{ "status": "completed_bounded_diagnostic", "diagnostic_only": true, "box": { "x0": "0.125", "x1": "2", "y0": "0.125", "y1": "0.625" }, "protocol_version": 1, "grid_size": 9, "cell_cap": 4, "step_cap": 12, "precisions_bits": [ 128, 256 ], "calls": [ { "z": { "re": "0.125", "im": "0.125" }, "bits": 128, "replay": false, "purpose": "grid_0_0", "values": { "m": { "re": "0.16222522340652579019687994948956127407", "im": "0.038527859142471457725119880850813022256" }, "c": { "re": "0.004041950025430119020033635509021450889", "im": "0.00055829000014282903008935178582010575978" }, "dm": { "re": "0.31859945495883498172483542164413808111", "im": "-0.13737587771074550065477561096791775887" } }, "metadata": { "metadata": { "classification": "diagnostic, not a certificate", "bits": 128, "lattice_cutoff": 24, "gauss_legendre_order_per_segment": 48, "positive_half_segments": [ "0.0", "0.125", "0.25", "0.5", "1.0", "2.0", "4.0" ], "normalization": "B=exp(2*pi*exp(2*z)-9*z)/(4*pi^4), analytic and nonzero", "derivative": "dm=(B*M)' includes B' contribution", "majorants": { "status": "analytic majorants evaluated as floating numbers; NOT interval bounds", "quadrature_error": "NOT bounded: fixed Gauss-Legendre approximation and replay only", "roundoff_error": "NOT bounded: ordinary mpmath arithmetic", "normalized_lattice_m": "2.3469735475722720081956798542733344844e-818", "normalized_lattice_c": "1.2517192253718784043710292556124450583e-817", "normalized_lattice_dm": "9.2783564559979635095200158449496365132e-815", "normalized_real_tail_m": "1.0083552782890376165648987366359964705e-1972", "normalized_real_tail_c": "1.6134573500762681528334900057283770895e-1971", "normalized_real_tail_dm": "3.623543643088937502081920537402718659e-1971", "phi_lattice_tail": "4.5885262662854514740333947116012359699e-820", "phi_derivative_lattice_tail": "1.8039741874006024900445183341996020805e-816", "envelope_K0": "7.0806448041385032092774528790706719056", "envelope_K1": "99.811506129080957217155350239768137982", "envelope_d": "1.5219640730090286703744177804891892666" } } }, "elapsed_seconds": 0.21527966600842774 }, { "z": { "re": "0.125", "im": "0.1875" }, "bits": 128, "replay": false, "purpose": "grid_0_1", "values": { "m": { "re": "0.17374858514743541932398967622618640944", "im": "0.058862787698680902224966925084734650374" }, "c": { "re": "0.0046726794863345783084478704376929818807", "im": "0.0008238571917961069074267761839655279206" }, "dm": { "re": "0.33143166924880362845831793105017094783", "im": "-0.23693562933470219307816986013418716418" } }, "metadata": { "metadata": { "classification": "diagnostic, not a certificate", "bits": 128, "lattice_cutoff": 24, "gauss_legendre_order_per_segment": 48, "positive_half_segments": [ "0.0", "0.125", "0.25", "0.5", "1.0", "2.0", "4.0" ], "normalization": "B=exp(2*pi*exp(2*z)-9*z)/(4*pi^4), analytic and nonzero", "derivative": "dm=(B*M)' includes B' contribution", "majorants": { "status": "analytic majorants evaluated as floating numbers; NOT interval bounds", "quadrature_error": "NOT bounded: fixed Gauss-Legendre approximation and replay only", "roundoff_error": "NOT bounded: ordinary mpmath arithmetic", "normalized_lattice_m": "1.1148547349994364354352315343483459024e-785", "normalized_lattice_c": "5.9458919199969943223212348498578448127e-785", "normalized_lattice_dm": "4.4086668777184799761334412718497288947e-782", "normalized_real_tail_m": "1.1416284236805389013458283170503015553e-1894", "normalized_real_tail_c": "1.8267102876078511063134068230741076303e-1893", "normalized_real_tail_dm": "4.285950547075124240589324986219517334e-1893", "phi_lattice_tail": "2.575127112483722287169904859455751326e-787", "phi_derivative_lattice_tail": "1.0124084663803664294249623722467560192e-783", "envelope_K0": "7.6916660011049469339417991865339105462", "envelope_K1": "111.95370680359173350893646533622747631", "envelope_d": "1.461637954554517745521968003740990655" } } }, "elapsed_seconds": 0.15413062501465902 }, { "z": { "re": "0.125", "im": "0.25" }, "bits": 128, "replay": false, "purpose": "grid_0_2", "values": { "m": { "re": "0.19274636187444031688049191464939231617", "im": "0.079663880451295760944004044412912090898" }, "c": { "re": "0.005768695537553080432763290254865239463", "im": "0.0010009495012638749311425339516234613434" }, "dm": { "re": "0.32947392979869769826091852412114438938", "im": "-0.38008423092230821461439562496308741029" } }, "metadata": { "metadata": { "classification": "diagnostic, not a certificate", "bits": 128, "lattice_cutoff": 24, "gauss_legendre_order_per_segment": 48, "positive_half_segments": [ "0.0", "0.125", "0.25", "0.5", "1.0", "2.0", "4.0" ], "normalization": "B=exp(2*pi*exp(2*z)-9*z)/(4*pi^4), analytic and nonzero", "derivative": "dm=(B*M)' includes B' contribution", "majorants": { "status": "analytic majorants evaluated as floating numbers; NOT interval bounds", "quadrature_error": "NOT bounded: fixed Gauss-Legendre approximation and replay only", "roundoff_error": "NOT bounded: ordinary mpmath arithmetic", "normalized_lattice_m": "1.2045451208318648860040197662759987518e-740", "normalized_lattice_c": "6.4242406444366127253547720868053266762e-740", "normalized_lattice_dm": "4.7652697089127635251343670274312919124e-737", "normalized_real_tail_m": "4.2492361093810088248265372756480940139e-1787", "normalized_real_tail_c": "6.7991914129320597355826675467409321994e-1786", "normalized_real_tail_dm": "1.6941948824274382430270957411622972829e-1785", "phi_lattice_tail": "3.4822619197001443260025646128996249337e-742", "phi_derivative_lattice_tail": "1.3690475443202646147289599099099827161e-738", "envelope_K0": "8.6675384390440944838131174022670163717", "envelope_K1": "132.49029078751267542542390489224169672", "envelope_d": "1.3785034646766524887891155021962680546" } } }, "elapsed_seconds": 0.1879898749757558 }, { "z": { "re": "0.125", "im": "0.3125" }, "bits": 128, "replay": false, "purpose": "grid_0_3", "values": { "m": { "re": "0.22265083467723123993722309263852253155", "im": "0.098942272246976533089084767159270588354" }, "c": { "re": "0.007621870275254828295269861975414361614", "im": "0.00084733566983641930603513348781693811593" }, "dm": { "re": "0.27272470084846379244574727657847329665", "im": "-0.58998663051752122290814954647911712819" } }, "metadata": { "metadata": { "classification": "diagnostic, not a certificate", "bits": 128, "lattice_cutoff": 24, "gauss_legendre_order_per_segment": 48, "positive_half_segments": [ "0.0", "0.125", "0.25", "0.5", "1.0", "2.0", "4.0" ], "normalization": "B=exp(2*pi*exp(2*z)-9*z)/(4*pi^4), analytic and nonzero", "derivative": "dm=(B*M)' includes B' contribution", "majorants": { "status": "analytic majorants evaluated as floating numbers; NOT interval bounds", "quadrature_error": "NOT bounded: fixed Gauss-Legendre approximation and replay only", "roundoff_error": "NOT bounded: ordinary mpmath arithmetic", "normalized_lattice_m": "5.9090575157420505790690323889666157713e-684", "normalized_lattice_c": "3.1514973417290936421701506074488617447e-683", "normalized_lattice_dm": "2.3389208718537611313478347969647471751e-680", "normalized_real_tail_m": "1.1081795234753653144556210441763464281e-1651", "normalized_real_tail_c": "1.7732039743035482605656026932574687121e-1650", "normalized_real_tail_dm": "4.7792292812255599687589717415212051793e-1650", "phi_lattice_tail": "2.241849059997265044919279156096387541e-685", "phi_derivative_lattice_tail": "8.8138055697724088568987923655992442035e-682", "envelope_K0": "10.18167853949153246670305287452827837", "envelope_K1": "167.18305268120390240767790001762444874", "envelope_d": "1.2738578892849270606047326496499107661" } } }, "elapsed_seconds": 0.15570679202210158 }, { "z": { "re": "0.125", "im": "0.375" }, "bits": 128, "replay": false, "purpose": "grid_0_4", "values": { "m": { "re": "0.26828408388066465688872873001010081422", "im": "0.11065842132772843041700053548442828694" }, "c": { "re": "0.010689158494023966823277271996576917727", "im": "-0.00036409496358262107044986045966668532878" }, "dm": { "re": "0.063073083472890534783011062792818608913", "im": "-0.88426465297059085832236245497879086482" } }, "metadata": { "metadata": { "classification": "diagnostic, not a certificate", "bits": 128, "lattice_cutoff": 24, "gauss_legendre_order_per_segment": 48, "positive_half_segments": [ "0.0", "0.125", "0.25", "0.5", "1.0", "2.0", "4.0" ], "normalization": "B=exp(2*pi*exp(2*z)-9*z)/(4*pi^4), analytic and nonzero", "derivative": "dm=(B*M)' includes B' contribution", "majorants": { "status": "analytic majorants evaluated as floating numbers; NOT interval bounds", "quadrature_error": "NOT bounded: fixed Gauss-Legendre approximation and replay only", "roundoff_error": "NOT bounded: ordinary mpmath arithmetic", "normalized_lattice_m": "1.7384810742248279854632801065884273225e-616", "normalized_lattice_c": "9.2718990625324159224708272351382790532e-616", "normalized_lattice_dm": "6.8862360498179053708516425106186508498e-613", "normalized_real_tail_m": "1.608331409489629808495131189169615809e-1490", "normalized_real_tail_c": "2.573518035124746380963309806437715779e-1489", "normalized_real_tail_dm": "7.6878092039618426579079664543992403919e-1489", "phi_lattice_tail": "8.9238448836090041519537254011336962523e-618", "phi_derivative_lattice_tail": "3.5084000587904882233411529679191517387e-614", "envelope_K0": "12.595217910474195352796490529722614478", "envelope_K1": "229.54126205164252921382369277640260385", "envelope_d": "1.1493341875837106139976900705596868057" } } }, "elapsed_seconds": 0.15582666697446257 }, { "z": { "re": "0.125", "im": "0.4375" }, "bits": 128, "replay": false, "purpose": "grid_0_5", "values": { "m": { "re": "0.33415577701846332738494114817413057484", "im": "0.098886879705919973843368817113642785252" }, "c": { "re": "0.015340708204593329650168957960714392318", "im": "-0.0047352371058544482828756308026278297039" }, "dm": { "re": "-0.53758745383113079809848228578413445607", "im": "-1.2166586646314249089163172785262811589" } }, "metadata": { "metadata": { "classification": "diagnostic, not a certificate", "bits": 128, "lattice_cutoff": 24, "gauss_legendre_order_per_segment": 48, "positive_half_segments": [ "0.0", "0.125", "0.25", "0.5", "1.0", "2.0", "4.0" ], "normalization": "B=exp(2*pi*exp(2*z)-9*z)/(4*pi^4), analytic and nonzero", "derivative": "dm=(B*M)' includes B' contribution", "majorants": { "status": "analytic majorants evaluated as floating numbers; NOT interval bounds", "quadrature_error": "NOT bounded: fixed Gauss-Legendre approximation and replay only", "roundoff_error": "NOT bounded: ordinary mpmath arithmetic", "normalized_lattice_m": "2.783310902429432279214214952825280537e-539", "normalized_lattice_c": "1.4844324812956972155809146415068162864e-538", "normalized_lattice_dm": "1.1036624557075879889262393244193755409e-535", "normalized_real_tail_m": "4.198123580446010280365751635123700448e-1306", "normalized_real_tail_c": "6.7175572307396271398601474251319153585e-1305", "normalized_real_tail_dm": "2.3147060126717202320316535640810389402e-1304", "phi_lattice_tail": "1.9356365872969653834965440138348783136e-540", "phi_derivative_lattice_tail": "7.6099345128052750467898755680309622573e-537", "envelope_K0": "16.757999595347284854867734621554433003", "envelope_K1": "357.61040338926418324104642749144832606", "envelope_d": "1.0068755102900204581994763865832455735" } } }, "elapsed_seconds": 0.1553927079658024 }, { "z": { "re": "0.125", "im": "0.5" }, "bits": 128, "replay": false, "purpose": "grid_0_6", "values": { "m": { "re": "0.41400905675384810134416919850428182646", "im": "0.024440344120582713370549314143724812567" }, "c": { "re": "0.019764549056862589088828355098139922591", "im": "-0.017886351913816319572379543140305022339" }, "dm": { "re": "-2.0652503428671332761256049732219971302", "im": "-1.2044372955657580293506853613983688355" } }, "metadata": { "metadata": { "classification": "diagnostic, not a certificate", "bits": 128, "lattice_cutoff": 24, "gauss_legendre_order_per_segment": 48, "positive_half_segments": [ "0.0", "0.125", "0.25", "0.5", "1.0", "2.0", "4.0" ], "normalization": "B=exp(2*pi*exp(2*z)-9*z)/(4*pi^4), analytic and nonzero", "derivative": "dm=(B*M)' includes B' contribution", "majorants": { "status": "analytic majorants evaluated as floating numbers; NOT interval bounds", "quadrature_error": "NOT bounded: fixed Gauss-Legendre approximation and replay only", "roundoff_error": "NOT bounded: ordinary mpmath arithmetic", "normalized_lattice_m": "1.5836744795384249765928157512905621007e-453", "normalized_lattice_c": "8.4462638908715998751616840068829978702e-453", "normalized_lattice_dm": "6.2915451336063027484323747121523003194e-450", "normalized_real_tail_m": "2.8918801740815027349148289734519961079e-1101", "normalized_real_tail_c": "4.6274655237661460226064345023398560283e-1100", "normalized_real_tail_dm": "1.9937739947727618252411325373371978593e-1099", "phi_lattice_tail": "1.4210689249680573121153852115435788848e-454", "phi_derivative_lattice_tail": "5.5869172592419013598919352956561404267e-451", "envelope_K0": "24.983585560594923710980841691774397433", "envelope_K1": "691.58751112121217564683229655248525689", "envelope_d": "0.84870487741648658484554125650222836214" } } }, "elapsed_seconds": 0.1571749160066247 }, { "z": { "re": "0.125", "im": "0.5625" }, "bits": 128, "replay": false, "purpose": "grid_0_7", "values": { "m": { "re": "0.44241343684704988347967524680410893743", "im": "-0.19428810928262408228605172326147162357" }, "c": { "re": "0.0088140042791516255081939197331429724469", "im": "-0.050107137291038523858212662024221281807" }, "dm": { "re": "-5.1981862892273387174719915563422605527", "im": "0.97760506167256938294535108350599881863" } }, "metadata": { "metadata": { "classification": "diagnostic, not a certificate", "bits": 128, "lattice_cutoff": 24, "gauss_legendre_order_per_segment": 48, "positive_half_segments": [ "0.0", "0.125", "0.25", "0.5", "1.0", "2.0", "4.0" ], "normalization": "B=exp(2*pi*exp(2*z)-9*z)/(4*pi^4), analytic and nonzero", "derivative": "dm=(B*M)' includes B' contribution", "majorants": { "status": "analytic majorants evaluated as floating numbers; NOT interval bounds", "quadrature_error": "NOT bounded: fixed Gauss-Legendre approximation and replay only", "roundoff_error": "NOT bounded: ordinary mpmath arithmetic", "normalized_lattice_m": "1.6224646236435343587758626067587225828e-360", "normalized_lattice_c": "8.6531446594321832468046005693798537748e-360", "normalized_lattice_dm": "6.4725473833872433137120499821447531319e-357", "normalized_real_tail_m": "4.151809341552826697227656118180653077e-879", "normalized_real_tail_c": "6.643717555468874934796492014353460904e-878", "normalized_real_tail_dm": "4.1925368081959448991203705839562333288e-877", "phi_lattice_tail": "1.6144292525175739343768210704242839689e-361", "phi_derivative_lattice_tail": "6.3471113161651743543353377638863142176e-358", "envelope_K0": "45.779336961551260847650165707650203536", "envelope_K1": "1974.9153743821504788261579387588952755", "envelope_d": "0.67729048878756286732349724939914712065" } } }, "elapsed_seconds": 0.1559806250152178 }, { "z": { "re": "0.125", "im": "0.625" }, "bits": 128, "replay": false, "purpose": "grid_0_8", "values": { "m": { "re": "0.13692521170771949913910914528094158162", "im": "-0.59267545874315895956902751607295850706" }, "c": { "re": "-0.078557361788862318589643078245184221359", "im": "-0.076151807620338720467337696369353285836" }, "dm": { "re": "-5.8669657599779564567165238713935587164", "im": "10.434618733875781458992918134684658931" } }, "metadata": { "metadata": { "classification": "diagnostic, not a certificate", "bits": 128, "lattice_cutoff": 24, "gauss_legendre_order_per_segment": 48, "positive_half_segments": [ "0.0", "0.125", "0.25", "0.5", "1.0", "2.0", "4.0" ], "normalization": "B=exp(2*pi*exp(2*z)-9*z)/(4*pi^4), analytic and nonzero", "derivative": "dm=(B*M)' includes B' contribution", "majorants": { "status": "analytic majorants evaluated as floating numbers; NOT interval bounds", "quadrature_error": "NOT bounded: fixed Gauss-Legendre approximation and replay only", "roundoff_error": "NOT bounded: ordinary mpmath arithmetic", "normalized_lattice_m": "1.3084544008029800790707310999091938453e-261", "normalized_lattice_c": "6.9784234709492270883772325328490338416e-261", "normalized_lattice_dm": "5.2764936213834893908718277077255368722e-258", "normalized_real_tail_m": "6.7198336301407489897717222741657517979e-643", "normalized_real_tail_c": "1.0753554451135352088931477689298137116e-641", "normalized_real_tail_dm": "1.2529021250820129700555132843421803091e-640", "phi_lattice_tail": "1.0021598388692270941092068707959257556e-262", "phi_derivative_lattice_tail": "3.9399806736491836923747700781666945459e-259", "envelope_K0": "126.24928292784368352612039481684046491", "envelope_K1": "10771.851462133738538848956859875684407", "envelope_d": "0.49530720860677725930394940995503526598" } } }, "elapsed_seconds": 0.1549767919932492 }, { "z": { "re": "0.359375", "im": "0.125" }, "bits": 128, "replay": false, "purpose": "grid_1_0", "values": { "m": { "re": "0.2035649710798327797269006591076931236", "im": "0.0089041502574320684077543484223257764245" }, "c": { "re": "0.0035882980781479723628424164374434113708", "im": "-0.00057825749818925194091243907092670759651" }, "dm": { "re": "0.059475189328703879749366887238108382869", "im": "-0.097130592004151356724533666336624138537" } }, "metadata": { "metadata": { "classification": "diagnostic, not a certificate", "bits": 128, "lattice_cutoff": 24, "gauss_legendre_order_per_segment": 48, "positive_half_segments": [ "0.0", "0.125", "0.25", "0.5", "1.0", "2.0", "4.0" ], "normalization": "B=exp(2*pi*exp(2*z)-9*z)/(4*pi^4), analytic and nonzero", "derivative": "dm=(B*M)' includes B' contribution", "majorants": { "status": "analytic majorants evaluated as floating numbers; NOT interval bounds", "quadrature_error": "NOT bounded: fixed Gauss-Legendre approximation and replay only", "roundoff_error": "NOT bounded: ordinary mpmath arithmetic", "normalized_lattice_m": "3.0516254660709241900580786457533149782e-817", "normalized_lattice_c": "1.627533581904492901364308611068434655e-816", "normalized_lattice_dm": "1.2092965044624221068003971957880429662e-813", "normalized_real_tail_m": "1.3111023979187412965493034104036760804e-1971", "normalized_real_tail_c": "2.0978794341355618255094448586581223185e-1970", "normalized_real_tail_dm": "5.9526327188095611545126934387101202775e-1970", "phi_lattice_tail": "4.5885262662854514740333947116012359699e-820", "phi_derivative_lattice_tail": "1.8039741874006024900445183341996020805e-816", "envelope_K0": "7.0806448041385032092774528790706719056", "envelope_K1": "99.811506129080957217155350239768137982", "envelope_d": "1.5219640730090286703744177804891892666" } } }, "elapsed_seconds": 0.1557240840047598 }, { "z": { "re": "0.359375", "im": "0.1875" }, "bits": 128, "replay": false, "purpose": "grid_1_1", "values": { "m": { "re": "0.21111523785085748271330689576975241932", "im": "0.011943251975210423202417191766994403144" }, "c": { "re": "0.0037144413769759074382977449673957242281", "im": "-0.00097113688287513955030176763364321770111" }, "dm": { "re": "0.035953447530150240923602143752742297278", "im": "-0.14403051739073850609214667414056689587" } }, "metadata": { "metadata": { "classification": "diagnostic, not a certificate", "bits": 128, "lattice_cutoff": 24, "gauss_legendre_order_per_segment": 48, "positive_half_segments": [ "0.0", "0.125", "0.25", "0.5", "1.0", "2.0", "4.0" ], "normalization": "B=exp(2*pi*exp(2*z)-9*z)/(4*pi^4), analytic and nonzero", "derivative": "dm=(B*M)' includes B' contribution", "majorants": { "status": "analytic majorants evaluated as floating numbers; NOT interval bounds", "quadrature_error": "NOT bounded: fixed Gauss-Legendre approximation and replay only", "roundoff_error": "NOT bounded: ordinary mpmath arithmetic", "normalized_lattice_m": "1.2044081706734865366722549595598099453e-784", "normalized_lattice_c": "6.4235102435919281955853597843189863747e-784", "normalized_lattice_dm": "4.7739894690692669169065942182766946438e-781", "normalized_real_tail_m": "1.2333325214379871280006811821054818852e-1893", "normalized_real_tail_c": "1.9734452631170127985443763722824458968e-1892", "normalized_real_tail_dm": "5.7756559956126819463739681579625775424e-1892", "phi_lattice_tail": "2.575127112483722287169904859455751326e-787", "phi_derivative_lattice_tail": "1.0124084663803664294249623722467560192e-783", "envelope_K0": "7.6916660011049469339417991865339105462", "envelope_K1": "111.95370680359173350893646533622747631", "envelope_d": "1.461637954554517745521968003740990655" } } }, "elapsed_seconds": 0.15418166702147573 }, { "z": { "re": "0.359375", "im": "0.25" }, "bits": 128, "replay": false, "purpose": "grid_1_2", "values": { "m": { "re": "0.2214736350023683181158264592590458214", "im": "0.013164979152833634823736667474416914238" }, "c": { "re": "0.003836238958776863251750416875107881208", "im": "-0.0014875165949324408713963956320749825486" }, "dm": { "re": "0.0013256324892980298835114884514550444456", "im": "-0.18629109853825097078513183295359938773" } }, "metadata": { "metadata": { "classification": "diagnostic, not a certificate", "bits": 128, "lattice_cutoff": 24, "gauss_legendre_order_per_segment": 48, "positive_half_segments": [ "0.0", "0.125", "0.25", "0.5", "1.0", "2.0", "4.0" ], "normalization": "B=exp(2*pi*exp(2*z)-9*z)/(4*pi^4), analytic and nonzero", "derivative": "dm=(B*M)' includes B' contribution", "majorants": { "status": "analytic majorants evaluated as floating numbers; NOT interval bounds", "quadrature_error": "NOT bounded: fixed Gauss-Legendre approximation and replay only", "roundoff_error": "NOT bounded: ordinary mpmath arithmetic", "normalized_lattice_m": "1.0080621175248825252264625801258123173e-739", "normalized_lattice_c": "5.3763312934660401345411337606709990254e-739", "normalized_lattice_dm": "3.9971421605223954031570838530813691639e-736", "normalized_real_tail_m": "3.5561091703460728356260404824961455369e-1786", "normalized_real_tail_c": "5.6901208386813092976716878552362551161e-1785", "normalized_real_tail_dm": "1.7414612057623878841771357459570149931e-1784", "phi_lattice_tail": "3.4822619197001443260025646128996249337e-742", "phi_derivative_lattice_tail": "1.3690475443202646147289599099099827161e-738", "envelope_K0": "8.6675384390440944838131174022670163717", "envelope_K1": "132.49029078751267542542390489224169672", "envelope_d": "1.3785034646766524887891155021962680546" } } }, "elapsed_seconds": 0.16155737498775125 }, { "z": { "re": "0.359375", "im": "0.3125" }, "bits": 128, "replay": false, "purpose": "grid_1_3", "values": { "m": { "re": "0.2342025966369635320447992974254572995", "im": "0.011920034628335445367788227373126987732" }, "c": { "re": "0.0038793527571119041142017544395480384878", "im": "-0.0021473283843775701939779704301816304046" }, "dm": { "re": "-0.042107904615022773170117286722014670472", "im": "-0.21903578205269815328126067693564572206" } }, "metadata": { "metadata": { "classification": "diagnostic, not a certificate", "bits": 128, "lattice_cutoff": 24, "gauss_legendre_order_per_segment": 48, "positive_half_segments": [ "0.0", "0.125", "0.25", "0.5", "1.0", "2.0", "4.0" ], "normalization": "B=exp(2*pi*exp(2*z)-9*z)/(4*pi^4), analytic and nonzero", "derivative": "dm=(B*M)' includes B' contribution", "majorants": { "status": "analytic majorants evaluated as floating numbers; NOT interval bounds", "quadrature_error": "NOT bounded: fixed Gauss-Legendre approximation and replay only", "roundoff_error": "NOT bounded: ordinary mpmath arithmetic", "normalized_lattice_m": "3.5858994429380800963206645111794157083e-683", "normalized_lattice_c": "1.9124797029003093847043544059623550444e-682", "normalized_lattice_dm": "1.422573112360073460399087568276537362e-679", "normalized_real_tail_m": "6.7249647263023351009603066318098509489e-1651", "normalized_real_tail_c": "1.0760651976615916553914784645611769742e-1649", "normalized_real_tail_dm": "3.5010986512272691877541034686239447939e-1649", "phi_lattice_tail": "2.241849059997265044919279156096387541e-685", "phi_derivative_lattice_tail": "8.8138055697724088568987923655992442035e-682", "envelope_K0": "10.18167853949153246670305287452827837", "envelope_K1": "167.18305268120390240767790001762444874", "envelope_d": "1.2738578892849270606047326496499107661" } } }, "elapsed_seconds": 0.15630133298691362 }, { "z": { "re": "0.359375", "im": "0.375" }, "bits": 128, "replay": false, "purpose": "grid_1_4", "values": { "m": { "re": "0.24859426765931540682588700732937889178", "im": "0.0079233269473358130830667101387214335452" }, "c": { "re": "0.0037452832012045584495160395111442394595", "im": "-0.0029044355446057233011376572986780650001" }, "dm": { "re": "-0.084039044220237296283929662222236402262", "im": "-0.23991035654362978455852236102901778249" } }, "metadata": { "metadata": { "classification": "diagnostic, not a certificate", "bits": 128, "lattice_cutoff": 24, "gauss_legendre_order_per_segment": 48, "positive_half_segments": [ "0.0", "0.125", "0.25", "0.5", "1.0", "2.0", "4.0" ], "normalization": "B=exp(2*pi*exp(2*z)-9*z)/(4*pi^4), analytic and nonzero", "derivative": "dm=(B*M)' includes B' contribution", "majorants": { "status": "analytic majorants evaluated as floating numbers; NOT interval bounds", "quadrature_error": "NOT bounded: fixed Gauss-Legendre approximation and replay only", "roundoff_error": "NOT bounded: ordinary mpmath arithmetic", "normalized_lattice_m": "7.1969841785539785522596872731920934582e-616", "normalized_lattice_c": "3.838391561895455227871833212369116511e-615", "normalized_lattice_dm": "2.8571087165057803711717658072332850451e-612", "normalized_real_tail_m": "6.6581890821730847640052571090188503027e-1490", "normalized_real_tail_c": "1.0653879905062936220923899013500736683e-1488", "normalized_real_tail_dm": "3.7688395258654227772080179009745606003e-1488", "phi_lattice_tail": "8.9238448836090041519537254011336962523e-618", "phi_derivative_lattice_tail": "3.5084000587904882233411529679191517387e-614", "envelope_K0": "12.595217910474195352796490529722614478", "envelope_K1": "229.54126205164252921382369277640260385", "envelope_d": "1.1493341875837106139976900705596868057" } } }, "elapsed_seconds": 0.15791499998886138 }, { "z": { "re": "0.359375", "im": "0.4375" }, "bits": 128, "replay": false, "purpose": "grid_1_5", "values": { "m": { "re": "0.26428099610490344751901682721816338571", "im": "0.0019078005555236079036112780020273544879" }, "c": { "re": "0.0034035526003383739559701085096685608136", "im": "-0.0035704126701258404601650064287932287883" }, "dm": { "re": "-0.10220212452624302684898245697273282895", "im": "-0.26737376766498372051431991825260929035" } }, "metadata": { "metadata": { "classification": "diagnostic, not a certificate", "bits": 128, "lattice_cutoff": 24, "gauss_legendre_order_per_segment": 48, "positive_half_segments": [ "0.0", "0.125", "0.25", "0.5", "1.0", "2.0", "4.0" ], "normalization": "B=exp(2*pi*exp(2*z)-9*z)/(4*pi^4), analytic and nonzero", "derivative": "dm=(B*M)' includes B' contribution", "majorants": { "status": "analytic majorants evaluated as floating numbers; NOT interval bounds", "quadrature_error": "NOT bounded: fixed Gauss-Legendre approximation and replay only", "roundoff_error": "NOT bounded: ordinary mpmath arithmetic", "normalized_lattice_m": "7.4390921827671239997253200581519066976e-539", "normalized_lattice_c": "3.9675158308091327998535040310143502387e-538", "normalized_lattice_dm": "2.9562974945631386239720808316444012858e-535", "normalized_real_tail_m": "1.1220531735181550330843698403735071399e-1305", "normalized_real_tail_c": "1.795434618492208740716714726916077326e-1304", "normalized_real_tail_dm": "7.1646946595948395905170691900508744833e-1304", "phi_lattice_tail": "1.9356365872969653834965440138348783136e-540", "phi_derivative_lattice_tail": "7.6099345128052750467898755680309622573e-537", "envelope_K0": "16.757999595347284854867734621554433003", "envelope_K1": "357.61040338926418324104642749144832606", "envelope_d": "1.0068755102900204581994763865832455735" } } }, "elapsed_seconds": 0.15677837503608316 }, { "z": { "re": "0.359375", "im": "0.5" }, "bits": 128, "replay": false, "purpose": "grid_1_6", "values": { "m": { "re": "0.28407012871015101096919944091503313788", "im": "-0.0039677250356250946896109272720917345932" }, "c": { "re": "0.003255062467799155174380369260953552632", "im": "-0.0037944564239448946900532424004330923763" }, "dm": { "re": "-0.081387318785516366310606022760492945779", "im": "-0.40124001265748952206940283109082018839" } }, "metadata": { "metadata": { "classification": "diagnostic, not a certificate", "bits": 128, "lattice_cutoff": 24, "gauss_legendre_order_per_segment": 48, "positive_half_segments": [ "0.0", "0.125", "0.25", "0.5", "1.0", "2.0", "4.0" ], "normalization": "B=exp(2*pi*exp(2*z)-9*z)/(4*pi^4), analytic and nonzero", "derivative": "dm=(B*M)' includes B' contribution", "majorants": { "status": "analytic majorants evaluated as floating numbers; NOT interval bounds", "quadrature_error": "NOT bounded: fixed Gauss-Legendre approximation and replay only", "roundoff_error": "NOT bounded: ordinary mpmath arithmetic", "normalized_lattice_m": "2.6040178660498280529681178954312849581e-453", "normalized_lattice_c": "1.3888095285599082949163295442300186443e-452", "normalized_lattice_dm": "1.036769209167900970775926023460833152e-449", "normalized_real_tail_m": "4.7550855539317327044361180562781472634e-1101", "normalized_real_tail_c": "7.6088887294115785962776669119511703557e-1100", "normalized_real_tail_dm": "3.690595207943364344025436238404377116e-1099", "phi_lattice_tail": "1.4210689249680573121153852115435788848e-454", "phi_derivative_lattice_tail": "5.5869172592419013598919352956561404267e-451", "envelope_K0": "24.983585560594923710980841691774397433", "envelope_K1": "691.58751112121217564683229655248525689", "envelope_d": "0.84870487741648658484554125650222836214" } } }, "elapsed_seconds": 0.15671816701069474 }, { "z": { "re": "0.359375", "im": "0.5625" }, "bits": 128, "replay": false, "purpose": "grid_1_7", "values": { "m": { "re": "0.32412474539711214690479674389119043391", "im": "-0.0099755985725679100683384291459644279232" }, "c": { "re": "0.0053907270642169438739006704481318265724", "im": "-0.0035788940380407992597578977777300579607" }, "dm": { "re": "-0.16776115486480783510655717570460719736", "im": "-1.0309652911050391451371323699812933805" } }, "metadata": { "metadata": { "classification": "diagnostic, not a certificate", "bits": 128, "lattice_cutoff": 24, "gauss_legendre_order_per_segment": 48, "positive_half_segments": [ "0.0", "0.125", "0.25", "0.5", "1.0", "2.0", "4.0" ], "normalization": "B=exp(2*pi*exp(2*z)-9*z)/(4*pi^4), analytic and nonzero", "derivative": "dm=(B*M)' includes B' contribution", "majorants": { "status": "analytic majorants evaluated as floating numbers; NOT interval bounds", "quadrature_error": "NOT bounded: fixed Gauss-Legendre approximation and replay only", "roundoff_error": "NOT bounded: ordinary mpmath arithmetic", "normalized_lattice_m": "1.5758234439081478044605317304480064362e-360", "normalized_lattice_c": "8.4043917008434549571228358957227009929e-360", "normalized_lattice_dm": "6.3001262045036389201922144473595044644e-357", "normalized_real_tail_m": "4.0324567942587247235731377384171039611e-879", "normalized_real_tail_c": "6.4527298321619121895936479558734856819e-878", "normalized_real_tail_dm": "4.4212054010025908320743900712418003103e-877", "phi_lattice_tail": "1.6144292525175739343768210704242839689e-361", "phi_derivative_lattice_tail": "6.3471113161651743543353377638863142176e-358", "envelope_K0": "45.779336961551260847650165707650203536", "envelope_K1": "1974.9153743821504788261579387588952755", "envelope_d": "0.67729048878756286732349724939914712065" } } }, "elapsed_seconds": 0.15792133298236877 }, { "z": { "re": "0.359375", "im": "0.625" }, "bits": 128, "replay": false, "purpose": "grid_1_8", "values": { "m": { "re": "0.4556299307428310137931246370629680908", "im": "-0.051701932398636530849058730247986690007" }, "c": { "re": "0.020008194859862467915601680086814603735", "im": "-0.0077348493315742754666685189338346521119" }, "dm": { "re": "-1.7604296551370943672651955379062836228", "im": "-3.9115775161506321993455096544106126485" } }, "metadata": { "metadata": { "classification": "diagnostic, not a certificate", "bits": 128, "lattice_cutoff": 24, "gauss_legendre_order_per_segment": 48, "positive_half_segments": [ "0.0", "0.125", "0.25", "0.5", "1.0", "2.0", "4.0" ], "normalization": "B=exp(2*pi*exp(2*z)-9*z)/(4*pi^4), analytic and nonzero", "derivative": "dm=(B*M)' includes B' contribution", "majorants": { "status": "analytic majorants evaluated as floating numbers; NOT interval bounds", "quadrature_error": "NOT bounded: fixed Gauss-Legendre approximation and replay only", "roundoff_error": "NOT bounded: ordinary mpmath arithmetic", "normalized_lattice_m": "7.2668733492733111438647279461795618544e-262", "normalized_lattice_c": "3.8756657862790992767278549046290996557e-261", "normalized_lattice_dm": "2.9367585675844044786209302487557818728e-258", "normalized_real_tail_m": "3.7320505696226566820967974454466471843e-643", "normalized_real_tail_c": "5.9722920571751345458732978759292874208e-642", "normalized_real_tail_dm": "7.2823024354457595361037861188453510418e-641", "phi_lattice_tail": "1.0021598388692270941092068707959257556e-262", "phi_derivative_lattice_tail": "3.9399806736491836923747700781666945459e-259", "envelope_K0": "126.24928292784368352612039481684046491", "envelope_K1": "10771.851462133738538848956859875684407", "envelope_d": "0.49530720860677725930394940995503526598" } } }, "elapsed_seconds": 0.15703674999531358 }, { "z": { "re": "0.59375", "im": "0.125" }, "bits": 128, "replay": false, "purpose": "grid_2_0", "values": { "m": { "re": "0.20117151929708546136552173712559279515", "im": "-0.0069416643695919549424339770637861494874" }, "c": { "re": "0.0022662481451994948257016594367861928586", "im": "-0.00062318787639905721744754819662142257253" }, "dm": { "re": "-0.062728187212310199768860258668612139236", "im": "-0.042882001574616563921491940525825325544" } }, "metadata": { "metadata": { "classification": "diagnostic, not a certificate", "bits": 128, "lattice_cutoff": 24, "gauss_legendre_order_per_segment": 48, "positive_half_segments": [ "0.0", "0.125", "0.25", "0.5", "1.0", "2.0", "4.0" ], "normalization": "B=exp(2*pi*exp(2*z)-9*z)/(4*pi^4), analytic and nonzero", "derivative": "dm=(B*M)' includes B' contribution", "majorants": { "status": "analytic majorants evaluated as floating numbers; NOT interval bounds", "quadrature_error": "NOT bounded: fixed Gauss-Legendre approximation and replay only", "roundoff_error": "NOT bounded: ordinary mpmath arithmetic", "normalized_lattice_m": "6.4946025427199660833790554184792091675e-815", "normalized_lattice_c": "3.463788022783981911135496223188911556e-814", "normalized_lattice_dm": "2.5836472146625855521842157604606388032e-811", "normalized_real_tail_m": "2.7903453624840732691445651295611066223e-1969", "normalized_real_tail_c": "4.4647985995474325418748832310197692515e-1968", "normalized_real_tail_dm": "1.6951998071813590067106142111137698265e-1967", "phi_lattice_tail": "4.5885262662854514740333947116012359699e-820", "phi_derivative_lattice_tail": "1.8039741874006024900445183341996020805e-816", "envelope_K0": "7.0806448041385032092774528790706719056", "envelope_K1": "99.811506129080957217155350239768137982", "envelope_d": "1.5219640730090286703744177804891892666" } } }, "elapsed_seconds": 0.1590604159864597 }, { "z": { "re": "0.59375", "im": "0.1875" }, "bits": 128, "replay": false, "purpose": "grid_2_1", "values": { "m": { "re": "0.20446358713334421820508730358909033733", "im": "-0.011251910802058723177760813226463082135" }, "c": { "re": "0.0022057874954717937445201441954500451008", "im": "-0.00095166913073338835706725265317328499117" }, "dm": { "re": "-0.076053749199292560227820017012961572824", "im": "-0.062091017640412094134845104110689472699" } }, "metadata": { "metadata": { "classification": "diagnostic, not a certificate", "bits": 128, "lattice_cutoff": 24, "gauss_legendre_order_per_segment": 48, "positive_half_segments": [ "0.0", "0.125", "0.25", "0.5", "1.0", "2.0", "4.0" ], "normalization": "B=exp(2*pi*exp(2*z)-9*z)/(4*pi^4), analytic and nonzero", "derivative": "dm=(B*M)' includes B' contribution", "majorants": { "status": "analytic majorants evaluated as floating numbers; NOT interval bounds", "quadrature_error": "NOT bounded: fixed Gauss-Legendre approximation and replay only", "roundoff_error": "NOT bounded: ordinary mpmath arithmetic", "normalized_lattice_m": "1.9063741554988868842422449500706792438e-782", "normalized_lattice_c": "1.01673288293273967159586397337102893e-781", "normalized_lattice_dm": "7.5855362532086533844239520877242665843e-779", "normalized_real_tail_m": "1.9521565041284171892410363812754003064e-1891", "normalized_real_tail_c": "3.1236296286451223575187464801494422784e-1890", "normalized_real_tail_dm": "1.212376150472158449205770543548791966e-1889", "phi_lattice_tail": "2.575127112483722287169904859455751326e-787", "phi_derivative_lattice_tail": "1.0124084663803664294249623722467560192e-783", "envelope_K0": "7.6916660011049469339417991865339105462", "envelope_K1": "111.95370680359173350893646533622747631", "envelope_d": "1.461637954554517745521968003740990655" } } }, "elapsed_seconds": 0.16375895898090675 }, { "z": { "re": "0.59375", "im": "0.25" }, "bits": 128, "replay": false, "purpose": "grid_2_2", "values": { "m": { "re": "0.20887690218334766473916080464422447222", "im": "-0.01655205563969928107703967177043560432" }, "c": { "re": "0.0021060311237799169053733503804636219058", "im": "-0.0012954242710717627202838340041766849732" }, "dm": { "re": "-0.094352110098322193896626614966918542594", "im": "-0.078612622760680795251600916850683489472" } }, "metadata": { "metadata": { "classification": "diagnostic, not a certificate", "bits": 128, "lattice_cutoff": 24, "gauss_legendre_order_per_segment": 48, "positive_half_segments": [ "0.0", "0.125", "0.25", "0.5", "1.0", "2.0", "4.0" ], "normalization": "B=exp(2*pi*exp(2*z)-9*z)/(4*pi^4), analytic and nonzero", "derivative": "dm=(B*M)' includes B' contribution", "majorants": { "status": "analytic majorants evaluated as floating numbers; NOT interval bounds", "quadrature_error": "NOT bounded: fixed Gauss-Legendre approximation and replay only", "roundoff_error": "NOT bounded: ordinary mpmath arithmetic", "normalized_lattice_m": "1.061006704257653752561798361118874666e-737", "normalized_lattice_c": "5.6587024227074866803295912593006648852e-737", "normalized_lattice_dm": "4.2231873001964889153086057158585879983e-734", "normalized_real_tail_m": "3.7428801313091440931403542649883213319e-1784", "normalized_real_tail_c": "5.9889725572670693184804944109438285229e-1783", "normalized_real_tail_dm": "2.4012539398526141661526895077834135977e-1782", "phi_lattice_tail": "3.4822619197001443260025646128996249337e-742", "phi_derivative_lattice_tail": "1.3690475443202646147289599099099827161e-738", "envelope_K0": "8.6675384390440944838131174022670163717", "envelope_K1": "132.49029078751267542542390489224169672", "envelope_d": "1.3785034646766524887891155021962680546" } } }, "elapsed_seconds": 0.15580091701122 }, { "z": { "re": "0.59375", "im": "0.3125" }, "bits": 128, "replay": false, "purpose": "grid_2_3", "values": { "m": { "re": "0.21421543054106374385329409090366686801", "im": "-0.023141959330093802921347613767830432917" }, "c": { "re": "0.0019543738553396610251251394706678685475", "im": "-0.0016518183620274446090585408518992060854" }, "dm": { "re": "-0.11725622529310855334192162259091002247", "im": "-0.091544360360002008382805624881231313206" } }, "metadata": { "metadata": { "classification": "diagnostic, not a certificate", "bits": 128, "lattice_cutoff": 24, "gauss_legendre_order_per_segment": 48, "positive_half_segments": [ "0.0", "0.125", "0.25", "0.5", "1.0", "2.0", "4.0" ], "normalization": "B=exp(2*pi*exp(2*z)-9*z)/(4*pi^4), analytic and nonzero", "derivative": "dm=(B*M)' includes B' contribution", "majorants": { "status": "analytic majorants evaluated as floating numbers; NOT interval bounds", "quadrature_error": "NOT bounded: fixed Gauss-Legendre approximation and replay only", "roundoff_error": "NOT bounded: ordinary mpmath arithmetic", "normalized_lattice_m": "2.2582593278142636335236523295945481843e-681", "normalized_lattice_c": "1.2044049748342739378792812424504256983e-680", "normalized_lattice_dm": "8.9928869231640622967736504499455747333e-678", "normalized_real_tail_m": "4.2351199647559059835210635597773804409e-1649", "normalized_real_tail_c": "6.7766380753961080355349922619464295362e-1648", "normalized_real_tail_dm": "2.8439400936757392345054413753747316436e-1647", "phi_lattice_tail": "2.241849059997265044919279156096387541e-685", "phi_derivative_lattice_tail": "8.8138055697724088568987923655992442035e-682", "envelope_K0": "10.18167853949153246670305287452827837", "envelope_K1": "167.18305268120390240767790001762444874", "envelope_d": "1.2738578892849270606047326496499107661" } } }, "elapsed_seconds": 0.1582382500055246 }, { "z": { "re": "0.59375", "im": "0.375" }, "bits": 128, "replay": false, "purpose": "grid_2_4", "values": { "m": { "re": "0.22022479281754886932798296719535219652", "im": "-0.031294286110194762672684884578105136792" }, "c": { "re": "0.0017376077396330145140884451196102828987", "im": "-0.0020127964644160576790021434307553460656" }, "dm": { "re": "-0.1442311450941452408009866821391630548", "im": "-0.09990486038265697775099999331117561197" } }, "metadata": { "metadata": { "classification": "diagnostic, not a certificate", "bits": 128, "lattice_cutoff": 24, "gauss_legendre_order_per_segment": 48, "positive_half_segments": [ "0.0", "0.125", "0.25", "0.5", "1.0", "2.0", "4.0" ], "normalization": "B=exp(2*pi*exp(2*z)-9*z)/(4*pi^4), analytic and nonzero", "derivative": "dm=(B*M)' includes B' contribution", "majorants": { "status": "analytic majorants evaluated as floating numbers; NOT interval bounds", "quadrature_error": "NOT bounded: fixed Gauss-Legendre approximation and replay only", "roundoff_error": "NOT bounded: ordinary mpmath arithmetic", "normalized_lattice_m": "2.4598029293186319678822476579028071705e-614", "normalized_lattice_c": "1.3118948956366037162038654175481638243e-613", "normalized_lattice_dm": "9.8019985421622513604968635518541270355e-611", "normalized_real_tail_m": "2.2756522179234982550657075566068711849e-1488", "normalized_real_tail_c": "3.6413092413311557989446619553873337478e-1487", "normalized_real_tail_dm": "1.6295187299869862892613460485868464723e-1486", "phi_lattice_tail": "8.9238448836090041519537254011336962523e-618", "phi_derivative_lattice_tail": "3.5084000587904882233411529679191517387e-614", "envelope_K0": "12.595217910474195352796490529722614478", "envelope_K1": "229.54126205164252921382369277640260385", "envelope_d": "1.1493341875837106139976900705596868057" } } }, "elapsed_seconds": 0.15796670800773427 }, { "z": { "re": "0.59375", "im": "0.4375" }, "bits": 128, "replay": false, "purpose": "grid_2_5", "values": { "m": { "re": "0.22658911775328948435991667324923617864", "im": "-0.041231988045096855496471394396839688726" }, "c": { "re": "0.0014434544369291239178806156385763706218", "im": "-0.0023631219959435533219499879397483036213" }, "dm": { "re": "-0.17409064414861816086940418206875960272", "im": "-0.10284554706274934713812704186425066701" } }, "metadata": { "metadata": { "classification": "diagnostic, not a certificate", "bits": 128, "lattice_cutoff": 24, "gauss_legendre_order_per_segment": 48, "positive_half_segments": [ "0.0", "0.125", "0.25", "0.5", "1.0", "2.0", "4.0" ], "normalization": "B=exp(2*pi*exp(2*z)-9*z)/(4*pi^4), analytic and nonzero", "derivative": "dm=(B*M)' includes B' contribution", "majorants": { "status": "analytic majorants evaluated as floating numbers; NOT interval bounds", "quadrature_error": "NOT bounded: fixed Gauss-Legendre approximation and replay only", "roundoff_error": "NOT bounded: ordinary mpmath arithmetic", "normalized_lattice_m": "1.2636151906973516388531480067557418463e-537", "normalized_lattice_c": "6.7392810170525420738834560360306231801e-537", "normalized_lattice_dm": "5.0404733072746869432655240311046313106e-534", "normalized_real_tail_m": "1.9059361007949170316214204883082262061e-1304", "normalized_real_tail_c": "3.0497517735917543133449519174496312477e-1303", "normalized_real_tail_dm": "1.5015154836787588335115003255208304053e-1302", "phi_lattice_tail": "1.9356365872969653834965440138348783136e-540", "phi_derivative_lattice_tail": "7.6099345128052750467898755680309622573e-537", "envelope_K0": "16.757999595347284854867734621554433003", "envelope_K1": "357.61040338926418324104642749144832606", "envelope_d": "1.0068755102900204581994763865832455735" } } }, "elapsed_seconds": 0.15713970799697563 }, { "z": { "re": "0.59375", "im": "0.5" }, "bits": 128, "replay": false, "purpose": "grid_2_6", "values": { "m": { "re": "0.23301128504454390785892233052538171513", "im": "-0.053077629217455619703817736147613223243" }, "c": { "re": "0.0010723797652149598943897505573568811576", "im": "-0.0026763940285022348431840989671758680123" }, "dm": { "re": "-0.20534113763769762867541847970642817435", "im": "-0.10297456774920461289913036905094891344" } }, "metadata": { "metadata": { "classification": "diagnostic, not a certificate", "bits": 128, "lattice_cutoff": 24, "gauss_legendre_order_per_segment": 48, "positive_half_segments": [ "0.0", "0.125", "0.25", "0.5", "1.0", "2.0", "4.0" ], "normalization": "B=exp(2*pi*exp(2*z)-9*z)/(4*pi^4), analytic and nonzero", "derivative": "dm=(B*M)' includes B' contribution", "majorants": { "status": "analytic majorants evaluated as floating numbers; NOT interval bounds", "quadrature_error": "NOT bounded: fixed Gauss-Legendre approximation and replay only", "roundoff_error": "NOT bounded: ordinary mpmath arithmetic", "normalized_lattice_m": "2.0351362614344973596066691790039603687e-452", "normalized_lattice_c": "1.08540600609839859179022356213544553e-451", "normalized_lattice_dm": "8.1329998057468334680227470652000555237e-449", "normalized_real_tail_m": "3.716275208092077546956345573620552711e-1100", "normalized_real_tail_c": "5.946627926150124949150612648350302994e-1099", "normalized_real_tail_dm": "3.4369933711369732083677614915495231792e-1098", "phi_lattice_tail": "1.4210689249680573121153852115435788848e-454", "phi_derivative_lattice_tail": "5.5869172592419013598919352956561404267e-451", "envelope_K0": "24.983585560594923710980841691774397433", "envelope_K1": "691.58751112121217564683229655248525689", "envelope_d": "0.84870487741648658484554125650222836214" } } }, "elapsed_seconds": 0.15756379201775417 }, { "z": { "re": "0.59375", "im": "0.5625" }, "bits": 128, "replay": false, "purpose": "grid_2_7", "values": { "m": { "re": "0.23975957826395133387910560554836286911", "im": "-0.0673002873234830985274436857692261439" }, "c": { "re": "0.00070336584677845954323003049472305106361", "im": "-0.0029757872675418745793529696295596216129" }, "dm": { "re": "-0.26133175111883296869987464133837419886", "im": "-0.11788882079668956506720548099842226282" } }, "metadata": { "metadata": { "classification": "diagnostic, not a certificate", "bits": 128, "lattice_cutoff": 24, "gauss_legendre_order_per_segment": 48, "positive_half_segments": [ "0.0", "0.125", "0.25", "0.5", "1.0", "2.0", "4.0" ], "normalization": "B=exp(2*pi*exp(2*z)-9*z)/(4*pi^4), analytic and nonzero", "derivative": "dm=(B*M)' includes B' contribution", "majorants": { "status": "analytic majorants evaluated as floating numbers; NOT interval bounds", "quadrature_error": "NOT bounded: fixed Gauss-Legendre approximation and replay only", "roundoff_error": "NOT bounded: ordinary mpmath arithmetic", "normalized_lattice_m": "5.3098502070035868178608560216186406062e-360", "normalized_lattice_c": "2.8319201104019129695257898781966083233e-359", "normalized_lattice_dm": "2.1307501255204442094311766647964657608e-356", "normalized_real_tail_m": "1.3587652618382903877079071509461176103e-878", "normalized_real_tail_c": "2.1742936347024093331734948224429302747e-877", "normalized_real_tail_dm": "1.6913352432559020839549464521196487283e-876", "phi_lattice_tail": "1.6144292525175739343768210704242839689e-361", "phi_derivative_lattice_tail": "6.3471113161651743543353377638863142176e-358", "envelope_K0": "45.779336961551260847650165707650203536", "envelope_K1": "1974.9153743821504788261579387588952755", "envelope_d": "0.67729048878756286732349724939914712065" } } }, "elapsed_seconds": 0.1660870419582352 }, { "z": { "re": "0.59375", "im": "0.625" }, "bits": 128, "replay": false, "purpose": "grid_2_8", "values": { "m": { "re": "0.24750382949631120901154815287299280823", "im": "-0.091752103501016929557285176946967526587" }, "c": { "re": "0.00042708298106667575236006310502728242101", "im": "-0.0042047097670023089521478221509005664034" }, "dm": { "re": "-0.65698708039227228560701926091545252334", "im": "-0.088717003754888834009622425258282303936" } }, "metadata": { "metadata": { "classification": "diagnostic, not a certificate", "bits": 128, "lattice_cutoff": 24, "gauss_legendre_order_per_segment": 48, "positive_half_segments": [ "0.0", "0.125", "0.25", "0.5", "1.0", "2.0", "4.0" ], "normalization": "B=exp(2*pi*exp(2*z)-9*z)/(4*pi^4), analytic and nonzero", "derivative": "dm=(B*M)' includes B' contribution", "majorants": { "status": "analytic majorants evaluated as floating numbers; NOT interval bounds", "quadrature_error": "NOT bounded: fixed Gauss-Legendre approximation and replay only", "roundoff_error": "NOT bounded: ordinary mpmath arithmetic", "normalized_lattice_m": "1.0023504256681346029154706067065327449e-261", "normalized_lattice_c": "5.3458689368967178822158432357681746394e-261", "normalized_lattice_dm": "4.0656497890068162967514833997108414541e-258", "normalized_real_tail_m": "5.1477744241274786646932068123717832185e-643", "normalized_real_tail_c": "8.2378337945335865738219033319689121949e-642", "normalized_real_tail_dm": "1.0807699869720850508948857161453861191e-640", "phi_lattice_tail": "1.0021598388692270941092068707959257556e-262", "phi_derivative_lattice_tail": "3.9399806736491836923747700781666945459e-259", "envelope_K0": "126.24928292784368352612039481684046491", "envelope_K1": "10771.851462133738538848956859875684407", "envelope_d": "0.49530720860677725930394940995503526598" } } }, "elapsed_seconds": 0.1581974580185488 }, { "z": { "re": "0.828125", "im": "0.125" }, "bits": 128, "replay": false, "purpose": "grid_3_0", "values": { "m": { "re": "0.1800271665827350031011115768531465011", "im": "-0.013150078173251390135673602972754144473" }, "c": { "re": "0.0012770899942684412759777925408333469356", "im": "-0.00041738919726380925439571483131639680867" }, "dm": { "re": "-0.10884416776074263136544295742598471756", "im": "-0.013416795385703830294028707797826855602" } }, "metadata": { "metadata": { "classification": "diagnostic, not a certificate", "bits": 128, "lattice_cutoff": 24, "gauss_legendre_order_per_segment": 48, "positive_half_segments": [ "0.0", "0.125", "0.25", "0.5", "1.0", "2.0", "4.0" ], "normalization": "B=exp(2*pi*exp(2*z)-9*z)/(4*pi^4), analytic and nonzero", "derivative": "dm=(B*M)' includes B' contribution", "majorants": { "status": "analytic majorants evaluated as floating numbers; NOT interval bounds", "quadrature_error": "NOT bounded: fixed Gauss-Legendre approximation and replay only", "roundoff_error": "NOT bounded: ordinary mpmath arithmetic", "normalized_lattice_m": "1.2037538936699754343291699535065578206e-810", "normalized_lattice_c": "6.4200207662398689830889064187016417097e-810", "normalized_lattice_dm": "4.8183282085973639029291919973969758691e-807", "normalized_real_tail_m": "5.171816246922241551488281993165160023e-1965", "normalized_real_tail_c": "8.2753619845173850296983210862416082052e-1964", "normalized_real_tail_dm": "4.4146114506143421593765609548259196896e-1963", "phi_lattice_tail": "4.5885262662854514740333947116012359699e-820", "phi_derivative_lattice_tail": "1.8039741874006024900445183341996020805e-816", "envelope_K0": "7.0806448041385032092774528790706719056", "envelope_K1": "99.811506129080957217155350239768137982", "envelope_d": "1.5219640730090286703744177804891892666" } } }, "elapsed_seconds": 0.1560897909803316 }, { "z": { "re": "0.828125", "im": "0.1875" }, "bits": 128, "replay": false, "purpose": "grid_3_1", "values": { "m": { "re": "0.1810403443860587788895556370266279645", "im": "-0.020148855362265730480976196785199361696" }, "c": { "re": "0.0012073660732635579766108339029983132651", "im": "-0.00062202912397941566362230343662763897095" }, "dm": { "re": "-0.11553406081347773883682120225330208529", "im": "-0.018782567375812423172810677892524512845" } }, "metadata": { "metadata": { "classification": "diagnostic, not a certificate", "bits": 128, "lattice_cutoff": 24, "gauss_legendre_order_per_segment": 48, "positive_half_segments": [ "0.0", "0.125", "0.25", "0.5", "1.0", "2.0", "4.0" ], "normalization": "B=exp(2*pi*exp(2*z)-9*z)/(4*pi^4), analytic and nonzero", "derivative": "dm=(B*M)' includes B' contribution", "majorants": { "status": "analytic majorants evaluated as floating numbers; NOT interval bounds", "quadrature_error": "NOT bounded: fixed Gauss-Legendre approximation and replay only", "roundoff_error": "NOT bounded: ordinary mpmath arithmetic", "normalized_lattice_m": "2.2014660308986326967804787568524999235e-778", "normalized_lattice_c": "1.1741152164792707716162553369879999592e-777", "normalized_lattice_dm": "8.8138058203909679417737792735104128796e-775", "normalized_real_tail_m": "2.2543351306144195152890290664197571706e-1887", "normalized_real_tail_c": "3.6071431731989626629778204017856470668e-1886", "normalized_real_tail_dm": "1.9539080949181075602156120653316744408e-1885", "phi_lattice_tail": "2.575127112483722287169904859455751326e-787", "phi_derivative_lattice_tail": "1.0124084663803664294249623722467560192e-783", "envelope_K0": "7.6916660011049469339417991865339105462", "envelope_K1": "111.95370680359173350893646533622747631", "envelope_d": "1.461637954554517745521968003740990655" } } }, "elapsed_seconds": 0.15804495802149177 }, { "z": { "re": "0.828125", "im": "0.25" }, "bits": 128, "replay": false, "purpose": "grid_3_2", "values": { "m": { "re": "0.18234189932482399502115557653069438852", "im": "-0.027641565744098579662067164175940962172" }, "c": { "re": "0.0011072631761434475376639111599337741863", "im": "-0.00082050925305316585897959762464826116826" }, "dm": { "re": "-0.12460813999149373308496735951140045149", "im": "-0.022561031491292096185037333770420858777" } }, "metadata": { "metadata": { "classification": "diagnostic, not a certificate", "bits": 128, "lattice_cutoff": 24, "gauss_legendre_order_per_segment": 48, "positive_half_segments": [ "0.0", "0.125", "0.25", "0.5", "1.0", "2.0", "4.0" ], "normalization": "B=exp(2*pi*exp(2*z)-9*z)/(4*pi^4), analytic and nonzero", "derivative": "dm=(B*M)' includes B' contribution", "majorants": { "status": "analytic majorants evaluated as floating numbers; NOT interval bounds", "quadrature_error": "NOT bounded: fixed Gauss-Legendre approximation and replay only", "roundoff_error": "NOT bounded: ordinary mpmath arithmetic", "normalized_lattice_m": "6.3833903771304279921677463107225160048e-734", "normalized_lattice_c": "3.4044748678028949291561313657186752026e-733", "normalized_lattice_dm": "2.5564714711208052544523090449239779641e-730", "normalized_real_tail_m": "2.2518486374379676530619812543279916145e-1780", "normalized_real_tail_c": "3.6031770240042800482230370093451671753e-1779", "normalized_real_tail_dm": "1.9968688227958123171886219159080394987e-1778", "phi_lattice_tail": "3.4822619197001443260025646128996249337e-742", "phi_derivative_lattice_tail": "1.3690475443202646147289599099099827161e-738", "envelope_K0": "8.6675384390440944838131174022670163717", "envelope_K1": "132.49029078751267542542390489224169672", "envelope_d": "1.3785034646766524887891155021962680546" } } }, "elapsed_seconds": 0.15827820799313486 }, { "z": { "re": "0.828125", "im": "0.3125" }, "bits": 128, "replay": false, "purpose": "grid_3_3", "values": { "m": { "re": "0.18381723357513530723953331224560249731", "im": "-0.035768472608088110046552731233617514659" }, "c": { "re": "0.00097502733784097550345270454729378343524", "im": "-0.0010087992476912981415486786896225738857" }, "dm": { "re": "-0.13577213558570556213539089825885846914", "im": "-0.024265338757730935975291347923702414179" } }, "metadata": { "metadata": { "classification": "diagnostic, not a certificate", "bits": 128, "lattice_cutoff": 24, "gauss_legendre_order_per_segment": 48, "positive_half_segments": [ "0.0", "0.125", "0.25", "0.5", "1.0", "2.0", "4.0" ], "normalization": "B=exp(2*pi*exp(2*z)-9*z)/(4*pi^4), analytic and nonzero", "derivative": "dm=(B*M)' includes B' contribution", "majorants": { "status": "analytic majorants evaluated as floating numbers; NOT interval bounds", "quadrature_error": "NOT bounded: fixed Gauss-Legendre approximation and replay only", "roundoff_error": "NOT bounded: ordinary mpmath arithmetic", "normalized_lattice_m": "5.9795156957720646601930540232315293466e-678", "normalized_lattice_c": "3.1890750377451011521029621457234823182e-677", "normalized_lattice_dm": "2.395806593819806512793436856872099586e-674", "normalized_real_tail_m": "1.1213931894724540729502107697375583608e-1645", "normalized_real_tail_c": "1.7943472318397251612600066899400503018e-1644", "normalized_real_tail_dm": "1.0274286450188104776508011409087619579e-1643", "phi_lattice_tail": "2.241849059997265044919279156096387541e-685", "phi_derivative_lattice_tail": "8.8138055697724088568987923655992442035e-682", "envelope_K0": "10.18167853949153246670305287452827837", "envelope_K1": "167.18305268120390240767790001762444874", "envelope_d": "1.2738578892849270606047326496499107661" } } }, "elapsed_seconds": 0.15994216699618846 }, { "z": { "re": "0.828125", "im": "0.375" }, "bits": 128, "replay": false, "purpose": "grid_3_4", "values": { "m": { "re": "0.18532252402821288265420417733083639111", "im": "-0.044648760529104586698058543269963606564" }, "c": { "re": "0.00080936911426485461490117683518254334618", "im": "-0.0011815177402606417350482486405673200854" }, "dm": { "re": "-0.14864583533418680168523172323340251142", "im": "-0.023449458763264594279887704001862827551" } }, "metadata": { "metadata": { "classification": "diagnostic, not a certificate", "bits": 128, "lattice_cutoff": 24, "gauss_legendre_order_per_segment": 48, "positive_half_segments": [ "0.0", "0.125", "0.25", "0.5", "1.0", "2.0", "4.0" ], "normalization": "B=exp(2*pi*exp(2*z)-9*z)/(4*pi^4), analytic and nonzero", "derivative": "dm=(B*M)' includes B' contribution", "majorants": { "status": "analytic majorants evaluated as floating numbers; NOT interval bounds", "quadrature_error": "NOT bounded: fixed Gauss-Legendre approximation and replay only", "roundoff_error": "NOT bounded: ordinary mpmath arithmetic", "normalized_lattice_m": "2.4526923019550863292385409643482220451e-611", "normalized_lattice_c": "1.3081025610427127089272218476523850907e-610", "normalized_lattice_dm": "9.8335506710651811542251166296989339034e-608", "normalized_real_tail_m": "2.269073920638860745101278050847368376e-1485", "normalized_real_tail_c": "3.6307831976298772433951430951365894794e-1484", "normalized_real_tail_dm": "2.1788450229775830830618093585333845493e-1483", "phi_lattice_tail": "8.9238448836090041519537254011336962523e-618", "phi_derivative_lattice_tail": "3.5084000587904882233411529679191517387e-614", "envelope_K0": "12.595217910474195352796490529722614478", "envelope_K1": "229.54126205164252921382369277640260385", "envelope_d": "1.1493341875837106139976900705596868057" } } }, "elapsed_seconds": 0.1589225839707069 }, { "z": { "re": "0.828125", "im": "0.4375" }, "bits": 128, "replay": false, "purpose": "grid_3_5", "values": { "m": { "re": "0.18668773568423372158609461699278395493", "im": "-0.054375198020769137265484306922620681116" }, "c": { "re": "0.00061004623519967774208280209750434042332", "im": "-0.0013319887870199999502133124580876122425" }, "dm": { "re": "-0.16276473774140111211482766103581237703", "im": "-0.019723291951434699656873199402899821786" } }, "metadata": { "metadata": { "classification": "diagnostic, not a certificate", "bits": 128, "lattice_cutoff": 24, "gauss_legendre_order_per_segment": 48, "positive_half_segments": [ "0.0", "0.125", "0.25", "0.5", "1.0", "2.0", "4.0" ], "normalization": "B=exp(2*pi*exp(2*z)-9*z)/(4*pi^4), analytic and nonzero", "derivative": "dm=(B*M)' includes B' contribution", "majorants": { "status": "analytic majorants evaluated as floating numbers; NOT interval bounds", "quadrature_error": "NOT bounded: fixed Gauss-Legendre approximation and replay only", "roundoff_error": "NOT bounded: ordinary mpmath arithmetic", "normalized_lattice_m": "4.1220997164490054475306704204912792438e-535", "normalized_lattice_c": "2.1984531821061362386830242242620155967e-534", "normalized_lattice_dm": "1.6543218419382622739567931120113876746e-531", "normalized_real_tail_m": "6.2174455629335262338849972277371992347e-1302", "normalized_real_tail_c": "9.9487415264647544375700777597312875719e-1301", "normalized_real_tail_dm": "6.4132535787359344235678371078971754413e-1300", "phi_lattice_tail": "1.9356365872969653834965440138348783136e-540", "phi_derivative_lattice_tail": "7.6099345128052750467898755680309622573e-537", "envelope_K0": "16.757999595347284854867734621554433003", "envelope_K1": "357.61040338926418324104642749144832606", "envelope_d": "1.0068755102900204581994763865832455735" } } }, "elapsed_seconds": 0.15863400005036965 }, { "z": { "re": "0.828125", "im": "0.5" }, "bits": 128, "replay": false, "purpose": "grid_3_6", "values": { "m": { "re": "0.18772053078835680027351349960024403405", "im": "-0.06500897674624689830184202350912860033" }, "c": { "re": "0.00037841797133317413996373632891899542606", "im": "-0.0014525077510784561714801768330799789001" }, "dm": { "re": "-0.17758086139244191848887602129690527232", "im": "-0.012763871562894108188001319063190813419" } }, "metadata": { "metadata": { "classification": "diagnostic, not a certificate", "bits": 128, "lattice_cutoff": 24, "gauss_legendre_order_per_segment": 48, "positive_half_segments": [ "0.0", "0.125", "0.25", "0.5", "1.0", "2.0", "4.0" ], "normalization": "B=exp(2*pi*exp(2*z)-9*z)/(4*pi^4), analytic and nonzero", "derivative": "dm=(B*M)' includes B' contribution", "majorants": { "status": "analytic majorants evaluated as floating numbers; NOT interval bounds", "quadrature_error": "NOT bounded: fixed Gauss-Legendre approximation and replay only", "roundoff_error": "NOT bounded: ordinary mpmath arithmetic", "normalized_lattice_m": "1.9201731325258517718051277277190516889e-450", "normalized_lattice_c": "1.0240923373471209449627347881168275674e-449", "normalized_lattice_dm": "7.7202860885035056439921296627835190809e-447", "normalized_real_tail_m": "3.50634595966585656009516929731072638e-1098", "normalized_real_tail_c": "5.610707936024317721744439738918259875e-1097", "normalized_real_tail_dm": "4.0958388380601650688161715728561254056e-1096", "phi_lattice_tail": "1.4210689249680573121153852115435788848e-454", "phi_derivative_lattice_tail": "5.5869172592419013598919352956561404267e-451", "envelope_K0": "24.983585560594923710980841691774397433", "envelope_K1": "691.58751112121217564683229655248525689", "envelope_d": "0.84870487741648658484554125650222836214" } } }, "elapsed_seconds": 0.15724420797778293 }, { "z": { "re": "0.828125", "im": "0.5625" }, "bits": 128, "replay": false, "purpose": "grid_3_7", "values": { "m": { "re": "0.18821291917208839261306099072586654789", "im": "-0.076571814369412604606839389902232637334" }, "c": { "re": "0.00011812619204369840464227916107100428419", "im": "-0.0015344338077568679304510843944491914766" }, "dm": { "re": "-0.19233370851158040536721792974107279278", "im": "-0.0025149544878615113794006810494980533495" } }, "metadata": { "metadata": { "classification": "diagnostic, not a certificate", "bits": 128, "lattice_cutoff": 24, "gauss_legendre_order_per_segment": 48, "positive_half_segments": [ "0.0", "0.125", "0.25", "0.5", "1.0", "2.0", "4.0" ], "normalization": "B=exp(2*pi*exp(2*z)-9*z)/(4*pi^4), analytic and nonzero", "derivative": "dm=(B*M)' includes B' contribution", "majorants": { "status": "analytic majorants evaluated as floating numbers; NOT interval bounds", "quadrature_error": "NOT bounded: fixed Gauss-Legendre approximation and replay only", "roundoff_error": "NOT bounded: ordinary mpmath arithmetic", "normalized_lattice_m": "1.3060561995502188317996597170051029284e-358", "normalized_lattice_c": "6.9656330642678337695981851573605489515e-358", "normalized_lattice_dm": "5.2727075645628345243078966104055201461e-355", "normalized_real_tail_m": "3.342135323547700162871013656395618062e-877", "normalized_real_tail_c": "5.348078703802391981639735115213989867e-876", "normalized_real_tail_dm": "4.9721647901360134131474466858079841795e-875", "phi_lattice_tail": "1.6144292525175739343768210704242839689e-361", "phi_derivative_lattice_tail": "6.3471113161651743543353377638863142176e-358", "envelope_K0": "45.779336961551260847650165707650203536", "envelope_K1": "1974.9153743821504788261579387588952755", "envelope_d": "0.67729048878756286732349724939914712065" } } }, "elapsed_seconds": 0.15831374999834225 }, { "z": { "re": "0.828125", "im": "0.625" }, "bits": 128, "replay": false, "purpose": "grid_3_8", "values": { "m": { "re": "0.18808086240018465588191827217244092716", "im": "-0.089110087084811429612684224605279752104" }, "c": { "re": "-0.00014863249381270317874314575106841997453", "im": "-0.0015775984281086719229082299178192002558" }, "dm": { "re": "-0.21313321987770223462534818026795202181", "im": "0.0040139236968359844999283797234732437789" } }, "metadata": { "metadata": { "classification": "diagnostic, not a certificate", "bits": 128, "lattice_cutoff": 24, "gauss_legendre_order_per_segment": 48, "positive_half_segments": [ "0.0", "0.125", "0.25", "0.5", "1.0", "2.0", "4.0" ], "normalization": "B=exp(2*pi*exp(2*z)-9*z)/(4*pi^4), analytic and nonzero", "derivative": "dm=(B*M)' includes B' contribution", "majorants": { "status": "analytic majorants evaluated as floating numbers; NOT interval bounds", "quadrature_error": "NOT bounded: fixed Gauss-Legendre approximation and replay only", "roundoff_error": "NOT bounded: ordinary mpmath arithmetic", "normalized_lattice_m": "5.9160574946156658217508133093369088519e-261", "normalized_lattice_c": "3.155230663795021771600433764979684721e-260", "normalized_lattice_dm": "2.4139838403953249515210818142088057055e-257", "normalized_real_tail_m": "3.0383116206241147705215064202792719088e-642", "normalized_real_tail_c": "4.8621217801212700387127723442368561977e-641", "normalized_real_tail_dm": "7.1165033144910642251158065810018975577e-640", "phi_lattice_tail": "1.0021598388692270941092068707959257556e-262", "phi_derivative_lattice_tail": "3.9399806736491836923747700781666945459e-259", "envelope_K0": "126.24928292784368352612039481684046491", "envelope_K1": "10771.851462133738538848956859875684407", "envelope_d": "0.49530720860677725930394940995503526598" } } }, "elapsed_seconds": 0.15842312498716637 }, { "z": { "re": "1.0625", "im": "0.125" }, "bits": 128, "replay": false, "purpose": "grid_4_0", "values": { "m": { "re": "0.15307226147764495264261363927276555681", "im": "-0.01442328187226936525925517970911378177" }, "c": { "re": "0.0006810552809561423091131397533287733424", "im": "-0.00024125855567189118411117138124794389268" }, "dm": { "re": "-0.11701159401988109821779866271609488622", "im": "0.00067991359858892589697740437480991255028" } }, "metadata": { "metadata": { "classification": "diagnostic, not a certificate", "bits": 128, "lattice_cutoff": 24, "gauss_legendre_order_per_segment": 48, "positive_half_segments": [ "0.0", "0.125", "0.25", "0.5", "1.0", "2.0", "4.0" ], "normalization": "B=exp(2*pi*exp(2*z)-9*z)/(4*pi^4), analytic and nonzero", "derivative": "dm=(B*M)' includes B' contribution", "majorants": { "status": "analytic majorants evaluated as floating numbers; NOT interval bounds", "quadrature_error": "NOT bounded: fixed Gauss-Legendre approximation and replay only", "roundoff_error": "NOT bounded: ordinary mpmath arithmetic", "normalized_lattice_m": "2.809157720183157437667402923781129154e-803", "normalized_lattice_c": "1.4982174507643506334226148926832688822e-802", "normalized_lattice_dm": "1.1354919130131258282693227535510464719e-799", "normalized_real_tail_m": "1.2069283940686847652618358251231710525e-1957", "normalized_real_tail_c": "1.9311918431468545861966541606708097091e-1956", "normalized_real_tail_dm": "1.505222923104746916349489461367037186e-1955", "phi_lattice_tail": "4.5885262662854514740333947116012359699e-820", "phi_derivative_lattice_tail": "1.8039741874006024900445183341996020805e-816", "envelope_K0": "7.0806448041385032092774528790706719056", "envelope_K1": "99.811506129080957217155350239768137982", "envelope_d": "1.5219640730090286703744177804891892666" } } }, "elapsed_seconds": 0.1593689169967547 }, { "z": { "re": "1.0625", "im": "0.1875" }, "bits": 128, "replay": false, "purpose": "grid_4_1", "values": { "m": { "re": "0.15300047583026472808748974764788332337", "im": "-0.021823379364395407147936155308125386805" }, "c": { "re": "0.00063376112507387587035644543771432166299", "im": "-0.00035582325781447848885600220380551323044" }, "dm": { "re": "-0.11997113723681493196182193905335033023", "im": "0.0017351168845572710962429977145451292211" } }, "metadata": { "metadata": { "classification": "diagnostic, not a certificate", "bits": 128, "lattice_cutoff": 24, "gauss_legendre_order_per_segment": 48, "positive_half_segments": [ "0.0", "0.125", "0.25", "0.5", "1.0", "2.0", "4.0" ], "normalization": "B=exp(2*pi*exp(2*z)-9*z)/(4*pi^4), analytic and nonzero", "derivative": "dm=(B*M)' includes B' contribution", "majorants": { "status": "analytic majorants evaluated as floating numbers; NOT interval bounds", "quadrature_error": "NOT bounded: fixed Gauss-Legendre approximation and replay only", "roundoff_error": "NOT bounded: ordinary mpmath arithmetic", "normalized_lattice_m": "2.4120830502592157678173152428468734354e-771", "normalized_lattice_c": "1.2864442934715817428359014628516658322e-770", "normalized_lattice_dm": "9.7519141364176335391457289779678839477e-768", "normalized_real_tail_m": "2.4700102031278241801012902726423581103e-1880", "normalized_real_tail_c": "3.952243089746810964032104868995437245e-1879", "normalized_real_tail_dm": "3.1124313245954887137069799432254301905e-1878", "phi_lattice_tail": "2.575127112483722287169904859455751326e-787", "phi_derivative_lattice_tail": "1.0124084663803664294249623722467560192e-783", "envelope_K0": "7.6916660011049469339417991865339105462", "envelope_K1": "111.95370680359173350893646533622747631", "envelope_d": "1.461637954554517745521968003740990655" } } }, "elapsed_seconds": 0.15740283305058256 }, { "z": { "re": "1.0625", "im": "0.25" }, "bits": 128, "replay": false, "purpose": "grid_4_2", "values": { "m": { "re": "0.15283791879989467996156011953659497438", "im": "-0.029440642102091267210665025161821155504" }, "c": { "re": "0.00056798245072854748371631054845882856064", "im": "-0.00046287477498034256391993177962001952596" }, "dm": { "re": "-0.12393553193377992414491159225429727638", "im": "0.0036272982523650782763263518553581860021" } }, "metadata": { "metadata": { "classification": "diagnostic, not a certificate", "bits": 128, "lattice_cutoff": 24, "gauss_legendre_order_per_segment": 48, "positive_half_segments": [ "0.0", "0.125", "0.25", "0.5", "1.0", "2.0", "4.0" ], "normalization": "B=exp(2*pi*exp(2*z)-9*z)/(4*pi^4), analytic and nonzero", "derivative": "dm=(B*M)' includes B' contribution", "majorants": { "status": "analytic majorants evaluated as floating numbers; NOT interval bounds", "quadrature_error": "NOT bounded: fixed Gauss-Legendre approximation and replay only", "roundoff_error": "NOT bounded: ordinary mpmath arithmetic", "normalized_lattice_m": "2.4673251735939550896083562389380082446e-727", "normalized_lattice_c": "1.3159067592501093811244566607669377305e-726", "normalized_lattice_dm": "9.9783302897382401926269017421998346485e-724", "normalized_real_tail_m": "8.7039057648415248727955473720356822736e-1774", "normalized_real_tail_c": "1.3927096497328103848163397301784079495e-1772", "normalized_real_tail_dm": "1.1139772459229630698736281652052709877e-1771", "phi_lattice_tail": "3.4822619197001443260025646128996249337e-742", "phi_derivative_lattice_tail": "1.3690475443202646147289599099099827161e-738", "envelope_K0": "8.6675384390440944838131174022670163717", "envelope_K1": "132.49029078751267542542390489224169672", "envelope_d": "1.3785034646766524887891155021962680546" } } }, "elapsed_seconds": 0.1612241250113584 }, { "z": { "re": "1.0625", "im": "0.3125" }, "bits": 128, "replay": false, "purpose": "grid_4_3", "values": { "m": { "re": "0.15252453820562586813430066796075372827", "im": "-0.037332623580246400822695670417062671469" }, "c": { "re": "0.00048434408022861602563349698137399349719", "im": "-0.0005595700829701143013066110945322553407" }, "dm": { "re": "-0.12872893949167958929591654334018375546", "im": "0.0065996602537595501062463966318030822663" } }, "metadata": { "metadata": { "classification": "diagnostic, not a certificate", "bits": 128, "lattice_cutoff": 24, "gauss_legendre_order_per_segment": 48, "positive_half_segments": [ "0.0", "0.125", "0.25", "0.5", "1.0", "2.0", "4.0" ], "normalization": "B=exp(2*pi*exp(2*z)-9*z)/(4*pi^4), analytic and nonzero", "derivative": "dm=(B*M)' includes B' contribution", "majorants": { "status": "analytic majorants evaluated as floating numbers; NOT interval bounds", "quadrature_error": "NOT bounded: fixed Gauss-Legendre approximation and replay only", "roundoff_error": "NOT bounded: ordinary mpmath arithmetic", "normalized_lattice_m": "6.2265828760812723648517158660465785595e-672", "normalized_lattice_c": "3.3208442005766785945875817952248418984e-671", "normalized_lattice_dm": "2.51925615233470512006832341011437997e-668", "normalized_real_tail_m": "1.167727954265664452705683792241607037e-1639", "normalized_real_tail_c": "1.8684877364594779542961238524357255482e-1638", "normalized_real_tail_dm": "1.528552810500130783961443397999679309e-1637", "phi_lattice_tail": "2.241849059997265044919279156096387541e-685", "phi_derivative_lattice_tail": "8.8138055697724088568987923655992442035e-682", "envelope_K0": "10.18167853949153246670305287452827837", "envelope_K1": "167.18305268120390240767790001762444874", "envelope_d": "1.2738578892849270606047326496499107661" } } }, "elapsed_seconds": 0.16407233400968835 }, { "z": { "re": "1.0625", "im": "0.375" }, "bits": 128, "replay": false, "purpose": "grid_4_4", "values": { "m": { "re": "0.15198601115196930491309800676577994282", "im": "-0.045544450508869370760915444105804885775" }, "c": { "re": "0.00038389529362082458771885072263845951619", "im": "-0.00064287845451472148577954116999889594345" }, "dm": { "re": "-0.13413013656856456133896299251240865721", "im": "0.010864323509009361058823040517030608078" } }, "metadata": { "metadata": { "classification": "diagnostic, not a certificate", "bits": 128, "lattice_cutoff": 24, "gauss_legendre_order_per_segment": 48, "positive_half_segments": [ "0.0", "0.125", "0.25", "0.5", "1.0", "2.0", "4.0" ], "normalization": "B=exp(2*pi*exp(2*z)-9*z)/(4*pi^4), analytic and nonzero", "derivative": "dm=(B*M)' includes B' contribution", "majorants": { "status": "analytic majorants evaluated as floating numbers; NOT interval bounds", "quadrature_error": "NOT bounded: fixed Gauss-Legendre approximation and replay only", "roundoff_error": "NOT bounded: ordinary mpmath arithmetic", "normalized_lattice_m": "5.3633723587732120789435595534954951945e-606", "normalized_lattice_c": "2.8604652580123797754365650951975974371e-605", "normalized_lattice_dm": "2.171380662642776885165710348321914529e-602", "normalized_real_tail_m": "4.9618487962255942317313489787955143642e-1480", "normalized_real_tail_c": "7.9395373921726011577875552269591951997e-1479", "normalized_real_tail_dm": "6.7119568552932143387384850132480432966e-1478", "phi_lattice_tail": "8.9238448836090041519537254011336962523e-618", "phi_derivative_lattice_tail": "3.5084000587904882233411529679191517387e-614", "envelope_K0": "12.595217910474195352796490529722614478", "envelope_K1": "229.54126205164252921382369277640260385", "envelope_d": "1.1493341875837106139976900705596868057" } } }, "elapsed_seconds": 0.1670367500046268 }, { "z": { "re": "1.0625", "im": "0.4375" }, "bits": 128, "replay": false, "purpose": "grid_4_5", "values": { "m": { "re": "0.15113593779314710078180869712956896894", "im": "-0.054106111896362611459182933410818037136" }, "c": { "re": "0.00026824816783816396216839747900316461957", "im": "-0.0007096500422629902585074874726093891932" }, "dm": { "re": "-0.13987676730192432785154122024944407685", "im": "0.016594298234353334583503790172438886942" } }, "metadata": { "metadata": { "classification": "diagnostic, not a certificate", "bits": 128, "lattice_cutoff": 24, "gauss_legendre_order_per_segment": 48, "positive_half_segments": [ "0.0", "0.125", "0.25", "0.5", "1.0", "2.0", "4.0" ], "normalization": "B=exp(2*pi*exp(2*z)-9*z)/(4*pi^4), analytic and nonzero", "derivative": "dm=(B*M)' includes B' contribution", "majorants": { "status": "analytic majorants evaluated as floating numbers; NOT interval bounds", "quadrature_error": "NOT bounded: fixed Gauss-Legendre approximation and replay only", "roundoff_error": "NOT bounded: ordinary mpmath arithmetic", "normalized_lattice_m": "1.5118318956546037798272204094567402768e-530", "normalized_lattice_c": "8.0631034434912201590785088504359481431e-530", "normalized_lattice_dm": "6.1267238011157425804763381972189276642e-527", "normalized_real_tail_m": "2.2803263283588210867997624305220069343e-1297", "normalized_real_tail_c": "3.648826034293475930391487192205161285e-1296", "normalized_real_tail_dm": "3.2464312331961583658018409573496083343e-1295", "phi_lattice_tail": "1.9356365872969653834965440138348783136e-540", "phi_derivative_lattice_tail": "7.6099345128052750467898755680309622573e-537", "envelope_K0": "16.757999595347284854867734621554433003", "envelope_K1": "357.61040338926418324104642749144832606", "envelope_d": "1.0068755102900204581994763865832455735" } } }, "elapsed_seconds": 0.15726624999660999 }, { "z": { "re": "1.0625", "im": "0.5" }, "bits": 128, "replay": false, "purpose": "grid_4_6", "values": { "m": { "re": "0.14987853270882835706243471569205394624", "im": "-0.06303005963240246558600385808027650852" }, "c": { "re": "0.00013970063280219428665591961037011748086", "im": "-0.00075674284448749462211382896457408733157" }, "dm": { "re": "-0.14567109307331499031678739411556946045", "im": "0.023915635210003052813561979200727953458" } }, "metadata": { "metadata": { "classification": "diagnostic, not a certificate", "bits": 128, "lattice_cutoff": 24, "gauss_legendre_order_per_segment": 48, "positive_half_segments": [ "0.0", "0.125", "0.25", "0.5", "1.0", "2.0", "4.0" ], "normalization": "B=exp(2*pi*exp(2*z)-9*z)/(4*pi^4), analytic and nonzero", "derivative": "dm=(B*M)' includes B' contribution", "majorants": { "status": "analytic majorants evaluated as floating numbers; NOT interval bounds", "quadrature_error": "NOT bounded: fixed Gauss-Legendre approximation and replay only", "roundoff_error": "NOT bounded: ordinary mpmath arithmetic", "normalized_lattice_m": "9.7005095845184140743716834482993973128e-447", "normalized_lattice_c": "5.1736051117431541729982311724263452335e-446", "normalized_lattice_dm": "3.9382230956937931976881155095870767072e-443", "normalized_real_tail_m": "1.7713685298592796524150127417702923886e-1094", "normalized_real_tail_c": "2.8344697250160416059706693970838025684e-1093", "normalized_real_tail_dm": "2.7633865469081628565644888108368648826e-1092", "phi_lattice_tail": "1.4210689249680573121153852115435788848e-454", "phi_derivative_lattice_tail": "5.5869172592419013598919352956561404267e-451", "envelope_K0": "24.983585560594923710980841691774397433", "envelope_K1": "691.58751112121217564683229655248525689", "envelope_d": "0.84870487741648658484554125650222836214" } } }, "elapsed_seconds": 0.15833291597664356 }, { "z": { "re": "1.0625", "im": "0.5625" }, "bits": 128, "replay": false, "purpose": "grid_4_7", "values": { "m": { "re": "0.14811179254945865366838705285623783671", "im": "-0.072309219437229606316127948195534859175" }, "c": { "re": "0.0000013234998288106850610337589801264050833", "im": "-0.00078120299202318970510057815870739436036" }, "dm": { "re": "-0.15118735410487632500851066956436915383", "im": "0.032900101197782575245008678591316685291" } }, "metadata": { "metadata": { "classification": "diagnostic, not a certificate", "bits": 128, "lattice_cutoff": 24, "gauss_legendre_order_per_segment": 48, "positive_half_segments": [ "0.0", "0.125", "0.25", "0.5", "1.0", "2.0", "4.0" ], "normalization": "B=exp(2*pi*exp(2*z)-9*z)/(4*pi^4), analytic and nonzero", "derivative": "dm=(B*M)' includes B' contribution", "majorants": { "status": "analytic majorants evaluated as floating numbers; NOT interval bounds", "quadrature_error": "NOT bounded: fixed Gauss-Legendre approximation and replay only", "roundoff_error": "NOT bounded: ordinary mpmath arithmetic", "normalized_lattice_m": "7.6983692032571320013001429898826351868e-356", "normalized_lattice_c": "4.105796908403803734026742927937405433e-355", "normalized_lattice_dm": "3.1380788148813214988562529335906783028e-352", "normalized_real_tail_m": "1.969975844590608424564591877173006313e-874", "normalized_real_tail_c": "3.1523516678781770468203617680365777907e-873", "normalized_real_tail_dm": "3.7023913719651652677086990144555508312e-872", "phi_lattice_tail": "1.6144292525175739343768210704242839689e-361", "phi_derivative_lattice_tail": "6.3471113161651743543353377638863142176e-358", "envelope_K0": "45.779336961551260847650165707650203536", "envelope_K1": "1974.9153743821504788261579387588952755", "envelope_d": "0.67729048878756286732349724939914712065" } } }, "elapsed_seconds": 0.1575278749805875 }, { "z": { "re": "1.0625", "im": "0.625" }, "bits": 128, "replay": false, "purpose": "grid_4_8", "values": { "m": { "re": "0.14573133159109027420213736711199454695", "im": "-0.081915576629104549167167568203915157221" }, "c": { "re": "-0.00014297891608473148736584536908211209496", "im": "-0.00078049405169187571221215849951565557856" }, "dm": { "re": "-0.15609462129306050657762774166083576162", "im": "0.043537182171460881614005564213918655343" } }, "metadata": { "metadata": { "classification": "diagnostic, not a certificate", "bits": 128, "lattice_cutoff": 24, "gauss_legendre_order_per_segment": 48, "positive_half_segments": [ "0.0", "0.125", "0.25", "0.5", "1.0", "2.0", "4.0" ], "normalization": "B=exp(2*pi*exp(2*z)-9*z)/(4*pi^4), analytic and nonzero", "derivative": "dm=(B*M)' includes B' contribution", "majorants": { "status": "analytic majorants evaluated as floating numbers; NOT interval bounds", "quadrature_error": "NOT bounded: fixed Gauss-Legendre approximation and replay only", "roundoff_error": "NOT bounded: ordinary mpmath arithmetic", "normalized_lattice_m": "3.5638953975471805890183110983236419457e-259", "normalized_lattice_c": "1.9007442120251629808097659191059423711e-258", "normalized_lattice_dm": "1.4681631174591969490208759287688568066e-255", "normalized_real_tail_m": "1.8303109479431874747481346761504931389e-640", "normalized_real_tail_c": "2.9289934133092483288804594986170817529e-639", "normalized_real_tail_dm": "5.0036826700105003567793702873163817959e-638", "phi_lattice_tail": "1.0021598388692270941092068707959257556e-262", "phi_derivative_lattice_tail": "3.9399806736491836923747700781666945459e-259", "envelope_K0": "126.24928292784368352612039481684046491", "envelope_K1": "10771.851462133738538848956859875684407", "envelope_d": "0.49530720860677725930394940995503526598" } } }, "elapsed_seconds": 0.1571596250287257 }, { "z": { "re": "1.296875", "im": "0.125" }, "bits": 128, "replay": false, "purpose": "grid_5_0", "values": { "m": { "re": "0.1264657766562641485029435928940159338", "im": "-0.013471444554102144785752996563411415423" }, "c": { "re": "0.0003524294539716132124276445326905277896", "im": "-0.00013033888618250556463844603221620888082" }, "dm": { "re": "-0.10835924340833628074217799221697426842", "im": "0.0064841738252048014270703870654212972649" } }, "metadata": { "metadata": { "classification": "diagnostic, not a certificate", "bits": 128, "lattice_cutoff": 24, "gauss_legendre_order_per_segment": 48, "positive_half_segments": [ "0.0", "0.125", "0.25", "0.5", "1.0", "2.0", "4.0" ], "normalization": "B=exp(2*pi*exp(2*z)-9*z)/(4*pi^4), analytic and nonzero", "derivative": "dm=(B*M)' includes B' contribution", "majorants": { "status": "analytic majorants evaluated as floating numbers; NOT interval bounds", "quadrature_error": "NOT bounded: fixed Gauss-Legendre approximation and replay only", "roundoff_error": "NOT bounded: ordinary mpmath arithmetic", "normalized_lattice_m": "5.8950242593158161788476146955900393626e-791", "normalized_lattice_c": "3.1440129383017686287187278376480209934e-790", "normalized_lattice_dm": "2.4199175947005045292692013343829517869e-787", "normalized_real_tail_m": "2.5327421494255172524235109637426247678e-1945", "normalized_real_tail_c": "4.0526107462564496070912286122632264944e-1944", "normalized_real_tail_dm": "4.7520394972832394192149633635373758248e-1943", "phi_lattice_tail": "4.5885262662854514740333947116012359699e-820", "phi_derivative_lattice_tail": "1.8039741874006024900445183341996020805e-816", "envelope_K0": "7.0806448041385032092774528790706719056", "envelope_K1": "99.811506129080957217155350239768137982", "envelope_d": "1.5219640730090286703744177804891892666" } } }, "elapsed_seconds": 0.15790145797654986 }, { "z": { "re": "1.296875", "im": "0.1875" }, "bits": 128, "replay": false, "purpose": "grid_5_1", "values": { "m": { "re": "0.12595003559613295086296446910537684381", "im": "-0.020274930790757394544940822214458468241" }, "c": { "re": "0.00032496983902788171617347165143024461475", "im": "-0.00019120717387020559459916871874369243779" }, "dm": { "re": "-0.1094128658117698985383904864273159712", "im": "0.010077192880305195700136384264779040019" } }, "metadata": { "metadata": { "classification": "diagnostic, not a certificate", "bits": 128, "lattice_cutoff": 24, "gauss_legendre_order_per_segment": 48, "positive_half_segments": [ "0.0", "0.125", "0.25", "0.5", "1.0", "2.0", "4.0" ], "normalization": "B=exp(2*pi*exp(2*z)-9*z)/(4*pi^4), analytic and nonzero", "derivative": "dm=(B*M)' includes B' contribution", "majorants": { "status": "analytic majorants evaluated as floating numbers; NOT interval bounds", "quadrature_error": "NOT bounded: fixed Gauss-Legendre approximation and replay only", "roundoff_error": "NOT bounded: ordinary mpmath arithmetic", "normalized_lattice_m": "1.5121222376844441362768396899479760397e-759", "normalized_lattice_c": "8.0646519343170353934764783463892055453e-759", "normalized_lattice_dm": "6.2085321241829931476180765527740232864e-756", "normalized_real_tail_m": "1.5484364665867017923075477882701186945e-1868", "normalized_real_tail_c": "2.477640504168621259041171068953907756e-1867", "normalized_real_tail_dm": "2.9250895286140944357010195654560120127e-1866", "phi_lattice_tail": "2.575127112483722287169904859455751326e-787", "phi_derivative_lattice_tail": "1.0124084663803664294249623722467560192e-783", "envelope_K0": "7.6916660011049469339417991865339105462", "envelope_K1": "111.95370680359173350893646533622747631", "envelope_d": "1.461637954554517745521968003740990655" } } }, "elapsed_seconds": 0.15659612498711795 }, { "z": { "re": "1.296875", "im": "0.25" }, "bits": 128, "replay": false, "purpose": "grid_5_2", "values": { "m": { "re": "0.12519762444556193931366788205350479953", "im": "-0.027154815007965683302224298022561932165" }, "c": { "re": "0.00028728073171379527756058699825457482003", "im": "-0.00024693159645237631172837148696915771216" }, "dm": { "re": "-0.11079022717368324122683563768925417391", "im": "0.014077885681819097627541956220481086158" } }, "metadata": { "metadata": { "classification": "diagnostic, not a certificate", "bits": 128, "lattice_cutoff": 24, "gauss_legendre_order_per_segment": 48, "positive_half_segments": [ "0.0", "0.125", "0.25", "0.5", "1.0", "2.0", "4.0" ], "normalization": "B=exp(2*pi*exp(2*z)-9*z)/(4*pi^4), analytic and nonzero", "derivative": "dm=(B*M)' includes B' contribution", "majorants": { "status": "analytic majorants evaluated as floating numbers; NOT interval bounds", "quadrature_error": "NOT bounded: fixed Gauss-Legendre approximation and replay only", "roundoff_error": "NOT bounded: ordinary mpmath arithmetic", "normalized_lattice_m": "2.926305406633290552769012902241863991e-716", "normalized_lattice_c": "1.5606962168710882948101402145289941286e-715", "normalized_lattice_dm": "1.2018544407944487752095735286101254053e-712", "normalized_real_tail_m": "1.0323035962617725260570696940330802086e-1762", "normalized_real_tail_c": "1.6517862426487684129913125949372439028e-1761", "normalized_real_tail_dm": "1.9703333873888371548234458535450611486e-1760", "phi_lattice_tail": "3.4822619197001443260025646128996249337e-742", "phi_derivative_lattice_tail": "1.3690475443202646147289599099099827161e-738", "envelope_K0": "8.6675384390440944838131174022670163717", "envelope_K1": "132.49029078751267542542390489224169672", "envelope_d": "1.3785034646766524887891155021962680546" } } }, "elapsed_seconds": 0.154644416004885 }, { "z": { "re": "1.296875", "im": "0.3125" }, "bits": 128, "replay": false, "purpose": "grid_5_3", "values": { "m": { "re": "0.12417942569500212903503807242088073314", "im": "-0.034128494683935978565742264706731393382" }, "c": { "re": "0.00024015261075959829857455339553820276708", "im": "-0.00029584105510080071755471189301822439923" }, "dm": { "re": "-0.11239652655716012558869201077480702531", "im": "0.018599916324095293060526207862026256016" } }, "metadata": { "metadata": { "classification": "diagnostic, not a certificate", "bits": 128, "lattice_cutoff": 24, "gauss_legendre_order_per_segment": 48, "positive_half_segments": [ "0.0", "0.125", "0.25", "0.5", "1.0", "2.0", "4.0" ], "normalization": "B=exp(2*pi*exp(2*z)-9*z)/(4*pi^4), analytic and nonzero", "derivative": "dm=(B*M)' includes B' contribution", "majorants": { "status": "analytic majorants evaluated as floating numbers; NOT interval bounds", "quadrature_error": "NOT bounded: fixed Gauss-Legendre approximation and replay only", "roundoff_error": "NOT bounded: ordinary mpmath arithmetic", "normalized_lattice_m": "9.0811082167441231367280523557940129862e-662", "normalized_lattice_c": "4.8432577155968656729216279230901402593e-661", "normalized_lattice_dm": "3.7312756861479654447007839445550148506e-658", "normalized_real_tail_m": "1.7030631618409569412247346653431219862e-1629", "normalized_real_tail_c": "2.7250804613278737998633533061333404775e-1628", "normalized_real_tail_dm": "3.2999176990841909822375507809984414224e-1627", "phi_lattice_tail": "2.241849059997265044919279156096387541e-685", "phi_derivative_lattice_tail": "8.8138055697724088568987923655992442035e-682", "envelope_K0": "10.18167853949153246670305287452827837", "envelope_K1": "167.18305268120390240767790001762444874", "envelope_d": "1.2738578892849270606047326496499107661" } } }, "elapsed_seconds": 0.15660758299054578 }, { "z": { "re": "1.296875", "im": "0.375" }, "bits": 128, "replay": false, "purpose": "grid_5_4", "values": { "m": { "re": "0.12285977865152054825363666994892116673", "im": "-0.041206712295052155577937115366105861464" }, "c": { "re": "0.0001846450854526733893858020362037461724", "im": "-0.0003363285008700225232627765449494767157" }, "dm": { "re": "-0.11411407756628645922373748505163518255", "im": "0.023738285863035479672587396482784672326" } }, "metadata": { "metadata": { "classification": "diagnostic, not a certificate", "bits": 128, "lattice_cutoff": 24, "gauss_legendre_order_per_segment": 48, "positive_half_segments": [ "0.0", "0.125", "0.25", "0.5", "1.0", "2.0", "4.0" ], "normalization": "B=exp(2*pi*exp(2*z)-9*z)/(4*pi^4), analytic and nonzero", "derivative": "dm=(B*M)' includes B' contribution", "majorants": { "status": "analytic majorants evaluated as floating numbers; NOT interval bounds", "quadrature_error": "NOT bounded: fixed Gauss-Legendre approximation and replay only", "roundoff_error": "NOT bounded: ordinary mpmath arithmetic", "normalized_lattice_m": "6.4598655522613686451330919065436486614e-597", "normalized_lattice_c": "3.4452616278727299440709823501566126194e-596", "normalized_lattice_dm": "2.655896969910897287610891297678311591e-593", "normalized_real_tail_m": "5.9762541121793102303830070841494429248e-1471", "normalized_real_tail_c": "9.5627043340914440925187365713354886335e-1470", "normalized_real_tail_dm": "1.1839937918258593124358223784856754601e-1468", "phi_lattice_tail": "8.9238448836090041519537254011336962523e-618", "phi_derivative_lattice_tail": "3.5084000587904882233411529679191517387e-614", "envelope_K0": "12.595217910474195352796490529722614478", "envelope_K1": "229.54126205164252921382369277640260385", "envelope_d": "1.1493341875837106139976900705596868057" } } }, "elapsed_seconds": 0.1577676250017248 }, { "z": { "re": "1.296875", "im": "0.4375" }, "bits": 128, "replay": false, "purpose": "grid_5_5", "values": { "m": { "re": "0.12119777666269375843571375112780773295", "im": "-0.048392221400477272989004856326410629249" }, "c": { "re": "0.00012210572253010133340059639365712275193", "im": "-0.00036689628807347072588846634829812214573" }, "dm": { "re": "-0.11580551872151753790762029176291339444", "im": "0.02956520912302900617004709431487538552" } }, "metadata": { "metadata": { "classification": "diagnostic, not a certificate", "bits": 128, "lattice_cutoff": 24, "gauss_legendre_order_per_segment": 48, "positive_half_segments": [ "0.0", "0.125", "0.25", "0.5", "1.0", "2.0", "4.0" ], "normalization": "B=exp(2*pi*exp(2*z)-9*z)/(4*pi^4), analytic and nonzero", "derivative": "dm=(B*M)' includes B' contribution", "majorants": { "status": "analytic majorants evaluated as floating numbers; NOT interval bounds", "quadrature_error": "NOT bounded: fixed Gauss-Legendre approximation and replay only", "roundoff_error": "NOT bounded: ordinary mpmath arithmetic", "normalized_lattice_m": "1.0499958609739640463452474065675062699e-522", "normalized_lattice_c": "5.599977925194474913841319501693366773e-522", "normalized_lattice_dm": "4.3210931827917499669692521025790753055e-519", "normalized_real_tail_m": "1.5837297872393432263344174393206711618e-1289", "normalized_real_tail_c": "2.5341787300785251294251323767591877031e-1288", "normalized_real_tail_dm": "3.2497098863172067146765428794733358792e-1287", "phi_lattice_tail": "1.9356365872969653834965440138348783136e-540", "phi_derivative_lattice_tail": "7.6099345128052750467898755680309622573e-537", "envelope_K0": "16.757999595347284854867734621554433003", "envelope_K1": "357.61040338926418324104642749144832606", "envelope_d": "1.0068755102900204581994763865832455735" } } }, "elapsed_seconds": 0.1575759999686852 }, { "z": { "re": "1.296875", "im": "0.5" }, "bits": 128, "replay": false, "purpose": "grid_5_6", "values": { "m": { "re": "0.11914880902595256538233433189943548339", "im": "-0.055678676728601204331723205045525681724" }, "c": { "re": "0.000054179711648220609330483175254354690683", "im": "-0.00038621514837587312002974562936798656921" }, "dm": { "re": "-0.11731776968986051876167336202040994617", "im": "0.036126431211180204545940180761132972615" } }, "metadata": { "metadata": { "classification": "diagnostic, not a certificate", "bits": 128, "lattice_cutoff": 24, "gauss_legendre_order_per_segment": 48, "positive_half_segments": [ "0.0", "0.125", "0.25", "0.5", "1.0", "2.0", "4.0" ], "normalization": "B=exp(2*pi*exp(2*z)-9*z)/(4*pi^4), analytic and nonzero", "derivative": "dm=(B*M)' includes B' contribution", "majorants": { "status": "analytic majorants evaluated as floating numbers; NOT interval bounds", "quadrature_error": "NOT bounded: fixed Gauss-Legendre approximation and replay only", "roundoff_error": "NOT bounded: ordinary mpmath arithmetic", "normalized_lattice_m": "2.8360576332274901924167098275888310581e-440", "normalized_lattice_c": "1.512564071054661435955578574714043231e-439", "normalized_lattice_dm": "1.1691987830742096568941238557382241225e-436", "normalized_real_tail_m": "5.1788034397532852153043311085122114121e-1088", "normalized_real_tail_c": "8.2869043422351873868354082562775189631e-1087", "normalized_real_tail_dm": "1.1331861710908726946221330306266043355e-1085", "phi_lattice_tail": "1.4210689249680573121153852115435788848e-454", "phi_derivative_lattice_tail": "5.5869172592419013598919352956561404267e-451", "envelope_K0": "24.983585560594923710980841691774397433", "envelope_K1": "691.58751112121217564683229655248525689", "envelope_d": "0.84870487741648658484554125650222836214" } } }, "elapsed_seconds": 0.15675620903493837 }, { "z": { "re": "1.296875", "im": "0.5625" }, "bits": 128, "replay": false, "purpose": "grid_5_7", "values": { "m": { "re": "0.11666631553649125434629240068404661174", "im": "-0.06304979430691853628739864471810929376" }, "c": { "re": "-0.000017195285864800021315904283901100734307", "im": "-0.00039319429850927267040147641293295569001" }, "dm": { "re": "-0.11848670981166376267999603836534441086", "im": "0.043438132876175222195530564704553451808" } }, "metadata": { "metadata": { "classification": "diagnostic, not a certificate", "bits": 128, "lattice_cutoff": 24, "gauss_legendre_order_per_segment": 48, "positive_half_segments": [ "0.0", "0.125", "0.25", "0.5", "1.0", "2.0", "4.0" ], "normalization": "B=exp(2*pi*exp(2*z)-9*z)/(4*pi^4), analytic and nonzero", "derivative": "dm=(B*M)' includes B' contribution", "majorants": { "status": "analytic majorants evaluated as floating numbers; NOT interval bounds", "quadrature_error": "NOT bounded: fixed Gauss-Legendre approximation and replay only", "roundoff_error": "NOT bounded: ordinary mpmath arithmetic", "normalized_lattice_m": "7.2671120122182129351689764037885642007e-351", "normalized_lattice_c": "3.875793073183046898756787415353900907e-350", "normalized_lattice_dm": "3.007919702689647770856031652860760517e-347", "normalized_real_tail_m": "1.8596191928476364490996174633778300579e-869", "normalized_real_tail_c": "2.9757591598336409342497205408314274115e-868", "normalized_real_tail_dm": "4.6627341791354956640227391760835602515e-867", "phi_lattice_tail": "1.6144292525175739343768210704242839689e-361", "phi_derivative_lattice_tail": "6.3471113161651743543353377638863142176e-358", "envelope_K0": "45.779336961551260847650165707650203536", "envelope_K1": "1974.9153743821504788261579387588952755", "envelope_d": "0.67729048878756286732349724939914712065" } } }, "elapsed_seconds": 0.15847908396972343 }, { "z": { "re": "1.296875", "im": "0.625" }, "bits": 128, "replay": false, "purpose": "grid_5_8", "values": { "m": { "re": "0.11370371181875397036222790001325765911", "im": "-0.070478825120861065023586509694055301778" }, "c": { "re": "-0.000089813921227030993551946246130863271244", "im": "-0.00038705821665925572043326913657392557958" }, "dm": { "re": "-0.11914251807758082620730266434853309216", "im": "0.051484587182135055911917852262776423565" } }, "metadata": { "metadata": { "classification": "diagnostic, not a certificate", "bits": 128, "lattice_cutoff": 24, "gauss_legendre_order_per_segment": 48, "positive_half_segments": [ "0.0", "0.125", "0.25", "0.5", "1.0", "2.0", "4.0" ], "normalization": "B=exp(2*pi*exp(2*z)-9*z)/(4*pi^4), analytic and nonzero", "derivative": "dm=(B*M)' includes B' contribution", "majorants": { "status": "analytic majorants evaluated as floating numbers; NOT interval bounds", "quadrature_error": "NOT bounded: fixed Gauss-Legendre approximation and replay only", "roundoff_error": "NOT bounded: ordinary mpmath arithmetic", "normalized_lattice_m": "8.7902812541138284471747339580754764329e-256", "normalized_lattice_c": "4.6881500021940418384931914443069207642e-255", "normalized_lattice_dm": "3.6763858342073068215373078176232009123e-252", "normalized_real_tail_m": "4.5144276753962498453299946946670967581e-637", "normalized_real_tail_c": "7.2243074003112111215701635055499582135e-636", "normalized_real_tail_dm": "1.5175832935179834370451655912747317262e-634", "phi_lattice_tail": "1.0021598388692270941092068707959257556e-262", "phi_derivative_lattice_tail": "3.9399806736491836923747700781666945459e-259", "envelope_K0": "126.24928292784368352612039481684046491", "envelope_K1": "10771.851462133738538848956859875684407", "envelope_d": "0.49530720860677725930394940995503526598" } } }, "elapsed_seconds": 0.15709691605297849 }, { "z": { "re": "1.53125", "im": "0.125" }, "bits": 128, "replay": false, "purpose": "grid_6_0", "values": { "m": { "re": "0.10273452457876599882302921063053797995", "im": "-0.011699532743613530447183275493849831252" }, "c": { "re": "0.00017922872081162200996757122716642983171", "im": "-0.00006793603207633685460674740538379619838" }, "dm": { "re": "-0.093692002589079511094881623483315310683", "im": "0.0081835482019480323503981496932422505613" } }, "metadata": { "metadata": { "classification": "diagnostic, not a certificate", "bits": 128, "lattice_cutoff": 24, "gauss_legendre_order_per_segment": 48, "positive_half_segments": [ "0.0", "0.125", "0.25", "0.5", "1.0", "2.0", "4.0" ], "normalization": "B=exp(2*pi*exp(2*z)-9*z)/(4*pi^4), analytic and nonzero", "derivative": "dm=(B*M)' includes B' contribution", "majorants": { "status": "analytic majorants evaluated as floating numbers; NOT interval bounds", "quadrature_error": "NOT bounded: fixed Gauss-Legendre approximation and replay only", "roundoff_error": "NOT bounded: ordinary mpmath arithmetic", "normalized_lattice_m": "1.020136942897503788529568709192457639e-770", "normalized_lattice_c": "5.440730362120020205491033115693107408e-770", "normalized_lattice_dm": "4.2902428895467215265949934912540719094e-767", "normalized_real_tail_m": "4.3829231565579212941875061935421635756e-1925", "normalized_real_tail_c": "7.0130634846945454393265064326247920484e-1924", "normalized_real_tail_dm": "1.2629960567259842764490831535344511619e-1922", "phi_lattice_tail": "4.5885262662854514740333947116012359699e-820", "phi_derivative_lattice_tail": "1.8039741874006024900445183341996020805e-816", "envelope_K0": "7.0806448041385032092774528790706719056", "envelope_K1": "99.811506129080957217155350239768137982", "envelope_d": "1.5219640730090286703744177804891892666" } } }, "elapsed_seconds": 0.1571173329721205 }, { "z": { "re": "1.53125", "im": "0.1875" }, "bits": 128, "replay": false, "purpose": "grid_6_1", "values": { "m": { "re": "0.10209106119482035940442161679909516383", "im": "-0.017559952054196242674687463853543493231" }, "c": { "re": "0.00016436404683465659523643541901827410763", "im": "-0.000099364153767761047004505517571184248921" }, "dm": { "re": "-0.093846773801986654515436778598762003826", "im": "0.012433111336644699444415824685797737861" } }, "metadata": { "metadata": { "classification": "diagnostic, not a certificate", "bits": 128, "lattice_cutoff": 24, "gauss_legendre_order_per_segment": 48, "positive_half_segments": [ "0.0", "0.125", "0.25", "0.5", "1.0", "2.0", "4.0" ], "normalization": "B=exp(2*pi*exp(2*z)-9*z)/(4*pi^4), analytic and nonzero", "derivative": "dm=(B*M)' includes B' contribution", "majorants": { "status": "analytic majorants evaluated as floating numbers; NOT interval bounds", "quadrature_error": "NOT bounded: fixed Gauss-Legendre approximation and replay only", "roundoff_error": "NOT bounded: ordinary mpmath arithmetic", "normalized_lattice_m": "3.7954901457609718831686793897401013845e-740", "normalized_lattice_c": "2.0242614110725183376899623411947207384e-739", "normalized_lattice_dm": "1.5965242110643461953251972298028854518e-736", "normalized_real_tail_m": "3.8866403811814169068305758479932350567e-1849", "normalized_real_tail_c": "6.2189814314950139793487740211229959468e-1848", "normalized_real_tail_dm": "1.1249396550318046218655240002633563969e-1846", "phi_lattice_tail": "2.575127112483722287169904859455751326e-787", "phi_derivative_lattice_tail": "1.0124084663803664294249623722467560192e-783", "envelope_K0": "7.6916660011049469339417991865339105462", "envelope_K1": "111.95370680359173350893646533622747631", "envelope_d": "1.461637954554517745521968003740990655" } } }, "elapsed_seconds": 0.1580737080075778 }, { "z": { "re": "1.53125", "im": "0.25" }, "bits": 128, "replay": false, "purpose": "grid_6_2", "values": { "m": { "re": "0.10117659154247323372776502685491767617", "im": "-0.023430638470551802245897831152848683068" }, "c": { "re": "0.00014409892709451868009782664552018890796", "im": "-0.00012779638187508425688903131445202168533" }, "dm": { "re": "-0.094013554739079193935354842814702507942", "im": "0.016864529958048921945374351478657823601" } }, "metadata": { "metadata": { "classification": "diagnostic, not a certificate", "bits": 128, "lattice_cutoff": 24, "gauss_legendre_order_per_segment": 48, "positive_half_segments": [ "0.0", "0.125", "0.25", "0.5", "1.0", "2.0", "4.0" ], "normalization": "B=exp(2*pi*exp(2*z)-9*z)/(4*pi^4), analytic and nonzero", "derivative": "dm=(B*M)' includes B' contribution", "majorants": { "status": "analytic majorants evaluated as floating numbers; NOT interval bounds", "quadrature_error": "NOT bounded: fixed Gauss-Legendre approximation and replay only", "roundoff_error": "NOT bounded: ordinary mpmath arithmetic", "normalized_lattice_m": "5.1343786868229115874393374691412614675e-698", "normalized_lattice_c": "2.7383352996388861799676466502086727827e-697", "normalized_lattice_dm": "2.1603377850892470242633064781109276216e-694", "normalized_real_tail_m": "1.8112386940073364207708330031314133767e-1744", "normalized_real_tail_c": "2.8981582237516320739522516955393473599e-1743", "normalized_real_tail_dm": "5.277766774025899519341984831606578549e-1742", "phi_lattice_tail": "3.4822619197001443260025646128996249337e-742", "phi_derivative_lattice_tail": "1.3690475443202646147289599099099827161e-738", "envelope_K0": "8.6675384390440944838131174022670163717", "envelope_K1": "132.49029078751267542542390489224169672", "envelope_d": "1.3785034646766524887891155021962680546" } } }, "elapsed_seconds": 0.15921845799311996 }, { "z": { "re": "1.53125", "im": "0.3125" }, "bits": 128, "replay": false, "purpose": "grid_6_3", "values": { "m": { "re": "0.099978192562164100275551934253072541719", "im": "-0.029310903506295652135439746914612123289" }, "c": { "re": "0.00011897739679479210613680536534328959741", "im": "-0.00015232358938550206707078338935492753799" }, "dm": { "re": "-0.094144305537502685512280437281455771539", "im": "0.021526123316744754089241398313620993277" } }, "metadata": { "metadata": { "classification": "diagnostic, not a certificate", "bits": 128, "lattice_cutoff": 24, "gauss_legendre_order_per_segment": 48, "positive_half_segments": [ "0.0", "0.125", "0.25", "0.5", "1.0", "2.0", "4.0" ], "normalization": "B=exp(2*pi*exp(2*z)-9*z)/(4*pi^4), analytic and nonzero", "derivative": "dm=(B*M)' includes B' contribution", "majorants": { "status": "analytic majorants evaluated as floating numbers; NOT interval bounds", "quadrature_error": "NOT bounded: fixed Gauss-Legendre approximation and replay only", "roundoff_error": "NOT bounded: ordinary mpmath arithmetic", "normalized_lattice_m": "5.5950626936811357844331159375065217354e-645", "normalized_lattice_c": "2.9840334366299390850309951666701449256e-644", "normalized_lattice_dm": "2.3551546381133762299897442051893218756e-641", "normalized_real_tail_m": "1.0492932067728784448585540788236172014e-1612", "normalized_real_tail_c": "1.6789796644358805801830205976775136191e-1611", "normalized_real_tail_dm": "3.087809680810807596614366219840442202e-1610", "phi_lattice_tail": "2.241849059997265044919279156096387541e-685", "phi_derivative_lattice_tail": "8.8138055697724088568987923655992442035e-682", "envelope_K0": "10.18167853949153246670305287452827837", "envelope_K1": "167.18305268120390240767790001762444874", "envelope_d": "1.2738578892849270606047326496499107661" } } }, "elapsed_seconds": 0.15779287501936778 }, { "z": { "re": "1.53125", "im": "0.375" }, "bits": 128, "replay": false, "purpose": "grid_6_4", "values": { "m": { "re": "0.098480227438361968401473084098285099724", "im": "-0.035196700471863339831192229034214312475" }, "c": { "re": "0.000089694741759314954534749075235957770241", "im": "-0.0001721185442257437743955192421004881459" }, "dm": { "re": "-0.0941798921344633919283252388530708578", "im": "0.02645604481740524506729330449954201832" } }, "metadata": { "metadata": { "classification": "diagnostic, not a certificate", "bits": 128, "lattice_cutoff": 24, "gauss_legendre_order_per_segment": 48, "positive_half_segments": [ "0.0", "0.125", "0.25", "0.5", "1.0", "2.0", "4.0" ], "normalization": "B=exp(2*pi*exp(2*z)-9*z)/(4*pi^4), analytic and nonzero", "derivative": "dm=(B*M)' includes B' contribution", "majorants": { "status": "analytic majorants evaluated as floating numbers; NOT interval bounds", "quadrature_error": "NOT bounded: fixed Gauss-Legendre approximation and replay only", "roundoff_error": "NOT bounded: ordinary mpmath arithmetic", "normalized_lattice_m": "7.3976715194659868334505985385262585815e-582", "normalized_lattice_c": "3.9454248103818596445069858872140045768e-581", "normalized_lattice_dm": "3.1158113635264796203340057574225385712e-578", "normalized_real_tail_m": "6.8438521639639848768192767103147597698e-1456", "normalized_real_tail_c": "1.0950962512930020309154329935602646443e-1454", "normalized_real_tail_dm": "2.0436864418941038563234551063080122854e-1453", "phi_lattice_tail": "8.9238448836090041519537254011336962523e-618", "phi_derivative_lattice_tail": "3.5084000587904882233411529679191517387e-614", "envelope_K0": "12.595217910474195352796490529722614478", "envelope_K1": "229.54126205164252921382369277640260385", "envelope_d": "1.1493341875837106139976900705596868057" } } }, "elapsed_seconds": 0.15835745900403708 }, { "z": { "re": "1.53125", "im": "0.4375" }, "bits": 128, "replay": false, "purpose": "grid_6_5", "values": { "m": { "re": "0.096665046982332703547692582675469313523", "im": "-0.041079989294363394259431652303503056198" }, "c": { "re": "0.000057090801190596828224642988857270511295", "im": "-0.00018646164211269950964728014580472472389" }, "dm": { "re": "-0.094052013421274032914001435819897142083", "im": "0.031680218106763538434893128969190761155" } }, "metadata": { "metadata": { "classification": "diagnostic, not a certificate", "bits": 128, "lattice_cutoff": 24, "gauss_legendre_order_per_segment": 48, "positive_half_segments": [ "0.0", "0.125", "0.25", "0.5", "1.0", "2.0", "4.0" ], "normalization": "B=exp(2*pi*exp(2*z)-9*z)/(4*pi^4), analytic and nonzero", "derivative": "dm=(B*M)' includes B' contribution", "majorants": { "status": "analytic majorants evaluated as floating numbers; NOT interval bounds", "quadrature_error": "NOT bounded: fixed Gauss-Legendre approximation and replay only", "roundoff_error": "NOT bounded: ordinary mpmath arithmetic", "normalized_lattice_m": "1.2588694030945802648124704689239661488e-509", "normalized_lattice_c": "6.7139701498377614123331758342611527934e-509", "normalized_lattice_dm": "5.3071813944956635618265873138963150943e-506", "normalized_real_tail_m": "1.8987779343013382625270492035657421058e-1276", "normalized_real_tail_c": "3.0382977532023236686497622194146975059e-1275", "normalized_real_tail_dm": "5.8042220006168743618016862611850950171e-1274", "phi_lattice_tail": "1.9356365872969653834965440138348783136e-540", "phi_derivative_lattice_tail": "7.6099345128052750467898755680309622573e-537", "envelope_K0": "16.757999595347284854867734621554433003", "envelope_K1": "357.61040338926418324104642749144832606", "envelope_d": "1.0068755102900204581994763865832455735" } } }, "elapsed_seconds": 0.15894929197384045 }, { "z": { "re": "1.53125", "im": "0.5" }, "bits": 128, "replay": false, "purpose": "grid_6_6", "values": { "m": { "re": "0.094513810163374766366755729142914232714", "im": "-0.046948233508274136914024375137304045115" }, "c": { "re": "0.000022138403588992635669173064662806749729", "im": "-0.00019476840365693800670052614250940622957" }, "dm": { "re": "-0.093685497146345104737244341446482647451", "im": "0.037210599836015808254584298528007338927" } }, "metadata": { "metadata": { "classification": "diagnostic, not a certificate", "bits": 128, "lattice_cutoff": 24, "gauss_legendre_order_per_segment": 48, "positive_half_segments": [ "0.0", "0.125", "0.25", "0.5", "1.0", "2.0", "4.0" ], "normalization": "B=exp(2*pi*exp(2*z)-9*z)/(4*pi^4), analytic and nonzero", "derivative": "dm=(B*M)' includes B' contribution", "majorants": { "status": "analytic majorants evaluated as floating numbers; NOT interval bounds", "quadrature_error": "NOT bounded: fixed Gauss-Legendre approximation and replay only", "roundoff_error": "NOT bounded: ordinary mpmath arithmetic", "normalized_lattice_m": "2.1530008502977544027245143207736890646e-429", "normalized_lattice_c": "1.1482671201588023481197409710793008345e-428", "normalized_lattice_dm": "9.0923330968478231016357708409553160214e-426", "normalized_real_tail_m": "3.931502688337427055671320470516380843e-1077", "normalized_real_tail_c": "6.2910259249084043203107263549224681483e-1076", "normalized_real_tail_dm": "1.2552901171546294273400603701836062997e-1074", "phi_lattice_tail": "1.4210689249680573121153852115435788848e-454", "phi_derivative_lattice_tail": "5.5869172592419013598919352956561404267e-451", "envelope_K0": "24.983585560594923710980841691774397433", "envelope_K1": "691.58751112121217564683229655248525689", "envelope_d": "0.84870487741648658484554125650222836214" } } }, "elapsed_seconds": 0.15923545800615102 }, { "z": { "re": "1.53125", "im": "0.5625" }, "bits": 128, "replay": false, "purpose": "grid_6_7", "values": { "m": { "re": "0.09200740120489292682884795118550374107", "im": "-0.052784051120175645933784249652388207468" }, "c": { "re": "-0.000014074352362298269664776623265803206361", "im": "-0.00019661759259575577832432500565715751181" }, "dm": { "re": "-0.093000919238617032365609354727763190383", "im": "0.043043838186923781110060164183458333096" } }, "metadata": { "metadata": { "classification": "diagnostic, not a certificate", "bits": 128, "lattice_cutoff": 24, "gauss_legendre_order_per_segment": 48, "positive_half_segments": [ "0.0", "0.125", "0.25", "0.5", "1.0", "2.0", "4.0" ], "normalization": "B=exp(2*pi*exp(2*z)-9*z)/(4*pi^4), analytic and nonzero", "derivative": "dm=(B*M)' includes B' contribution", "majorants": { "status": "analytic majorants evaluated as floating numbers; NOT interval bounds", "quadrature_error": "NOT bounded: fixed Gauss-Legendre approximation and replay only", "roundoff_error": "NOT bounded: ordinary mpmath arithmetic", "normalized_lattice_m": "2.286377235773881691577338697131469989e-342", "normalized_lattice_c": "1.2194011924127369021745806384701173275e-341", "normalized_lattice_dm": "9.6932195724498866007731263697930941985e-339", "normalized_real_tail_m": "5.8507299496505484053749677750042786247e-861", "normalized_real_tail_c": "9.3623271400663123053110127889815551784e-860", "normalized_real_tail_dm": "2.0548027780462086841798258302984486147e-858", "phi_lattice_tail": "1.6144292525175739343768210704242839689e-361", "phi_derivative_lattice_tail": "6.3471113161651743543353377638863142176e-358", "envelope_K0": "45.779336961551260847650165707650203536", "envelope_K1": "1974.9153743821504788261579387588952755", "envelope_d": "0.67729048878756286732349724939914712065" } } }, "elapsed_seconds": 0.160840124997776 }, { "z": { "re": "1.53125", "im": "0.625" }, "bits": 128, "replay": false, "purpose": "grid_6_8", "values": { "m": { "re": "0.089127416421860611860086291432734043549", "im": "-0.058565037762406193646230230552263627355" }, "c": { "re": "-0.000050368920501163744271087263167806318091", "im": "-0.00019177828355615954334258148326288119493" }, "dm": { "re": "-0.091917486395992682690129419719671599513", "im": "0.049160393176722315013766064928561443455" } }, "metadata": { "metadata": { "classification": "diagnostic, not a certificate", "bits": 128, "lattice_cutoff": 24, "gauss_legendre_order_per_segment": 48, "positive_half_segments": [ "0.0", "0.125", "0.25", "0.5", "1.0", "2.0", "4.0" ], "normalization": "B=exp(2*pi*exp(2*z)-9*z)/(4*pi^4), analytic and nonzero", "derivative": "dm=(B*M)' includes B' contribution", "majorants": { "status": "analytic majorants evaluated as floating numbers; NOT interval bounds", "quadrature_error": "NOT bounded: fixed Gauss-Legendre approximation and replay only", "roundoff_error": "NOT bounded: ordinary mpmath arithmetic", "normalized_lattice_m": "8.1723188447468929179624950224097988623e-250", "normalized_lattice_c": "4.3585700505316762229133306786185593932e-249", "normalized_lattice_dm": "3.500033754387058316732939176435390928e-246", "normalized_real_tail_m": "4.1970605147158055832830192163687013054e-631", "normalized_real_tail_c": "6.7164339571248063389730918386715824228e-630", "normalized_real_tail_dm": "1.8325384959316214538720428597589793207e-628", "phi_lattice_tail": "1.0021598388692270941092068707959257556e-262", "phi_derivative_lattice_tail": "3.9399806736491836923747700781666945459e-259", "envelope_K0": "126.24928292784368352612039481684046491", "envelope_K1": "10771.851462133738538848956859875684407", "envelope_d": "0.49530720860677725930394940995503526598" } } }, "elapsed_seconds": 0.1585310420487076 }, { "z": { "re": "1.765625", "im": "0.125" }, "bits": 128, "replay": false, "purpose": "grid_7_0", "values": { "m": { "re": "0.082611790482424460123234552296278453588", "im": "-0.0097781530242477314429393844024786902043" }, "c": { "re": "0.00009020597822884085090634948039071908847", "im": "-0.000034695021280155350130334039313925897527" }, "dm": { "re": "-0.078110886460869574868748098662516225434", "im": "0.0080199277986890063759715022164075642365" } }, "metadata": { "metadata": { "classification": "diagnostic, not a certificate", "bits": 128, "lattice_cutoff": 24, "gauss_legendre_order_per_segment": 48, "positive_half_segments": [ "0.0", "0.125", "0.25", "0.5", "1.0", "2.0", "4.0" ], "normalization": "B=exp(2*pi*exp(2*z)-9*z)/(4*pi^4), analytic and nonzero", "derivative": "dm=(B*M)' includes B' contribution", "majorants": { "status": "analytic majorants evaluated as floating numbers; NOT interval bounds", "quadrature_error": "NOT bounded: fixed Gauss-Legendre approximation and replay only", "roundoff_error": "NOT bounded: ordinary mpmath arithmetic", "normalized_lattice_m": "7.8883152065916811299398786073969482083e-738", "normalized_lattice_c": "4.2071014435155632693012685906117057111e-737", "normalized_lattice_dm": "3.4442136466453658584384797428992747773e-734", "normalized_real_tail_m": "3.3891409997365817597415890169061378427e-1892", "normalized_real_tail_c": "5.4229244138516725059298689761205136189e-1891", "normalized_real_tail_dm": "1.5211455511353259078288037806698231767e-1889", "phi_lattice_tail": "4.5885262662854514740333947116012359699e-820", "phi_derivative_lattice_tail": "1.8039741874006024900445183341996020805e-816", "envelope_K0": "7.0806448041385032092774528790706719056", "envelope_K1": "99.811506129080957217155350239768137982", "envelope_d": "1.5219640730090286703744177804891892666" } } }, "elapsed_seconds": 0.15692770900204778 }, { "z": { "re": "1.765625", "im": "0.1875" }, "bits": 128, "replay": false, "purpose": "grid_7_1", "values": { "m": { "re": "0.081983629019275064177856854920213581627", "im": "-0.014653555621124394953457409665618080946" }, "c": { "re": "0.000082450247812047972102289982896963647631", "im": "-0.000050656358061979734848137742956285454959" }, "dm": { "re": "-0.077884500729223310087142359789944104074", "im": "0.012091215150823050100663463543809542269" } }, "metadata": { "metadata": { "classification": "diagnostic, not a certificate", "bits": 128, "lattice_cutoff": 24, "gauss_legendre_order_per_segment": 48, "positive_half_segments": [ "0.0", "0.125", "0.25", "0.5", "1.0", "2.0", "4.0" ], "normalization": "B=exp(2*pi*exp(2*z)-9*z)/(4*pi^4), analytic and nonzero", "derivative": "dm=(B*M)' includes B' contribution", "majorants": { "status": "analytic majorants evaluated as floating numbers; NOT interval bounds", "quadrature_error": "NOT bounded: fixed Gauss-Legendre approximation and replay only", "roundoff_error": "NOT bounded: ordinary mpmath arithmetic", "normalized_lattice_m": "1.3417987747622627866216839862663523047e-708", "normalized_lattice_c": "7.1562601320654015286489812600872122919e-708", "normalized_lattice_dm": "5.8596803352198781077129250635302096228e-705", "normalized_real_tail_m": "1.3740226166138989215167135584799090864e-1817", "normalized_real_tail_c": "2.1985623317634062102556777633424450865e-1816", "normalized_real_tail_dm": "6.1844690213839066734761983881533631905e-1815", "phi_lattice_tail": "2.575127112483722287169904859455751326e-787", "phi_derivative_lattice_tail": "1.0124084663803664294249623722467560192e-783", "envelope_K0": "7.6916660011049469339417991865339105462", "envelope_K1": "111.95370680359173350893646533622747631", "envelope_d": "1.461637954554517745521968003740990655" } } }, "elapsed_seconds": 0.15971558302408084 }, { "z": { "re": "1.765625", "im": "0.25" }, "bits": 128, "replay": false, "purpose": "grid_7_2", "values": { "m": { "re": "0.081098934256231699167840237889066812388", "im": "-0.019511330278872488180864371006070465644" }, "c": { "re": "0.0000719164365097772089663657280763324038", "im": "-0.000064993774292038050480445552816584261365" }, "dm": { "re": "-0.07754341868199012206555169102942191213", "im": "0.016232174073477842197610993449299535015" } }, "metadata": { "metadata": { "classification": "diagnostic, not a certificate", "bits": 128, "lattice_cutoff": 24, "gauss_legendre_order_per_segment": 48, "positive_half_segments": [ "0.0", "0.125", "0.25", "0.5", "1.0", "2.0", "4.0" ], "normalization": "B=exp(2*pi*exp(2*z)-9*z)/(4*pi^4), analytic and nonzero", "derivative": "dm=(B*M)' includes B' contribution", "majorants": { "status": "analytic majorants evaluated as floating numbers; NOT interval bounds", "quadrature_error": "NOT bounded: fixed Gauss-Legendre approximation and replay only", "roundoff_error": "NOT bounded: ordinary mpmath arithmetic", "normalized_lattice_m": "2.5846595715600406159386996881677144576e-668", "normalized_lattice_c": "1.378485104832021661833973167022781044e-667", "normalized_lattice_dm": "1.1290438436729387083536166392994172686e-664", "normalized_real_tail_m": "9.1178226468970922865256858141159828357e-1715", "normalized_real_tail_c": "1.4589403800969507879738823837332318018e-1713", "normalized_real_tail_dm": "4.1216773382992934897487100637776582055e-1712", "phi_lattice_tail": "3.4822619197001443260025646128996249337e-742", "phi_derivative_lattice_tail": "1.3690475443202646147289599099099827161e-738", "envelope_K0": "8.6675384390440944838131174022670163717", "envelope_K1": "132.49029078751267542542390489224169672", "envelope_d": "1.3785034646766524887891155021962680546" } } }, "elapsed_seconds": 0.16002141602803022 }, { "z": { "re": "1.765625", "im": "0.3125" }, "bits": 128, "replay": false, "purpose": "grid_7_3", "values": { "m": { "re": "0.079952801727327211962522615566417421936", "im": "-0.024343615858387078396850350356332668216" }, "c": { "re": "0.000058921887346022553698837405209027213715", "im": "-0.000077231823402106767039232598068537397226" }, "dm": { "re": "-0.07706454405863886678357244777119203874", "im": "0.02045962303174603191547386718036130105" } }, "metadata": { "metadata": { "classification": "diagnostic, not a certificate", "bits": 128, "lattice_cutoff": 24, "gauss_legendre_order_per_segment": 48, "positive_half_segments": [ "0.0", "0.125", "0.25", "0.5", "1.0", "2.0", "4.0" ], "normalization": "B=exp(2*pi*exp(2*z)-9*z)/(4*pi^4), analytic and nonzero", "derivative": "dm=(B*M)' includes B' contribution", "majorants": { "status": "analytic majorants evaluated as floating numbers; NOT interval bounds", "quadrature_error": "NOT bounded: fixed Gauss-Legendre approximation and replay only", "roundoff_error": "NOT bounded: ordinary mpmath arithmetic", "normalized_lattice_m": "1.3348504328792602340902916228816241158e-617", "normalized_lattice_c": "7.1192023086893879151482219887019952844e-617", "normalized_lattice_dm": "5.8332887002853872634796803094209199342e-614", "normalized_real_tail_m": "2.5033669289530704976709471074941401024e-1585", "normalized_real_tail_c": "4.0056507935091176502072676657887899683e-1584", "normalized_real_tail_dm": "1.1388440425493627090461900884246731717e-1582", "phi_lattice_tail": "2.241849059997265044919279156096387541e-685", "phi_derivative_lattice_tail": "8.8138055697724088568987923655992442035e-682", "envelope_K0": "10.18167853949153246670305287452827837", "envelope_K1": "167.18305268120390240767790001762444874", "envelope_d": "1.2738578892849270606047326496499107661" } } }, "elapsed_seconds": 0.1591582500259392 }, { "z": { "re": "1.765625", "im": "0.375" }, "bits": 128, "replay": false, "purpose": "grid_7_4", "values": { "m": { "re": "0.078539434069575586470096307927295486285", "im": "-0.029140942378924959345854950185226522124" }, "c": { "re": "0.000043864348199961954268157872650573730895", "im": "-0.000086951452712578597591453226706650585969" }, "dm": { "re": "-0.076419649248866632406834678363955903507", "im": "0.02478513338582392143950685340544109752" } }, "metadata": { "metadata": { "classification": "diagnostic, not a certificate", "bits": 128, "lattice_cutoff": 24, "gauss_legendre_order_per_segment": 48, "positive_half_segments": [ "0.0", "0.125", "0.25", "0.5", "1.0", "2.0", "4.0" ], "normalization": "B=exp(2*pi*exp(2*z)-9*z)/(4*pi^4), analytic and nonzero", "derivative": "dm=(B*M)' includes B' contribution", "majorants": { "status": "analytic majorants evaluated as floating numbers; NOT interval bounds", "quadrature_error": "NOT bounded: fixed Gauss-Legendre approximation and replay only", "roundoff_error": "NOT bounded: ordinary mpmath arithmetic", "normalized_lattice_m": "3.0263621014399145232193216640710326247e-557", "normalized_lattice_c": "1.6140597874346210790503048875045507332e-556", "normalized_lattice_dm": "1.3232840476508711805743055729408791463e-553", "normalized_real_tail_m": "2.7997964984491876865151115547952346961e-1431", "normalized_real_tail_c": "4.4800012863795016211449939598975028677e-1430", "normalized_real_tail_dm": "1.2858318521163051635238735453369213059e-1428", "phi_lattice_tail": "8.9238448836090041519537254011336962523e-618", "phi_derivative_lattice_tail": "3.5084000587904882233411529679191517387e-614", "envelope_K0": "12.595217910474195352796490529722614478", "envelope_K1": "229.54126205164252921382369277640260385", "envelope_d": "1.1493341875837106139976900705596868057" } } }, "elapsed_seconds": 0.158354084007442 }, { "z": { "re": "1.765625", "im": "0.4375" }, "bits": 128, "replay": false, "purpose": "grid_7_5", "values": { "m": { "re": "0.076852501480044701516567812462693653845", "im": "-0.033891942225224646023152874164345725954" }, "c": { "re": "0.00002721357034239413791295601324780541135", "im": "-0.000093803708352241764700752260317503545651" }, "dm": { "re": "-0.075576429218141589118014523365042698924", "im": "0.029214018607540833865429701000345725237" } }, "metadata": { "metadata": { "classification": "diagnostic, not a certificate", "bits": 128, "lattice_cutoff": 24, "gauss_legendre_order_per_segment": 48, "positive_half_segments": [ "0.0", "0.125", "0.25", "0.5", "1.0", "2.0", "4.0" ], "normalization": "B=exp(2*pi*exp(2*z)-9*z)/(4*pi^4), analytic and nonzero", "derivative": "dm=(B*M)' includes B' contribution", "majorants": { "status": "analytic majorants evaluated as floating numbers; NOT interval bounds", "quadrature_error": "NOT bounded: fixed Gauss-Legendre approximation and replay only", "roundoff_error": "NOT bounded: ordinary mpmath arithmetic", "normalized_lattice_m": "3.5289876129527557301930128089240187804e-488", "normalized_lattice_c": "1.8821267269081363894362734980928100162e-487", "normalized_lattice_dm": "1.5444498195111514706409839546894596835e-484", "normalized_real_tail_m": "5.3228426979204357458076792470821972096e-1255", "normalized_real_tail_c": "8.5172577148637114508752635278631026599e-1254", "normalized_real_tail_dm": "2.4821346786437631865115317486288432002e-1252", "phi_lattice_tail": "1.9356365872969653834965440138348783136e-540", "phi_derivative_lattice_tail": "7.6099345128052750467898755680309622573e-537", "envelope_K0": "16.757999595347284854867734621554433003", "envelope_K1": "357.61040338926418324104642749144832606", "envelope_d": "1.0068755102900204581994763865832455735" } } }, "elapsed_seconds": 0.15972308296477422 }, { "z": { "re": "1.765625", "im": "0.5" }, "bits": 128, "replay": false, "purpose": "grid_7_6", "values": { "m": { "re": "0.074885559424254073019320432949779179146", "im": "-0.038583133041683107426572350866832671566" }, "c": { "re": "0.0000095004275615218149869042769750187752983", "im": "-0.000097522723455852279708569690393520254927" }, "dm": { "re": "-0.074499736624800560745853393689214627746", "im": "0.033744518773304915786059444328836141055" } }, "metadata": { "metadata": { "classification": "diagnostic, not a certificate", "bits": 128, "lattice_cutoff": 24, "gauss_legendre_order_per_segment": 48, "positive_half_segments": [ "0.0", "0.125", "0.25", "0.5", "1.0", "2.0", "4.0" ], "normalization": "B=exp(2*pi*exp(2*z)-9*z)/(4*pi^4), analytic and nonzero", "derivative": "dm=(B*M)' includes B' contribution", "majorants": { "status": "analytic majorants evaluated as floating numbers; NOT interval bounds", "quadrature_error": "NOT bounded: fixed Gauss-Legendre approximation and replay only", "roundoff_error": "NOT bounded: ordinary mpmath arithmetic", "normalized_lattice_m": "1.8517326375696069226175495107093079377e-411", "normalized_lattice_c": "9.8759074003712369206269307237829756678e-411", "normalized_lattice_dm": "8.1174895701818472903889754688055511578e-408", "normalized_real_tail_m": "3.381369701586623330535708098138594239e-1059", "normalized_real_tail_c": "5.4107261626665627632403338621977526589e-1058", "normalized_real_tail_dm": "1.6227834263869739883208668122144839703e-1056", "phi_lattice_tail": "1.4210689249680573121153852115435788848e-454", "phi_derivative_lattice_tail": "5.5869172592419013598919352956561404267e-451", "envelope_K0": "24.983585560594923710980841691774397433", "envelope_K1": "691.58751112121217564683229655248525689", "envelope_d": "0.84870487741648658484554125650222836214" } } }, "elapsed_seconds": 0.15982066601281986 }, { "z": { "re": "1.765625", "im": "0.5625" }, "bits": 128, "replay": false, "purpose": "grid_7_7", "values": { "m": { "re": "0.072632510351362195819950117193893619711", "im": "-0.043198782643694877146231959404092326271" }, "c": { "re": "-0.0000086965963920288141849222112483742413332", "im": "-0.00009793746911419962334806980492075478504" }, "dm": { "re": "-0.073152965230584150510636533890738334115", "im": "0.038367212942522747051431730101811508212" } }, "metadata": { "metadata": { "classification": "diagnostic, not a certificate", "bits": 128, "lattice_cutoff": 24, "gauss_legendre_order_per_segment": 48, "positive_half_segments": [ "0.0", "0.125", "0.25", "0.5", "1.0", "2.0", "4.0" ], "normalization": "B=exp(2*pi*exp(2*z)-9*z)/(4*pi^4), analytic and nonzero", "derivative": "dm=(B*M)' includes B' contribution", "majorants": { "status": "analytic majorants evaluated as floating numbers; NOT interval bounds", "quadrature_error": "NOT bounded: fixed Gauss-Legendre approximation and replay only", "roundoff_error": "NOT bounded: ordinary mpmath arithmetic", "normalized_lattice_m": "3.0647066353404430991715255864773947196e-328", "normalized_lattice_c": "1.6345102055149029862248136461212771838e-327", "normalized_lattice_dm": "1.3485251187335663783964274658669587069e-324", "normalized_real_tail_m": "7.842437642277335462151174613985263402e-847", "normalized_real_tail_c": "1.2549454070591001394645002543370399666e-845", "normalized_real_tail_dm": "4.0139748222925364272899653106693101973e-844", "phi_lattice_tail": "1.6144292525175739343768210704242839689e-361", "phi_derivative_lattice_tail": "6.3471113161651743543353377638863142176e-358", "envelope_K0": "45.779336961551260847650165707650203536", "envelope_K1": "1974.9153743821504788261579387588952755", "envelope_d": "0.67729048878756286732349724939914712065" } } }, "elapsed_seconds": 0.15908149996539578 }, { "z": { "re": "1.765625", "im": "0.625" }, "bits": 128, "replay": false, "purpose": "grid_7_8", "values": { "m": { "re": "0.070088094272150627761955382251039014376", "im": "-0.047720864019490485607469433651060781905" }, "c": { "re": "-0.000026767568750457066014683544482999752481", "im": "-0.000094981631019592774110992217732706263136" }, "dm": { "re": "-0.071499542321946971981707951257759326808", "im": "0.043064687361519110468671625108001341174" } }, "metadata": { "metadata": { "classification": "diagnostic, not a certificate", "bits": 128, "lattice_cutoff": 24, "gauss_legendre_order_per_segment": 48, "positive_half_segments": [ "0.0", "0.125", "0.25", "0.5", "1.0", "2.0", "4.0" ], "normalization": "B=exp(2*pi*exp(2*z)-9*z)/(4*pi^4), analytic and nonzero", "derivative": "dm=(B*M)' includes B' contribution", "majorants": { "status": "analytic majorants evaluated as floating numbers; NOT interval bounds", "quadrature_error": "NOT bounded: fixed Gauss-Legendre approximation and replay only", "roundoff_error": "NOT bounded: ordinary mpmath arithmetic", "normalized_lattice_m": "9.9436794761624037918238403381030273418e-240", "normalized_lattice_c": "5.303295720619948688972714846988281249e-239", "normalized_lattice_dm": "4.4183842361427523730612675738180113168e-236", "normalized_real_tail_m": "5.1067787849733281387012705212004281898e-621", "normalized_real_tail_c": "8.1722296647042562017985647297380356505e-620", "normalized_real_tail_dm": "3.0499855466268214003190264124325087545e-618", "phi_lattice_tail": "1.0021598388692270941092068707959257556e-262", "phi_derivative_lattice_tail": "3.9399806736491836923747700781666945459e-259", "envelope_K0": "126.24928292784368352612039481684046491", "envelope_K1": "10771.851462133738538848956859875684407", "envelope_d": "0.49530720860677725930394940995503526598" } } }, "elapsed_seconds": 0.15766104101203382 }, { "z": { "re": "2.0", "im": "0.125" }, "bits": 128, "replay": false, "purpose": "grid_8_0", "values": { "m": { "re": "0.066018641216084349993714677056642057656", "im": "-0.0079962182966944409046650917748842493473" }, "c": { "re": "0.000045115191929084438786482346605260913058", "im": "-0.000017506284187195130298448082943220937621" }, "dm": { "re": "-0.06378292984099407613044789992788333316", "im": "0.0071203510933571160571365217203573949217" } }, "metadata": { "metadata": { "classification": "diagnostic, not a certificate", "bits": 128, "lattice_cutoff": 24, "gauss_legendre_order_per_segment": 48, "positive_half_segments": [ "0.0", "0.125", "0.25", "0.5", "1.0", "2.0", "4.0" ], "normalization": "B=exp(2*pi*exp(2*z)-9*z)/(4*pi^4), analytic and nonzero", "derivative": "dm=(B*M)' includes B' contribution", "majorants": { "status": "analytic majorants evaluated as floating numbers; NOT interval bounds", "quadrature_error": "NOT bounded: fixed Gauss-Legendre approximation and replay only", "roundoff_error": "NOT bounded: ordinary mpmath arithmetic", "normalized_lattice_m": "1.0004532882591316008192479129419706636e-684", "normalized_lattice_c": "5.3357508707153685377026555356905102058e-684", "normalized_lattice_dm": "4.6250652506888778415645653873088293994e-681", "normalized_real_tail_m": "4.2983541716575497385891002725424101803e-1839", "normalized_real_tail_c": "6.8777456525634763731132753326992163815e-1838", "normalized_real_tail_dm": "3.0328190206998898031371011360671395595e-1836", "phi_lattice_tail": "4.5885262662854514740333947116012359699e-820", "phi_derivative_lattice_tail": "1.8039741874006024900445183341996020805e-816", "envelope_K0": "7.0806448041385032092774528790706719056", "envelope_K1": "99.811506129080957217155350239768137982", "envelope_d": "1.5219640730090286703744177804891892666" } } }, "elapsed_seconds": 0.15774541604332626 }, { "z": { "re": "2.0", "im": "0.1875" }, "bits": 128, "replay": false, "purpose": "grid_8_1", "values": { "m": { "re": "0.065461949057564783458596720702744052501", "im": "-0.01197230964957726102587180870916237604" }, "c": { "re": "0.000041152125541251424074491413836273533988", "im": "-0.000025532994300655105955272541013889098102" }, "dm": { "re": "-0.063427183937637265767468089622117002354", "im": "0.01069630512847955593587653217571606165" } }, "metadata": { "metadata": { "classification": "diagnostic, not a certificate", "bits": 128, "lattice_cutoff": 24, "gauss_legendre_order_per_segment": 48, "positive_half_segments": [ "0.0", "0.125", "0.25", "0.5", "1.0", "2.0", "4.0" ], "normalization": "B=exp(2*pi*exp(2*z)-9*z)/(4*pi^4), analytic and nonzero", "derivative": "dm=(B*M)' includes B' contribution", "majorants": { "status": "analytic majorants evaluated as floating numbers; NOT interval bounds", "quadrature_error": "NOT bounded: fixed Gauss-Legendre approximation and replay only", "roundoff_error": "NOT bounded: ordinary mpmath arithmetic", "normalized_lattice_m": "1.229520706244664020295323030258658269e-657", "normalized_lattice_c": "6.5574437666382081082417228280461774347e-657", "normalized_lattice_dm": "5.6850314349091843632914031077874278113e-654", "normalized_real_tail_m": "1.2590481447373394913051085837589695592e-1766", "normalized_real_tail_c": "2.0145926212755725339159084232932355284e-1765", "normalized_real_tail_dm": "8.899511664983596558694673027114174831e-1764", "phi_lattice_tail": "2.575127112483722287169904859455751326e-787", "phi_derivative_lattice_tail": "1.0124084663803664294249623722467560192e-783", "envelope_K0": "7.6916660011049469339417991865339105462", "envelope_K1": "111.95370680359173350893646533622747631", "envelope_d": "1.461637954554517745521968003740990655" } } }, "elapsed_seconds": 0.15740033297333866 }, { "z": { "re": "2.0", "im": "0.25" }, "bits": 128, "replay": false, "purpose": "grid_8_2", "values": { "m": { "re": "0.064681248079328406118234412971193609915", "im": "-0.015921425279965561350757185053539301306" }, "c": { "re": "0.000035781302104630919362406593421730864165", "im": "-0.000032711862195598376182157388022971523467" }, "dm": { "re": "-0.062918180976569984389409123581688363933", "im": "0.014289230863266000585438257443311615807" } }, "metadata": { "metadata": { "classification": "diagnostic, not a certificate", "bits": 128, "lattice_cutoff": 24, "gauss_legendre_order_per_segment": 48, "positive_half_segments": [ "0.0", "0.125", "0.25", "0.5", "1.0", "2.0", "4.0" ], "normalization": "B=exp(2*pi*exp(2*z)-9*z)/(4*pi^4), analytic and nonzero", "derivative": "dm=(B*M)' includes B' contribution", "majorants": { "status": "analytic majorants evaluated as floating numbers; NOT interval bounds", "quadrature_error": "NOT bounded: fixed Gauss-Legendre approximation and replay only", "roundoff_error": "NOT bounded: ordinary mpmath arithmetic", "normalized_lattice_m": "2.6530577513974613220478561422704994161e-620", "normalized_lattice_c": "1.4149641340786460384255232758775996886e-619", "normalized_lattice_dm": "1.2270368659696874184002053439451398737e-616", "normalized_real_tail_m": "9.3591087644153689578883497382505440498e-1667", "normalized_real_tail_c": "1.4975485076770622041522463985249452626e-1665", "normalized_real_tail_dm": "6.6336209703082078003108074684173071777e-1664", "phi_lattice_tail": "3.4822619197001443260025646128996249337e-742", "phi_derivative_lattice_tail": "1.3690475443202646147289599099099827161e-738", "envelope_K0": "8.6675384390440944838131174022670163717", "envelope_K1": "132.49029078751267542542390489224169672", "envelope_d": "1.3785034646766524887891155021962680546" } } }, "elapsed_seconds": 0.1578098749741912 }, { "z": { "re": "2.0", "im": "0.3125" }, "bits": 128, "replay": false, "purpose": "grid_8_3", "values": { "m": { "re": "0.063675388636950477812479298550185463592", "im": "-0.019833674165225967579880851357772360069" }, "c": { "re": "0.000029174835063721793352572774663553989586", "im": "-0.000038799651335876477889746314858222128956" }, "dm": { "re": "-0.062245515129083361172783369180000805023", "im": "0.01790158438647635783755467251829439472" } }, "metadata": { "metadata": { "classification": "diagnostic, not a certificate", "bits": 128, "lattice_cutoff": 24, "gauss_legendre_order_per_segment": 48, "positive_half_segments": [ "0.0", "0.125", "0.25", "0.5", "1.0", "2.0", "4.0" ], "normalization": "B=exp(2*pi*exp(2*z)-9*z)/(4*pi^4), analytic and nonzero", "derivative": "dm=(B*M)' includes B' contribution", "majorants": { "status": "analytic majorants evaluated as floating numbers; NOT interval bounds", "quadrature_error": "NOT bounded: fixed Gauss-Legendre approximation and replay only", "roundoff_error": "NOT bounded: ordinary mpmath arithmetic", "normalized_lattice_m": "2.6459073118167332273155082493449238734e-573", "normalized_lattice_c": "1.4111505663022577212349377329839593991e-572", "normalized_lattice_dm": "1.2241903035456776060168710487225860686e-569", "normalized_real_tail_m": "4.9621116331287536494558921056200965045e-1541", "normalized_real_tail_c": "7.9399013268244830119264375963086644015e-1540", "normalized_real_tail_dm": "3.5313478951800536077009901733014893318e-1538", "phi_lattice_tail": "2.241849059997265044919279156096387541e-685", "phi_derivative_lattice_tail": "8.8138055697724088568987923655992442035e-682", "envelope_K0": "10.18167853949153246670305287452827837", "envelope_K1": "167.18305268120390240767790001762444874", "envelope_d": "1.2738578892849270606047326496499107661" } } }, "elapsed_seconds": 0.15828408300876617 }, { "z": { "re": "2.0", "im": "0.375" }, "bits": 128, "replay": false, "purpose": "grid_8_4", "values": { "m": { "re": "0.062443146255985972244643589430743000126", "im": "-0.023698443543840447833337191137839138472" }, "c": { "re": "0.000021546343952379317107898174238705304328", "im": "-0.000043586012760745537328355388059540864543" }, "dm": { "re": "-0.061396579749306077096331211716306389188", "im": "0.021533215721786489034599653908112896218" } }, "metadata": { "metadata": { "classification": "diagnostic, not a certificate", "bits": 128, "lattice_cutoff": 24, "gauss_legendre_order_per_segment": 48, "positive_half_segments": [ "0.0", "0.125", "0.25", "0.5", "1.0", "2.0", "4.0" ], "normalization": "B=exp(2*pi*exp(2*z)-9*z)/(4*pi^4), analytic and nonzero", "derivative": "dm=(B*M)' includes B' contribution", "majorants": { "status": "analytic majorants evaluated as floating numbers; NOT interval bounds", "quadrature_error": "NOT bounded: fixed Gauss-Legendre approximation and replay only", "roundoff_error": "NOT bounded: ordinary mpmath arithmetic", "normalized_lattice_m": "2.2820450458833283127127147352955986796e-517", "normalized_lattice_c": "1.2170906911377751001134478588243192958e-516", "normalized_lattice_dm": "1.0564172655928099817910400941587622356e-513", "normalized_real_tail_m": "2.1112020024727074253245326357972510243e-1391", "normalized_real_tail_c": "3.3781696963060051649937643924355594138e-1390", "normalized_real_tail_dm": "1.5116038178172661992419643998885140705e-1388", "phi_lattice_tail": "8.9238448836090041519537254011336962523e-618", "phi_derivative_lattice_tail": "3.5084000587904882233411529679191517387e-614", "envelope_K0": "12.595217910474195352796490529722614478", "envelope_K1": "229.54126205164252921382369277640260385", "envelope_d": "1.1493341875837106139976900705596868057" } } }, "elapsed_seconds": 0.15997333300765604 }, { "z": { "re": "2.0", "im": "0.4375" }, "bits": 128, "replay": false, "purpose": "grid_8_5", "values": { "m": { "re": "0.060983400111256199295143534481068274398", "im": "-0.027504278004714026120718127594982916387" }, "c": { "re": "0.000013145195554910276097933463689265505328", "im": "-0.000046900558894922555117264509063715228868" }, "dm": { "re": "-0.060357116058616790521548654894978135248", "im": "0.02518088597328413847752669997016312679" } }, "metadata": { "metadata": { "classification": "diagnostic, not a certificate", "bits": 128, "lattice_cutoff": 24, "gauss_legendre_order_per_segment": 48, "positive_half_segments": [ "0.0", "0.125", "0.25", "0.5", "1.0", "2.0", "4.0" ], "normalization": "B=exp(2*pi*exp(2*z)-9*z)/(4*pi^4), analytic and nonzero", "derivative": "dm=(B*M)' includes B' contribution", "majorants": { "status": "analytic majorants evaluated as floating numbers; NOT interval bounds", "quadrature_error": "NOT bounded: fixed Gauss-Legendre approximation and replay only", "roundoff_error": "NOT bounded: ordinary mpmath arithmetic", "normalized_lattice_m": "2.3374694418931639750490862789805521242e-453", "normalized_lattice_c": "1.2466503690096874533595126821229611329e-452", "normalized_lattice_dm": "1.0829953272258903559388150163539693318e-449", "normalized_real_tail_m": "3.5256519758602368891506199208604614622e-1220", "normalized_real_tail_c": "5.6415130402128883634535231413716974126e-1219", "normalized_real_tail_dm": "2.5492087434004829773664761211795904186e-1217", "phi_lattice_tail": "1.9356365872969653834965440138348783136e-540", "phi_derivative_lattice_tail": "7.6099345128052750467898755680309622573e-537", "envelope_K0": "16.757999595347284854867734621554433003", "envelope_K1": "357.61040338926418324104642749144832606", "envelope_d": "1.0068755102900204581994763865832455735" } } }, "elapsed_seconds": 0.17024612496607006 }, { "z": { "re": "2.0", "im": "0.5" }, "bits": 128, "replay": false, "purpose": "grid_8_6", "values": { "m": { "re": "0.059295338435383207743698710744226736792", "im": "-0.031238795724848168132627265529089961985" }, "c": { "re": "0.0000042495023807484702648465907323164047914", "im": "-0.000048619080651099263316505088901504262158" }, "dm": { "re": "-0.059111850214370240802463059819729446962", "im": "0.028837891283600155929648905704269256569" } }, "metadata": { "metadata": { "classification": "diagnostic, not a certificate", "bits": 128, "lattice_cutoff": 24, "gauss_legendre_order_per_segment": 48, "positive_half_segments": [ "0.0", "0.125", "0.25", "0.5", "1.0", "2.0", "4.0" ], "normalization": "B=exp(2*pi*exp(2*z)-9*z)/(4*pi^4), analytic and nonzero", "derivative": "dm=(B*M)' includes B' contribution", "majorants": { "status": "analytic majorants evaluated as floating numbers; NOT interval bounds", "quadrature_error": "NOT bounded: fixed Gauss-Legendre approximation and replay only", "roundoff_error": "NOT bounded: ordinary mpmath arithmetic", "normalized_lattice_m": "2.9833193398720661357186607083359749287e-382", "normalized_lattice_c": "1.5911036479317686057166190444458532953e-381", "normalized_lattice_dm": "1.3843946997408657632374973507227359883e-378", "normalized_real_tail_m": "5.4477117383646114653414770215952292636e-1030", "normalized_real_tail_c": "8.7172001380399874714042847205874000932e-1029", "normalized_real_tail_dm": "4.0130204217786659549359070770644532123e-1027", "phi_lattice_tail": "1.4210689249680573121153852115435788848e-454", "phi_derivative_lattice_tail": "5.5869172592419013598919352956561404267e-451", "envelope_K0": "24.983585560594923710980841691774397433", "envelope_K1": "691.58751112121217564683229655248525689", "envelope_d": "0.84870487741648658484554125650222836214" } } }, "elapsed_seconds": 0.15910345903830603 }, { "z": { "re": "2.0", "im": "0.5625" }, "bits": 128, "replay": false, "purpose": "grid_8_7", "values": { "m": { "re": "0.057378683678219960719264496746602229416", "im": "-0.034888646785395856139562747540148423708" }, "c": { "re": "-0.0000048420432012826089405634350607463847892", "im": "-0.000048668667777664469358440818885072609277" }, "dm": { "re": "-0.057645199246018608938046441566234084621", "im": "0.032493809188817487492851011585334272973" } }, "metadata": { "metadata": { "classification": "diagnostic, not a certificate", "bits": 128, "lattice_cutoff": 24, "gauss_legendre_order_per_segment": 48, "positive_half_segments": [ "0.0", "0.125", "0.25", "0.5", "1.0", "2.0", "4.0" ], "normalization": "B=exp(2*pi*exp(2*z)-9*z)/(4*pi^4), analytic and nonzero", "derivative": "dm=(B*M)' includes B' contribution", "majorants": { "status": "analytic majorants evaluated as floating numbers; NOT interval bounds", "quadrature_error": "NOT bounded: fixed Gauss-Legendre approximation and replay only", "roundoff_error": "NOT bounded: ordinary mpmath arithmetic", "normalized_lattice_m": "4.0688659900997066987958365458836154534e-305", "normalized_lattice_c": "2.1700618613865102393577794911379282418e-304", "normalized_lattice_dm": "1.8948291866412820313404943727949196604e-301", "normalized_real_tail_m": "1.0412033384916555010934396156977205671e-823", "normalized_real_tail_c": "1.6661316379625947208230930990280473451e-822", "normalized_real_tail_dm": "8.0021484536992775479429954029232373279e-821", "phi_lattice_tail": "1.6144292525175739343768210704242839689e-361", "phi_derivative_lattice_tail": "6.3471113161651743543353377638863142176e-358", "envelope_K0": "45.779336961551260847650165707650203536", "envelope_K1": "1974.9153743821504788261579387588952755", "envelope_d": "0.67729048878756286732349724939914712065" } } }, "elapsed_seconds": 0.15883866703370586 }, { "z": { "re": "2.0", "im": "0.625" }, "bits": 128, "replay": false, "purpose": "grid_8_8", "values": { "m": { "re": "0.055233929364448427842080191177415485427", "im": "-0.038439517184922448702715047303862354583" }, "c": { "re": "-0.000013819365623693773948085289396848418231", "im": "-0.000047031480748386734445946472336938098296" }, "dm": { "re": "-0.055942023486078897555191636117729230776", "im": "0.036134379665903320705475182231636423601" } }, "metadata": { "metadata": { "classification": "diagnostic, not a certificate", "bits": 128, "lattice_cutoff": 24, "gauss_legendre_order_per_segment": 48, "positive_half_segments": [ "0.0", "0.125", "0.25", "0.5", "1.0", "2.0", "4.0" ], "normalization": "B=exp(2*pi*exp(2*z)-9*z)/(4*pi^4), analytic and nonzero", "derivative": "dm=(B*M)' includes B' contribution", "majorants": { "status": "analytic majorants evaluated as floating numbers; NOT interval bounds", "quadrature_error": "NOT bounded: fixed Gauss-Legendre approximation and replay only", "roundoff_error": "NOT bounded: ordinary mpmath arithmetic", "normalized_lattice_m": "4.5863937162174271417108611288043773115e-223", "normalized_lattice_c": "2.4460766486492944755791259353623345662e-222", "normalized_lattice_dm": "2.155663493934500230009343272544272903e-219", "normalized_real_tail_m": "2.3554357504847240935178094314820330182e-604", "normalized_real_tail_c": "3.7693353724380544205148566211558007553e-603", "normalized_real_tail_dm": "2.0114484467570987956105619504011708751e-601", "phi_lattice_tail": "1.0021598388692270941092068707959257556e-262", "phi_derivative_lattice_tail": "3.9399806736491836923747700781666945459e-259", "envelope_K0": "126.24928292784368352612039481684046491", "envelope_K1": "10771.851462133738538848956859875684407", "envelope_d": "0.49530720860677725930394940995503526598" } } }, "elapsed_seconds": 0.16030491702258587 }, { "z": { "re": "0.2421875", "im": "0.59375" }, "bits": 128, "replay": false, "purpose": "cell_0_7_step_0", "values": { "m": { "re": "0.19333576060874026365519907272340131948", "im": "0.057979299093506573992428430424645359394" }, "c": { "re": "-0.012519745081136390792848864521385382645", "im": "-0.00094569379303306057482543007510119339126" }, "dm": { "re": "1.7810205490860276321488957294946191393", "im": "1.9722122222323539334215376172589971082" } }, "metadata": { "metadata": { "classification": "diagnostic, not a certificate", "bits": 128, "lattice_cutoff": 24, "gauss_legendre_order_per_segment": 48, "positive_half_segments": [ "0.0", "0.125", "0.25", "0.5", "1.0", "2.0", "4.0" ], "normalization": "B=exp(2*pi*exp(2*z)-9*z)/(4*pi^4), analytic and nonzero", "derivative": "dm=(B*M)' includes B' contribution", "majorants": { "status": "analytic majorants evaluated as floating numbers; NOT interval bounds", "quadrature_error": "NOT bounded: fixed Gauss-Legendre approximation and replay only", "roundoff_error": "NOT bounded: ordinary mpmath arithmetic", "normalized_lattice_m": "7.9513550132465291594087763856677431948e-312", "normalized_lattice_c": "4.2407226737314822183513474056894630372e-311", "normalized_lattice_dm": "3.1879538275220390802096635328668178347e-308", "normalized_real_tail_m": "1.1519172303993744201288794418963598964e-762", "normalized_real_tail_c": "1.8433307096776388759976395900522980426e-761", "normalized_real_tail_dm": "1.5746421887050431574966726327228123317e-760", "phi_lattice_tail": "9.5899916368770065877852292299326725313e-313", "phi_derivative_lattice_tail": "3.7702949414123579212972797743894434158e-309", "envelope_K0": "70.873113161494437037846370353104916622", "envelope_K1": "4171.970167435341205168775349782120994", "envelope_d": "0.58744583039528823332246294434438261735" } } }, "elapsed_seconds": 0.17176720802672207 }, { "z": { "re": "0.20971052195016394915473619513351983776", "im": "0.61343637785919879282635807295505602743" }, "bits": 128, "replay": false, "purpose": "cell_0_7_step_1", "values": { "m": { "re": "0.080564127128848554513802498383617071786", "im": "-0.011878756280444612222886074428500447844" }, "c": { "re": "-0.024302986289613173893399359485275902", "im": "-0.005471697287064923918289281914188583187" }, "dm": { "re": "1.2138808574232990038271634955880469949", "im": "4.3324864206427338548471942388204131728" } }, "metadata": { "metadata": { "classification": "diagnostic, not a certificate", "bits": 128, "lattice_cutoff": 24, "gauss_legendre_order_per_segment": 48, "positive_half_segments": [ "0.0", "0.125", "0.25", "0.5", "1.0", "2.0", "4.0" ], "normalization": "B=exp(2*pi*exp(2*z)-9*z)/(4*pi^4), analytic and nonzero", "derivative": "dm=(B*M)' includes B' contribution", "majorants": { "status": "analytic majorants evaluated as floating numbers; NOT interval bounds", "quadrature_error": "NOT bounded: fixed Gauss-Legendre approximation and replay only", "roundoff_error": "NOT bounded: ordinary mpmath arithmetic", "normalized_lattice_m": "2.1009730814481427037645878174630044497e-280", "normalized_lattice_c": "1.1205189767723427753411135026469357065e-279", "normalized_lattice_dm": "8.4532854666773003838446148178644031563e-277", "normalized_real_tail_m": "1.267871716755953398959463871351973106e-687", "normalized_real_tail_c": "2.0289159853660647086632924472295519505e-686", "normalized_real_tail_dm": "2.1029573416384326465763302193543409377e-685", "phi_lattice_tail": "2.286606667247099754097315345378701368e-281", "phi_derivative_lattice_tail": "8.9897696233330711256237694622759479914e-278", "envelope_K0": "99.987242516986615141896333641399582481", "envelope_K1": "7383.5371294694462107988126747811164499", "envelope_d": "0.5296465728969732233933499888538344427" } } }, "elapsed_seconds": 0.16970333299832419 }, { "z": { "re": "0.20856621186873558427018883738799649583", "im": "0.6224134417632680006649664128418227517" }, "bits": 128, "replay": false, "purpose": "cell_0_7_step_2", "values": { "m": { "re": "0.037378557708846397677597901547922038405", "im": "-0.0048635469801233748660110609369981362376" }, "c": { "re": "-0.027032270638813440229840833423691709043", "im": "-0.0034632002373904931674316837000350966413" }, "dm": { "re": "1.5333846572590918214808206454843601341", "im": "4.9502021801899650083684061312641142099" } }, "metadata": { "metadata": { "classification": "diagnostic, not a certificate", "bits": 128, "lattice_cutoff": 24, "gauss_legendre_order_per_segment": 48, "positive_half_segments": [ "0.0", "0.125", "0.25", "0.5", "1.0", "2.0", "4.0" ], "normalization": "B=exp(2*pi*exp(2*z)-9*z)/(4*pi^4), analytic and nonzero", "derivative": "dm=(B*M)' includes B' contribution", "majorants": { "status": "analytic majorants evaluated as floating numbers; NOT interval bounds", "quadrature_error": "NOT bounded: fixed Gauss-Legendre approximation and replay only", "roundoff_error": "NOT bounded: ordinary mpmath arithmetic", "normalized_lattice_m": "6.3360328599609187420276196879126561705e-266", "normalized_lattice_c": "3.3792175253124899957480638335534166243e-265", "normalized_lattice_dm": "2.5548991408790799954235415357109411301e-262", "normalized_real_tail_m": "4.937031915018117542377393312103816482e-653", "normalized_real_tail_c": "7.9005681920926253918253617121542678595e-652", "normalized_real_tail_dm": "9.0540128453374136750111323172110564884e-651", "phi_lattice_tail": "6.5811072719337613734572193024598300281e-267", "phi_derivative_lattice_tail": "2.5873552757700044240314855956743823905e-263", "envelope_K0": "119.56706618197650701646867812611116522", "envelope_K1": "9869.8498366501008118646632007340350364", "envelope_d": "0.50301191257889817578047719459247028554" } } }, "elapsed_seconds": 0.16321987501578405 }, { "z": { "re": "0.20825677961382788685529139842652398396", "im": "0.62420532024261016314515117684667960121" }, "bits": 128, "replay": false, "purpose": "cell_0_7_step_3", "values": { "m": { "re": "0.02790366959261160853086275895503921767", "im": "-0.0036151219499676757602047439358200845602" }, "c": { "re": "-0.027556407820519689674986752174452556449", "im": "-0.0030503489656217110115411605366526330717" }, "dm": { "re": "1.5930256746558679321345962987837927693", "im": "5.0858256006210789483004060307549478277" } }, "metadata": { "metadata": { "classification": "diagnostic, not a certificate", "bits": 128, "lattice_cutoff": 24, "gauss_legendre_order_per_segment": 48, "positive_half_segments": [ "0.0", "0.125", "0.25", "0.5", "1.0", "2.0", "4.0" ], "normalization": "B=exp(2*pi*exp(2*z)-9*z)/(4*pi^4), analytic and nonzero", "derivative": "dm=(B*M)' includes B' contribution", "majorants": { "status": "analytic majorants evaluated as floating numbers; NOT interval bounds", "quadrature_error": "NOT bounded: fixed Gauss-Legendre approximation and replay only", "roundoff_error": "NOT bounded: ordinary mpmath arithmetic", "normalized_lattice_m": "5.0533712396211459023237074224557180547e-263", "normalized_lattice_c": "2.6951313277979444812393106253097162959e-262", "normalized_lattice_dm": "2.0386628148630839944988299792575378566e-259", "normalized_real_tail_m": "4.2194729061346057183145617058508193525e-646", "normalized_real_tail_c": "6.7522944144347840561140014887239344523e-645", "normalized_real_tail_dm": "7.9000834180564342939174048191809417878e-644", "phi_lattice_tail": "5.1893815209955761286926893844102171308e-264", "phi_derivative_lattice_tail": "2.0401997872898999767548457967478666461e-260", "envelope_K0": "124.13991332165329992527499088461057023", "envelope_K1": "10484.303021509898455374383289161552137", "envelope_d": "0.49767577914527312753347977038114619668" } } }, "elapsed_seconds": 0.16178349999245256 }, { "z": { "re": "0.20814206876233783640486859749652997952", "im": "0.62485520909587472103498939154256419831" }, "bits": 128, "replay": false, "purpose": "cell_0_7_step_4", "values": { "m": { "re": "0.024398216895282276615989540702472896155", "im": "-0.003159133379244850417288761156559114133" }, "c": { "re": "-0.027742884711151328747460290692880501033", "im": "-0.0028984719988006128034322517204185572284" }, "dm": { "re": "1.6144693116803568021965720021458668686", "im": "5.1359521859841955270785227982531472268" } }, "metadata": { "metadata": { "classification": "diagnostic, not a certificate", "bits": 128, "lattice_cutoff": 24, "gauss_legendre_order_per_segment": 48, "positive_half_segments": [ "0.0", "0.125", "0.25", "0.5", "1.0", "2.0", "4.0" ], "normalization": "B=exp(2*pi*exp(2*z)-9*z)/(4*pi^4), analytic and nonzero", "derivative": "dm=(B*M)' includes B' contribution", "majorants": { "status": "analytic majorants evaluated as floating numbers; NOT interval bounds", "quadrature_error": "NOT bounded: fixed Gauss-Legendre approximation and replay only", "roundoff_error": "NOT bounded: ordinary mpmath arithmetic", "normalized_lattice_m": "5.714018841422883266170580761600847629e-262", "normalized_lattice_c": "3.0474767154255377419576430728537854021e-261", "normalized_lattice_dm": "2.3055942096487847372419385717863583506e-258", "normalized_real_tail_m": "1.3852373407176296957612946568828172716e-643", "normalized_real_tail_c": "2.2167547285973725396613485915366786213e-642", "normalized_real_tail_dm": "2.6132819329583183343518338074489851103e-641", "phi_lattice_tail": "5.8426413724477979706913368902426412662e-263", "phi_derivative_lattice_tail": "2.2970281982644244367211216374816907059e-259", "envelope_K0": "125.86111530868465662488653873074179547", "envelope_K1": "10718.743700735064952627932909105744004", "envelope_d": "0.49573885630147622970818200645041912202" } } }, "elapsed_seconds": 0.1658226249855943 }, { "z": { "re": "0.20811709312702776346794591730574104551", "im": "0.6249958104595712872330239390812473354" }, "bits": 128, "replay": false, "purpose": "cell_0_7_step_5", "values": { "m": { "re": "0.023634948008475734098275822619122638583", "im": "-0.0030602214944233928353822501779159820733" }, "c": { "re": "-0.027782954699225456604026262454698017031", "im": "-0.0028654607936006101933005289348701016944" }, "dm": { "re": "1.6190947411673552742095121686652965809", "im": "5.1468638336118233243667652352897156277" } }, "metadata": { "metadata": { "classification": "diagnostic, not a certificate", "bits": 128, "lattice_cutoff": 24, "gauss_legendre_order_per_segment": 48, "positive_half_segments": [ "0.0", "0.125", "0.25", "0.5", "1.0", "2.0", "4.0" ], "normalization": "B=exp(2*pi*exp(2*z)-9*z)/(4*pi^4), analytic and nonzero", "derivative": "dm=(B*M)' includes B' contribution", "majorants": { "status": "analytic majorants evaluated as floating numbers; NOT interval bounds", "quadrature_error": "NOT bounded: fixed Gauss-Legendre approximation and replay only", "roundoff_error": "NOT bounded: ordinary mpmath arithmetic", "normalized_lattice_m": "9.6582361403076781827841027541957091894e-262", "normalized_lattice_c": "5.1510592748307616974848548022377115677e-261", "normalized_lattice_dm": "3.8972278758901202554300733012411522476e-258", "normalized_real_tail_m": "4.8535994193824391625473334563518469034e-643", "normalized_real_tail_c": "7.7670740512639338812438185833263858731e-642", "normalized_real_tail_dm": "9.1714763943800093925303872759915070495e-641", "phi_lattice_tail": "9.8663468410795316487994019125220504092e-263", "phi_derivative_lattice_tail": "3.8789436939755112269254561276455704961e-259", "envelope_K0": "126.23802697826178924851650628945480219", "envelope_K1": "10770.310241016511215393049810083184639", "envelope_d": "0.4953196989630838745170993957948856295" } } }, "elapsed_seconds": 0.16362104198196903 }, { "z": { "re": "0.20811671546167514755066653646371395198", "im": "0.62499793389363215154130364854802648275" }, "bits": 128, "replay": false, "purpose": "cell_0_7_step_6", "values": { "m": { "re": "0.023623407318174955585346630792895936339", "im": "-0.0030587272026777349966312713619069838789" }, "c": { "re": "-0.027783559107645680958090029902378375551", "im": "-0.0028649618337091961380015058948264929398" }, "dm": { "re": "1.6191645548275523638181816071359792744", "im": "5.147028812857032541314870416856019445" } }, "metadata": { "metadata": { "classification": "diagnostic, not a certificate", "bits": 128, "lattice_cutoff": 24, "gauss_legendre_order_per_segment": 48, "positive_half_segments": [ "0.0", "0.125", "0.25", "0.5", "1.0", "2.0", "4.0" ], "normalization": "B=exp(2*pi*exp(2*z)-9*z)/(4*pi^4), analytic and nonzero", "derivative": "dm=(B*M)' includes B' contribution", "majorants": { "status": "analytic majorants evaluated as floating numbers; NOT interval bounds", "quadrature_error": "NOT bounded: fixed Gauss-Legendre approximation and replay only", "roundoff_error": "NOT bounded: ordinary mpmath arithmetic", "normalized_lattice_m": "9.7351065137158204487654029065002442294e-262", "normalized_lattice_c": "5.1920568073151042393415482168001302557e-261", "normalized_lattice_dm": "3.9282483975513160287392272115460104268e-258", "normalized_real_tail_m": "4.946388999146805462440237323862663037e-643", "normalized_real_tail_c": "7.9155625353933902061863753679059247107e-642", "normalized_real_tail_dm": "9.3470457176143516726935540177268242523e-641", "phi_lattice_tail": "9.9447318110370764703065490334401719952e-263", "phi_derivative_lattice_tail": "3.9097606609661031054265983523309079219e-259", "envelope_K0": "126.24373178245801257652561556460306388", "envelope_K1": "10771.091362336480483409639962845468116", "envelope_d": "0.49531336833320767388818382645946384268" } } }, "elapsed_seconds": 0.16345733299385756 }, { "z": { "re": "0.20811652672407991959256788931691875277", "im": "0.62499899505656741409541631388857035529" }, "bits": 128, "replay": false, "purpose": "cell_0_7_step_7", "values": { "m": { "re": "0.023617639837709727804795039986987787752", "im": "-0.0030579804323762484072235714303816476379" }, "c": { "re": "-0.027783861145266613605065483687101203479", "im": "-0.0028647124789998652147831647242090700136" }, "dm": { "re": "1.6191994430930889406457228807067028621", "im": "5.1471112614257520648117745822804878552" } }, "metadata": { "metadata": { "classification": "diagnostic, not a certificate", "bits": 128, "lattice_cutoff": 24, "gauss_legendre_order_per_segment": 48, "positive_half_segments": [ "0.0", "0.125", "0.25", "0.5", "1.0", "2.0", "4.0" ], "normalization": "B=exp(2*pi*exp(2*z)-9*z)/(4*pi^4), analytic and nonzero", "derivative": "dm=(B*M)' includes B' contribution", "majorants": { "status": "analytic majorants evaluated as floating numbers; NOT interval bounds", "quadrature_error": "NOT bounded: fixed Gauss-Legendre approximation and replay only", "roundoff_error": "NOT bounded: ordinary mpmath arithmetic", "normalized_lattice_m": "9.7737506536489118603792219046272490859e-262", "normalized_lattice_c": "5.2126670152794196588689183491345328458e-261", "normalized_lattice_dm": "3.9438429869077069340142154027032153775e-258", "normalized_real_tail_m": "4.9934222835764819196348845750223817244e-643", "normalized_real_tail_c": "7.9908285419607004304996680352430974133e-642", "normalized_real_tail_dm": "9.4360401439858463092831877719017531468e-641", "phi_lattice_tail": "9.9841369418814777236569695355568419561e-263", "phi_derivative_lattice_tail": "3.9252527459557329609213088222456880123e-259", "envelope_K0": "126.2465828354565998583345837804631959", "envelope_K1": "10771.481745287650273864378544171015078", "envelope_d": "0.49531020466685516565939871220305239004" } } }, "elapsed_seconds": 0.16511075000744313 }, { "z": { "re": "0.2081164323790404598947492267077536198", "im": "0.62499952549958709610192458963196426634" }, "bits": 128, "replay": false, "purpose": "cell_0_7_step_8", "values": { "m": { "re": "0.023614756813280728394270240533341831967", "im": "-0.003057607141068086639486910834647270124" }, "c": { "re": "-0.027784012122453804261798045201024284007", "im": "-0.0028645878329379249752114597404299527456" }, "dm": { "re": "1.6192168825873191217396609606640090887", "im": "5.1471524754519334481590511745482813964" } }, "metadata": { "metadata": { "classification": "diagnostic, not a certificate", "bits": 128, "lattice_cutoff": 24, "gauss_legendre_order_per_segment": 48, "positive_half_segments": [ "0.0", "0.125", "0.25", "0.5", "1.0", "2.0", "4.0" ], "normalization": "B=exp(2*pi*exp(2*z)-9*z)/(4*pi^4), analytic and nonzero", "derivative": "dm=(B*M)' includes B' contribution", "majorants": { "status": "analytic majorants evaluated as floating numbers; NOT interval bounds", "quadrature_error": "NOT bounded: fixed Gauss-Legendre approximation and replay only", "roundoff_error": "NOT bounded: ordinary mpmath arithmetic", "normalized_lattice_m": "9.7931251600461862695769586861978590875e-262", "normalized_lattice_c": "5.22300008535796601044104463263885818e-261", "normalized_lattice_dm": "3.9516614436825601930615936084546583758e-258", "normalized_real_tail_m": "5.0171001876877377719713636503647467191e-643", "normalized_real_tail_c": "8.0287196080300656320948263219937869132e-642", "normalized_real_tail_dm": "9.4808429068151551452810749611577589983e-641", "phi_lattice_tail": "1.0003892869941248574026133538706293508e-262", "phi_derivative_lattice_tail": "3.93301976791435865734615670960766231e-259", "envelope_K0": "126.24800802484393460585762334375288508", "envelope_K1": "10771.676892356375724874756401383970256", "envelope_d": "0.49530862324560022246166310298724582689" } } }, "elapsed_seconds": 0.16840625001350418 }, { "z": { "re": "0.20811638521245875492481972995005715754", "im": "0.62499979068649442467742219746864044644" }, "bits": 128, "replay": false, "purpose": "cell_0_7_step_9", "values": { "m": { "re": "0.023613315479971197654174853675010842735", "im": "-0.0030574205188683730851175970633377969321" }, "c": { "re": "-0.027784087600644581268162063639136778046", "im": "-0.0028645255177280911976270813750587674737" }, "dm": { "re": "1.6192256011751247894042678236878209374", "im": "5.1471730799011407972905388149857199376" } }, "metadata": { "metadata": { "classification": "diagnostic, not a certificate", "bits": 128, "lattice_cutoff": 24, "gauss_legendre_order_per_segment": 48, "positive_half_segments": [ "0.0", "0.125", "0.25", "0.5", "1.0", "2.0", "4.0" ], "normalization": "B=exp(2*pi*exp(2*z)-9*z)/(4*pi^4), analytic and nonzero", "derivative": "dm=(B*M)' includes B' contribution", "majorants": { "status": "analytic majorants evaluated as floating numbers; NOT interval bounds", "quadrature_error": "NOT bounded: fixed Gauss-Legendre approximation and replay only", "roundoff_error": "NOT bounded: ordinary mpmath arithmetic", "normalized_lattice_m": "9.8028255471840880333607033789278637426e-262", "normalized_lattice_c": "5.2281736251648469511257084687615273294e-261", "normalized_lattice_dm": "3.9555759726165035792553861791460309086e-258", "normalized_real_tail_m": "5.0289796616160405085236775187215328087e-643", "normalized_real_tail_c": "8.047729987054926735985340794933330174e-642", "normalized_real_tail_dm": "9.5033210672685986255245655405027009929e-641", "phi_lattice_tail": "1.0013784199843910811614793967345260871e-262", "phi_derivative_lattice_tail": "3.9369085336722392152997298246272097059e-259", "envelope_K0": "126.24872053527996720647729952473608035", "envelope_K1": "10771.774454791565412044712904746711179", "envelope_d": "0.49530783263792495898719843151176743242" } } }, "elapsed_seconds": 0.1747086250106804 }, { "z": { "re": "0.20811636163065221949650578544218539785", "im": "0.62499992327129864487584747661140845087" }, "bits": 128, "replay": false, "purpose": "cell_0_7_step_10", "values": { "m": { "re": "0.023612594858036934244641360770231120096", "im": "-0.0030573272136313236151683913333133963437" }, "c": { "re": "-0.027784125337139640152294778570209631264", "im": "-0.0028644943620782028450042534585476032409" }, "dm": { "re": "1.6192299601792408933836077864985702779", "im": "5.1471833814848562702693000378376131978" } }, "metadata": { "metadata": { "classification": "diagnostic, not a certificate", "bits": 128, "lattice_cutoff": 24, "gauss_legendre_order_per_segment": 48, "positive_half_segments": [ "0.0", "0.125", "0.25", "0.5", "1.0", "2.0", "4.0" ], "normalization": "B=exp(2*pi*exp(2*z)-9*z)/(4*pi^4), analytic and nonzero", "derivative": "dm=(B*M)' includes B' contribution", "majorants": { "status": "analytic majorants evaluated as floating numbers; NOT interval bounds", "quadrature_error": "NOT bounded: fixed Gauss-Legendre approximation and replay only", "roundoff_error": "NOT bounded: ordinary mpmath arithmetic", "normalized_lattice_m": "9.8076790273459448127482183467587166111e-262", "normalized_lattice_c": "5.2307621479178372334657164516046488593e-261", "normalized_lattice_dm": "3.9575345634745704270884656919653642358e-258", "normalized_real_tail_m": "5.0349295549498186453107086855818041393e-643", "normalized_real_tail_c": "8.0572514295142672269392576417885424283e-642", "normalized_real_tail_dm": "9.5145793914016408459383926437525078579e-641", "phi_lattice_tail": "1.0018733209419303741436948335093278413e-262", "phi_derivative_lattice_tail": "3.9388542314865473919180017607281761123e-259", "envelope_K0": "126.24907676943611853731234465846850709", "envelope_K1": "10771.823233234684648261166082520442827", "envelope_d": "0.49530743735982186534755440800985501341" } } }, "elapsed_seconds": 0.16876891703577712 }, { "z": { "re": "0.20811634984012000740414410514067041294", "im": "0.62499998956153854193346158813727035093" }, "bits": 128, "replay": false, "purpose": "cell_0_7_step_11", "values": { "m": { "re": "0.023612234558249210591819892185238525555", "im": "-0.0030572805624784026558174143576979454954" }, "c": { "re": "-0.027784144204737134052727144138323722065", "im": "-0.0028644787847419838635007541952038962038" }, "dm": { "re": "1.6192321396088573403858675122395282659", "im": "5.1471885321165022842147405199374897414" } }, "metadata": { "metadata": { "classification": "diagnostic, not a certificate", "bits": 128, "lattice_cutoff": 24, "gauss_legendre_order_per_segment": 48, "positive_half_segments": [ "0.0", "0.125", "0.25", "0.5", "1.0", "2.0", "4.0" ], "normalization": "B=exp(2*pi*exp(2*z)-9*z)/(4*pi^4), analytic and nonzero", "derivative": "dm=(B*M)' includes B' contribution", "majorants": { "status": "analytic majorants evaluated as floating numbers; NOT interval bounds", "quadrature_error": "NOT bounded: fixed Gauss-Legendre approximation and replay only", "roundoff_error": "NOT bounded: ordinary mpmath arithmetic", "normalized_lattice_m": "9.8101065894638700098923055553190436111e-262", "normalized_lattice_c": "5.2320568477140640052758962961701565926e-261", "normalized_lattice_dm": "3.9585141906582904780943916260983289608e-258", "normalized_real_tail_m": "5.0379070439531687105408243167794283233e-643", "normalized_real_tail_c": "8.062016219172032627048703389265342225e-642", "normalized_real_tail_dm": "9.520213370600178556636277163792447887e-641", "phi_lattice_tail": "1.0021208550757761514225527936444517191e-262", "phi_derivative_lattice_tail": "3.9398274092827373648158459022699716391e-259", "envelope_K0": "126.24925488124904588553819590052037115", "envelope_K1": "10771.847621762665066328847661408382087", "envelope_d": "0.49530723972720351387398854135221360201" } } }, "elapsed_seconds": 0.1682742919656448 }, { "z": { "re": "0.4765625", "im": "0.59375" }, "bits": 128, "replay": false, "purpose": "cell_1_7_step_0", "values": { "m": { "re": "0.25931656163177871818690457609486358615", "im": "-0.063579312949005699511988326532405486647" }, "c": { "re": "-0.00092032972335829699576249552576219090562", "im": "-0.0044577546119330775535714711730615193899" }, "dm": { "re": "-0.17882589985482454635745042199650977234", "im": "0.31322791172876480060051166802401807006" } }, "metadata": { "metadata": { "classification": "diagnostic, not a certificate", "bits": 128, "lattice_cutoff": 24, "gauss_legendre_order_per_segment": 48, "positive_half_segments": [ "0.0", "0.125", "0.25", "0.5", "1.0", "2.0", "4.0" ], "normalization": "B=exp(2*pi*exp(2*z)-9*z)/(4*pi^4), analytic and nonzero", "derivative": "dm=(B*M)' includes B' contribution", "majorants": { "status": "analytic majorants evaluated as floating numbers; NOT interval bounds", "quadrature_error": "NOT bounded: fixed Gauss-Legendre approximation and replay only", "roundoff_error": "NOT bounded: ordinary mpmath arithmetic", "normalized_lattice_m": "9.4382136983396122552703049219192907608e-312", "normalized_lattice_c": "5.0337139724477932028108292916902884058e-311", "normalized_lattice_dm": "3.7948716321179133748808004709136703861e-308", "normalized_real_tail_m": "1.3673192764247814625066136681307040824e-762", "normalized_real_tail_c": "2.188023189213141298041203963131956542e-761", "normalized_real_tail_dm": "2.0253830190360579424482230605647444451e-760", "phi_lattice_tail": "9.5899916368770065877852292299326725313e-313", "phi_derivative_lattice_tail": "3.7702949414123579212972797743894434158e-309", "envelope_K0": "70.873113161494437037846370353104916622", "envelope_K1": "4171.970167435341205168775349782120994", "envelope_d": "0.58744583039528823332246294434438261735" } } }, "elapsed_seconds": 0.16692679200787097 }, { "z": { "re": "0.49248587882772789735474457048318192554", "im": "0.61053052883086246979188866964546056996" }, "bits": 128, "replay": false, "purpose": "cell_1_7_step_1", "values": { "m": { "re": "0.25420860616864853518552113973934182932", "im": "-0.058136561635618569126330551120501396038" }, "c": { "re": "-0.0014617506854332383111818562414574613313", "im": "-0.0028155146226595013738262643070921705526" }, "dm": { "re": "0.23800346305731852996122172023963397938", "im": "0.28410044332873040610246476009253380414" } }, "metadata": { "metadata": { "classification": "diagnostic, not a certificate", "bits": 128, "lattice_cutoff": 24, "gauss_legendre_order_per_segment": 48, "positive_half_segments": [ "0.0", "0.125", "0.25", "0.5", "1.0", "2.0", "4.0" ], "normalization": "B=exp(2*pi*exp(2*z)-9*z)/(4*pi^4), analytic and nonzero", "derivative": "dm=(B*M)' includes B' contribution", "majorants": { "status": "analytic majorants evaluated as floating numbers; NOT interval bounds", "quadrature_error": "NOT bounded: fixed Gauss-Legendre approximation and replay only", "roundoff_error": "NOT bounded: ordinary mpmath arithmetic", "normalized_lattice_m": "4.2959829971103902368286888691019525358e-285", "normalized_lattice_c": "2.2911909317922081263086340635210413524e-284", "normalized_lattice_dm": "1.7332187082013392818495018508507460719e-281", "normalized_real_tail_m": "8.563344558698120779678650888065808844e-699", "normalized_real_tail_c": "1.3703486362834069840587736274032004637e-697", "normalized_real_tail_dm": "1.4928330780137689293380397186760333908e-696", "phi_lattice_tail": "4.9940513496934464838280475040520191062e-286", "phi_derivative_lattice_tail": "1.9634059396358831056529270594894233829e-282", "envelope_K0": "94.658438758989379634079453027515663239", "envelope_K1": "6749.846848797493586221700596573363991", "envelope_d": "0.53823197042081346802890331646436833244" } } }, "elapsed_seconds": 0.1650962500134483 }, { "z": { "re": "0.48748233901214250662786266482616159919", "im": "0.62031984712668993131887523744349247668" }, "bits": 128, "replay": false, "purpose": "cell_1_7_step_2", "values": { "m": { "re": "0.24877975026869851452742703765795681914", "im": "-0.056911088583531567182983404946686200029" }, "c": { "re": "-0.0025076548128952588509870129267108489566", "im": "-0.0024639153377716729529632684013257956453" }, "dm": { "re": "0.41733703190825208623026720065705019501", "im": "0.50878785325168429013679264985465241052" } }, "metadata": { "metadata": { "classification": "diagnostic, not a certificate", "bits": 128, "lattice_cutoff": 24, "gauss_legendre_order_per_segment": 48, "positive_half_segments": [ "0.0", "0.125", "0.25", "0.5", "1.0", "2.0", "4.0" ], "normalization": "B=exp(2*pi*exp(2*z)-9*z)/(4*pi^4), analytic and nonzero", "derivative": "dm=(B*M)' includes B' contribution", "majorants": { "status": "analytic majorants evaluated as floating numbers; NOT interval bounds", "quadrature_error": "NOT bounded: fixed Gauss-Legendre approximation and replay only", "roundoff_error": "NOT bounded: ordinary mpmath arithmetic", "normalized_lattice_m": "2.1341086477326597182743592219760969743e-269", "normalized_lattice_c": "1.1381912787907518497463249183872517196e-268", "normalized_lattice_dm": "8.6291575533339255027852364313798917518e-266", "normalized_real_tail_m": "3.3023776637507153613076481226094988452e-661", "normalized_real_tail_c": "5.2846745149992885570196518277695414628e-660", "normalized_real_tail_dm": "6.3521605868395115569810072344664415424e-659", "phi_lattice_tail": "2.7425980504989373447204601663745149598e-270", "phi_derivative_lattice_tail": "1.0782494863041302995531104186385455177e-266", "envelope_K0": "114.52804329922297906729372372063677518", "envelope_K1": "9207.1747494591217858424015328352764487", "envelope_d": "0.50923835467794649349347639810916694877" } } }, "elapsed_seconds": 0.16383316699648276 }, { "z": { "re": "0.48613160227975949750314030964813164178", "im": "0.62303193887843511344948995659022703211" }, "bits": 128, "replay": false, "purpose": "cell_1_7_step_3", "values": { "m": { "re": "0.24669263088193023938985251159280606243", "im": "-0.056440501793464312361671877711756638577" }, "c": { "re": "-0.0028609194601813763037783957158913764685", "im": "-0.0023459380563869704583385183749233965779" }, "dm": { "re": "0.47553043914466365876761362899007500317", "im": "0.58734695655669030434414093171065080224" } }, "metadata": { "metadata": { "classification": "diagnostic, not a certificate", "bits": 128, "lattice_cutoff": 24, "gauss_legendre_order_per_segment": 48, "positive_half_segments": [ "0.0", "0.125", "0.25", "0.5", "1.0", "2.0", "4.0" ], "normalization": "B=exp(2*pi*exp(2*z)-9*z)/(4*pi^4), analytic and nonzero", "derivative": "dm=(B*M)' includes B' contribution", "majorants": { "status": "analytic majorants evaluated as floating numbers; NOT interval bounds", "quadrature_error": "NOT bounded: fixed Gauss-Legendre approximation and replay only", "roundoff_error": "NOT bounded: ordinary mpmath arithmetic", "normalized_lattice_m": "4.995063757189941206802824709996152557e-265", "normalized_lattice_c": "2.6640340038346353102948398453312813638e-264", "normalized_lattice_dm": "2.0211109563328894592698897695851425246e-261", "normalized_real_tail_m": "9.5639815648355403994990267102036687919e-651", "normalized_real_tail_c": "1.5304931408675890215108861861910532073e-649", "normalized_real_tail_dm": "1.8929585608678824581150261213189965104e-648", "phi_lattice_tail": "6.5733942499566732204319610139282538987e-266", "phi_derivative_lattice_tail": "2.5843229094401534975876041001673103554e-262", "envelope_K0": "121.11743850417184847044416196800224452", "envelope_K1": "10076.794215163120204901561128887756699", "envelope_d": "0.50117078265001586852510942062002366611" } } }, "elapsed_seconds": 0.16552916599903256 }, { "z": { "re": "0.48555596654018882291302298886041990586", "im": "0.62420656107687421300772421352681055755" }, "bits": 128, "replay": false, "purpose": "cell_1_7_step_4", "values": { "m": { "re": "0.24570017475659077870270477381890053601", "im": "-0.056214934267601473609572375120916051935" }, "c": { "re": "-0.0030231486684761609114655017873379515079", "im": "-0.0022914526989731991845042032313221645452" }, "dm": { "re": "0.50203289515651269413554678243580135757", "im": "0.62375221351093638706097478377006484978" } }, "metadata": { "metadata": { "classification": "diagnostic, not a certificate", "bits": 128, "lattice_cutoff": 24, "gauss_legendre_order_per_segment": 48, "positive_half_segments": [ "0.0", "0.125", "0.25", "0.5", "1.0", "2.0", "4.0" ], "normalization": "B=exp(2*pi*exp(2*z)-9*z)/(4*pi^4), analytic and nonzero", "derivative": "dm=(B*M)' includes B' contribution", "majorants": { "status": "analytic majorants evaluated as floating numbers; NOT interval bounds", "quadrature_error": "NOT bounded: fixed Gauss-Legendre approximation and replay only", "roundoff_error": "NOT bounded: ordinary mpmath arithmetic", "normalized_lattice_m": "3.9233789759640825309022031650492682823e-263", "normalized_lattice_c": "2.0924687871808440164811750213596097506e-262", "normalized_lattice_dm": "1.5879716289537773417837320020619152698e-259", "normalized_real_tail_m": "3.2970819710716292638355448517514456274e-646", "normalized_real_tail_c": "5.2762202057761965512520337449536070806e-645", "normalized_real_tail_dm": "6.6082352046240880251115124051974964476e-644", "phi_lattice_tail": "5.2134208662978661852617404316666778079e-264", "phi_derivative_lattice_tail": "2.0496508301499962213273528165770369895e-260", "envelope_K0": "124.14316709963819908168471876233203702", "envelope_K1": "10484.744591055838991390648978457884049", "envelope_d": "0.4976720817741690255600580010265286854" } } }, "elapsed_seconds": 0.1723936659982428 }, { "z": { "re": "0.48528700483745377703847215903078804066", "im": "0.62475943371450393023905276192004946463" }, "bits": 128, "replay": false, "purpose": "cell_1_7_step_5", "values": { "m": { "re": "0.24521371737668273827301714923946599839", "im": "-0.056103986604419314190122552893435211441" }, "c": { "re": "-0.0031015026175881760612923784867645096317", "im": "-0.0022650706923463475317356433847232640338" }, "dm": { "re": "0.51478733163535505065667949883011766487", "im": "0.64140495986600642246934092231001255334" } }, "metadata": { "metadata": { "classification": "diagnostic, not a certificate", "bits": 128, "lattice_cutoff": 24, "gauss_legendre_order_per_segment": 48, "positive_half_segments": [ "0.0", "0.125", "0.25", "0.5", "1.0", "2.0", "4.0" ], "normalization": "B=exp(2*pi*exp(2*z)-9*z)/(4*pi^4), analytic and nonzero", "derivative": "dm=(B*M)' includes B' contribution", "majorants": { "status": "analytic majorants evaluated as floating numbers; NOT interval bounds", "quadrature_error": "NOT bounded: fixed Gauss-Legendre approximation and replay only", "roundoff_error": "NOT bounded: ordinary mpmath arithmetic", "normalized_lattice_m": "3.0635604875113747603557181803090508315e-262", "normalized_lattice_c": "1.6338989266727332055230496961648271101e-261", "normalized_lattice_dm": "1.2401456797507374399564093510676255317e-258", "normalized_real_tail_m": "4.5203846789796105905975118153572287148e-644", "normalized_real_tail_c": "7.2338384491487726194732852112010992626e-643", "normalized_real_tail_dm": "9.1141201814912970103605318257434202233e-642", "phi_lattice_tail": "4.0890268835499677680131274230321053931e-263", "phi_derivative_lattice_tail": "1.6075965400286934584117468420101430729e-259", "envelope_K0": "125.6052993887368186322731285585588956", "envelope_K1": "10683.791295777847695236203431039177463", "envelope_d": "0.49602435707621795891574181531663761241" } } }, "elapsed_seconds": 0.16783158300677314 }, { "z": { "re": "0.48522185733606836659091292232771230847", "im": "0.6248938201901790392252124541081879884" }, "bits": 128, "replay": false, "purpose": "cell_1_7_step_6", "values": { "m": { "re": "0.24509359086420007685659938263022467109", "im": "-0.056076523251527812245050181594562319627" }, "c": { "re": "-0.0031207401953228757770173079168469689985", "im": "-0.0022585820368207168655266952380598774644" }, "dm": { "re": "0.51791562847810298775023738651472770618", "im": "0.64574547994377126487902518612835953104" } }, "metadata": { "metadata": { "classification": "diagnostic, not a certificate", "bits": 128, "lattice_cutoff": 24, "gauss_legendre_order_per_segment": 48, "positive_half_segments": [ "0.0", "0.125", "0.25", "0.5", "1.0", "2.0", "4.0" ], "normalization": "B=exp(2*pi*exp(2*z)-9*z)/(4*pi^4), analytic and nonzero", "derivative": "dm=(B*M)' includes B' contribution", "majorants": { "status": "analytic majorants evaluated as floating numbers; NOT interval bounds", "quadrature_error": "NOT bounded: fixed Gauss-Legendre approximation and replay only", "roundoff_error": "NOT bounded: ordinary mpmath arithmetic", "normalized_lattice_m": "5.049367392995620422657094276802215546e-262", "normalized_lattice_c": "2.6929959429309975587504502809611816246e-261", "normalized_lattice_dm": "2.0440843543700593651724270564741968767e-258", "normalized_real_tail_m": "1.495390511712822325646193110255930264e-643", "normalized_real_tail_c": "2.3930297146475279318158489249993894048e-642", "normalized_real_tail_dm": "3.0194205865484200968818887021394366933e-641", "phi_lattice_tail": "6.7467517397011147377023052018162224545e-263", "phi_derivative_lattice_tail": "2.6524782208719224994379598309894617216e-259", "envelope_K0": "125.96445842326308076577754958587947434", "envelope_K1": "10732.874277743007751717790586241248887", "envelope_d": "0.49562375375673982253787228404905958119" } } }, "elapsed_seconds": 0.1647179169813171 }, { "z": { "re": "0.48518953204646093839857094904733561352", "im": "0.62496055783080188153572014487564210985" }, "bits": 128, "replay": false, "purpose": "cell_1_7_step_7", "values": { "m": { "re": "0.24503365624829668099115327644487998015", "im": "-0.056062815678255740675888316234266624123" }, "c": { "re": "-0.0031303223768156588091678837627833492439", "im": "-0.0022553491349732358213806683766274994666" }, "dm": { "re": "0.51947317924957628697508381811725055714", "im": "0.64790846830185318271857027671778583314" } }, "metadata": { "metadata": { "classification": "diagnostic, not a certificate", "bits": 128, "lattice_cutoff": 24, "gauss_legendre_order_per_segment": 48, "positive_half_segments": [ "0.0", "0.125", "0.25", "0.5", "1.0", "2.0", "4.0" ], "normalization": "B=exp(2*pi*exp(2*z)-9*z)/(4*pi^4), analytic and nonzero", "derivative": "dm=(B*M)' includes B' contribution", "majorants": { "status": "analytic majorants evaluated as floating numbers; NOT interval bounds", "quadrature_error": "NOT bounded: fixed Gauss-Legendre approximation and replay only", "roundoff_error": "NOT bounded: ordinary mpmath arithmetic", "normalized_lattice_m": "6.4716419518933912907171530246259743338e-262", "normalized_lattice_c": "3.4515423743431420217158149464671863113e-261", "normalized_lattice_dm": "2.6198961991784918765632014464133059443e-258", "normalized_real_tail_m": "2.7089526866909668931199146824862438222e-643", "normalized_real_tail_c": "4.3350580765137919483997158329038305186e-642", "normalized_real_tail_dm": "5.4737294937456654750791832551602842725e-641", "phi_lattice_tail": "8.6517119630953081987334934629623500898e-263", "phi_derivative_lattice_tail": "3.4014112925376446128073836878389441157e-259", "envelope_K0": "126.143371869456512325072855643968541", "envelope_K1": "10757.352471641079239225896367420935161", "envelope_d": "0.49542479691605278691064592207059295178" } } }, "elapsed_seconds": 0.16796891699777916 }, { "z": { "re": "0.48517343068586377081265014770242030693", "im": "0.62499381424133787424947503868363831717" }, "bits": 128, "replay": false, "purpose": "cell_1_7_step_8", "values": { "m": { "re": "0.24500372070788526632279215436255544921", "im": "-0.05605596784236070393202632547833235336" }, "c": { "re": "-0.0031351044287776368215446133169741729367", "im": "-0.002253735505168423559781636794426431772" }, "dm": { "re": "0.5202503256923315929602697119035242541", "im": "0.6489881671579925288954804782830504466" } }, "metadata": { "metadata": { "classification": "diagnostic, not a certificate", "bits": 128, "lattice_cutoff": 24, "gauss_legendre_order_per_segment": 48, "positive_half_segments": [ "0.0", "0.125", "0.25", "0.5", "1.0", "2.0", "4.0" ], "normalization": "B=exp(2*pi*exp(2*z)-9*z)/(4*pi^4), analytic and nonzero", "derivative": "dm=(B*M)' includes B' contribution", "majorants": { "status": "analytic majorants evaluated as floating numbers; NOT interval bounds", "quadrature_error": "NOT bounded: fixed Gauss-Legendre approximation and replay only", "roundoff_error": "NOT bounded: ordinary mpmath arithmetic", "normalized_lattice_m": "7.3235841101503205403881727779098629299e-262", "normalized_lattice_c": "3.905911525413504288207025481551926896e-261", "normalized_lattice_dm": "2.9648119165349191116778920765055512952e-258", "normalized_real_tail_m": "3.6424600719157352509437799482321294455e-643", "normalized_real_tail_c": "5.8289229508329264893962166802449208144e-642", "normalized_real_tail_dm": "7.3626253713050392803626750872525757323e-641", "phi_lattice_tail": "9.7932215578971967625671656437146774443e-263", "phi_derivative_lattice_tail": "3.8501945672076085673773979520535088255e-259", "envelope_K0": "126.23266429080577976684943531569883348", "envelope_K1": "10769.57598055929628308879565696031705", "envelope_d": "0.49532565031411553468072340071081792736" } } }, "elapsed_seconds": 0.1992535840254277 }, { "z": { "re": "0.48517142182053746703914053753054876594", "im": "0.62499796431277187627193381276144721368" }, "bits": 128, "replay": false, "purpose": "cell_1_7_step_9", "values": { "m": { "re": "0.24499998187058813757329452845631908348", "im": "-0.056055112430250040321385696962788510792" }, "c": { "re": "-0.0031357015031878970019692340251431540599", "im": "-0.0022535340071435361712487825246244868397" }, "dm": { "re": "0.52034735417058583153855300625511948357", "im": "0.64912298588465713334737142603162566213" } }, "metadata": { "metadata": { "classification": "diagnostic, not a certificate", "bits": 128, "lattice_cutoff": 24, "gauss_legendre_order_per_segment": 48, "positive_half_segments": [ "0.0", "0.125", "0.25", "0.5", "1.0", "2.0", "4.0" ], "normalization": "B=exp(2*pi*exp(2*z)-9*z)/(4*pi^4), analytic and nonzero", "derivative": "dm=(B*M)' includes B' contribution", "majorants": { "status": "analytic majorants evaluated as floating numbers; NOT interval bounds", "quadrature_error": "NOT bounded: fixed Gauss-Legendre approximation and replay only", "roundoff_error": "NOT bounded: ordinary mpmath arithmetic", "normalized_lattice_m": "7.4374856761641632068098266325743228039e-262", "normalized_lattice_c": "3.9666590272875537102985742040396388287e-261", "normalized_lattice_dm": "3.0109261207418586660202984941842608536e-258", "normalized_real_tail_m": "3.7795683086401602363597521054927355071e-643", "normalized_real_tail_c": "6.0483333013072964922049912901908432615e-642", "normalized_real_tail_dm": "7.6401092897445648000674844437189357469e-641", "phi_lattice_tail": "9.9458592241638871801780979879610381126e-263", "phi_derivative_lattice_tail": "3.910203902229479279566024432999823349e-259", "envelope_K0": "126.24381350902690960120262980807807438", "envelope_K1": "10771.102552754062393184368975358340455", "envelope_d": "0.49531327764404707345416556747315088207" } } }, "elapsed_seconds": 0.16188299999339506 }, { "z": { "re": "0.2421875", "im": "0.53125" }, "bits": 128, "replay": false, "purpose": "cell_0_6_step_0", "values": { "m": { "re": "0.2697247124805976359467257024546990676", "im": "0.011120050797520824744791108657355120062" }, "c": { "re": "-0.0014615082693746377413461112433944748851", "im": "-0.0074867993102034398712350080200193383137" }, "dm": { "re": "0.063578488062214770200029243130330762904", "im": "0.61544452341784566560639690131719629491" } }, "metadata": { "metadata": { "classification": "diagnostic, not a certificate", "bits": 128, "lattice_cutoff": 24, "gauss_legendre_order_per_segment": 48, "positive_half_segments": [ "0.0", "0.125", "0.25", "0.5", "1.0", "2.0", "4.0" ], "normalization": "B=exp(2*pi*exp(2*z)-9*z)/(4*pi^4), analytic and nonzero", "derivative": "dm=(B*M)' includes B' contribution", "majorants": { "status": "analytic majorants evaluated as floating numbers; NOT interval bounds", "quadrature_error": "NOT bounded: fixed Gauss-Legendre approximation and replay only", "roundoff_error": "NOT bounded: ordinary mpmath arithmetic", "normalized_lattice_m": "7.4891023979000137335659876988498850819e-408", "normalized_lattice_c": "3.994187945546673991235193439386605377e-407", "normalized_lattice_dm": "2.9828563804138235147476932413040089858e-404", "normalized_real_tail_m": "3.7064687339483659566685721032910856159e-992", "normalized_real_tail_c": "5.9310005776661832480816935637136640822e-991", "normalized_real_tail_dm": "3.1518693035705009817372517078049988777e-990", "phi_lattice_tail": "7.4131025121277860699325724745896154215e-409", "phi_derivative_lattice_tail": "2.9144533134075237843732796217023061305e-405", "envelope_K0": "32.655940532879415933669079343997813933", "envelope_K1": "1097.1476971337962654627243950799547334", "envelope_d": "0.76449034231527283458538549127537770114" } } }, "elapsed_seconds": 0.160355250001885 }, { "z": { "re": "0.23827038030432312208413625177168416359", "im": "0.55823659156148061650237768148629437405" }, "bits": 128, "replay": false, "purpose": "cell_0_6_step_1", "values": { "m": { "re": "0.2448799948953459937615917481171721811", "im": "0.014302925004887338507130217592989879076" }, "c": { "re": "-0.005885570953555815137689990798291813643", "im": "-0.0066312582115753762309520682994691291953" }, "dm": { "re": "0.47175965977710386896845652869587772908", "im": "1.1916916946960498064043895402334531819" } }, "metadata": { "metadata": { "classification": "diagnostic, not a certificate", "bits": 128, "lattice_cutoff": 24, "gauss_legendre_order_per_segment": 48, "positive_half_segments": [ "0.0", "0.125", "0.25", "0.5", "1.0", "2.0", "4.0" ], "normalization": "B=exp(2*pi*exp(2*z)-9*z)/(4*pi^4), analytic and nonzero", "derivative": "dm=(B*M)' includes B' contribution", "majorants": { "status": "analytic majorants evaluated as floating numbers; NOT interval bounds", "quadrature_error": "NOT bounded: fixed Gauss-Legendre approximation and replay only", "roundoff_error": "NOT bounded: ordinary mpmath arithmetic", "normalized_lattice_m": "4.0811935775167412996404833335663746485e-367", "normalized_lattice_c": "2.1766365746755953598082577779020664792e-366", "normalized_lattice_dm": "1.6288941277068352097319160444550321934e-363", "normalized_real_tail_m": "8.4735825182137575974888047038055671886e-895", "normalized_real_tail_c": "1.3559381548668197855775253184343939268e-893", "normalized_real_tail_dm": "8.5816954308718446443116573873953095806e-893", "phi_lattice_tail": "4.5811180810994629967678112696638120626e-368", "phi_derivative_lattice_tail": "1.8010616673287003100797299526450429445e-364", "envelope_K0": "43.495679067651487579594362961826106833", "envelope_K1": "1807.0371137008395548862011129113994708", "envelope_d": "0.68935059602781350452086604020810781656" } } }, "elapsed_seconds": 0.1638260409818031 }, { "z": { "re": "0.23700940097229086064503881993138272917", "im": "0.56094817439280887202734267155433065337" }, "bits": 128, "replay": false, "purpose": "cell_0_6_step_2", "values": { "m": { "re": "0.24090689332628002389760123264000165612", "im": "0.014070037509074137007303884498001946101" }, "c": { "re": "-0.0064979464212758641490508864551545677709", "im": "-0.0066288430582608742674532098409582035136" }, "dm": { "re": "0.50768652350799231635684888577105709938", "im": "1.2841929997177763822950657092790797035" } }, "metadata": { "metadata": { "classification": "diagnostic, not a certificate", "bits": 128, "lattice_cutoff": 24, "gauss_legendre_order_per_segment": 48, "positive_half_segments": [ "0.0", "0.125", "0.25", "0.5", "1.0", "2.0", "4.0" ], "normalization": "B=exp(2*pi*exp(2*z)-9*z)/(4*pi^4), analytic and nonzero", "derivative": "dm=(B*M)' includes B' contribution", "majorants": { "status": "analytic majorants evaluated as floating numbers; NOT interval bounds", "quadrature_error": "NOT bounded: fixed Gauss-Legendre approximation and replay only", "roundoff_error": "NOT bounded: ordinary mpmath arithmetic", "normalized_lattice_m": "5.8577279943678802350138978003947519618e-363", "normalized_lattice_c": "3.1241215969962027920074121602105343796e-362", "normalized_lattice_dm": "2.3385366819628484890703381290022733319e-359", "normalized_real_tail_m": "7.2851340468283541409447988787325183439e-885", "normalized_real_tail_c": "1.1657648590159581202702668606772731759e-883", "normalized_real_tail_dm": "7.5242571473287886321589840354810562414e-883", "phi_lattice_tail": "6.6352743104879949670512178773694194974e-364", "phi_derivative_lattice_tail": "2.608650988966144546162039768873537208e-360", "envelope_K0": "44.9252475735621428790273072224695424", "envelope_K1": "1911.4281851757894957506318905629304823", "envelope_d": "0.68168595819500219438342838348090402528" } } }, "elapsed_seconds": 0.16119524999521673 }, { "z": { "re": "0.23643429368081381441350896320707363253", "im": "0.56218639238886315501152574942793309998" }, "bits": 128, "replay": false, "purpose": "cell_0_6_step_3", "values": { "m": { "re": "0.23899294825188044180052227873717818817", "im": "0.013957967978534381311762457621876816231" }, "c": { "re": "-0.0067867791386990557916357640891535427226", "im": "-0.0066258278964012074103234446503523159907" }, "dm": { "re": "0.52453878122534433153332643641025897259", "im": "1.3280172825306090654828297654744031957" } }, "metadata": { "metadata": { "classification": "diagnostic, not a certificate", "bits": 128, "lattice_cutoff": 24, "gauss_legendre_order_per_segment": 48, "positive_half_segments": [ "0.0", "0.125", "0.25", "0.5", "1.0", "2.0", "4.0" ], "normalization": "B=exp(2*pi*exp(2*z)-9*z)/(4*pi^4), analytic and nonzero", "derivative": "dm=(B*M)' includes B' contribution", "majorants": { "status": "analytic majorants evaluated as floating numbers; NOT interval bounds", "quadrature_error": "NOT bounded: fixed Gauss-Legendre approximation and replay only", "roundoff_error": "NOT bounded: ordinary mpmath arithmetic", "normalized_lattice_m": "4.6742526411406744816629706526447591843e-361", "normalized_lattice_c": "2.4929347419416930568869176814105382316e-360", "normalized_lattice_dm": "1.8662880502201827381942878751135358476e-357", "normalized_real_tail_m": "2.5572546923498348790677003363303688698e-880", "normalized_real_tail_c": "4.0921135193289880053669742595878119592e-879", "normalized_real_tail_dm": "2.6653715423490644434487156122232389455e-878", "phi_lattice_tail": "5.3151422564304415716830670204984528572e-362", "phi_derivative_lattice_tail": "2.0896424857397163805267904083416881302e-358", "envelope_K0": "45.60455019861480257964395405038134107", "envelope_K1": "1961.8554856081867593790063482429552008", "envelope_d": "0.67817929423290002068764947020428352217" } } }, "elapsed_seconds": 0.1615402500028722 }, { "z": { "re": "0.23629644111537569145666399286726293045", "im": "0.56248343226219903671834932859184071108" }, "bits": 128, "replay": false, "purpose": "cell_0_6_step_4", "values": { "m": { "re": "0.2385243016242476549906971522693672133", "im": "0.013930578456597019041947720769952244134" }, "c": { "re": "-0.0068569293017458121923296285197144071659", "im": "-0.0066249109148947635159781394081755197696" }, "dm": { "re": "0.52862413336774581064220545305765802013", "im": "1.3386796841565250143001022112941469131" } }, "metadata": { "metadata": { "classification": "diagnostic, not a certificate", "bits": 128, "lattice_cutoff": 24, "gauss_legendre_order_per_segment": 48, "positive_half_segments": [ "0.0", "0.125", "0.25", "0.5", "1.0", "2.0", "4.0" ], "normalization": "B=exp(2*pi*exp(2*z)-9*z)/(4*pi^4), analytic and nonzero", "derivative": "dm=(B*M)' includes B' contribution", "majorants": { "status": "analytic majorants evaluated as floating numbers; NOT interval bounds", "quadrature_error": "NOT bounded: fixed Gauss-Legendre approximation and replay only", "roundoff_error": "NOT bounded: ordinary mpmath arithmetic", "normalized_lattice_m": "1.337620830084305823035782267342033875e-360", "normalized_lattice_c": "7.1339777604496310561908387591575139999e-360", "normalized_lattice_dm": "5.3408702129217099164804655110764033585e-357", "normalized_real_tail_m": "3.154962879096024935489465857944951268e-879", "normalized_real_tail_c": "5.0485656643645971613570963112273784994e-878", "normalized_real_tail_dm": "3.295594265440497352821001958206510785e-877", "phi_lattice_tail": "1.5223865518751698570396378914005984609e-361", "phi_derivative_lattice_tail": "5.9852464243423924870332304199630991065e-358", "envelope_K0": "45.770075002246404873054215576153825419", "envelope_K1": "1974.2224631159266819380193115154022016", "envelope_d": "0.67733745061695562053732550697073293858" } } }, "elapsed_seconds": 0.16091254097409546 }, { "z": { "re": "0.23629217652694226550583286362987240139", "im": "0.56249262341061182575845400773695562459" }, "bits": 128, "replay": false, "purpose": "cell_0_6_step_5", "values": { "m": { "re": "0.23850974146574874391721109688232660819", "im": "0.013929728078282764612540270236589339281" }, "c": { "re": "-0.0068591052315213281014263298476814297426", "im": "-0.0066248812866354064733659326577726712746" }, "dm": { "re": "0.52875081248131535471373424579228944188", "im": "1.3390105266929408138472466678976077363" } }, "metadata": { "metadata": { "classification": "diagnostic, not a certificate", "bits": 128, "lattice_cutoff": 24, "gauss_legendre_order_per_segment": 48, "positive_half_segments": [ "0.0", "0.125", "0.25", "0.5", "1.0", "2.0", "4.0" ], "normalization": "B=exp(2*pi*exp(2*z)-9*z)/(4*pi^4), analytic and nonzero", "derivative": "dm=(B*M)' includes B' contribution", "majorants": { "status": "analytic majorants evaluated as floating numbers; NOT interval bounds", "quadrature_error": "NOT bounded: fixed Gauss-Legendre approximation and replay only", "roundoff_error": "NOT bounded: ordinary mpmath arithmetic", "normalized_lattice_m": "1.3818603237779609616163377490714335039e-360", "normalized_lattice_c": "7.369921726815791795287134661714312021e-360", "normalized_lattice_dm": "5.5175151798453709053802758723385467831e-357", "normalized_real_tail_m": "3.4100786402566124558625063867764722127e-879", "normalized_real_tail_c": "5.4568014514667663750803225879710835257e-878", "normalized_real_tail_dm": "3.5623246017423593474785438006146674884e-877", "phi_lattice_tail": "1.572780191975618691797413204185090026e-361", "phi_derivative_lattice_tail": "6.1833684806948322039413890864346876006e-358", "envelope_K0": "45.775212796049874013315896634120462036", "envelope_K1": "1974.6068228593115478035745459903165322", "envelope_d": "0.67731139807874891272564687084573943929" } } }, "elapsed_seconds": 0.1605884999735281 }, { "z": { "re": "0.23629004489931548986395037608482544232", "im": "0.56249721757899703068090570271831277551" }, "bits": 128, "replay": false, "purpose": "cell_0_6_step_6", "values": { "m": { "re": "0.23850246227867389672484406000374316705", "im": "0.013929302945907654483780093157806599845" }, "c": { "re": "-0.006860192983719348753210582351236037976", "im": "-0.0066248664499271274571017102933688521732" }, "dm": { "re": "0.52881413854606730781364917531962055183", "im": "1.3391759182722043542623593752887816267" } }, "metadata": { "metadata": { "classification": "diagnostic, not a certificate", "bits": 128, "lattice_cutoff": 24, "gauss_legendre_order_per_segment": 48, "positive_half_segments": [ "0.0", "0.125", "0.25", "0.5", "1.0", "2.0", "4.0" ], "normalization": "B=exp(2*pi*exp(2*z)-9*z)/(4*pi^4), analytic and nonzero", "derivative": "dm=(B*M)' includes B' contribution", "majorants": { "status": "analytic majorants evaluated as floating numbers; NOT interval bounds", "quadrature_error": "NOT bounded: fixed Gauss-Legendre approximation and replay only", "roundoff_error": "NOT bounded: ordinary mpmath arithmetic", "normalized_lattice_m": "1.4045189283836676780324818606854050559e-360", "normalized_lattice_c": "7.4907676180462276161732365903221602979e-360", "normalized_lattice_dm": "5.6079893424660297574453300816132536847e-357", "normalized_real_tail_m": "3.5452299854585073816743353553100439514e-879", "normalized_real_tail_c": "5.6730703943630842029539145324020161333e-878", "normalized_real_tail_dm": "3.7036361248129392174311241197223603947e-877", "phi_lattice_tail": "1.5985913557239763823987381403949058541e-361", "phi_derivative_lattice_tail": "6.2848447945408055062975071480797990555e-358", "envelope_K0": "45.777781269175565097917246451470666379", "envelope_K1": "1974.7989822140995489791126362413658454", "envelope_d": "0.67729837570868898757444389482861646659" } } }, "elapsed_seconds": 0.16074804100207984 }, { "z": { "re": "0.23628897925206121968335256031003708843", "im": "0.56249951431192514707485625588666797336" }, "bits": 128, "replay": false, "purpose": "cell_0_6_step_7", "values": { "m": { "re": "0.23849882290808629237677759583432488032", "im": "0.013929090393910928763799568353381421628" }, "c": { "re": "-0.0068607368066702985995811158074063648802", "im": "-0.0066248590259310732131875097709910718836" }, "dm": { "re": "0.52884579820706599749358316418888992373", "im": "1.3392586066430084886811603716036326018" } }, "metadata": { "metadata": { "classification": "diagnostic, not a certificate", "bits": 128, "lattice_cutoff": 24, "gauss_legendre_order_per_segment": 48, "positive_half_segments": [ "0.0", "0.125", "0.25", "0.5", "1.0", "2.0", "4.0" ], "normalization": "B=exp(2*pi*exp(2*z)-9*z)/(4*pi^4), analytic and nonzero", "derivative": "dm=(B*M)' includes B' contribution", "majorants": { "status": "analytic majorants evaluated as floating numbers; NOT interval bounds", "quadrature_error": "NOT bounded: fixed Gauss-Legendre approximation and replay only", "roundoff_error": "NOT bounded: ordinary mpmath arithmetic", "normalized_lattice_m": "1.4159854571494866028035756671715715368e-360", "normalized_lattice_c": "7.5519224381305952149524035582483815298e-360", "normalized_lattice_dm": "5.6537743744554942950240043578305451551e-357", "normalized_real_tail_m": "3.6147907443156169095786372247175655991e-879", "normalized_real_tail_c": "5.7843813975160253087718654438452167075e-878", "normalized_real_tail_dm": "3.7763693072757875485852231007372989722e-877", "phi_lattice_tail": "1.6116533898866871571465174100825586297e-361", "phi_derivative_lattice_tail": "6.3361980419605930625166649909664121182e-358", "envelope_K0": "45.779065399849353071450455378067577823", "envelope_K1": "1974.8950567651809412815232870368715429", "envelope_d": "0.67729186549789480967796861725134424131" } } }, "elapsed_seconds": 0.16501629102276638 }, { "z": { "re": "0.2421875", "im": "0.46875" }, "bits": 128, "replay": false, "purpose": "cell_0_5_step_0", "values": { "m": { "re": "0.28397486666669995372153992006634205833", "im": "0.021717836494381494066484435638345982756" }, "c": { "re": "0.0041341631418207781352000186686367978895", "im": "-0.0067697141183706178546287117499397100385" }, "dm": { "re": "-0.27386423259244249931720616208979469675", "im": "-0.069986749045779594084577065162795622331" } }, "metadata": { "metadata": { "classification": "diagnostic, not a certificate", "bits": 128, "lattice_cutoff": 24, "gauss_legendre_order_per_segment": 48, "positive_half_segments": [ "0.0", "0.125", "0.25", "0.5", "1.0", "2.0", "4.0" ], "normalization": "B=exp(2*pi*exp(2*z)-9*z)/(4*pi^4), analytic and nonzero", "derivative": "dm=(B*M)' includes B' contribution", "majorants": { "status": "analytic majorants evaluated as floating numbers; NOT interval bounds", "quadrature_error": "NOT bounded: fixed Gauss-Legendre approximation and replay only", "roundoff_error": "NOT bounded: ordinary mpmath arithmetic", "normalized_lattice_m": "2.6408168471927742542926826619408032566e-497", "normalized_lattice_c": "1.4084356518361462689560974197017617369e-496", "normalized_lattice_dm": "1.0489593971017903916158843200204226169e-493", "normalized_real_tail_m": "5.8576068256535441339210468367730901277e-1206", "normalized_real_tail_c": "9.3730164828976671871998387506068326873e-1205", "normalized_real_tail_dm": "3.778114712345831471205254133611136387e-1204", "phi_lattice_tail": "1.7154965076199756935453698454036671324e-498", "phi_derivative_lattice_tail": "6.7444561471968604275641594493997744632e-495", "envelope_K0": "20.091478866486302716992862467220967022", "envelope_K1": "479.91599823200924684947053362153336359", "envelope_d": "0.92960523813384162925531083446433595776" } } }, "elapsed_seconds": 0.15922191698336974 }, { "z": { "re": "0.304210931605665319422852495180841582", "im": "0.45785608540004263193088440193342373827" }, "bits": 128, "replay": false, "purpose": "cell_0_5_step_1", "values": { "m": { "re": "0.27392681143513542936383803142696344172", "im": "0.014357514892977283122337162222534204729" }, "c": { "re": "0.0035255229763382625619424733531486775499", "im": "-0.0043520287214149680134811653189711369024" }, "dm": { "re": "-0.066968843954020392351537222948275417432", "im": "-0.21970171047283026049377699188033142914" } }, "metadata": { "metadata": { "classification": "diagnostic, not a certificate", "bits": 128, "lattice_cutoff": 24, "gauss_legendre_order_per_segment": 48, "positive_half_segments": [ "0.0", "0.125", "0.25", "0.5", "1.0", "2.0", "4.0" ], "normalization": "B=exp(2*pi*exp(2*z)-9*z)/(4*pi^4), analytic and nonzero", "derivative": "dm=(B*M)' includes B' contribution", "majorants": { "status": "analytic majorants evaluated as floating numbers; NOT interval bounds", "quadrature_error": "NOT bounded: fixed Gauss-Legendre approximation and replay only", "roundoff_error": "NOT bounded: ordinary mpmath arithmetic", "normalized_lattice_m": "5.2059751010101905428897919270158267249e-512", "normalized_lattice_c": "2.7765200538721016228745556944084409199e-511", "normalized_lattice_dm": "2.0685301567863611304025560899071181112e-508", "normalized_real_tail_m": "2.8936418886475130370204600440007718061e-1241", "normalized_real_tail_c": "4.6302327822318441339653124812316882227e-1240", "normalized_real_tail_dm": "1.8743825692790109578161355080012760302e-1239", "phi_lattice_tail": "2.3931496865619248463662942124753329256e-513", "phi_derivative_lattice_tail": "9.4086423627219220112349243714408831375e-510", "envelope_K0": "18.792058020548764749334094027981449217", "envelope_K1": "430.11677639554542296292027916417612074", "envelope_d": "0.95696993300074697283358954946354654501" } } }, "elapsed_seconds": 0.16415158298332244 }, { "z": { "re": "0.31057865606611512777169043973268955338", "im": "0.44031563350894778003315997006244609012" }, "bits": 128, "replay": false, "purpose": "cell_0_5_step_2", "values": { "m": { "re": "0.26936804647074164978464877178884014775", "im": "0.014263280182800773413763986812757932648" }, "c": { "re": "0.0037882967904835743198514641314731894772", "im": "-0.0040931544609745977145302926052752736067" }, "dm": { "re": "-0.087457919623080591669955125002153546017", "im": "-0.24115220718929161713113566510000737721" } }, "metadata": { "metadata": { "classification": "diagnostic, not a certificate", "bits": 128, "lattice_cutoff": 24, "gauss_legendre_order_per_segment": 48, "positive_half_segments": [ "0.0", "0.125", "0.25", "0.5", "1.0", "2.0", "4.0" ], "normalization": "B=exp(2*pi*exp(2*z)-9*z)/(4*pi^4), analytic and nonzero", "derivative": "dm=(B*M)' includes B' contribution", "majorants": { "status": "analytic majorants evaluated as floating numbers; NOT interval bounds", "quadrature_error": "NOT bounded: fixed Gauss-Legendre approximation and replay only", "roundoff_error": "NOT bounded: ordinary mpmath arithmetic", "normalized_lattice_m": "2.5729339863221242872782520780133870941e-535", "normalized_lattice_c": "1.3722314593717996198817344416071397835e-534", "normalized_lattice_dm": "1.0219678732790515912943200901476712587e-531", "normalized_real_tail_m": "5.1442101134391571792874242355958904347e-1297", "normalized_real_tail_c": "8.2314264380738965676280933337301042267e-1296", "normalized_real_tail_dm": "3.1913476713219541730445353003890116276e-1295", "phi_lattice_tail": "9.5763349534238244149338336770063122392e-537", "phi_derivative_lattice_tail": "3.7649258309386839009837114216923850109e-533", "envelope_K0": "17.01303984984370868839354147758447145", "envelope_K1": "366.33848020093987725335446627821471205", "envelope_d": "1.0000702191164262275163557865364392369" } } }, "elapsed_seconds": 0.16479533299570903 }, { "z": { "re": "0.31137999080695178901577205629098701453", "im": "0.43842460210714959513459929026967462538" }, "bits": 128, "replay": false, "purpose": "cell_0_5_step_3", "values": { "m": { "re": "0.26883973165856775438262745022060889025", "im": "0.014235879472847615077343735080565765509" }, "c": { "re": "0.0038088131359849324174950715324452814348", "im": "-0.0040612236593342699507104224577783311498" }, "dm": { "re": "-0.088681473925107637121122117746635473745", "im": "-0.24293424312997224299773632173714300143" } }, "metadata": { "metadata": { "classification": "diagnostic, not a certificate", "bits": 128, "lattice_cutoff": 24, "gauss_legendre_order_per_segment": 48, "positive_half_segments": [ "0.0", "0.125", "0.25", "0.5", "1.0", "2.0", "4.0" ], "normalization": "B=exp(2*pi*exp(2*z)-9*z)/(4*pi^4), analytic and nonzero", "derivative": "dm=(B*M)' includes B' contribution", "majorants": { "status": "analytic majorants evaluated as floating numbers; NOT interval bounds", "quadrature_error": "NOT bounded: fixed Gauss-Legendre approximation and replay only", "roundoff_error": "NOT bounded: ordinary mpmath arithmetic", "normalized_lattice_m": "8.6651275482892909070946007163150732538e-538", "normalized_lattice_c": "4.6214013590876218171171203820347057354e-537", "normalized_lattice_dm": "3.4416728620158516563214484723983868779e-534", "normalized_real_tail_m": "6.2476555283037040997609953371477543843e-1303", "normalized_real_tail_c": "9.9970833465892620239755048906903157719e-1302", "normalized_real_tail_dm": "3.8597703324246682093124561733331315507e-1301", "phi_lattice_tail": "3.1483492049556880099927098739449333525e-539", "phi_derivative_lattice_tail": "1.2377701181301131240277060665652383325e-535", "envelope_K0": "16.840907390102397462608158368454874034", "envelope_K1": "360.4363304174904326110585800838309321", "envelope_d": "1.0046442886192338116444019130248076817" } } }, "elapsed_seconds": 0.16370716696837917 }, { "z": { "re": "0.31157929610332558594958747482094065727", "im": "0.43795700762019360429246480630550255129" }, "bits": 128, "replay": false, "purpose": "cell_0_5_step_4", "values": { "m": { "re": "0.26870833532302467657253692727520284297", "im": "0.014228951917451255753523204487971657197" }, "c": { "re": "0.0038136869681275128607141803417705194996", "im": "-0.0040532791504655473630808170918049864747" }, "dm": { "re": "-0.088961139771621874186821650165810516937", "im": "-0.24335605834746918481812503862939047157" } }, "metadata": { "metadata": { "classification": "diagnostic, not a certificate", "bits": 128, "lattice_cutoff": 24, "gauss_legendre_order_per_segment": 48, "positive_half_segments": [ "0.0", "0.125", "0.25", "0.5", "1.0", "2.0", "4.0" ], "normalization": "B=exp(2*pi*exp(2*z)-9*z)/(4*pi^4), analytic and nonzero", "derivative": "dm=(B*M)' includes B' contribution", "majorants": { "status": "analytic majorants evaluated as floating numbers; NOT interval bounds", "quadrature_error": "NOT bounded: fixed Gauss-Legendre approximation and replay only", "roundoff_error": "NOT bounded: ordinary mpmath arithmetic", "normalized_lattice_m": "2.1260665232575854082149334016540918138e-538", "normalized_lattice_c": "1.133902145737378884381297814215515634e-537", "normalized_lattice_dm": "8.4443859783725393445483395975546127347e-535", "normalized_real_tail_m": "2.16698018885955931738640852210832963e-1304", "normalized_real_tail_c": "3.4674574215299998521358725529242627598e-1303", "normalized_real_tail_dm": "1.3373861467165965594294781314583576187e-1302", "phi_lattice_tail": "7.6786599528407257287144681258215465257e-540", "phi_derivative_lattice_tail": "3.018856936818863939734043619694754558e-536", "envelope_K0": "16.798877032138012498412719838376875247", "envelope_K1": "359.00234984396165192138240567509066704", "envelope_d": "1.0057731032591668230113948066229740188" } } }, "elapsed_seconds": 0.1630157500039786 }, { "z": { "re": "0.31167881714487651187799395116094813262", "im": "0.4377238138545392647400299243775646456" }, "bits": 128, "replay": false, "purpose": "cell_0_5_step_5", "values": { "m": { "re": "0.26864270166859389750737674798437310512", "im": "0.014225483628086689767838455479183032311" }, "c": { "re": "0.0038160889684253681189489532181838674189", "im": "-0.004049310982175244813421931225886699602" }, "dm": { "re": "-0.08909732772777429884141266307568161673", "im": "-0.24356362554204338462804179985423701923" } }, "metadata": { "metadata": { "classification": "diagnostic, not a certificate", "bits": 128, "lattice_cutoff": 24, "gauss_legendre_order_per_segment": 48, "positive_half_segments": [ "0.0", "0.125", "0.25", "0.5", "1.0", "2.0", "4.0" ], "normalization": "B=exp(2*pi*exp(2*z)-9*z)/(4*pi^4), analytic and nonzero", "derivative": "dm=(B*M)' includes B' contribution", "majorants": { "status": "analytic majorants evaluated as floating numbers; NOT interval bounds", "quadrature_error": "NOT bounded: fixed Gauss-Legendre approximation and replay only", "roundoff_error": "NOT bounded: ordinary mpmath arithmetic", "normalized_lattice_m": "1.0554688694052590167840773263963726701e-538", "normalized_lattice_c": "5.6291673034947147561817457407806542404e-538", "normalized_lattice_dm": "4.1921321723982052415552808865606551827e-535", "normalized_real_tail_m": "4.0572929156163300920376512314428712522e-1305", "normalized_real_tail_c": "6.4922096879564690227669571182081775831e-1304", "normalized_real_tail_dm": "2.5027549219167444487202681110917571409e-1303", "phi_lattice_tail": "3.8006335943913279882522368631398593789e-540", "phi_derivative_lattice_tail": "1.4942150272575122853321338075595052556e-536", "envelope_K0": "16.777994037305229378891273035370921895", "envelope_K1": "358.29091577357083347165387387566050611", "envelope_d": "1.00633572506590951792774942467232662" } } }, "elapsed_seconds": 0.16915349999908358 }, { "z": { "re": "0.31172854458326531406091100511812604465", "im": "0.43760736495292179473029795997224809012" }, "bits": 128, "replay": false, "purpose": "cell_0_5_step_6", "values": { "m": { "re": "0.26860990069785043756040724135263277397", "im": "0.014223748474561171252697702544833073714" }, "c": { "re": "0.0038172813583362903643794515294316502142", "im": "-0.0040473279267547888662858983517988017857" }, "dm": { "re": "-0.089164523898138904984937329598917684363", "im": "-0.24366658269128434562231498400331954215" } }, "metadata": { "metadata": { "classification": "diagnostic, not a certificate", "bits": 128, "lattice_cutoff": 24, "gauss_legendre_order_per_segment": 48, "positive_half_segments": [ "0.0", "0.125", "0.25", "0.5", "1.0", "2.0", "4.0" ], "normalization": "B=exp(2*pi*exp(2*z)-9*z)/(4*pi^4), analytic and nonzero", "derivative": "dm=(B*M)' includes B' contribution", "majorants": { "status": "analytic majorants evaluated as floating numbers; NOT interval bounds", "quadrature_error": "NOT bounded: fixed Gauss-Legendre approximation and replay only", "roundoff_error": "NOT bounded: ordinary mpmath arithmetic", "normalized_lattice_m": "7.4407654612915912287690248956231614447e-539", "normalized_lattice_c": "3.9684082460221819886768132776656861038e-538", "normalized_lattice_dm": "2.9553322475440774574005080201058538113e-535", "normalized_real_tail_m": "1.7579058305200352431859796176522129902e-1305", "normalized_real_tail_c": "2.8128836727826759521440959725407776026e-1304", "normalized_real_tail_dm": "1.0840964901562751651738943807417516354e-1303", "phi_lattice_tail": "2.6753437375895332255548475368934365081e-540", "phi_derivative_lattice_tail": "1.0518085252113774452044709006612867069e-536", "envelope_K0": "16.767585132707784539602871284520704098", "envelope_K1": "357.93656845828353618558604504407667701", "envelope_d": "1.0066165969987684496504872028432304069" } } }, "elapsed_seconds": 0.16224708297522739 }, { "z": { "re": "0.31175340001089588367694274036787401294", "im": "0.43754917714262862298733361406334052217" }, "bits": 128, "replay": false, "purpose": "cell_0_5_step_7", "values": { "m": { "re": "0.26859350414322920548404370229747370599", "im": "0.014222880660052231242740210472989716318" }, "c": { "re": "0.0038178754153184326247278953835191375905", "im": "-0.0040463366570586496787128651370727952198" }, "dm": { "re": "-0.089197899178304970450236470428823164978", "im": "-0.24371785572348885420832388739814596358" } }, "metadata": { "metadata": { "classification": "diagnostic, not a certificate", "bits": 128, "lattice_cutoff": 24, "gauss_legendre_order_per_segment": 48, "positive_half_segments": [ "0.0", "0.125", "0.25", "0.5", "1.0", "2.0", "4.0" ], "normalization": "B=exp(2*pi*exp(2*z)-9*z)/(4*pi^4), analytic and nonzero", "derivative": "dm=(B*M)' includes B' contribution", "majorants": { "status": "analytic majorants evaluated as floating numbers; NOT interval bounds", "quadrature_error": "NOT bounded: fixed Gauss-Legendre approximation and replay only", "roundoff_error": "NOT bounded: ordinary mpmath arithmetic", "normalized_lattice_m": "6.2483117617948459467598852446385769372e-539", "normalized_lattice_c": "3.3324329396239178382719387971405743665e-538", "normalized_lattice_dm": "2.4817096421769775556026576108803010605e-535", "normalized_real_tail_m": "1.1574871659588353036756521473181141819e-1305", "normalized_real_tail_c": "1.8521337470096828126588298234556280344e-1304", "normalized_real_tail_dm": "7.1372972270286788591479785508141363002e-1304", "phi_lattice_tail": "2.2449179111921852172049436639221564128e-540", "phi_derivative_lattice_tail": "8.8258707253786578897859195121601985777e-537", "envelope_K0": "16.762388772975923505682420995068154007", "envelope_K1": "357.75973485739874545495283239503808012", "envelope_d": "1.0067569241321851228534607513621597045" } } }, "elapsed_seconds": 0.16678420803509653 }, { "z": { "re": "0.31176582564929686618436081229292875834", "im": "0.4375200923536450703644608123395124695" }, "bits": 128, "replay": false, "purpose": "cell_0_5_step_8", "values": { "m": { "re": "0.2685853068444730122190619527369397188", "im": "0.014222446695143841534088615504943225776" }, "c": { "re": "0.0038181719111240019878588114707880700244", "im": "-0.0040458410868142613321949307439148132807" }, "dm": { "re": "-0.089214531321020364312448334386555599871", "im": "-0.24374344098692188706478249043798103831" } }, "metadata": { "metadata": { "classification": "diagnostic, not a certificate", "bits": 128, "lattice_cutoff": 24, "gauss_legendre_order_per_segment": 48, "positive_half_segments": [ "0.0", "0.125", "0.25", "0.5", "1.0", "2.0", "4.0" ], "normalization": "B=exp(2*pi*exp(2*z)-9*z)/(4*pi^4), analytic and nonzero", "derivative": "dm=(B*M)' includes B' contribution", "majorants": { "status": "analytic majorants evaluated as floating numbers; NOT interval bounds", "quadrature_error": "NOT bounded: fixed Gauss-Legendre approximation and replay only", "roundoff_error": "NOT bounded: ordinary mpmath arithmetic", "normalized_lattice_m": "5.7259811333733433356338549569602693747e-539", "normalized_lattice_c": "3.0538566044657831123380559770454769998e-538", "normalized_lattice_dm": "2.2742488320839396084621549895478949985e-535", "normalized_real_tail_m": "9.39315667403275999082741782310273957e-1306", "normalized_real_tail_c": "1.5030302605176311697136853213316660822e-1304", "normalized_real_tail_dm": "5.7916434645445472371960285258543881551e-1304", "phi_lattice_tail": "2.0564853119603001207218855982839179456e-540", "phi_derivative_lattice_tail": "8.0850499795614943088495989477438737358e-537", "envelope_K0": "16.759792609359102268104268284304069788", "envelope_K1": "357.67140277716084987355211289118388191", "envelope_d": "1.006827060603339997240418335584831871" } } }, "elapsed_seconds": 0.1655931249842979 }, { "z": { "re": "0.31177203794933434178190940429754046885", "im": "0.437505552232721989337429371579857033" }, "bits": 128, "replay": false, "purpose": "cell_0_5_step_9", "values": { "m": { "re": "0.26858120843921920703670246351350388967", "im": "0.014222229698497427450524792519891457657" }, "c": { "re": "0.0038183200260804337349626082018647541774", "im": "-0.0040455933178552646538802411046858488925" }, "dm": { "re": "-0.089222833543399704780212233296135119009", "im": "-0.24375622082204036314352204139998183255" } }, "metadata": { "metadata": { "classification": "diagnostic, not a certificate", "bits": 128, "lattice_cutoff": 24, "gauss_legendre_order_per_segment": 48, "positive_half_segments": [ "0.0", "0.125", "0.25", "0.5", "1.0", "2.0", "4.0" ], "normalization": "B=exp(2*pi*exp(2*z)-9*z)/(4*pi^4), analytic and nonzero", "derivative": "dm=(B*M)' includes B' contribution", "majorants": { "status": "analytic majorants evaluated as floating numbers; NOT interval bounds", "quadrature_error": "NOT bounded: fixed Gauss-Legendre approximation and replay only", "roundoff_error": "NOT bounded: ordinary mpmath arithmetic", "normalized_lattice_m": "5.4814718387702747928461881193931938085e-539", "normalized_lattice_c": "2.9234516473441465561846336636763700312e-538", "normalized_lattice_dm": "2.1771339492872503268956918728274572507e-535", "normalized_real_tail_m": "8.4619024092304200353267563533357503021e-1306", "normalized_real_tail_c": "1.3540171623974986613393767018094523039e-1304", "normalized_real_tail_dm": "5.2172854272250235145310615217770508022e-1304", "phi_lattice_tail": "1.968302550390211970132333882728833403e-540", "phi_derivative_lattice_tail": "7.7383603968626022380403057418412608608e-537", "envelope_K0": "16.758495030755237279395096273119346832", "envelope_K1": "357.62725788050988003728204055495387992", "envelope_d": "1.0068621220790545196914058836644178498" } } }, "elapsed_seconds": 0.16219975001877174 }, { "z": { "re": "0.125", "im": "0.5625" }, "bits": 256, "replay": true, "purpose": "replay_corner_0_7", "values": { "m": { "re": "0.4424134368470498834796752467803551900836518733224263236828772730240881613707", "im": "-0.1942881092826240822860517232249517031241440111542622167557257471154529050295" }, "c": { "re": "0.008814004279151625508193919696276888079816617422015906620807501856890707991212", "im": "-0.05010713729103852385821266198495289528293189926064949302712366306743413028943" }, "dm": { "re": "-5.198186289227338717471991544040203232483153837591200483473369218917173325232", "im": "0.9776050616725693829453510890865525921877994157041013896729112438448178622541" } }, "metadata": { "metadata": { "classification": "diagnostic, not a certificate", "bits": 256, "lattice_cutoff": 32, "gauss_legendre_order_per_segment": 96, "positive_half_segments": [ "0.0", "0.125", "0.25", "0.5", "1.0", "2.0", "4.0", "4.5" ], "normalization": "B=exp(2*pi*exp(2*z)-9*z)/(4*pi^4), analytic and nonzero", "derivative": "dm=(B*M)' includes B' contribution", "majorants": { "status": "analytic majorants evaluated as floating numbers; NOT interval bounds", "quadrature_error": "NOT bounded: fixed Gauss-Legendre approximation and replay only", "roundoff_error": "NOT bounded: ordinary mpmath arithmetic", "normalized_lattice_m": "6.001970521292359363011787832803478569837905991853900579626700883224931021642e-633", "normalized_lattice_c": "4.051330101872342570032956787142348034640586544501382891248023096176828439608e-632", "normalized_lattice_dm": "4.144197988035908507060091205620976177221753052448206876976690555834454301222e-629", "normalized_real_tail_m": "3.497671536013245374571102598370119279519364895211489710419582705652511545914e-2386", "normalized_real_tail_c": "7.08307165769817927228147414475273653062185660273440282246280464763768148002e-2385", "normalized_real_tail_dm": "3.53198219170397248137960595858783306655798839887910562286163740883602964333e-2384", "phi_lattice_tail": "5.308662521405219350019878815441029402457386582129341401866411931453612849439e-634", "phi_derivative_lattice_tail": "3.634781730517774112514689734083475256179900250033568722694892158181764510492e-630", "envelope_K0": "45.77933696155126084765016570765020353591667391661649659058173348829585538802", "envelope_K1": "1974.915374382150478826157938758895275515797618955465117684194588053427814691", "envelope_d": "0.6772904887875628673234972493991471206495588414680672589271832706483651107667" } } }, "elapsed_seconds": 0.8690809170366265 }, { "z": { "re": "0.359375", "im": "0.5625" }, "bits": 256, "replay": true, "purpose": "replay_corner_1_7", "values": { "m": { "re": "0.3241247453971121469055826040156528565820546044974106474446838147677002664022", "im": "-0.009975598572567910068031033953378199767976620244505733019458063321761203739433" }, "c": { "re": "0.005390727064216943875125966483383222673307214790652569245974505824151690852614", "im": "-0.003578894038040799258647962553733257116509718408898454868423939100205714422206" }, "dm": { "re": "-0.1677611548648078350013787177224920400576884138361676906650938725047537584656", "im": "-1.030965291105039145283815056131662142784093103467038691911626473161390707925" } }, "metadata": { "metadata": { "classification": "diagnostic, not a certificate", "bits": 256, "lattice_cutoff": 32, "gauss_legendre_order_per_segment": 96, "positive_half_segments": [ "0.0", "0.125", "0.25", "0.5", "1.0", "2.0", "4.0", "4.5" ], "normalization": "B=exp(2*pi*exp(2*z)-9*z)/(4*pi^4), analytic and nonzero", "derivative": "dm=(B*M)' includes B' contribution", "majorants": { "status": "analytic majorants evaluated as floating numbers; NOT interval bounds", "quadrature_error": "NOT bounded: fixed Gauss-Legendre approximation and replay only", "roundoff_error": "NOT bounded: ordinary mpmath arithmetic", "normalized_lattice_m": "5.829431174812535582325608030533859349939729514028288291912475233354465588055e-633", "normalized_lattice_c": "3.934866042998461518069785420610355061209317421969094597040920782514264271937e-632", "normalized_lattice_dm": "4.030112260524026577528458877726749624368911308740156152505370406283156431262e-629", "normalized_real_tail_m": "3.397123564495574096197074343019455984491418984417529438039806848524061723521e-2386", "normalized_real_tail_c": "6.879453770780291102437037710925668020857242618296450244802382368280997314696e-2385", "normalized_real_tail_dm": "3.724622932750349853520031602060828158707204484609667827970446407355811363135e-2384", "phi_lattice_tail": "5.308662521405219350019878815441029402457386582129341401866411931453612849439e-634", "phi_derivative_lattice_tail": "3.634781730517774112514689734083475256179900250033568722694892158181764510492e-630", "envelope_K0": "45.77933696155126084765016570765020353591667391661649659058173348829585538802", "envelope_K1": "1974.915374382150478826157938758895275515797618955465117684194588053427814691", "envelope_d": "0.6772904887875628673234972493991471206495588414680672589271832706483651107667" } } }, "elapsed_seconds": 0.5588222920196131 }, { "z": { "re": "0.359375", "im": "0.625" }, "bits": 256, "replay": true, "purpose": "replay_corner_1_8", "values": { "m": { "re": "0.4556299307428301982613145423941256486316265394145446642078556416105936264725", "im": "-0.05170193239863692232348957296429451851435278634479157890544929281305334289818" }, "c": { "re": "0.02000819485986106618020072591270523686048114708587597572632983283794048036744", "im": "-0.007734849331575507041111997972047835464026340550103050410958443127327908316271" }, "dm": { "re": "-1.760429655137226855887699058269824874749263541104341675603023396561603702939", "im": "-3.911577516150457566981514997745073349207437016711653268652341506163502804365" } }, "metadata": { "metadata": { "classification": "diagnostic, not a certificate", "bits": 256, "lattice_cutoff": 32, "gauss_legendre_order_per_segment": 96, "positive_half_segments": [ "0.0", "0.125", "0.25", "0.5", "1.0", "2.0", "4.0", "4.5" ], "normalization": "B=exp(2*pi*exp(2*z)-9*z)/(4*pi^4), analytic and nonzero", "derivative": "dm=(B*M)' includes B' contribution", "majorants": { "status": "analytic majorants evaluated as floating numbers; NOT interval bounds", "quadrature_error": "NOT bounded: fixed Gauss-Legendre approximation and replay only", "roundoff_error": "NOT bounded: ordinary mpmath arithmetic", "normalized_lattice_m": "5.933740081067129090125935220186667278909365181185913067271967071635959155277e-461", "normalized_lattice_c": "4.005274554720312135835006273626000413263821497300491320408577773354272429812e-460", "normalized_lattice_dm": "4.127921734697351558866816981355610436411027868886503107611434644522633080744e-457", "normalized_real_tail_m": "2.095576248531151969974133793294932878784138857451398408417313777837060614545e-1745", "normalized_real_tail_c": "4.243776868190690978561208571021119080343739123933635068263509172024510773841e-1744", "normalized_real_tail_dm": "4.089071070621553744284707775941509641045650379440032295539297749942735899501e-1743", "phi_lattice_tail": "7.273867734636615468343701099086336534586537544654409491266217575773554548569e-462", "phi_derivative_lattice_tail": "4.980335714590012097526369578262461458973490865323419345274280198831878213279e-458", "envelope_K0": "126.2492829278436835261203948168404649069660071060487721886868609718869742379", "envelope_K1": "10771.85146213373853884895685987568440713214333778226012962950582542118672571", "envelope_d": "0.495307208606777259303949409955035265976351690422319468296460584906557471819" } } }, "elapsed_seconds": 0.5551680829958059 }, { "z": { "re": "0.125", "im": "0.625" }, "bits": 256, "replay": true, "purpose": "replay_corner_0_8", "values": { "m": { "re": "0.1369252117077194991564623794768534942397624725692765048981971799125737571177", "im": "-0.5926754587431589595755214134653954887757885301438938704570774658841433158655" }, "c": { "re": "-0.07855736178886231856663107280316436430569482027009378617344119003138181470568", "im": "-0.07615180762033872047253477060842902139217962361561403329915766677776329322474" }, "dm": { "re": "-5.866965759977956459449778597072290579797705764437598032054304052597172827293", "im": "10.43461873387578145351192656863908578396874348965824477132767629122635129202" } }, "metadata": { "metadata": { "classification": "diagnostic, not a certificate", "bits": 256, "lattice_cutoff": 32, "gauss_legendre_order_per_segment": 96, "positive_half_segments": [ "0.0", "0.125", "0.25", "0.5", "1.0", "2.0", "4.0", "4.5" ], "normalization": "B=exp(2*pi*exp(2*z)-9*z)/(4*pi^4), analytic and nonzero", "derivative": "dm=(B*M)' includes B' contribution", "majorants": { "status": "analytic majorants evaluated as floating numbers; NOT interval bounds", "quadrature_error": "NOT bounded: fixed Gauss-Legendre approximation and replay only", "roundoff_error": "NOT bounded: ordinary mpmath arithmetic", "normalized_lattice_m": "1.068413876109416615927774550712020336005517556895487638745986324581659985982e-460", "normalized_lattice_c": "7.211793663738562157512478217306137268037243509044541561535407690926204905379e-460", "normalized_lattice_dm": "7.423354811810366856542888458251911744225231199950770731140526037920932699602e-457", "normalized_real_tail_m": "3.773240337101763971674019366871228461548494616202467184156832247821407611761e-1745", "normalized_real_tail_c": "7.641234754373802248017323909806826512575408875077769834439262817805931098105e-1744", "normalized_real_tail_dm": "7.035145655385745173200893705883144479852147799031111526487210193938190893563e-1743", "phi_lattice_tail": "7.273867734636615468343701099086336534586537544654409491266217575773554548569e-462", "phi_derivative_lattice_tail": "4.980335714590012097526369578262461458973490865323419345274280198831878213279e-458", "envelope_K0": "126.2492829278436835261203948168404649069660071060487721886868609718869742379", "envelope_K1": "10771.85146213373853884895685987568440713214333778226012962950582542118672571", "envelope_d": "0.495307208606777259303949409955035265976351690422319468296460584906557471819" } } }, "elapsed_seconds": 0.557331666990649 }, { "z": { "re": "0.59375", "im": "0.5625" }, "bits": 256, "replay": true, "purpose": "replay_corner_2_7", "values": { "m": { "re": "0.2397595782639513338678309012960639890587290484409804539006331637277671180131", "im": "-0.06730028732348309851540678599337525230992401238648699802735872687119316408856" }, "c": { "re": "0.0007033658467784595230174672828758873363969938835151544401942992001438530005654", "im": "-0.002975787267541874565706521517183112392906279448662170609008909653910624557916" }, "dm": { "re": "-0.2613317511188329660110235718445719243367647448466012177166037383159049812039", "im": "-0.1178888207966895629445806209287905158230291070290133789901438431826855397473" } }, "metadata": { "metadata": { "classification": "diagnostic, not a certificate", "bits": 256, "lattice_cutoff": 32, "gauss_legendre_order_per_segment": 96, "positive_half_segments": [ "0.0", "0.125", "0.25", "0.5", "1.0", "2.0", "4.0", "4.5" ], "normalization": "B=exp(2*pi*exp(2*z)-9*z)/(4*pi^4), analytic and nonzero", "derivative": "dm=(B*M)' includes B' contribution", "majorants": { "status": "analytic majorants evaluated as floating numbers; NOT interval bounds", "quadrature_error": "NOT bounded: fixed Gauss-Legendre approximation and replay only", "roundoff_error": "NOT bounded: ordinary mpmath arithmetic", "normalized_lattice_m": "1.964268678064909425408932609148835711768298815573561581829842580132056644646e-632", "normalized_lattice_c": "1.325881357693813862151029511175464105443601700512154067735143741589138235136e-631", "normalized_lattice_dm": "1.36088932676923323893782126718859928648909849415196820626962597236065412939e-628", "normalized_real_tail_m": "1.144685169641695296994396331200497082881453028498739439634869202165335762289e-2385", "normalized_real_tail_c": "2.318081328848318822472804462212660064277834365635527993349189641783558122888e-2384", "normalized_real_tail_dm": "1.424857128911331670727891868433674330034900625763878791878048044393124500624e-2383", "phi_lattice_tail": "5.308662521405219350019878815441029402457386582129341401866411931453612849439e-634", "phi_derivative_lattice_tail": "3.634781730517774112514689734083475256179900250033568722694892158181764510492e-630", "envelope_K0": "45.77933696155126084765016570765020353591667391661649659058173348829585538802", "envelope_K1": "1974.915374382150478826157938758895275515797618955465117684194588053427814691", "envelope_d": "0.6772904887875628673234972493991471206495588414680672589271832706483651107667" } } }, "elapsed_seconds": 0.563067790993955 }, { "z": { "re": "0.59375", "im": "0.625" }, "bits": 256, "replay": true, "purpose": "replay_corner_2_8", "values": { "m": { "re": "0.2475038294963139213329746271082222272143273633014244510555208280481530037305", "im": "-0.09175210350100738378078566956667046381284764418410084447140743269156843210308" }, "c": { "re": "0.0004270829810684541557275844653995336432860089575549081337160953993075465508138", "im": "-0.004204709766987386642442496701090740649737441878523704591306968457951055165082" }, "dm": { "re": "-0.6569870803902298801347602009734060301256902853644168920443943272623477941349", "im": "-0.08871700375563097794268007876507123848965399136034947438442868081046233125839" } }, "metadata": { "metadata": { "classification": "diagnostic, not a certificate", "bits": 256, "lattice_cutoff": 32, "gauss_legendre_order_per_segment": 96, "positive_half_segments": [ "0.0", "0.125", "0.25", "0.5", "1.0", "2.0", "4.0", "4.5" ], "normalization": "B=exp(2*pi*exp(2*z)-9*z)/(4*pi^4), analytic and nonzero", "derivative": "dm=(B*M)' includes B' contribution", "majorants": { "status": "analytic majorants evaluated as floating numbers; NOT interval bounds", "quadrature_error": "NOT bounded: fixed Gauss-Legendre approximation and replay only", "roundoff_error": "NOT bounded: ordinary mpmath arithmetic", "normalized_lattice_m": "8.184657431323580594049780446869151262046044303073032370233798924158572789034e-461", "normalized_lattice_c": "5.524643766143416900983601801636677101881079904574296849907814273807036632598e-460", "normalized_lattice_dm": "5.705946059671147181326613287862553160671792527103184759574832032700739397789e-457", "normalized_real_tail_m": "2.890516517595952627570981805439778435129885320520692384572306441364885982016e-1745", "normalized_real_tail_c": "5.853620045128347119988573731989928240845529218026559597827253442759996105231e-1744", "normalized_real_tail_dm": "6.068609930580385785037441738767302133759303172082997342853450242953797054964e-1743", "phi_lattice_tail": "7.273867734636615468343701099086336534586537544654409491266217575773554548569e-462", "phi_derivative_lattice_tail": "4.980335714590012097526369578262461458973490865323419345274280198831878213279e-458", "envelope_K0": "126.2492829278436835261203948168404649069660071060487721886868609718869742379", "envelope_K1": "10771.85146213373853884895685987568440713214333778226012962950582542118672571", "envelope_d": "0.495307208606777259303949409955035265976351690422319468296460584906557471819" } } }, "elapsed_seconds": 0.5609067080076784 }, { "z": { "re": "0.125", "im": "0.5" }, "bits": 256, "replay": true, "purpose": "replay_corner_0_6", "values": { "m": { "re": "0.4140090567538481013441691985042818266881289465130146072412444026331877863392", "im": "0.02444034412058271337054931414372481253653011303532512871925613299255362344771" }, "c": { "re": "0.0197645490568625890888283550981399227386618201325436823733772926770594159813", "im": "-0.01788635191381631957237954314030502216398969071356124475484433449637415192798" }, "dm": { "re": "-2.065250342867133276125604973221997195473657240071330120961328906183383944468", "im": "-1.204437295565758029350685361398368866815449634960599810918138718559070649949" } }, "metadata": { "metadata": { "classification": "diagnostic, not a certificate", "bits": 256, "lattice_cutoff": 32, "gauss_legendre_order_per_segment": 96, "positive_half_segments": [ "0.0", "0.125", "0.25", "0.5", "1.0", "2.0", "4.0", "4.5" ], "normalization": "B=exp(2*pi*exp(2*z)-9*z)/(4*pi^4), analytic and nonzero", "derivative": "dm=(B*M)' includes B' contribution", "majorants": { "status": "analytic majorants evaluated as floating numbers; NOT interval bounds", "quadrature_error": "NOT bounded: fixed Gauss-Legendre approximation and replay only", "roundoff_error": "NOT bounded: ordinary mpmath arithmetic", "normalized_lattice_m": "4.824504357380927089265119962573648041696825283143127500769679192249881245606e-795", "normalized_lattice_c": "3.256540441232125785253955974737212428145357066121611063019533454768669840784e-794", "normalized_lattice_dm": "3.323191023685657042741728599653251171462085137905241738078093804334878779295e-791", "normalized_real_tail_m": "1.184468286118804074236010657153622860987675855318675381729342165693672580317e-2989", "normalized_real_tail_c": "2.398625785499149144356561436227296679418266854744224881305039120971109458489e-2988", "normalized_real_tail_dm": "8.166182290892451110466822164481315697160994882675560524853302085110034151206e-2988", "phi_lattice_tail": "3.848127073659310480112728546712962877935804122156839931289037583715960921408e-796", "phi_derivative_lattice_tail": "2.634769478686932523943207330815543157054247305396869180730711204308512557347e-792", "envelope_K0": "24.98358556059492371098084169177439743280792252808812131232102861750641657677", "envelope_K1": "691.5875111212121756468322965524852568972249488655562644948558656178324871281", "envelope_d": "0.848704877416486584845541256502228362138203201447800350869254093646723901502" } } }, "elapsed_seconds": 0.558542207989376 }, { "z": { "re": "0.359375", "im": "0.5" }, "bits": 256, "replay": true, "purpose": "replay_corner_1_6", "values": { "m": { "re": "0.2840701287101510109691994364038816205537753289332676473116250234877700369923", "im": "-0.003967725035625094689610928652127108398070407572839858165719316816862368689651" }, "c": { "re": "0.00325506246779915517438036277543435158205968714730180251277116597164789300006", "im": "-0.003794456423944894690053248292138722520071157082691902708573064755509408047408" }, "dm": { "re": "-0.08138731878551636631060649387000887444363779363611279875882281913645325756737", "im": "-0.4012400126574895220694020853965467897814999204137867480023883908975605978044" } }, "metadata": { "metadata": { "classification": "diagnostic, not a certificate", "bits": 256, "lattice_cutoff": 32, "gauss_legendre_order_per_segment": 96, "positive_half_segments": [ "0.0", "0.125", "0.25", "0.5", "1.0", "2.0", "4.0", "4.5" ], "normalization": "B=exp(2*pi*exp(2*z)-9*z)/(4*pi^4), analytic and nonzero", "derivative": "dm=(B*M)' includes B' contribution", "majorants": { "status": "analytic majorants evaluated as floating numbers; NOT interval bounds", "quadrature_error": "NOT bounded: fixed Gauss-Legendre approximation and replay only", "roundoff_error": "NOT bounded: ordinary mpmath arithmetic", "normalized_lattice_m": "7.932877433951449955812071840192000600632533859107040900334946964439403684657e-795", "normalized_lattice_c": "5.354692267917228720173148492129600405426960354897252607726089200996597487144e-794", "normalized_lattice_dm": "5.471162688825349016802501964291966956567319136593040714387878952562785180604e-791", "normalized_real_tail_m": "1.947607679907648961297482372044320054920574492055390061081283666386615681628e-2989", "normalized_real_tail_c": "3.944032994222432676960590027812808755932252753384346615365909633663124632389e-2988", "normalized_real_tail_dm": "1.51160930521589025016189759416121907907443397714587207129255316801502203494e-2987", "phi_lattice_tail": "3.848127073659310480112728546712962877935804122156839931289037583715960921408e-796", "phi_derivative_lattice_tail": "2.634769478686932523943207330815543157054247305396869180730711204308512557347e-792", "envelope_K0": "24.98358556059492371098084169177439743280792252808812131232102861750641657677", "envelope_K1": "691.5875111212121756468322965524852568972249488655562644948558656178324871281", "envelope_d": "0.848704877416486584845541256502228362138203201447800350869254093646723901502" } } }, "elapsed_seconds": 0.5634247499983758 }, { "z": { "re": "0.125", "im": "0.4375" }, "bits": 256, "replay": true, "purpose": "replay_corner_0_5", "values": { "m": { "re": "0.3341557770184633273849411481741305748413432325481176387225170350779226085382", "im": "0.0988868797059199738433688171136427852567358269976624350181046330165282244272" }, "c": { "re": "0.01534070820459332965016895796071439231928433959851277353392107063408120655414", "im": "-0.004735237105854448282875630802627829703482300269511338418156268173282132167595" }, "dm": { "re": "-0.5375874538311307980984822857841344560320445141730499361810297815024578249626", "im": "-1.216658664631424908916317278526281158948576945702133724192791667800746274812" } }, "metadata": { "metadata": { "classification": "diagnostic, not a certificate", "bits": 256, "lattice_cutoff": 32, "gauss_legendre_order_per_segment": 96, "positive_half_segments": [ "0.0", "0.125", "0.25", "0.5", "1.0", "2.0", "4.0", "4.5" ], "normalization": "B=exp(2*pi*exp(2*z)-9*z)/(4*pi^4), analytic and nonzero", "derivative": "dm=(B*M)' includes B' contribution", "majorants": { "status": "analytic majorants evaluated as floating numbers; NOT interval bounds", "quadrature_error": "NOT bounded: fixed Gauss-Legendre approximation and replay only", "roundoff_error": "NOT bounded: ordinary mpmath arithmetic", "normalized_lattice_m": "1.519095332774698770596086458042631287725292666991525878623104220096194633115e-944", "normalized_lattice_c": "1.025389349622921670152358359178776119214572550219279968070595348564931377352e-943", "normalized_lattice_dm": "1.045241634964012165623547253636064300123484444836057662103096664095228029575e-940", "normalized_real_tail_m": "2.415909500541067392564035341176763809463027208285785170464802089507223916236e-3546", "normalized_real_tail_c": "4.892349990362089096778807486988342894597440384945080738946582039323495504021e-3545", "normalized_real_tail_dm": "1.332052318092797117916581421334557069690312380813033497429799887424168667566e-3544", "phi_lattice_tail": "9.390627393980322415840738444587875203718719124464803625921976797748713203453e-946", "phi_derivative_lattice_tail": "6.429657329338828034654878750269191130998586968046026946078245011084220475933e-942", "envelope_K0": "16.75799959534728485486773462155443300344343055674133582342672208436120203679", "envelope_K1": "357.6104033892641832410464274914483260646317182467297643828089997188902069127", "envelope_d": "1.006875510290020458199476386583245573465469766147046672378953444795552362874" } } }, "elapsed_seconds": 0.5572973749949597 }, { "z": { "re": "0.359375", "im": "0.4375" }, "bits": 256, "replay": true, "purpose": "replay_corner_1_5", "values": { "m": { "re": "0.2642809961049034475190168272182681991328031617577532894585025446576441542956", "im": "0.001907800555523607903611278002096903649607512034052438081963826021458076437699" }, "c": { "re": "0.003403552600338373955970108509770185319248376447927844528971544017065157328277", "im": "-0.003570412670125840460165006428596249706166274220342397187303740229665765148182" }, "dm": { "re": "-0.1022021245262430268489824569574385124552044359380346278864245376867587037573", "im": "-0.2673737676649837205143199182662055152021571919896189542088158810787254083552" } }, "metadata": { "metadata": { "classification": "diagnostic, not a certificate", "bits": 256, "lattice_cutoff": 32, "gauss_legendre_order_per_segment": 96, "positive_half_segments": [ "0.0", "0.125", "0.25", "0.5", "1.0", "2.0", "4.0", "4.5" ], "normalization": "B=exp(2*pi*exp(2*z)-9*z)/(4*pi^4), analytic and nonzero", "derivative": "dm=(B*M)' includes B' contribution", "majorants": { "status": "analytic majorants evaluated as floating numbers; NOT interval bounds", "quadrature_error": "NOT bounded: fixed Gauss-Legendre approximation and replay only", "roundoff_error": "NOT bounded: ordinary mpmath arithmetic", "normalized_lattice_m": "4.060160941797194998439325720447367992620822021499749177769031894313281097979e-944", "normalized_lattice_c": "2.740608635713106623946544861301973395019054864512330694994096528661464741136e-943", "normalized_lattice_dm": "2.79720795821277358158726765456291440114540046407620422187211839886622572564e-940", "normalized_real_tail_m": "6.457120354057732016236033718132952605363345676418108189994666111171720477873e-3546", "normalized_real_tail_c": "1.307602486552835852781486119214799902136904536114832839012518133909130078179e-3544", "normalized_real_tail_dm": "4.123092987832454402453185624388023121705148539841343578434944857284752487229e-3544", "phi_lattice_tail": "9.390627393980322415840738444587875203718719124464803625921976797748713203453e-946", "phi_derivative_lattice_tail": "6.429657329338828034654878750269191130998586968046026946078245011084220475933e-942", "envelope_K0": "16.75799959534728485486773462155443300344343055674133582342672208436120203679", "envelope_K1": "357.6104033892641832410464274914483260646317182467297643828089997188902069127", "envelope_d": "1.006875510290020458199476386583245573465469766147046672378953444795552362874" } } }, "elapsed_seconds": 0.5568416669848375 }, { "z": { "re": "0.2421875", "im": "0.59375" }, "bits": 256, "replay": true, "purpose": "cell_0_7_step_0", "values": { "m": { "re": "0.1933357606087402636551724844074496543667504373791615252503463754366290365585", "im": "0.05797929909350657399243285862558084676701059445365958823010965826740233774581" }, "c": { "re": "-0.01251974508113639079291057459496232813697340041433678532406572327934930412904", "im": "-0.0009456937930330605748432228929919592589129125681065828410533847287010319458137" }, "dm": { "re": "1.781020549086027632146461166607461748295767402801779986356257696723007598557", "im": "1.972212222232353933427899469738190091399625963808800399351003132341119957079" } }, "metadata": { "metadata": { "classification": "diagnostic, not a certificate", "bits": 256, "lattice_cutoff": 32, "gauss_legendre_order_per_segment": 96, "positive_half_segments": [ "0.0", "0.125", "0.25", "0.5", "1.0", "2.0", "4.0", "4.5" ], "normalization": "B=exp(2*pi*exp(2*z)-9*z)/(4*pi^4), analytic and nonzero", "derivative": "dm=(B*M)' includes B' contribution", "majorants": { "status": "analytic majorants evaluated as floating numbers; NOT interval bounds", "quadrature_error": "NOT bounded: fixed Gauss-Legendre approximation and replay only", "roundoff_error": "NOT bounded: ordinary mpmath arithmetic", "normalized_lattice_m": "4.766815029046165016188948897832102908808325459791466890878169836288274562398e-548", "normalized_lattice_c": "3.217600144606161385927540506036669463445619685359240151342764639494585329619e-547", "normalized_lattice_dm": "3.300885980078598004147854201246507305811836923717250977909064985301513155427e-544", "normalized_real_tail_m": "7.037146921905677404240013724384762861872849240806273517922632025907668943294e-2070", "normalized_real_tail_c": "1.425088779171036289462455418699221566638050424526067350666720714828492207798e-2068", "normalized_real_tail_dm": "9.619604724123007713373095155189108310662591248776952450189061453982171517421e-2068", "phi_lattice_tail": "5.110376079094360789875474422295703154618336676898510296147802634540412390595e-549", "phi_derivative_lattice_tail": "3.49901722580216895616243515246440807024827414882420258757637387260709959581e-545", "envelope_K0": "70.87311316149443703784637035310491662154555266677058707233581431761345409535", "envelope_K1": "4171.970167435341205168775349782120993961049640453464838267291510038175725116", "envelope_d": "0.5874458303952882333224629443443826173484982088182668184618485628214732475205" } } }, "elapsed_seconds": 0.5641562080127187 }, { "z": { "re": "0.2097105219501639491548216649211800177596422383770527720221005334709142505361", "im": "0.6134363778591987928264051037475765506039547622505328473607422570554653525157" }, "bits": 256, "replay": true, "purpose": "cell_0_7_step_1", "values": { "m": { "re": "0.08056412712884855451371375115490022239849690612622300704163723038831864702623", "im": "-0.01187875628044461222244996493924086333926796714523846324476642420159594263493" }, "c": { "re": "-0.02430298628961317389336948058247403703827491201848412590864947869181992039331", "im": "-0.005471697287064923918213403834397781372050694726640705242044687581273810153275" }, "dm": { "re": "1.213880857423299003839448756722281239608565712793040009170504612803749887203", "im": "4.332486420642733854846071105967222951711721007584040946373087430124535525899" } }, "metadata": { "metadata": { "classification": "diagnostic, not a certificate", "bits": 256, "lattice_cutoff": 32, "gauss_legendre_order_per_segment": 96, "positive_half_segments": [ "0.0", "0.125", "0.25", "0.5", "1.0", "2.0", "4.0", "4.5" ], "normalization": "B=exp(2*pi*exp(2*z)-9*z)/(4*pi^4), analytic and nonzero", "derivative": "dm=(B*M)' includes B' contribution", "majorants": { "status": "analytic majorants evaluated as floating numbers; NOT interval bounds", "quadrature_error": "NOT bounded: fixed Gauss-Legendre approximation and replay only", "roundoff_error": "NOT bounded: ordinary mpmath arithmetic", "normalized_lattice_m": "2.481815741527474103343068659720245224100992801678698058912645517733361236525e-493", "normalized_lattice_c": "1.675225625531045019756571345311165526268170141133121189766035724470018834655e-492", "normalized_lattice_dm": "1.722109180405812761749941945060831567759931075866589319849772727693022049014e-489", "normalized_real_tail_m": "2.911632646578603263644591013833815133250531916148556873701070439367596856834e-1866", "normalized_real_tail_c": "5.896361407233508058805754084030994894160091929417595709794016719845743730282e-1865", "normalized_real_tail_dm": "4.829383895354460634289533680275342992166045559117143408497054569667665587289e-1864", "phi_lattice_tail": "2.400976944790617459030759762687038535431792398466607857875576348760050743745e-494", "phi_derivative_lattice_tail": "1.643922004672703834142327282990280443393472225824466922853241852457329395512e-490", "envelope_K0": "99.98724251698661514198615703308564635236662429231037140393364714800291588613", "envelope_K1": "7383.537129469446210809655601288807139980867630862535699248680591441128254764", "envelope_d": "0.5296465728969732233932108897496453072906668735755021482469596718244493225704" } } }, "elapsed_seconds": 0.5714581250213087 }, { "z": { "re": "0.2085662118687355842702066618726665597282954385350474977317882757020641989562", "im": "0.6224134417632680006649833309801167886089278290964207163986691899263918656414" }, "bits": 256, "replay": true, "purpose": "cell_0_7_step_2", "values": { "m": { "re": "0.03737855770884639767731345089145585754761754675025720380225715876162741347556", "im": "-0.00486354698012337486577763983201040672080050793973991335240783114491310918394" }, "c": { "re": "-0.02703227063881344023032189092288455841938400760522377684624506239357806807019", "im": "-0.003463200237390493167268628958724245520872225256403962004829877857202359908592" }, "dm": { "re": "1.533384657259091821508401531337745212782651260765690640651504052823666980706", "im": "4.950202180189965008455521521459929220978295770733034864072319626068611665584" } }, "metadata": { "metadata": { "classification": "diagnostic, not a certificate", "bits": 256, "lattice_cutoff": 32, "gauss_legendre_order_per_segment": 96, "positive_half_segments": [ "0.0", "0.125", "0.25", "0.5", "1.0", "2.0", "4.0", "4.5" ], "normalization": "B=exp(2*pi*exp(2*z)-9*z)/(4*pi^4), analytic and nonzero", "derivative": "dm=(B*M)' includes B' contribution", "majorants": { "status": "analytic majorants evaluated as floating numbers; NOT interval bounds", "quadrature_error": "NOT bounded: fixed Gauss-Legendre approximation and replay only", "roundoff_error": "NOT bounded: ordinary mpmath arithmetic", "normalized_lattice_m": "4.060765203283835415028783235618437947958821972792490065928194659814911498256e-468", "normalized_lattice_c": "2.741016512216588905144428684042445614872204831634930794501531395375065261323e-467", "normalized_lattice_dm": "2.821310494517249336737670457546639880475560770832649615502770305700997071615e-464", "normalized_real_tail_m": "2.011976487884037292954444330283114821191548511211156581606023609309537101181e-1772", "normalized_real_tail_c": "4.07447452381123113253091405375065085084807951117103929941375951697867535249e-1771", "normalized_real_tail_dm": "3.689759612532721398367275499017866066456531424712483384375910174465009686008e-1770", "phi_lattice_tail": "3.749185298976448701716856761088743127748837466986874368679259990702721300423e-469", "phi_derivative_lattice_tail": "2.567025154471145608454063258723941239833198600724688708106352733647671964504e-465", "envelope_K0": "119.5670661819765070165106913448339977019868606661970619321908029357055469108", "envelope_K1": "9869.84983665010081187025182418991217068517021856621081783921040547961615526", "envelope_d": "0.5030119125788981757804268435284059301260168917194290935294851193794141134923" } } }, "elapsed_seconds": 0.5705373749951832 }, { "z": { "re": "0.2082567796138278868553077860928407597685053954532763638622493802924112007668", "im": "0.6242053202426101631451200261467148026122830097996875556597206391306865960767" }, "bits": 256, "replay": true, "purpose": "cell_0_7_step_3", "values": { "m": { "re": "0.02790366959261160853060259535037264573722721853431712946794334652289639989434", "im": "-0.003615121949967675760043364406925739708117994434472300079472962676878752615081" }, "c": { "re": "-0.02755640782051968967580662539248120939094600851209733907246420335001400359194", "im": "-0.003050348965621711011496372155317578922481675755465494401844436497384344058732" }, "dm": { "re": "1.593025674655867932157513253609535625846064587862373797456807183385710689937", "im": "5.085825600621078948449193403210959959181735088271998649503218693000636152395" } }, "metadata": { "metadata": { "classification": "diagnostic, not a certificate", "bits": 256, "lattice_cutoff": 32, "gauss_legendre_order_per_segment": 96, "positive_half_segments": [ "0.0", "0.125", "0.25", "0.5", "1.0", "2.0", "4.0", "4.5" ], "normalization": "B=exp(2*pi*exp(2*z)-9*z)/(4*pi^4), analytic and nonzero", "derivative": "dm=(B*M)' includes B' contribution", "majorants": { "status": "analytic majorants evaluated as floating numbers; NOT interval bounds", "quadrature_error": "NOT bounded: fixed Gauss-Legendre approximation and replay only", "roundoff_error": "NOT bounded: ordinary mpmath arithmetic", "normalized_lattice_m": "4.581084781872256507715672008470647858649845165760448034056198873392195683167e-463", "normalized_lattice_c": "3.092232227763773142708078605717687304588645486888302422987934239539732086138e-462", "normalized_lattice_dm": "3.183698872011434265133338024066294321444426403506769960551422520407176889013e-459", "normalized_real_tail_m": "1.275565775396777304287890278527052223616567653418132602567399601649830378474e-1753", "normalized_real_tail_c": "2.583163036336761888320008525553626245560246661132157682453290695371115400994e-1752", "normalized_real_tail_dm": "2.388231007764387539787738868146145342834721217980025059519824588450593543096e-1751", "phi_lattice_tail": "4.181674298582893492570436604142249639106936570863778046892513591181819288021e-464", "phi_derivative_lattice_tail": "2.86314552529541496678851070703389927053199485296715459561177207789731764688e-460", "envelope_K0": "124.1399133216532999251933075020428296544963103581699236331292762308128394839", "envelope_K1": "10484.30302150989845536329813121530930819055584232746338372466393481899451454", "envelope_d": "0.4976757791452731275335725915205365304811898641601545873902227568694532019971" } } }, "elapsed_seconds": 0.5808990419609472 }, { "z": { "re": "0.2081420687623378364048891570314145602832215280645709508238859094657142447174", "im": "0.6248552090958747210349336236722631747386862090887371027504874959171388726176" }, "bits": 256, "replay": true, "purpose": "cell_0_7_step_4", "values": { "m": { "re": "0.02439821689528227661575311661220162086602486517201744026511934532090112813428", "im": "-0.00315913337924485041715038606511208416402682691230839573335194092215120300822" }, "c": { "re": "-0.02774288471115132874843693572614383671965898645316420221345817277639298704114", "im": "-0.002898471998800612803463408177888113820601449295668405290113753001045946240143" }, "dm": { "re": "1.614469311680356802216365175411781188215681116928884969884187409830613549232", "im": "5.135952185984195527257843243596405289693413332986309699537187208688853606564" } }, "metadata": { "metadata": { "classification": "diagnostic, not a certificate", "bits": 256, "lattice_cutoff": 32, "gauss_legendre_order_per_segment": 96, "positive_half_segments": [ "0.0", "0.125", "0.25", "0.5", "1.0", "2.0", "4.0", "4.5" ], "normalization": "B=exp(2*pi*exp(2*z)-9*z)/(4*pi^4), analytic and nonzero", "derivative": "dm=(B*M)' includes B' contribution", "majorants": { "status": "analytic majorants evaluated as floating numbers; NOT interval bounds", "quadrature_error": "NOT bounded: fixed Gauss-Legendre approximation and replay only", "roundoff_error": "NOT bounded: ordinary mpmath arithmetic", "normalized_lattice_m": "3.125774637663469157482259002402856511010896450620249686014417761118741899582e-461", "normalized_lattice_c": "2.109897880422841681300524826621928144932355104168668538059731988755150782218e-460", "normalized_lattice_dm": "2.172531197445235454861105492401936178706340483948429651737175795275208065832e-457", "normalized_real_tail_m": "8.524620987574859453597896980543318533354519375402614512720059457067699250022e-1747", "normalized_real_tail_c": "1.72633124843057180179702659315971407341638443914454938267680274494704268959e-1745", "normalized_real_tail_dm": "1.608189250847499798495395835361768041168997474547629675402938276127963577326e-1744", "phi_lattice_tail": "2.841009605913628803653552524451312071836295588306930477860943578057644099871e-462", "phi_derivative_lattice_tail": "1.945207435990283298704251899525745360970912052281129241504552900814799335597e-458", "envelope_K0": "125.8611153086846566247373637432861423333151928691152447184075878675124703894", "envelope_K1": "10718.74370073506495260753997098045039401148828875670007876637877556118401975", "envelope_d": "0.4957388563014762297083482524861009617019381545552540292317146421527395768575" } } }, "elapsed_seconds": 0.5684195419889875 }, { "z": { "re": "0.2081170931270277634679678545195606694452440791500713633850984307856272838969", "im": "0.6249958104595712872329621604309444450314627344139543672894489604744180208714" }, "bits": 256, "replay": true, "purpose": "cell_0_7_step_5", "values": { "m": { "re": "0.02363494800847573409804632131769647768764278210590140599894705493475464582469", "im": "-0.003060221494423392835248350721543502415058980442923400965534342330698503588054" }, "c": { "re": "-0.02778295469922545660503948375334287024939134817575417166273835870139806194171", "im": "-0.002865460793600610193350986425939877524482776688335101380443375244380165689455" }, "dm": { "re": "1.619094741167355274228528252930525462224883776801764206082070426695962553627", "im": "5.146863833611823324553405064516068183904550333555718276395397484933038578839" } }, "metadata": { "metadata": { "classification": "diagnostic, not a certificate", "bits": 256, "lattice_cutoff": 32, "gauss_legendre_order_per_segment": 96, "positive_half_segments": [ "0.0", "0.125", "0.25", "0.5", "1.0", "2.0", "4.0", "4.5" ], "normalization": "B=exp(2*pi*exp(2*z)-9*z)/(4*pi^4), analytic and nonzero", "derivative": "dm=(B*M)' includes B' contribution", "majorants": { "status": "analytic majorants evaluated as floating numbers; NOT interval bounds", "quadrature_error": "NOT bounded: fixed Gauss-Legendre approximation and replay only", "roundoff_error": "NOT bounded: ordinary mpmath arithmetic", "normalized_lattice_m": "7.795515112216203026225653405171421857177006474466951828375470680050273444363e-461", "normalized_lattice_c": "5.261972700745937042702316048490709753594479370265192484153442709033934574945e-460", "normalized_lattice_dm": "5.418298357218799465359633075959454463272840111996423386528076228915735813968e-457", "normalized_real_tail_m": "2.556436103092973305922274154725039386525270782662335381601284822790521183906e-1745", "normalized_real_tail_c": "5.177069740015617391783250575224107947618115265565045205939809652959791155483e-1744", "normalized_real_tail_dm": "4.830702195905832971829502512127047621148267872231797211415932037735157767804e-1743", "phi_lattice_tail": "7.07865676365409937067895343239120314680266608192175446776476569902928168323e-462", "phi_derivative_lattice_tail": "4.846676950623967978554666948751568464352670591670231847466172263543516858797e-458", "envelope_K0": "126.2380269782617892483505375837503581076532560240823830971694510352490723377", "envelope_K1": "10770.31024101651121537032507900372373378487911497688835101859926609628694893", "envelope_d": "0.4953196989630838745172835773998515355077710042039086962091187073303207138706" } } }, "elapsed_seconds": 0.5643968749791384 }, { "z": { "re": "0.2081167154616751475506884961151864687499800810325239035610795612692283826445", "im": "0.6249979338936321515412417767863457340877808756829600716114345282571420301567" }, "bits": 256, "replay": true, "purpose": "cell_0_7_step_6", "values": { "m": { "re": "0.02362340731817495558511724144383931120052918613827422861973297205235777823008", "im": "-0.003058727202677734996497437321535713410405947748526572004272910540992288069597" }, "c": { "re": "-0.02778355910764568095910381099590968117122327199360084423174213871362406535637", "im": "-0.002864961833709196138052263252194378931187117845175353173500189022402907142485" }, "dm": { "re": "1.619164554827552363837185684740267844498944779625749550593263901681364231882", "im": "5.147028812857032541501622852358303413466304912717136144787313448648317080022" } }, "metadata": { "metadata": { "classification": "diagnostic, not a certificate", "bits": 256, "lattice_cutoff": 32, "gauss_legendre_order_per_segment": 96, "positive_half_segments": [ "0.0", "0.125", "0.25", "0.5", "1.0", "2.0", "4.0", "4.5" ], "normalization": "B=exp(2*pi*exp(2*z)-9*z)/(4*pi^4), analytic and nonzero", "derivative": "dm=(B*M)' includes B' contribution", "majorants": { "status": "analytic majorants evaluated as floating numbers; NOT interval bounds", "quadrature_error": "NOT bounded: fixed Gauss-Legendre approximation and replay only", "roundoff_error": "NOT bounded: ordinary mpmath arithmetic", "normalized_lattice_m": "7.903857646241785787821818617157794628396880102180532108850877633184576648249e-461", "normalized_lattice_c": "5.335103911213205406779727566581511374167894068971859173474342402399589237568e-460", "normalized_lattice_dm": "5.49360405391326915948364955208827835796113841725582924834595014842789105757e-457", "normalized_real_tail_m": "2.691174356390931837903294416537482048742870986895370700621409115705832070426e-1745", "normalized_real_tail_c": "5.44992981384524708397382976446614015298206978352858318054329881555763165061e-1744", "normalized_real_tail_dm": "5.085432979006762735253615701093338256086724199680089430890265895973840875912e-1743", "phi_lattice_tail": "7.176934047123124288515923497195378943108252263190511104203621670308298909631e-462", "phi_derivative_lattice_tail": "4.913966305153057901276383669479026807469520636078726475296187743839328684016e-458", "envelope_K0": "126.2437317824580125763593858659433198158922664700847180788666587640719463771", "envelope_K1": "10771.09136233648048338687895074928183458094746813062985793381710048038209874", "envelope_d": "0.4953133683332076738883682859190592960941639231388972007387955129981220348415" } } }, "elapsed_seconds": 0.5657384169753641 }, { "z": { "re": "0.2081165267240799195925898601937006677720280969020139499811300309093608888403", "im": "0.6249989950565674140953543955778627417422161703537683140477894923036583543764" }, "bits": 256, "replay": true, "purpose": "cell_0_7_step_7", "values": { "m": { "re": "0.02361763983770972780456570661400231611758330663417181610451256420392113634262", "im": "-0.003057980432376248407089770073183376941299770971408756122625601789668850173984" }, "c": { "re": "-0.02778386114526661360607954461902494934560310596142635826198366709112832474431", "im": "-0.002864712478999865214834072029369815562682366182986377268674647255792375183354" }, "dm": { "re": "1.619199443093088940664720955183196317798292549104214923131978408347460772263", "im": "5.147111261425752064998583315764842103727698676538769688159867290351624602583" } }, "metadata": { "metadata": { "classification": "diagnostic, not a certificate", "bits": 256, "lattice_cutoff": 32, "gauss_legendre_order_per_segment": 96, "positive_half_segments": [ "0.0", "0.125", "0.25", "0.5", "1.0", "2.0", "4.0", "4.5" ], "normalization": "B=exp(2*pi*exp(2*z)-9*z)/(4*pi^4), analytic and nonzero", "derivative": "dm=(B*M)' includes B' contribution", "majorants": { "status": "analytic majorants evaluated as floating numbers; NOT interval bounds", "quadrature_error": "NOT bounded: fixed Gauss-Legendre approximation and replay only", "roundoff_error": "NOT bounded: ordinary mpmath arithmetic", "normalized_lattice_m": "7.958563665713068171523740368384768345938545161766903078337339129940115656316e-461", "normalized_lattice_c": "5.372030474356321015778524748659718633508517984192659577877703912709578068013e-460", "normalized_lattice_dm": "5.531628602589772954981086783335078165006591935257636439044757270149548507245e-457", "normalized_real_tail_m": "2.761146652808156910463266991309309220224232484733518728725534838539933910334e-1745", "normalized_real_tail_c": "5.591631561561277346674123143101290894846236653854310133808164694766397884803e-1744", "normalized_real_tail_dm": "5.217722271361521853267984741126675659251614079624692295191791278094788935549e-1743", "phi_lattice_tail": "7.226557229320154040665056606088848892077808311233750918955204528729720283624e-462", "phi_derivative_lattice_tail": "4.947942741841705093002691922447234039129905000265747391631113517446070068058e-458", "envelope_K0": "126.2465828354565998581682235934860700429155289369789663873210624929089894769", "envelope_K1": "10771.48174528765027384159939217636111980309482987862920909757187166605275824", "envelope_d": "0.4953102046668551656595833105703254379056059240927592684729685732627241037381" } } }, "elapsed_seconds": 0.5674909169902094 }, { "z": { "re": "0.2081164323790404598947712031988086336900811120457349441475892393004080551285", "im": "0.6249995254995870961018626480484099381212668476846968970389189059388709857916" }, "bits": 256, "replay": true, "purpose": "cell_0_7_step_8", "values": { "m": { "re": "0.02361475681328072839404093514835780660698704175817110295224241142929225756309", "im": "-0.003057607141068086639353125812833534699814551651006586280830959949261602032544" }, "c": { "re": "-0.02778401212245380426281224603737969361211789258065529922010944510067615541684", "im": "-0.002864587832937924975262442023136812029341676440022664695746203162537533781903" }, "dm": { "re": "1.619216882587319121758656033627896160506656292433231583501850548787567771889", "im": "5.147152475451933448345888055733622774606567590410750013197814667405822264044" } }, "metadata": { "metadata": { "classification": "diagnostic, not a certificate", "bits": 256, "lattice_cutoff": 32, "gauss_legendre_order_per_segment": 96, "positive_half_segments": [ "0.0", "0.125", "0.25", "0.5", "1.0", "2.0", "4.0", "4.5" ], "normalization": "B=exp(2*pi*exp(2*z)-9*z)/(4*pi^4), analytic and nonzero", "derivative": "dm=(B*M)' includes B' contribution", "majorants": { "status": "analytic majorants evaluated as floating numbers; NOT interval bounds", "quadrature_error": "NOT bounded: fixed Gauss-Legendre approximation and replay only", "roundoff_error": "NOT bounded: ordinary mpmath arithmetic", "normalized_lattice_m": "7.986051332069690449485637590849771468723448996091091908291633646622901682634e-461", "normalized_lattice_c": "5.390584649147041053402805373823595741388328072361487038096852711470458635778e-460", "normalized_lattice_dm": "5.550734475226668316595973353997022685917128707228037744467169888170802259223e-457", "normalized_real_tail_m": "2.796802773315476440422660199100388757070361470240561219140026374857391285098e-1745", "normalized_real_tail_c": "5.663839204481434271390070994956826289181713004942895834518867699444909381343e-1744", "normalized_real_tail_dm": "5.285134189710013592155482934978833959701208928601604995894088684140882928314e-1743", "phi_lattice_tail": "7.251490832075826684921030938362348971737137062536051445403820535534721874804e-462", "phi_derivative_lattice_tail": "4.965014500200214759587558158214353642396012910701847410236190058253826851853e-458", "envelope_K0": "126.2480080248439346056911979146622305473500346618794683729576531135467815127", "envelope_K1": "10771.67689235637572485196817959334085687147226289480948941109557375308553615", "envelope_d": "0.4953086232456002224618477708034447463656752880736130944685092538931108318662" } } }, "elapsed_seconds": 0.5729386659804732 }, { "z": { "re": "0.2081163852124587549248417092486530287348101857725001721032584847829507337025", "im": "0.6249997906864944246773602442490795903852093304811764833559108024183695819037" }, "bits": 256, "replay": true, "purpose": "cell_0_7_step_9", "values": { "m": { "re": "0.0236133154799711976539455622840182926859744496068000393839345488846135819061", "im": "-0.00305742051886837308498382020766645471977109989760057342023243213161176996293" }, "c": { "re": "-0.02778408760064458126917633442401664856417434770118120721877471629245582465211", "im": "-0.002864525517728091197678101147449697167430357230660477819633753946619268881774" }, "dm": { "re": "1.619225601175124789423261395908305332789114251501491814906723240682380170184", "im": "5.147173079901140797477389769698908708524687443442235175021021682176243784161" } }, "metadata": { "metadata": { "classification": "diagnostic, not a certificate", "bits": 256, "lattice_cutoff": 32, "gauss_legendre_order_per_segment": 96, "positive_half_segments": [ "0.0", "0.125", "0.25", "0.5", "1.0", "2.0", "4.0", "4.5" ], "normalization": "B=exp(2*pi*exp(2*z)-9*z)/(4*pi^4), analytic and nonzero", "derivative": "dm=(B*M)' includes B' contribution", "majorants": { "status": "analytic majorants evaluated as floating numbers; NOT interval bounds", "quadrature_error": "NOT bounded: fixed Gauss-Legendre approximation and replay only", "roundoff_error": "NOT bounded: ordinary mpmath arithmetic", "normalized_lattice_m": "7.999828951128071025694872519104744289247085579225263781206187180318111131077e-461", "normalized_lattice_c": "5.399884542011447942344038950395702395241782765977053052314176346714725013477e-460", "normalized_lattice_dm": "5.560310895731665487774929139911218677005975799041614291916571375148852165655e-457", "normalized_real_tail_m": "2.814800779900960785873492111023568869693693468309786299024090158947179831051e-1745", "normalized_real_tail_c": "5.700287186328048921290882963618069813701620968731472564251004223030011830715e-1744", "normalized_real_tail_dm": "5.319161609653617449297008567939686352541560348297591981496978148643322632691e-1743", "phi_lattice_tail": "7.263988246533606911640680307705183975016561160010536413657765869453908803616e-462", "phi_derivative_lattice_tail": "4.973571339812205017638028367147303583966372467634211005106037322294803601707e-458", "envelope_K0": "126.2487205352799672063108414751005884060011292748081222697793220083444969914", "envelope_K1": "10771.77445479156541202192014809650666484842130423809070436738946721742874555", "envelope_d": "0.4953078326379249589873831340512006029476867506393339089131117995527252748583" } } }, "elapsed_seconds": 0.5671951660187915 }, { "z": { "re": "0.2081163616306522194965277661446527381650434918381000720677595784458972501384", "im": "0.6249999232712986448757855175739485570148252007490377910949665563510613110589" }, "bits": 256, "replay": true, "purpose": "cell_0_7_step_10", "values": { "m": { "re": "0.02361259485803693424441207637623190638438653008234601014165988666494564651368", "im": "-0.003057327213631323615034618560325859199566951770806790642585261816791432363514" }, "c": { "re": "-0.02778412533713964015330908432842886055462763316183560757452154402691641905043", "im": "-0.002864494362078202845055291976008145652245252497033307773750093100368405248472" }, "dm": { "re": "1.619229960179240893402600608350588174498496053586495346675352965576294847291", "im": "5.147183381484856270456158029234047356905337752258161232255458689828519630153" } }, "metadata": { "metadata": { "classification": "diagnostic, not a certificate", "bits": 256, "lattice_cutoff": 32, "gauss_legendre_order_per_segment": 96, "positive_half_segments": [ "0.0", "0.125", "0.25", "0.5", "1.0", "2.0", "4.0", "4.5" ], "normalization": "B=exp(2*pi*exp(2*z)-9*z)/(4*pi^4), analytic and nonzero", "derivative": "dm=(B*M)' includes B' contribution", "majorants": { "status": "analytic majorants evaluated as floating numbers; NOT interval bounds", "quadrature_error": "NOT bounded: fixed Gauss-Legendre approximation and replay only", "roundoff_error": "NOT bounded: ordinary mpmath arithmetic", "normalized_lattice_m": "8.006726222384401360267361993672678919941878320993731476412751484650380098887e-461", "normalized_lattice_c": "5.404540200109470918180469345729058270960767866670768746578607252139006566749e-460", "normalized_lattice_dm": "5.565104987636149026627316123917863378278422041470564191192316498437149033243e-457", "normalized_real_tail_m": "2.823842579985658842828218109681904261145436084527178228912483867858504038678e-1745", "normalized_real_tail_c": "5.718597845556022964754168701039248161166799881136235555242463606626629452133e-1744", "normalized_real_tail_dm": "5.336256271883782054786965054313134771839360663151011679390481314592805863561e-1743", "phi_lattice_tail": "7.270244620840719661006880788639895164468285744506313120758843965426059042967e-462", "phi_derivative_lattice_tail": "4.977855009180728885306117093999979694244038071174689206931080220950897849033e-458", "envelope_K0": "126.2490767694361185371458702986886576925558632820281182251111519898267761435", "envelope_K1": "10771.82323323468464823837105845006615246100439803231588670816948458229161259", "envelope_d": "0.495307437359821865347739127910598081650027292676905580281367547094265357582" } } }, "elapsed_seconds": 0.5675639580003917 }, { "z": { "re": "0.2081163498401200074041660865450987433769233540804510788824981553524498780692", "im": "0.6249999895615385419333996261908869970346372779413140303522101934113284522996" }, "bits": 256, "replay": true, "purpose": "cell_0_7_step_11", "values": { "m": { "re": "0.02361223455824921059159061128973536852595528569148084911773043718819571028044", "im": "-0.003057280562478402655683643625955472637732640403978799783693627681009657342925" }, "c": { "re": "-0.02778414420473713405374146738298190920693137125909545803893323509061730089833", "im": "-0.002864478784741983863551802085256117372387694896775320192811956753930676391959" }, "dm": { "re": "1.619232139608857340404859958908122836408392696068122762107892499119384067967", "im": "5.147188532116502284401602029655374922396208820527601600180115676423862957533" } }, "metadata": { "metadata": { "classification": "diagnostic, not a certificate", "bits": 256, "lattice_cutoff": 32, "gauss_legendre_order_per_segment": 96, "positive_half_segments": [ "0.0", "0.125", "0.25", "0.5", "1.0", "2.0", "4.0", "4.5" ], "normalization": "B=exp(2*pi*exp(2*z)-9*z)/(4*pi^4), analytic and nonzero", "derivative": "dm=(B*M)' includes B' contribution", "majorants": { "status": "analytic majorants evaluated as floating numbers; NOT interval bounds", "quadrature_error": "NOT bounded: fixed Gauss-Legendre approximation and replay only", "roundoff_error": "NOT bounded: ordinary mpmath arithmetic", "normalized_lattice_m": "8.010176975354092312144809382423072913229263817477868026640241219842293745134e-461", "normalized_lattice_c": "5.406869458364012310697746333135574216429753076797560917982162823393548277965e-460", "normalized_lattice_dm": "5.567503505328863119948263664304478482091749343821209379511899977397731642888e-457", "normalized_real_tail_m": "2.828374218226205096055257847907468914317364056437735569340708377583980461944e-1745", "normalized_real_tail_c": "5.727774921225974555507858274332239255984494128016947945981145644354739491402e-1744", "normalized_real_tail_dm": "5.344823914870996574028066967375708067877368662471455988705421606608910377924e-1743", "phi_lattice_tail": "7.273374726492211819664183717330581574187460795301261433710403362526810768395e-462", "phi_derivative_lattice_tail": "4.979998157439025504206480866470964305651542498191801154890983034933934923084e-458", "envelope_K0": "126.2492548812490458853717133857003682626103761891939547892692137601525187279", "envelope_K1": "10771.84762176266506630605150363032471166439190050872143542805608408470427621", "envelope_d": "0.4953072397272035138741732699335348050748958555515901363940823957850230615771" } } }, "elapsed_seconds": 0.5666520000086166 }, { "z": { "re": "0.4765625", "im": "0.59375" }, "bits": 256, "replay": true, "purpose": "cell_1_7_step_0", "values": { "m": { "re": "0.2593165616317787174712183172231062549086477729852209917558786467057302955807", "im": "-0.06357931294900568000200385641902776151175680549432533863319024520491857831451" }, "c": { "re": "-0.0009203297233583062525239317326944812817521491327675165581786522723597334110402", "im": "-0.004457754611933045362391141158646310265018221463728138745592859051270896326333" }, "dm": { "re": "-0.1788258998548203736460745478241596049986717260237394169344716138855832640518", "im": "0.3132279117287651358752981690814031760088814407799308053244325627912420164309" } }, "metadata": { "metadata": { "classification": "diagnostic, not a certificate", "bits": 256, "lattice_cutoff": 32, "gauss_legendre_order_per_segment": 96, "positive_half_segments": [ "0.0", "0.125", "0.25", "0.5", "1.0", "2.0", "4.0", "4.5" ], "normalization": "B=exp(2*pi*exp(2*z)-9*z)/(4*pi^4), analytic and nonzero", "derivative": "dm=(B*M)' includes B' contribution", "majorants": { "status": "analytic majorants evaluated as floating numbers; NOT interval bounds", "quadrature_error": "NOT bounded: fixed Gauss-Legendre approximation and replay only", "roundoff_error": "NOT bounded: ordinary mpmath arithmetic", "normalized_lattice_m": "5.658182640523957236932891989086016888399918102876371620642516859682261301262e-548", "normalized_lattice_c": "3.819273282353671134929702092633061399669944719441550843933698880285526378352e-547", "normalized_lattice_dm": "3.924600693271923373419697162830526639100138732681408220384726116988881337317e-544", "normalized_real_tail_m": "8.35305383358051940843396344263939870407905306381969724390748563990383477898e-2070", "normalized_real_tail_c": "1.691572369050895940934777014713978612211948745255609697144282637506406856966e-2068", "normalized_real_tail_dm": "1.237321354516771850718591398818875105013170139021659088543732892621001758541e-2067", "phi_lattice_tail": "5.110376079094360789875474422295703154618336676898510296147802634540412390595e-549", "phi_derivative_lattice_tail": "3.49901722580216895616243515246440807024827414882420258757637387260709959581e-545", "envelope_K0": "70.87311316149443703784637035310491662154555266677058707233581431761345409535", "envelope_K1": "4171.970167435341205168775349782120993961049640453464838267291510038175725116", "envelope_d": "0.5874458303952882333224629443443826173484982088182668184618485628214732475205" } } }, "elapsed_seconds": 0.5637037080014125 }, { "z": { "re": "0.4924858788277277980103217808324627340482857752009607847824485245893683927109", "im": "0.6105305288308627206014858329642470933734738140832391972780051660584790481705" }, "bits": 256, "replay": true, "purpose": "cell_1_7_step_1", "values": { "m": { "re": "0.2542086061686483209857262183173111330370930070430212699673921687000075801096", "im": "-0.05813656163561934536309236400558906586465707983711637184058780107013614971908" }, "c": { "re": "-0.001461750685433165486092172352595339349517362701727685955248271603607310007551", "im": "-0.002815514622660873056234706257677769755411323155896173800096485757705104075432" }, "dm": { "re": "0.2380034630571464568685368941612186572923694992153142821954729868358659269889", "im": "0.2841004433287569205258753506997419666228581705951170977232452082013266937465" } }, "metadata": { "metadata": { "classification": "diagnostic, not a certificate", "bits": 256, "lattice_cutoff": 32, "gauss_legendre_order_per_segment": 96, "positive_half_segments": [ "0.0", "0.125", "0.25", "0.5", "1.0", "2.0", "4.0", "4.5" ], "normalization": "B=exp(2*pi*exp(2*z)-9*z)/(4*pi^4), analytic and nonzero", "derivative": "dm=(B*M)' includes B' contribution", "majorants": { "status": "analytic majorants evaluated as floating numbers; NOT interval bounds", "quadrature_error": "NOT bounded: fixed Gauss-Legendre approximation and replay only", "roundoff_error": "NOT bounded: ordinary mpmath arithmetic", "normalized_lattice_m": "1.759054788535534171453399357102366908460164286106378945610807939854833412567e-501", "normalized_lattice_c": "1.187361982261485565731044566044097663210610893121805788287295359402012553483e-500", "normalized_lattice_dm": "1.222527035527802606842835085323756167574479866053930521247438197637230244658e-497", "normalized_real_tail_m": "1.568170150206800717588741157783183360300633363186338205460196579046398883477e-1896", "normalized_real_tail_c": "3.175706361029777347863494183225293723213962944390852417443538069230333947249e-1895", "normalized_real_tail_dm": "2.733763958854928330855880629455527479002880414871901194182185244892464655293e-1894", "phi_lattice_tail": "1.817679435112509353270357838687878696614274237008348967748329872146076871094e-502", "phi_derivative_lattice_tail": "1.244544737218661716956858997565746112577901094295054677179782654567082101532e-498", "envelope_K0": "94.65843875898982112947583920026109731483334104524623992528594145038621750965", "envelope_K1": "6749.846848797545285595745887586530506933386300287525213674535922930279148082", "envelope_d": "0.5382319704208127277865763676380372923007518143342115096009269750196066283245" } } }, "elapsed_seconds": 0.5847134590148926 }, { "z": { "re": "0.4874823390121451545036626997095388612292968819034232102915736488474955705852", "im": "0.620319847126694588730167884033894289911548219330350700556818374882535823905" }, "bits": 256, "replay": true, "purpose": "cell_1_7_step_2", "values": { "m": { "re": "0.2487797502687029587991329289045571757064664995830565716085463874880346416403", "im": "-0.05691108858353198115388656958012019061239359885321595945540999872304936209943" }, "c": { "re": "-0.002507654812884555617867122111606935003579840936333646670389397427246186436277", "im": "-0.002463915337775299650412829613369294831169065495026328892627548428450959980914" }, "dm": { "re": "0.4173370319076289475289876986940581226014327736795952912919233706155933174523", "im": "0.508787853250398618137093780165908951165150274037637782419153891165768326607" } }, "metadata": { "metadata": { "classification": "diagnostic, not a certificate", "bits": 256, "lattice_cutoff": 32, "gauss_legendre_order_per_segment": 96, "positive_half_segments": [ "0.0", "0.125", "0.25", "0.5", "1.0", "2.0", "4.0", "4.5" ], "normalization": "B=exp(2*pi*exp(2*z)-9*z)/(4*pi^4), analytic and nonzero", "derivative": "dm=(B*M)' includes B' contribution", "majorants": { "status": "analytic majorants evaluated as floating numbers; NOT interval bounds", "quadrature_error": "NOT bounded: fixed Gauss-Legendre approximation and replay only", "roundoff_error": "NOT bounded: ordinary mpmath arithmetic", "normalized_lattice_m": "4.232465417265511730393601313673698571530139196703794918091196213518412649766e-474", "normalized_lattice_c": "2.856914156654220418015680886729746535782843957775061569711557444124928538592e-473", "normalized_lattice_dm": "2.945307813340621256173349248002005966907059704746556871584901870240416339548e-470", "normalized_real_tail_m": "1.897555853148365773388372353288765069285662468590667158744333272538991958904e-1794", "normalized_real_tail_c": "3.842757544001347321008667786633403343681814814467097160854181987078711338255e-1793", "normalized_real_tail_dm": "3.649970030382981658670805930219502330342277609531217783690257795928208412594e-1792", "phi_lattice_tail": "4.834889280420379007615488750376791633254274389808274905337451343008027881707e-475", "phi_derivative_lattice_tail": "3.3103945023230428352731285536632175802890492184780107191439570719598098902e-471", "envelope_K0": "114.5280432992338419066740252171363391130407407229072954004927875211452758775", "envelope_K1": "9207.174749460533771065678139311875206637406316094746548243238176424758876694", "envelope_d": "0.5092383546779326520388399964497159825274172746475652490903022125779087583602" } } }, "elapsed_seconds": 0.5770221250131726 }, { "z": { "re": "0.4861316022797578893311352775247352325264208155297943771609685858766637764472", "im": "0.6230319388784448556348324783782016534327698827416895498688218161699026617974" }, "bits": 256, "replay": true, "purpose": "cell_1_7_step_3", "values": { "m": { "re": "0.2466926308819356266046811035814658106226789411524493896320520381070400126163", "im": "-0.05644050179346383193528145217393426750750237591063386193553446584357964310926" }, "c": { "re": "-0.002860919460161307487713467778152917876151415705879903849697933903989355580997", "im": "-0.0023459380563875590284049467715200895184862321100295749521632306910879348707" }, "dm": { "re": "0.4755304391442813679170677685140333534560768516090265715312919251614305265289", "im": "0.5873469565542490555545615900606145391779296890973280906403449973893800947438" } }, "metadata": { "metadata": { "classification": "diagnostic, not a certificate", "bits": 256, "lattice_cutoff": 32, "gauss_legendre_order_per_segment": 96, "positive_half_segments": [ "0.0", "0.125", "0.25", "0.5", "1.0", "2.0", "4.0", "4.5" ], "normalization": "B=exp(2*pi*exp(2*z)-9*z)/(4*pi^4), analytic and nonzero", "derivative": "dm=(B*M)' includes B' contribution", "majorants": { "status": "analytic majorants evaluated as floating numbers; NOT interval bounds", "quadrature_error": "NOT bounded: fixed Gauss-Legendre approximation and replay only", "roundoff_error": "NOT bounded: ordinary mpmath arithmetic", "normalized_lattice_m": "1.767475480251551503224834522934049274597306312144697825503133088618026848248e-466", "normalized_lattice_c": "1.193045949169797264676763302980483260353181760697671032214614834817168122567e-465", "normalized_lattice_dm": "1.230448411039127326533724923104273456369149473999408810949903583027026840167e-462", "normalized_real_tail_m": "4.85746337051771983974376208729254641782495284656430300959842770080674407566e-1766", "normalized_real_tail_c": "9.836901592414652852384145332209388072466257601878394968906946012355951309925e-1765", "normalized_real_tail_dm": "9.614172516948754484658906733687172733222961655828201760303307125265116890568e-1764", "phi_lattice_tail": "2.067519050111527961376960664069293554607189698462684112208827035254961153182e-467", "phi_derivative_lattice_tail": "1.415607121481439663741173871402793513637126777886833600851027913164643436253e-463", "envelope_K0": "121.1174385041964982442099509610363322696330926329075130223997018372421061837", "envelope_K1": "10076.79421516642177230557546061092641829992004852790908458917684169718761185", "envelope_d": "0.501170782649986862134245395225614198683315793694635632850149901696335277968" } } }, "elapsed_seconds": 0.5756245829979889 }, { "z": { "re": "0.4855559665401836409818469108658818742968680982788746702847837092693809454119", "im": "0.6242065610768863544867394662599014347542733757532309572227154362174768082984" }, "bits": 256, "replay": true, "purpose": "cell_1_7_step_4", "values": { "m": { "re": "0.2457001747565963718467626996719916917749069270779835334128399648458035275741", "im": "-0.0562149342676006793409967200654076261577004368753024812967714800995941335834" }, "c": { "re": "-0.003023148668450491435846349294392864153176222213763161551439854121998516538542", "im": "-0.002291452698970653288442970633758503916517013771836695473504536496214625153062" }, "dm": { "re": "0.502032895156426123310348301959181456676809740102001043651365766929475901213", "im": "0.6237522135077955572241340484755874739785561846215720916933231488230223659093" } }, "metadata": { "metadata": { "classification": "diagnostic, not a certificate", "bits": 256, "lattice_cutoff": 32, "gauss_legendre_order_per_segment": 96, "positive_half_segments": [ "0.0", "0.125", "0.25", "0.5", "1.0", "2.0", "4.0", "4.5" ], "normalization": "B=exp(2*pi*exp(2*z)-9*z)/(4*pi^4), analytic and nonzero", "derivative": "dm=(B*M)' includes B' contribution", "majorants": { "status": "analytic majorants evaluated as floating numbers; NOT interval bounds", "quadrature_error": "NOT bounded: fixed Gauss-Legendre approximation and replay only", "roundoff_error": "NOT bounded: ordinary mpmath arithmetic", "normalized_lattice_m": "3.568925806198540253534870486302467742678222107543172510008619977222092779894e-463", "normalized_lattice_c": "2.409024919184014671136037578254165726307799922591641444255818484624912626429e-462", "normalized_lattice_dm": "2.484992296615626265941049289113154393656477916323084927285619484632267913122e-459", "normalized_real_tail_m": "1.015779030610381063142704383349824838437602582393614953069550064767924498376e-1753", "normalized_real_tail_c": "2.057065889226091167324824718596735254366607291619507118704819533504116337294e-1752", "normalized_real_tail_dm": "2.035893195587613264322045448769517313812531237047512713523610644451926236259e-1751", "phi_lattice_tail": "4.21548474919640894720610988149247491247368094834027574441777941075744810546e-464", "phi_derivative_lattice_tail": "2.886295161893156185484298027897976245023822269892447733423970853836337853892e-460", "envelope_K0": "124.14316709967003768201839183384707247491505489313665433832509736857565764", "envelope_K1": "10484.74459106015983144068903913396245785304789492226457944495227740696633578", "envelope_d": "0.4976720817741328470198777713999648092570644290531617202751856262671980798561" } } }, "elapsed_seconds": 0.5743167920154519 }, { "z": { "re": "0.4852870048374464316837169243551370368987268865058633870002371157170765631872", "im": "0.6247594337145171692330820895290675746733679950686951345063532371247921306593" }, "bits": 256, "replay": true, "purpose": "cell_1_7_step_5", "values": { "m": { "re": "0.2452137173766883737434675127759100480341910948017932590656410136949605246714", "im": "-0.05610398660441843060557301076896679828885532795390780246680632937389002836699" }, "c": { "re": "-0.003101502617559507152743471359717516672533731428592084027055583165132936490252", "im": "-0.002265070692341749904625003896405821992834084810185138426232868640933533431569" }, "dm": { "re": "0.5147873316354692617292541472133142620971432121726004713444774967110772687566", "im": "0.6414049598624878533957529806403781768768451396173150140729810295661250388376" } }, "metadata": { "metadata": { "classification": "diagnostic, not a certificate", "bits": 256, "lattice_cutoff": 32, "gauss_legendre_order_per_segment": 96, "positive_half_segments": [ "0.0", "0.125", "0.25", "0.5", "1.0", "2.0", "4.0", "4.5" ], "normalization": "B=exp(2*pi*exp(2*z)-9*z)/(4*pi^4), analytic and nonzero", "derivative": "dm=(B*M)' includes B' contribution", "majorants": { "status": "analytic majorants evaluated as floating numbers; NOT interval bounds", "quadrature_error": "NOT bounded: fixed Gauss-Legendre approximation and replay only", "roundoff_error": "NOT bounded: ordinary mpmath arithmetic", "normalized_lattice_m": "1.285814814135737032049090724701868112994625612756857774115802169106436340263e-461", "normalized_lattice_c": "8.679249995416224966331362391737609762713722886108789975281664641468445296776e-461", "normalized_lattice_dm": "8.9537099281041535920997443200472650956468067529923800883650697586268896585e-458", "normalized_real_tail_m": "6.44505548474267119567793688980600973432340978159322599618708782075381681524e-1748", "normalized_real_tail_c": "1.30519589587893443146946463517793587058432313056369992056388038350240709454e-1746", "normalized_real_tail_dm": "1.299469280512479941684308407417966848074149878642417997133867673913573985307e-1745", "phi_lattice_tail": "1.525525280129755653529630680930326968840700647012254982207417703030088691528e-462", "phi_derivative_lattice_tail": "1.044510061677621885614188172835329007019872993854074695700223835674294499244e-458", "envelope_K0": "125.6052993887721280231186275702724108653340367270076903102233156927295881828", "envelope_K1": "10683.79129578266945090855651458406096134246270513774663536334246646874462232", "envelope_d": "0.4960243570761784955114043275484324841539732205634016874489313459473103778919" } } }, "elapsed_seconds": 0.5696904999786057 }, { "z": { "re": "0.4852218573360604326100740277678531287745981180137647031825758148436797503615", "im": "0.624893820190192535688368405042634508241362448188452359733753958379029707662" }, "bits": 256, "replay": true, "purpose": "cell_1_7_step_6", "values": { "m": { "re": "0.2450935908642057127548110492507063953196028572516131512422591534096876052566", "im": "-0.05607652325152692313998829816889658196136195152185828212383171244481165509123" }, "c": { "re": "-0.003120740195293442455537787576080661712857400508747157234005853615103179996492", "im": "-0.002258582036815556001132213326741909028999456744540110858166387676739817326384" }, "dm": { "re": "0.5179156284782728206763902716850174983452668740329328124588655370222617156856", "im": "0.645745479940156264014500773911981422762029843688261789361520100834523767517" } }, "metadata": { "metadata": { "classification": "diagnostic, not a certificate", "bits": 256, "lattice_cutoff": 32, "gauss_legendre_order_per_segment": 96, "positive_half_segments": [ "0.0", "0.125", "0.25", "0.5", "1.0", "2.0", "4.0", "4.5" ], "normalization": "B=exp(2*pi*exp(2*z)-9*z)/(4*pi^4), analytic and nonzero", "derivative": "dm=(B*M)' includes B' contribution", "majorants": { "status": "analytic majorants evaluated as floating numbers; NOT interval bounds", "quadrature_error": "NOT bounded: fixed Gauss-Legendre approximation and replay only", "roundoff_error": "NOT bounded: ordinary mpmath arithmetic", "normalized_lattice_m": "3.073563579909100575913201702058601284278769313679921889997490822941882104439e-461", "normalized_lattice_c": "2.074655416438642888741411148889555866888169286733947275748306305485770420497e-460", "normalized_lattice_dm": "2.140305977256712342652011623164054624649306792719983249629904855174382589419e-457", "normalized_real_tail_m": "1.659404984893952892412413864410455221385950517749880401347526593867559601096e-1746", "normalized_real_tail_c": "3.360481035113713504665912391681469626142571257206593792903222854657473009085e-1745", "normalized_real_tail_dm": "3.350590720996104579102637389390638279149161760566302682376347081283633618553e-1744", "phi_lattice_tail": "3.650458684054617718368779382774349027653899035369254455010736046064560050541e-462", "phi_derivative_lattice_tail": "2.499428147732290771629477640622682231384976095569505349420797811714395947319e-458", "envelope_K0": "125.9644584232992256524705440412992686650566892956197020785987657949040200298", "envelope_K1": "10732.87427774795108326557514453710141087958469646830011214283026177113901712", "envelope_d": "0.4956237537566995880604929161349475295544612563762110174834940639786282090066" } } }, "elapsed_seconds": 0.5701005409937352 }, { "z": { "re": "0.4851895320464527041679373154249845369632637373425513686739024013458410236349", "im": "0.6249605578308155044242606014360227023467418799429642719675999598157730730773" }, "bits": 256, "replay": true, "purpose": "cell_1_7_step_7", "values": { "m": { "re": "0.2450336562483023162998124038430463046708848563186558062503395436624595678909", "im": "-0.05606281567825485027640311221471012138226118002721433385063041053541816917522" }, "c": { "re": "-0.003130322376785840581802894289702206979212804872886711765843673627247780719901", "im": "-0.002255349134967784999183305792235377701280795765758392916234079191193873277455" }, "dm": { "re": "0.5194731792497748440918008987926941211908813699793119402971640656414714319607", "im": "0.6479084682981895660619298439808645702884508559401127100616071768026009317145" } }, "metadata": { "metadata": { "classification": "diagnostic, not a certificate", "bits": 256, "lattice_cutoff": 32, "gauss_legendre_order_per_segment": 96, "positive_half_segments": [ "0.0", "0.125", "0.25", "0.5", "1.0", "2.0", "4.0", "4.5" ], "normalization": "B=exp(2*pi*exp(2*z)-9*z)/(4*pi^4), analytic and nonzero", "derivative": "dm=(B*M)' includes B' contribution", "majorants": { "status": "analytic majorants evaluated as floating numbers; NOT interval bounds", "quadrature_error": "NOT bounded: fixed Gauss-Legendre approximation and replay only", "roundoff_error": "NOT bounded: ordinary mpmath arithmetic", "normalized_lattice_m": "4.738101370210770391761948292434639800510029800621932978093933241947384310418e-461", "normalized_lattice_c": "3.198218424892270014439315097393381865344270115419804760213404938314484409532e-460", "normalized_lattice_dm": "3.299457376749831476208197359681819325795971169071123991112509304444240281395e-457", "normalized_real_tail_m": "8.328770141064940465959038187225944407644606055114923862337181214232518457626e-1746", "normalized_real_tail_c": "1.686669317110601715438615408052488020530770366955024291203130549200215620392e-1744", "normalized_real_tail_dm": "1.682917350006226464541867624540733236813790842861329563952718450408198700775e-1743", "phi_lattice_tail": "5.630401903048860297382213747430771831672798972684570075046583601608208110637e-462", "phi_derivative_lattice_tail": "3.855073079171226308826890297190034799895199922015281964706127208845390232763e-458", "envelope_K0": "126.1433718694930706671458700834020830770632579917334431924880289570168822159", "envelope_K1": "10757.35247164608288192912128686225235356540148198750404475192643089882725617", "envelope_d": "0.4954247969160121737429080934946518109115135257183707894935775067148416147778" } } }, "elapsed_seconds": 0.5750722080119886 }, { "z": { "re": "0.4851734306858553849706949822076274895222242454419047848951811461584708992124", "im": "0.6249938142413515597573367606966991323492411324198746080586916781281336543633" }, "bits": 256, "replay": true, "purpose": "cell_1_7_step_8", "values": { "m": { "re": "0.2450037207078909011390667356802198863940155659576122325817143670820197732383", "im": "-0.05605596784235981326041850828620924987972810093621118134477429404112626540213" }, "c": { "re": "-0.003135104428747625476960545080075483062274421711159478613791027821472586165804", "im": "-0.002253735505162825653949775998194661841017089409814624274249152078906058247217" }, "dm": { "re": "0.5202503256925447427793072204690109759006079349606256299766022518621167228131", "im": "0.6489881671543045053137575367500293959696826762056428708920432657494778817395" } }, "metadata": { "metadata": { "classification": "diagnostic, not a certificate", "bits": 256, "lattice_cutoff": 32, "gauss_legendre_order_per_segment": 96, "positive_half_segments": [ "0.0", "0.125", "0.25", "0.5", "1.0", "2.0", "4.0", "4.5" ], "normalization": "B=exp(2*pi*exp(2*z)-9*z)/(4*pi^4), analytic and nonzero", "derivative": "dm=(B*M)' includes B' contribution", "majorants": { "status": "analytic majorants evaluated as floating numbers; NOT interval bounds", "quadrature_error": "NOT bounded: fixed Gauss-Legendre approximation and replay only", "roundoff_error": "NOT bounded: ordinary mpmath arithmetic", "normalized_lattice_m": "5.878575862625002712118809345555866068799991600100060731133245288187461171528e-461", "normalized_lattice_c": "3.968038707271876830680196308250209596439994330067540993514940569526536290782e-460", "normalized_lattice_dm": "4.093667373113758309019101286678875034743760280270560766024341374943491139437e-457", "normalized_real_tail_m": "1.860916840797500101859828361373508640369520915167707918846489327779717029092e-1745", "normalized_real_tail_c": "3.768565248751248040985061644401641844965380641746662980249336280148664687874e-1744", "normalized_real_tail_dm": "3.761532940768904960938646102790035743124824270016523138082850028086411952213e-1743", "phi_lattice_tail": "6.987495011758116799974634921571127918885176383914859184434554932502045822797e-462", "phi_derivative_lattice_tail": "4.784259520814208415343529706720503384636782588602372294585267648350784893786e-458", "envelope_K0": "126.2326642908425437081385759707252128942970646599990225682290132841772427351", "envelope_K1": "10769.57598056432995408298849576928264128978553616681571067771524489014543536", "envelope_d": "0.4953256503140747339276077232332537700577060359636228729677581606488315737751" } } }, "elapsed_seconds": 0.592229750007391 }, { "z": { "re": "0.4851714218205290621528010034155596368980397644770142282967955453995515065141", "im": "0.6249979643127855695696222097051404137220393959055699584742106874546902578414" }, "bits": 256, "replay": true, "purpose": "cell_1_7_step_9", "values": { "m": { "re": "0.2449999818705937723066336459943721434361201323891329419582643691989657182905", "im": "-0.05605511243024914965740477303371984058533605212132864516709262171736872106249" }, "c": { "re": "-0.003135701503157861499210350047878899729671593467752720032381537492938746974128", "im": "-0.002253534007137919793031881327925322634466997885872215319642794849629560242291" }, "dm": { "re": "0.5203473541708008147039635996186886554090028760869241519450321582302779889339", "im": "0.6491229858809660564420196232096830294409839188710189064859337705029217748758" } }, "metadata": { "metadata": { "classification": "diagnostic, not a certificate", "bits": 256, "lattice_cutoff": 32, "gauss_legendre_order_per_segment": 96, "positive_half_segments": [ "0.0", "0.125", "0.25", "0.5", "1.0", "2.0", "4.0", "4.5" ], "normalization": "B=exp(2*pi*exp(2*z)-9*z)/(4*pi^4), analytic and nonzero", "derivative": "dm=(B*M)' includes B' contribution", "majorants": { "status": "analytic majorants evaluated as floating numbers; NOT interval bounds", "quadrature_error": "NOT bounded: fixed Gauss-Legendre approximation and replay only", "roundoff_error": "NOT bounded: ordinary mpmath arithmetic", "normalized_lattice_m": "6.038945281706964858112737158054854892277821106033104784577330198906001604472e-461", "normalized_lattice_c": "4.076288065152201279226097581687027052287529246572345729589697884261551083019e-460", "normalized_lattice_dm": "4.205346640902719715615840205758355289203355378424544668299998659275664334872e-457", "normalized_real_tail_m": "2.057299432175430652584921616679016107834869514919960393005245456857474010407e-1745", "normalized_real_tail_c": "4.16626202048453094061433880846092921131778818185237675360448614770398697112e-1744", "normalized_real_tail_dm": "4.158674012484556041147196230906145044658232066514280563629623247891905903718e-1743", "phi_lattice_tail": "7.178351782903985854745447751712289785352947554972356118933604388486844506771e-462", "phi_derivative_lattice_tail": "4.914937012952658790973316462262937946508987889492285573464923923853459394284e-458", "envelope_K0": "126.2438135090636991610076462290623764887270403158651817649567468199821542594", "envelope_K1": "10771.10255275909980773742789777160693385769864236382556526304333603822108563", "envelope_d": "0.4953132776440062493645626996888238735997711944075632463538266820818442130049" } } }, "elapsed_seconds": 0.580835249973461 }, { "z": { "re": "0.2421875", "im": "0.53125" }, "bits": 256, "replay": true, "purpose": "cell_0_6_step_0", "values": { "m": { "re": "0.269724712480597635946725702430609012094907888158886773742078658777998635579", "im": "0.0111200507975208247447911087889842771952717272965286410608886015131531938777" }, "c": { "re": "-0.001461508269374637741346111434194298516088480344609404154396141050329776228535", "im": "-0.00748679931020343987123500779621583918964191541290984619551112868363535105343" }, "dm": { "re": "0.06357848806221477020002926351426137061790389287740952547378618134831402749335", "im": "0.6154445234178456656063969202275741028570066522902307206662690450756133988681" } }, "metadata": { "metadata": { "classification": "diagnostic, not a certificate", "bits": 256, "lattice_cutoff": 32, "gauss_legendre_order_per_segment": 96, "positive_half_segments": [ "0.0", "0.125", "0.25", "0.5", "1.0", "2.0", "4.0", "4.5" ], "normalization": "B=exp(2*pi*exp(2*z)-9*z)/(4*pi^4), analytic and nonzero", "derivative": "dm=(B*M)' includes B' contribution", "majorants": { "status": "analytic majorants evaluated as floating numbers; NOT interval bounds", "quadrature_error": "NOT bounded: fixed Gauss-Legendre approximation and replay only", "roundoff_error": "NOT bounded: ordinary mpmath arithmetic", "normalized_lattice_m": "1.989770903301720602162076938592359517390528829339403426755716235155699986407e-715", "normalized_lattice_c": "1.343095359728661406459401933549842674238606959804097313060108458730097490825e-714", "normalized_lattice_dm": "1.3726091785643097045260053137474085426624570050125521316464832739380884126e-711", "normalized_real_tail_m": "3.292045558821673356516608386247443342164324703852979657094680639880016676646e-2693", "normalized_real_tail_c": "6.666631402987493320083229201991090826942188310215822175536005063966545697579e-2692", "normalized_real_tail_dm": "2.799456325577135052111972505759484702135990303437943639861448729918202721808e-2691", "phi_lattice_tail": "1.750736517394583844222771985393492895922739468451452844610895243501162033297e-716", "phi_derivative_lattice_tail": "1.198709671733229065519807525723357095490099476499315838805975468246720147881e-712", "envelope_K0": "32.6559405328794159336690793439978139333272935177638307373138610351726096609", "envelope_K1": "1097.147697133796265462724395079954733395596660523133833561779626743912289642", "envelope_d": "0.7644903423152728345853854912753777011399174705335727305545602438564616563638" } } }, "elapsed_seconds": 0.5613874169648625 }, { "z": { "re": "0.2382703803043231220841362510914372655914334533286672844611615890730737342279", "im": "0.5582365915614806165023776804546373979494172297336130821007920279159302428946" }, "bits": 256, "replay": true, "purpose": "cell_0_6_step_1", "values": { "m": { "re": "0.2448799948953459937615917582840741956050318718495877792351300686153997925494", "im": "0.01430292500488733850713020901403024569165090617748386260687366377793094837517" }, "c": { "re": "-0.005885570953555815137689964135458035878982666437510961827567970177512073895009", "im": "-0.006631258211575376230952073026895674259099933681309475308832524835327330077856" }, "dm": { "re": "0.4717596597771038689684562272175317339044449948004163020800298896523234807813", "im": "1.191691694696049806404386879207200547880835692986210821038727358351388557914" } }, "metadata": { "metadata": { "classification": "diagnostic, not a certificate", "bits": 256, "lattice_cutoff": 32, "gauss_legendre_order_per_segment": 96, "positive_half_segments": [ "0.0", "0.125", "0.25", "0.5", "1.0", "2.0", "4.0", "4.5" ], "normalization": "B=exp(2*pi*exp(2*z)-9*z)/(4*pi^4), analytic and nonzero", "derivative": "dm=(B*M)' includes B' contribution", "majorants": { "status": "analytic majorants evaluated as floating numbers; NOT interval bounds", "quadrature_error": "NOT bounded: fixed Gauss-Legendre approximation and replay only", "roundoff_error": "NOT bounded: ordinary mpmath arithmetic", "normalized_lattice_m": "2.081506295068582632956775560333267754486924778747972162129538508672013827727e-644", "normalized_lattice_c": "1.405016749171293277245823503224955734278674225654881209437438493353609333716e-643", "normalized_lattice_dm": "1.437617008347555913721209570171202495438907556887206816710246938574402730096e-640", "normalized_real_tail_m": "1.061126318114905531261966399196559241491351660350145482563895180940357787372e-2428", "normalized_real_tail_c": "2.148866280723912855449486800091624586746585424268982229554687295248517585676e-2427", "normalized_real_tail_dm": "1.074665037623798413023431002322481149601170651903868270471377046229420775804e-2426", "phi_lattice_tail": "2.076870883348704961879392362726633194002604680889397379828284823716205970228e-645", "phi_derivative_lattice_tail": "1.422010216886408465900803096682718883145061021459941888632714089031955012563e-641", "envelope_K0": "43.49567906765148757959436243257225049180991244202973646343809576277914783517", "envelope_K1": "1807.037113700839554886201074702870542583516053077699984941568642334346355174", "envelope_d": "0.6893505960278135045208660431203764997635083838659445486981627971895772886347" } } }, "elapsed_seconds": 0.5697284169727936 }, { "z": { "re": "0.2370094009722908606450388152801390030061937533561228988558630694610177754167", "im": "0.5609481743928088720273426754578870560564979601771878375195265245627833565725" }, "bits": 256, "replay": true, "purpose": "cell_0_6_step_2", "values": { "m": { "re": "0.2409068933262800238976012421592106896200860329301823706018582243060736939047", "im": "0.01407003750907413700730387894110857395532978546586982186356269658643173612845" }, "c": { "re": "-0.006497946421275864149050851777736213593346697444322091237012570324124786014658", "im": "-0.006628843058260874267453195063744610673120219524120171570221124832962755646896" }, "dm": { "re": "0.5076865235079923163568506552840153149116358289666849934609487755300716579069", "im": "1.284192999717776382295062473058492272666292556696425578674288320429455957925" } }, "metadata": { "metadata": { "classification": "diagnostic, not a certificate", "bits": 256, "lattice_cutoff": 32, "gauss_legendre_order_per_segment": 96, "positive_half_segments": [ "0.0", "0.125", "0.25", "0.5", "1.0", "2.0", "4.0", "4.5" ], "normalization": "B=exp(2*pi*exp(2*z)-9*z)/(4*pi^4), analytic and nonzero", "derivative": "dm=(B*M)' includes B' contribution", "majorants": { "status": "analytic majorants evaluated as floating numbers; NOT interval bounds", "quadrature_error": "NOT bounded: fixed Gauss-Legendre approximation and replay only", "roundoff_error": "NOT bounded: ordinary mpmath arithmetic", "normalized_lattice_m": "3.667435950489998773588990420473501145323928285702217599389069142969282282788e-637", "normalized_lattice_c": "2.475519266580749172172568533819613273093651592848996879587621671504265540882e-636", "normalized_lattice_dm": "2.533326641508726021241579245697628944261003547978307611160568882221935789522e-633", "normalized_real_tail_m": "1.02378551910265084743135029006515135120116689520084819062640430584917111804e-2401", "normalized_real_tail_c": "2.07324908184734048875180803079503918196319624548794710800162283021204461525e-2400", "normalized_real_tail_dm": "1.057389673261194182760093325679121428042512344297622643529684618382027106538e-2399", "phi_lattice_tail": "3.692663180604208853016116585815377328623354363080096206023321691740053345573e-638", "phi_derivative_lattice_tail": "2.528325093504527908221008861066912109459674028943255288657853004228066974499e-634", "envelope_K0": "44.92524757356214287902730933719306865903054054937626391521659288367462324417", "envelope_K1": "1911.428185175789495750632046727923215331850231976418549757271716536418484987", "envelope_d": "0.6816859581950021943834283724325143320914109857442976947792178363949823199973" } } }, "elapsed_seconds": 0.5708065840299241 }, { "z": { "re": "0.2364342936808138144135089550404041675627371741867522766113869294082902728578", "im": "0.5621863923888631550115257543275401857053443490037179228902414999516030810392" }, "bits": 256, "replay": true, "purpose": "cell_0_6_step_3", "values": { "m": { "re": "0.2389929482518804418005222877087114627324251494434602324660731750676593719772", "im": "0.01395796797853438131176245277271405711872020418276113896243241823908139468883" }, "c": { "re": "-0.006786779138699055791635729509973023596845466883007628321943112968836076953591", "im": "-0.006625827896401207410323417207913841574949121751969755497453127671218455271342" }, "dm": { "re": "0.524538781225344331533329476003960724728848586972770657790339054540942633299", "im": "1.328017282530609065482826699257733326164486180915176527769991385670201944595" } }, "metadata": { "metadata": { "classification": "diagnostic, not a certificate", "bits": 256, "lattice_cutoff": 32, "gauss_legendre_order_per_segment": 96, "positive_half_segments": [ "0.0", "0.125", "0.25", "0.5", "1.0", "2.0", "4.0", "4.5" ], "normalization": "B=exp(2*pi*exp(2*z)-9*z)/(4*pi^4), analytic and nonzero", "derivative": "dm=(B*M)' includes B' contribution", "majorants": { "status": "analytic majorants evaluated as floating numbers; NOT interval bounds", "quadrature_error": "NOT bounded: fixed Gauss-Legendre approximation and replay only", "roundoff_error": "NOT bounded: ordinary mpmath arithmetic", "normalized_lattice_m": "7.579136717126272130200509399461506268324662694587710000222992794030039289556e-634", "normalized_lattice_c": "5.115917284060233687885343844636516731119147318846704250150520135970276520451e-633", "normalized_lattice_dm": "5.235741099196902223979454001553715487024580059961394503743528652778016905992e-630", "normalized_real_tail_m": "2.270691253606366006322962311953746608947530584539411967377670962300177278596e-2389", "normalized_real_tail_c": "4.598335733558840195360704941247212303171167323527327890026656044894056403448e-2388", "normalized_real_tail_dm": "2.366692636024452260486597373588605010386797367820802946855701384254322396821e-2387", "phi_lattice_tail": "7.660726000301781703629138587707098054882158855456975699398599991418286616515e-635", "phi_derivative_lattice_tail": "5.245213233300191231295330054829277990017549548808891905192883415745220054471e-631", "envelope_K0": "45.60455019861480257964395677240131853935205959504109233660399481274029985432", "envelope_K1": "1961.855485608186759379006551360202203368763615131593669424798052654514702311", "envelope_d": "0.6781792942329000206876494563202322641011125272394224936750637689274266591721" } } }, "elapsed_seconds": 0.5717937919544056 }, { "z": { "re": "0.2362964411153756914566639837122810547716884427736615342986913776244274910186", "im": "0.5624834322621990367183493334845858078742902606422324043978668781423157630567" }, "bits": 256, "replay": true, "purpose": "cell_0_6_step_4", "values": { "m": { "re": "0.2385243016242476549906971611852378446089186878635977967447805277646374554184", "im": "0.01393057845659701904194771596654660048134851056218972903458698474546298326665" }, "c": { "re": "-0.006856929301745812192329594488923603370915513447736760939374142388453793588042", "im": "-0.006624910914894763515978108640329305788640232963280830661817728453207217771032" }, "dm": { "re": "0.5286241333677458106422088175316398610311513396428544655020837590160962487139", "im": "1.338679684156525014300099242811372922510782965143197495840840064161908270129" } }, "metadata": { "metadata": { "classification": "diagnostic, not a certificate", "bits": 256, "lattice_cutoff": 32, "gauss_legendre_order_per_segment": 96, "positive_half_segments": [ "0.0", "0.125", "0.25", "0.5", "1.0", "2.0", "4.0", "4.5" ], "normalization": "B=exp(2*pi*exp(2*z)-9*z)/(4*pi^4), analytic and nonzero", "derivative": "dm=(B*M)' includes B' contribution", "majorants": { "status": "analytic majorants evaluated as floating numbers; NOT interval bounds", "quadrature_error": "NOT bounded: fixed Gauss-Legendre approximation and replay only", "roundoff_error": "NOT bounded: ordinary mpmath arithmetic", "normalized_lattice_m": "4.737234033078110974120566052290910947685654921073768182504694547461770229853e-633", "normalized_lattice_c": "3.197632972327724907531382085296364889687817071724793523190668819536694905151e-632", "normalized_lattice_dm": "3.272581657709928429894675626954193225076026545688902249500858295236224065463e-629", "normalized_real_tail_m": "2.08962698123617263564266590243976568223523438881034765661939049622184962539e-2386", "normalized_real_tail_c": "4.231665967489302844887784427838970001654117126316681679121917680803592624881e-2385", "normalized_real_tail_dm": "2.182771385964718293811109557433087648701849649251149356607349101632871132037e-2384", "phi_lattice_tail": "4.792523310603281191158239579000564269689475246740376289380898024000452256965e-634", "phi_derivative_lattice_tail": "3.281386997614287553464022538574874353305216265420997793850641965248595721046e-630", "envelope_K0": "45.77007500224640487305421831091031288996409463581116555683108343324540149707", "envelope_K1": "1974.222463115926681938019516095333560515660822791055263228316026988509318242", "envelope_d": "0.6773374506169556205373254931021864925269238994389811831872796945445336168286" } } }, "elapsed_seconds": 0.571803958970122 }, { "z": { "re": "0.2362921765269422655058328544434754078768397523588079158552639345909373811404", "im": "0.5624926234106118257584540126273648833128865530934715709361374497870248820185" }, "bits": 256, "replay": true, "purpose": "cell_0_6_step_5", "values": { "m": { "re": "0.2385097414657487439172111057976142143181639150515036819423081512053360997192", "im": "0.01392972807828276461254026543351083548888620863508512304749062193389117298549" }, "c": { "re": "-0.006859105231521328101426295837458130659435913680348434079079076759994430274128", "im": "-0.006624881286635406473365901785555130784473696350276727930457121770683905081361" }, "dm": { "re": "0.5287508124813153547137376203997975257403201621999265255435642600704861864051", "im": "1.339010526692940813847243702821415224599063648536018890276679749531611409415" } }, "metadata": { "metadata": { "classification": "diagnostic, not a certificate", "bits": 256, "lattice_cutoff": 32, "gauss_legendre_order_per_segment": 96, "positive_half_segments": [ "0.0", "0.125", "0.25", "0.5", "1.0", "2.0", "4.0", "4.5" ], "normalization": "B=exp(2*pi*exp(2*z)-9*z)/(4*pi^4), analytic and nonzero", "derivative": "dm=(B*M)' includes B' contribution", "majorants": { "status": "analytic majorants evaluated as floating numbers; NOT interval bounds", "quadrature_error": "NOT bounded: fixed Gauss-Legendre approximation and replay only", "roundoff_error": "NOT bounded: ordinary mpmath arithmetic", "normalized_lattice_m": "5.013670590416670374696013575454490371999870338898908689148698029563816860466e-633", "normalized_lattice_c": "3.384227648531252502919809163431781001099912478756763365175371169955576380815e-632", "normalized_lattice_dm": "3.463551677896164764645264994334655685881836968798888342733574052750012869843e-629", "normalized_real_tail_m": "2.581030083541228777918970033320361956826612954512396881206088292108695723048e-2386", "normalized_real_tail_c": "5.226797548400731798355423802099416067374060985240078680815913798436802911686e-2385", "normalized_real_tail_dm": "2.696262442717204244566796443589893969706096986943589623517800546037810325236e-2384", "phi_lattice_tail": "5.072325992890262959316734379623922164706464551900034535183862946699883024341e-634", "phi_derivative_lattice_tail": "3.472964758232112955744881744287546631924980494393215966037897578480604830678e-630", "envelope_K0": "45.7752127960498740133158993680852521404265386254663236951274279636559577761", "envelope_K1": "1974.606822859311547803574750526899862757030932397080898650202646044121210833", "envelope_d": "0.6773113980787489127256468569836921763104674695053377515878824327492383276931" } } }, "elapsed_seconds": 0.5709507499705069 }, { "z": { "re": "0.2362900448993154898639503668827136939546904990357494041969411126330295617601", "im": "0.5624972175789970306809057076075208011784234230768740957443339569072518136023" }, "bits": 256, "replay": true, "purpose": "cell_0_6_step_6", "values": { "m": { "re": "0.2385024622786738967248440689187489718120786291704048667356559300016181881713", "im": "0.01392930294590765448378008835488315290406585229515768309443939612452679095118" }, "c": { "re": "-0.006860192983719348753210548351378704982768074997616787107806691109162394754728", "im": "-0.006624866449927127457101679368947176507398394046943298976599002767143366517697" }, "dm": { "re": "0.5288141385460673078136525549945202422121075267392845684446117976596778566261", "im": "1.339175918272204354262356411924358815960389964900444201758724931600628481187" } }, "metadata": { "metadata": { "classification": "diagnostic, not a certificate", "bits": 256, "lattice_cutoff": 32, "gauss_legendre_order_per_segment": 96, "positive_half_segments": [ "0.0", "0.125", "0.25", "0.5", "1.0", "2.0", "4.0", "4.5" ], "normalization": "B=exp(2*pi*exp(2*z)-9*z)/(4*pi^4), analytic and nonzero", "derivative": "dm=(B*M)' includes B' contribution", "majorants": { "status": "analytic majorants evaluated as floating numbers; NOT interval bounds", "quadrature_error": "NOT bounded: fixed Gauss-Legendre approximation and replay only", "roundoff_error": "NOT bounded: ordinary mpmath arithmetic", "normalized_lattice_m": "5.157836720621143482565880447576304545778850773555503159921360630964013414665e-633", "normalized_lattice_c": "3.481539786419271850731969302114005568400724272149964632946918425900709054899e-632", "normalized_lattice_dm": "3.563145666827171118962527356025414122724439955164378248836132147211243972291e-629", "normalized_real_tail_m": "2.868411743555542142617010710340811466096533736899954757758616036698894398669e-2386", "normalized_real_tail_c": "5.808768978051408548138216929920370252104386418253751586881766093149803635696e-2385", "normalized_real_tail_dm": "2.996576638989479259170675112842517090052116177825216781014593191830247543409e-2384", "phi_lattice_tail": "5.218250592074820572701529090958352433748149869637952686542630039105007674835e-634", "phi_derivative_lattice_tail": "3.572877695814884613622215092078792621927212143831700955507349161299934969867e-630", "envelope_K0": "45.77778126917556509791724918502076633020420160586604509560118003683510808945", "envelope_K1": "1974.798982214099548979112840754860316047699881178930742314226287687329253233", "envelope_d": "0.6772983757086889875744438809699132893890845782783674156328033059595117406702" } } }, "elapsed_seconds": 0.6093520839931443 }, { "z": { "re": "0.2362889792520612196833525511000661753380650054068179826690345373970462296323", "im": "0.5624995143119251470748562607752670500094818035697699403555996031264552841846" }, "bits": 256, "replay": true, "purpose": "cell_0_6_step_7", "values": { "m": { "re": "0.2384988229080862923767776047491922186091286216666014976055514281217847658293", "im": "0.01392909039391092876379956355053337957130304375248714724652834427982092418261" }, "c": { "re": "-0.006860736806670298599581081812752579443697008005966217326484181195500050365092", "im": "-0.006624859025931073213187478820462732165598517475380652567973418677861630599312" }, "dm": { "re": "0.5288457982070659974935865463976402136276753535165724695798086153559198627883", "im": "1.339258606643008488681157409097215129834594552699505534787318989321930552034" } }, "metadata": { "metadata": { "classification": "diagnostic, not a certificate", "bits": 256, "lattice_cutoff": 32, "gauss_legendre_order_per_segment": 96, "positive_half_segments": [ "0.0", "0.125", "0.25", "0.5", "1.0", "2.0", "4.0", "4.5" ], "normalization": "B=exp(2*pi*exp(2*z)-9*z)/(4*pi^4), analytic and nonzero", "derivative": "dm=(B*M)' includes B' contribution", "majorants": { "status": "analytic majorants evaluated as floating numbers; NOT interval bounds", "quadrature_error": "NOT bounded: fixed Gauss-Legendre approximation and replay only", "roundoff_error": "NOT bounded: ordinary mpmath arithmetic", "normalized_lattice_m": "5.231455865126004029080996922766256057101604308479106846631589646660591845963e-633", "normalized_lattice_c": "3.531232708960052719629672922867222838543582908223397121476323011495899496025e-632", "normalized_lattice_dm": "3.614003837688566058501984890794454662982753084388608987149337992875083394207e-629", "normalized_real_tail_m": "3.023864143974028599199925622470860971050767931751712115160755337660487005036e-2386", "normalized_real_tail_c": "6.123572837706353447339469812571716849238303717662408123468995922437183535749e-2385", "normalized_real_tail_dm": "3.15902871020471214526689518588732709423182841024135363454030505905367827251e-2384", "phi_lattice_tail": "5.292768469872038811512651142331497697668367144542342081217700232233250319021e-634", "phi_derivative_lattice_tail": "3.623899251568741133000836067831635233787895437649958035041050286311830156027e-630", "envelope_K0": "45.77906539984935307145045811140561857968127172694873088335220652779081098219", "envelope_K1": "1974.895056765180941281523491538467544248961370117751960714066643798349331418", "envelope_d": "0.6772918654978948096779686033943367422130234788979349386977224766064522603869" } } }, "elapsed_seconds": 0.5829782919608988 }, { "z": { "re": "0.2421875", "im": "0.46875" }, "bits": 256, "replay": true, "purpose": "cell_0_5_step_0", "values": { "m": { "re": "0.283974866666699953721539920066341595701348078967645840979842142389176983437", "im": "0.02171783649438149406648443563835237472495787626028794651820142792692444505815" }, "c": { "re": "0.004134163141820778135200018668628752816377611364832186497764447896956085727706", "im": "-0.006769714118370617854628711749929391747568583076139653020551585542077879342051" }, "dm": { "re": "-0.2738642325924424993172061620889132334231614140832927527176633748236130868405", "im": "-0.06998674904577959408457706516213513407454030972036451514617696285977677108582" } }, "metadata": { "metadata": { "classification": "diagnostic, not a certificate", "bits": 256, "lattice_cutoff": 32, "gauss_legendre_order_per_segment": 96, "positive_half_segments": [ "0.0", "0.125", "0.25", "0.5", "1.0", "2.0", "4.0", "4.5" ], "normalization": "B=exp(2*pi*exp(2*z)-9*z)/(4*pi^4), analytic and nonzero", "derivative": "dm=(B*M)' includes B' contribution", "majorants": { "status": "analytic majorants evaluated as floating numbers; NOT interval bounds", "quadrature_error": "NOT bounded: fixed Gauss-Legendre approximation and replay only", "roundoff_error": "NOT bounded: ordinary mpmath arithmetic", "normalized_lattice_m": "1.998179967400703313405269936639402238515331504632400108071235288070064551051e-871", "normalized_lattice_c": "1.348771477995474736548557207231596510997848765626870072948083819447293571959e-870", "normalized_lattice_dm": "1.376246585841110658004274512413512691438567900318788448827581055367416766646e-867", "normalized_real_tail_m": "2.608065448459138742905481551053414425143852888439021224764557883536993898009e-3274", "normalized_real_tail_c": "5.281488340682477423892136001344721210580434707510149704732943346014515604658e-3273", "normalized_real_tail_dm": "1.682183651936201721521282143320403007216074178790827898097363822763153912279e-3272", "phi_lattice_tail": "1.153808235699151991157433992168784832099641295202035183678288901819201734671e-872", "phi_derivative_lattice_tail": "7.899995674485069340059414204261435843603809724163516398706868943729632692899e-869", "envelope_K0": "20.09147886648630271699286246722096702229643673055718000194078700199844721032", "envelope_K1": "479.9159982320092468494705336215333635799299221487881014660433457954128937652", "envelope_d": "0.9296052381338416292553108344643359577600314920394590424184296278423895717403" } } }, "elapsed_seconds": 0.5728242499753833 }, { "z": { "re": "0.3042109316056653194228524951810813589120902548365269474651320381980166428007", "im": "0.4578560854000426319308844019334784422122227047239406590125377278681087418413" }, "bits": 256, "replay": true, "purpose": "cell_0_5_step_1", "values": { "m": { "re": "0.2739268114351354293638380314268542589980883907757106433477247437822033672962", "im": "0.01435751489297728312233716222235226926530821648867200354641327688459176319144" }, "c": { "re": "0.003525522976338262561942473353096502159083422052151024645668956254400920178099", "im": "-0.00435202872141496801348116531927350866572470902839884128030064938772410330666" }, "dm": { "re": "-0.06696884395402039235153722297432396021912825285150912548740907067370080987582", "im": "-0.2197017104728302604937769918725867303745714840614333032202608559957446164061" } }, "metadata": { "metadata": { "classification": "diagnostic, not a certificate", "bits": 256, "lattice_cutoff": 32, "gauss_legendre_order_per_segment": 96, "positive_half_segments": [ "0.0", "0.125", "0.25", "0.5", "1.0", "2.0", "4.0", "4.5" ], "normalization": "B=exp(2*pi*exp(2*z)-9*z)/(4*pi^4), analytic and nonzero", "derivative": "dm=(B*M)' includes B' contribution", "majorants": { "status": "analytic majorants evaluated as floating numbers; NOT interval bounds", "quadrature_error": "NOT bounded: fixed Gauss-Legendre approximation and replay only", "roundoff_error": "NOT bounded: ordinary mpmath arithmetic", "normalized_lattice_m": "3.687521968055411472582748077901620392342173374081983433229751010417408225133e-897", "normalized_lattice_c": "2.489077328437402743993354952583593764830967027505338817430081932031750551965e-896", "normalized_lattice_dm": "2.540251136468557376653576622822429117434508138534303337900836404326593249627e-893", "normalized_real_tail_m": "1.725748256477573846175183408351900698599335881135596535583389447157432345188e-3370", "normalized_real_tail_c": "3.494740368582174272228514385573791451773213369845340283262655734961733547315e-3369", "normalized_real_tail_dm": "1.11786896077078550533160792676452735178273208183977076068168137662256190613e-3368", "phi_lattice_tail": "1.506780082640830379380083030501813779953273760676237939896123586780837760241e-898", "phi_derivative_lattice_tail": "1.031675435047474415603833416562531047432982272876220831708168073924371092618e-894", "envelope_K0": "18.79205802054876474933409402798756480944520623362971249828834627030018772755", "envelope_K1": "430.1167763955454229629202791644041022985187089970688528362420441756775299808", "envelope_d": "0.9569699330007469728335895494634102625848057283818570803192470575583278406343" } } }, "elapsed_seconds": 0.5799362499965355 }, { "z": { "re": "0.3105786560661151277716904397349854479271381725576965407413276369972745376694", "im": "0.4403156335089477800331599700632719588701403974520746129292907490397485681401" }, "bits": 256, "replay": true, "purpose": "cell_0_5_step_2", "values": { "m": { "re": "0.2693680464707416497846487717888322759269853450038543686618620430657457667887", "im": "0.0142632801828007734137639868121475300971513450913008735407690250461908646294" }, "c": { "re": "0.00378829679048357431985146413141197616221109613185704435646535331324487247708", "im": "-0.004093154460974597714530292605229618168975310010823371469949673379424379453677" }, "dm": { "re": "-0.0874579196230805916699551249980928063349913963427884258077698220415412236078", "im": "-0.2411522071892916171311356650998148747515849957914776182291997511996450880768" } }, "metadata": { "metadata": { "classification": "diagnostic, not a certificate", "bits": 256, "lattice_cutoff": 32, "gauss_legendre_order_per_segment": 96, "positive_half_segments": [ "0.0", "0.125", "0.25", "0.5", "1.0", "2.0", "4.0", "4.5" ], "normalization": "B=exp(2*pi*exp(2*z)-9*z)/(4*pi^4), analytic and nonzero", "derivative": "dm=(B*M)' includes B' contribution", "majorants": { "status": "analytic majorants evaluated as floating numbers; NOT interval bounds", "quadrature_error": "NOT bounded: fixed Gauss-Legendre approximation and replay only", "roundoff_error": "NOT bounded: ordinary mpmath arithmetic", "normalized_lattice_m": "7.765265830628712671598150270218910573834988939410674387618201097393126253256e-938", "normalized_lattice_c": "5.241554435674381053328751432397764637338617534102205211642285740740360220948e-937", "normalized_lattice_dm": "5.348243581018958736819003825966956684955689113284013215897738856133549834355e-934", "normalized_real_tail_m": "4.071828057300625338080934514470133627461850226521999001667410504408095617684e-3522", "normalized_real_tail_c": "8.245677929833002096524155709803754459574535332843444462166903484661334154944e-3521", "normalized_real_tail_dm": "2.526066918367415999039000946877051894089918883176449031661341216620091852472e-3520", "phi_lattice_tail": "2.569061433515877618042518543683312632242055056773687800148556802584992638184e-939", "phi_derivative_lattice_tail": "1.759007570262636258171249666209124652776855739518594439580534393465595107447e-935", "envelope_K0": "17.0130398498437086883935414776604099710850278240272629450318119300850062889", "envelope_K1": "366.3384802009398772533544662808289477659678323881098196271767422399432525686", "envelope_d": "1.000070219116426227516355786534438478379199989125076995317678662207966648426" } } }, "elapsed_seconds": 0.5775066660135053 }, { "z": { "re": "0.3113799908069517890157720562932557520283576542995464550338593879270235112212", "im": "0.4384246021071495951345992902704757057885237525445834057663584763170709877988" }, "bits": 256, "replay": true, "purpose": "cell_0_5_step_3", "values": { "m": { "re": "0.2688397316585677543826274502206003150874619846544411490383255986250498818992", "im": "0.01423587947284761507734373507995660293133689942027713026770070485993435762725" }, "c": { "re": "0.003808813135984932417495071532393514054761118097338474116211736568461990664137", "im": "-0.004061223659334269950710422457734100349977503096979595644572568353012009158767" }, "dm": { "re": "-0.08868147392510763712112211774287701354387593785559165524500477467849546462943", "im": "-0.2429342431299722429977363217375518927593085002965185134165789268185345527641" } }, "metadata": { "metadata": { "classification": "diagnostic, not a certificate", "bits": 256, "lattice_cutoff": 32, "gauss_legendre_order_per_segment": 96, "positive_half_segments": [ "0.0", "0.125", "0.25", "0.5", "1.0", "2.0", "4.0", "4.5" ], "normalization": "B=exp(2*pi*exp(2*z)-9*z)/(4*pi^4), analytic and nonzero", "derivative": "dm=(B*M)' includes B' contribution", "majorants": { "status": "analytic majorants evaluated as floating numbers; NOT interval bounds", "quadrature_error": "NOT bounded: fixed Gauss-Legendre approximation and replay only", "roundoff_error": "NOT bounded: ordinary mpmath arithmetic", "normalized_lattice_m": "3.750049542416439546020941681729174300216274872969338388787570785105475694522e-942", "normalized_lattice_c": "2.531283441131096693564135635167192652645985539254303412431610279946196093803e-941", "normalized_lattice_dm": "2.582758493715915963704141995576480416240721192033134908885807066148965810074e-938", "normalized_real_tail_m": "3.304606400363315573467232971851974051062519808601231399503836706048612212143e-3538", "normalized_real_tail_c": "6.692010634224931930685090423092599237357391670711476740009242790193268723709e-3537", "normalized_real_tail_dm": "2.041569303345715411660396225694292773396381567397961511069868011650230771229e-3536", "phi_lattice_tail": "1.211134624093675390385633970331799355311614411459732018404349734208652737246e-943", "phi_derivative_lattice_tail": "8.292503030853663496290265476226956941916207602189263316234506363975067314617e-940", "envelope_K0": "16.84090739010239746260815836852705948610215982661645523026105336957980566451", "envelope_K1": "360.4363304174904326110585800862961530121730328492539240353890237276947173289", "envelope_d": "1.004644288619233811644401913022873049472273913648894225414271422604885055919" } } }, "elapsed_seconds": 0.5884777500177734 }, { "z": { "re": "0.3115792961033255859495874748232023689765761730218617451786708398874739549524", "im": "0.4379570076201936042924648063062987877713308029870688141350205063713141902199" }, "bits": 256, "replay": true, "purpose": "cell_0_5_step_4", "values": { "m": { "re": "0.2687083353230246765725369272751942351473754692884632938097945044799501064672", "im": "0.0142289519174512557535232044873628039049709408629769175510998295400972267806" }, "c": { "re": "0.003813686968127512860714180341720745160279335793966434622775501399165926063078", "im": "-0.00405327915046554736308081709176140266245583807193709231483813218570844167378" }, "dm": { "re": "-0.08896113977162187418682165016214482770863790420988381990155849896762537130596", "im": "-0.2433560583474691848181250386299156132277776732128025104765379521834195213501" } }, "metadata": { "metadata": { "classification": "diagnostic, not a certificate", "bits": 256, "lattice_cutoff": 32, "gauss_legendre_order_per_segment": 96, "positive_half_segments": [ "0.0", "0.125", "0.25", "0.5", "1.0", "2.0", "4.0", "4.5" ], "normalization": "B=exp(2*pi*exp(2*z)-9*z)/(4*pi^4), analytic and nonzero", "derivative": "dm=(B*M)' includes B' contribution", "majorants": { "status": "analytic majorants evaluated as floating numbers; NOT interval bounds", "quadrature_error": "NOT bounded: fixed Gauss-Legendre approximation and replay only", "roundoff_error": "NOT bounded: ordinary mpmath arithmetic", "normalized_lattice_m": "3.227736395182109961045798787065556503163946933967504594194767761109305467666e-943", "normalized_lattice_c": "2.178722066747924223705914181269250639635664180428065601081468238748781190675e-942", "normalized_lattice_dm": "2.223017549198045343267912878122586038212997883838907113506712790589549699527e-939", "normalized_real_tail_m": "3.533434012601192435780783916764633702510280150018598976442663277920258055478e-3542", "normalized_real_tail_c": "7.155398979019673521612649248840029511896658853280916190775264264724640633257e-3541", "normalized_real_tail_dm": "2.180714767529576115396465214912987166337968913206769407150204884211063583894e-3540", "phi_lattice_tail": "1.036225136362711354005674561505402844554200165675964991585019530172326499531e-944", "phi_derivative_lattice_tail": "7.094917371687588299359904413350834007656737888658584958316903371827570020976e-941", "envelope_K0": "16.79887703213801249841271983844826825974332777415887010139219325728174574644", "envelope_K1": "359.0023498439616519213824056775240448259985403282880316386921988339264093368", "envelope_d": "1.005773103259166823011394806621052581788175983159680242048451249032236656465" } } }, "elapsed_seconds": 0.5834484589868225 }, { "z": { "re": "0.3116788171448765118779939511632063358878197869550861531948539545615341673006", "im": "0.4377238138545392647400299243783586122916128741474866658185937193358742384886" }, "bits": 256, "replay": true, "purpose": "cell_0_5_step_5", "values": { "m": { "re": "0.2686427016685938975073767479843644907353567478236364028415315317617715120944", "im": "0.01422548362808668976783845547857433109020704877555132029225067921782222622096" }, "c": { "re": "0.003816088968425368118948953218135037782437663920495997102978370327710862617994", "im": "-0.004049310982175244813421931225843471710489166305649468851733479764301996023749" }, "dm": { "re": "-0.08909732772777429884141266307206408363920725364475441844932478973739354776425", "im": "-0.2435636255420433846280417998548156355823341678278707041380468404000291911032" } }, "metadata": { "metadata": { "classification": "diagnostic, not a certificate", "bits": 256, "lattice_cutoff": 32, "gauss_legendre_order_per_segment": 96, "positive_half_segments": [ "0.0", "0.125", "0.25", "0.5", "1.0", "2.0", "4.0", "4.5" ], "normalization": "B=exp(2*pi*exp(2*z)-9*z)/(4*pi^4), analytic and nonzero", "derivative": "dm=(B*M)' includes B' contribution", "majorants": { "status": "analytic majorants evaluated as floating numbers; NOT interval bounds", "quadrature_error": "NOT bounded: fixed Gauss-Legendre approximation and replay only", "roundoff_error": "NOT bounded: ordinary mpmath arithmetic", "normalized_lattice_m": "9.506394389911583230759257814032067786438312911605685685466335941496405823975e-944", "normalized_lattice_c": "6.416816213190318680762499024471645755845861215333837837689776760510073931183e-943", "normalized_lattice_dm": "6.547261483881390444347518143589364956386760986579435191578622382168931469543e-940", "normalized_real_tail_m": "3.706977851967607230114177835886172731296362438404956006724079220530492792324e-3544", "normalized_real_tail_c": "7.50683472176522590345096522757047113886545225214057217060601727455550429264e-3543", "normalized_real_tail_dm": "2.286661884513938615975489881952939099830498671799419654424564632641364386787e-3542", "phi_lattice_tail": "3.042803307790392652279633690279520479071626949918792307073696546435334273013e-945", "phi_derivative_lattice_tail": "2.083373322022356425636786735480023001097409971007693778087577252067902824643e-941", "envelope_K0": "16.77799403730522937889127303544193529136005016117754179842995736489347600744", "envelope_K1": "358.2909157735708334716538738780785830875702387482366074073267415246862635742", "envelope_d": "1.006335725065909517927749424670411405403718780508288199383811308835761042572" } } }, "elapsed_seconds": 0.585355166986119 }, { "z": { "re": "0.3117285445832653140609110051203824968678877602592411683503248515636574297177", "im": "0.4376073649529217947302979599730409586438770841640287034183986657587424538606" }, "bits": 256, "replay": true, "purpose": "cell_0_5_step_6", "values": { "m": { "re": "0.2686099006978504375604072413526241585258955680503287917897907133323158546413", "im": "0.01422374847456117125269770254422444771254186579040109978726554811444066850799" }, "c": { "re": "0.003817281358336290364379451529383280206395308761162406274243642386393551252026", "im": "-0.004047327926754788866285898351755759203375739034309829241811501516603233726896" }, "dm": { "re": "-0.089164523898138904984937329595324613317328480819455042655075619917043113109", "im": "-0.2436665826912843456223149840039237659657200619892852887416019197393913406212" } }, "metadata": { "metadata": { "classification": "diagnostic, not a certificate", "bits": 256, "lattice_cutoff": 32, "gauss_legendre_order_per_segment": 96, "positive_half_segments": [ "0.0", "0.125", "0.25", "0.5", "1.0", "2.0", "4.0", "4.5" ], "normalization": "B=exp(2*pi*exp(2*z)-9*z)/(4*pi^4), analytic and nonzero", "derivative": "dm=(B*M)' includes B' contribution", "majorants": { "status": "analytic majorants evaluated as floating numbers; NOT interval bounds", "quadrature_error": "NOT bounded: fixed Gauss-Legendre approximation and replay only", "roundoff_error": "NOT bounded: ordinary mpmath arithmetic", "normalized_lattice_m": "5.164039144002999833918278947949609141013356858958238834956296830441371743924e-944", "normalized_lattice_c": "3.485726422202024887894838289865986170184015879796811213595500360547925927149e-943", "normalized_lattice_dm": "3.556582594393867771012294548101093722440689650088140654185461868477351623606e-940", "normalized_real_tail_m": "3.81045223569987540430918650822982574823444849847591675429445179565475494383e-3545", "normalized_real_tail_c": "7.716376000436753532805964179748982169996348147695398466609433446868988796961e-3544", "normalized_real_tail_dm": "2.349897146315475464248244349356448046576674812392176158107128639258608416924e-3543", "phi_lattice_tail": "1.65043709924106987146804014948024748531740739795623544847922724054874397891e-945", "phi_derivative_lattice_tail": "1.130035784249145129034225506488306874588202543376109432437865015835893829546e-941", "envelope_K0": "16.76758513270778453960287128459153168153975054242588368492186569901875510813", "envelope_K1": "357.9365684582835361855860450464872528706292887460654557770164843022685274553", "envelope_d": "1.006616596998768449650487202841318213103405190690621547790959580029859134939" } } }, "elapsed_seconds": 0.5849755420349538 }, { "z": { "re": "0.3117534000108958836769427403701295906731303895803141942843578005530601089058", "im": "0.4375491771426286229873336140641328506269319009079430517884462673559392312125" }, "bits": 256, "replay": true, "purpose": "cell_0_5_step_7", "values": { "m": { "re": "0.2685935041432292054840437022974650905626734050939409931065836372851059235438", "im": "0.01422288066005223124274021047238112769970597356312171040311504445117113257585" }, "c": { "re": "0.003817875415318432624727895383470994246906883419849716574136216120069723406481", "im": "-0.004046336657058649678712865137029847038913948443983473592428918593852917566806" }, "dm": { "re": "-0.08919789917830497045023647042524241393838039925636972992507809061412261890409", "im": "-0.2437178557234888542083238873987627128283359960068985210920859493916346594321" } }, "metadata": { "metadata": { "classification": "diagnostic, not a certificate", "bits": 256, "lattice_cutoff": 32, "gauss_legendre_order_per_segment": 96, "positive_half_segments": [ "0.0", "0.125", "0.25", "0.5", "1.0", "2.0", "4.0", "4.5" ], "normalization": "B=exp(2*pi*exp(2*z)-9*z)/(4*pi^4), analytic and nonzero", "derivative": "dm=(B*M)' includes B' contribution", "majorants": { "status": "analytic majorants evaluated as floating numbers; NOT interval bounds", "quadrature_error": "NOT bounded: fixed Gauss-Legendre approximation and replay only", "roundoff_error": "NOT bounded: ordinary mpmath arithmetic", "normalized_lattice_m": "3.806967933498781410276840460657082706295814203456459436903002077822161277354e-944", "normalized_lattice_c": "2.569703355111677451936867310943530826749674587333110119909526402529958862214e-943", "normalized_lattice_dm": "2.621937588664211977701031889422749616656220385973119325051857248871486152097e-940", "normalized_real_tail_m": "1.222750484304747054938280667590599768022141883970129494247971641358574082201e-3545", "normalized_real_tail_c": "2.476137180617101514866071842024686831973800185189581331385584408088646884737e-3544", "normalized_real_tail_dm": "7.539723892961605166932019300101882711297975889876565169249733703476570599619e-3544", "phi_lattice_tail": "1.215806527097383238613912169224187282298818084395233479614038263502603761727e-945", "phi_derivative_lattice_tail": "8.324491027107253532936383263417182861948621129125292759247495621838462458647e-942", "envelope_K0": "16.76238877297592350568242099513888966411367354219429539299931966629030955487", "envelope_K1": "357.7597348573987454549528323974449420093971347846732701079829015750304427371", "envelope_d": "1.006756924132185122853460751360248998826398544020509317337434274481198271493" } } }, "elapsed_seconds": 0.572919791971799 }, { "z": { "re": "0.3117658256492968661843608122951838991102977094943900146182014361467292721218", "im": "0.4375200923536450703644608123403045301600628145476101252648398018616177362055" }, "bits": 256, "replay": true, "purpose": "cell_0_5_step_8", "values": { "m": { "re": "0.2685853068444730122190619527369311035097070448792560840284227254534703183086", "im": "0.01422244669514384153408861550433465578020949157009456405397133982779518286297" }, "c": { "re": "0.003818171911124001987858811470740039228978530392156231901357153442639807175094", "im": "-0.004045841086814261332194930743871912726075027658920445874922134468518303408949" }, "dm": { "re": "-0.08921453132102036431244833438298103025383429291555563339678117680714293454623", "im": "-0.243743440986921887064782490438603981189318943903899885083911203428809758897" } }, "metadata": { "metadata": { "classification": "diagnostic, not a certificate", "bits": 256, "lattice_cutoff": 32, "gauss_legendre_order_per_segment": 96, "positive_half_segments": [ "0.0", "0.125", "0.25", "0.5", "1.0", "2.0", "4.0", "4.5" ], "normalization": "B=exp(2*pi*exp(2*z)-9*z)/(4*pi^4), analytic and nonzero", "derivative": "dm=(B*M)' includes B' contribution", "majorants": { "status": "analytic majorants evaluated as floating numbers; NOT interval bounds", "quadrature_error": "NOT bounded: fixed Gauss-Legendre approximation and replay only", "roundoff_error": "NOT bounded: ordinary mpmath arithmetic", "normalized_lattice_m": "3.268885207722050923853858424121584560916503191709659420754016109436196314706e-944", "normalized_lattice_c": "2.206497515212384373601354436282069578618639654404020109008960873869432512426e-943", "normalized_lattice_dm": "2.251348254508198194658658429786534891058802253949025590408084087735343260507e-940", "normalized_real_tail_m": "6.928095596861946117695765778503612551049108020880443893544243874422649169101e-3546", "normalized_real_tail_c": "1.402977572767906449630446153322545360913927323807293209459229609514244192231e-3544", "normalized_real_tail_dm": "4.271733239181506120957228019617122194109989081424770607089803090636930062823e-3544", "phi_lattice_tail": "1.043573029992669914304766078479451624614581311380361214080454976052759550671e-945", "phi_derivative_lattice_tail": "7.145227575842158700450686191824243727987871451443554114813236616933961936823e-942", "envelope_K0": "16.7597926093591022681042682843747597234099940338660973299456322152444658204", "envelope_K1": "357.6714027771608498735521128935888958734466952520668735267659152939082418006", "envelope_d": "1.006827060603339997240418335582921903883233179083282221416055029798018604877" } } }, "elapsed_seconds": 0.5712064589606598 }, { "z": { "re": "0.311772037949334341781909404299795391217921851069400598274038658247870136475", "im": "0.4375055522327219893374293715806489603059600767468189913065627176916393593295" }, "bits": 256, "replay": true, "purpose": "cell_0_5_step_9", "values": { "m": { "re": "0.2685812084392192070367024635134952744718672758330110680413337088685327893962", "im": "0.01422222969849742745052479251928289696672602632976804226591054580602847781049" }, "c": { "re": "0.003818320026080433734962608201816779460799379421465590419237313657313184888669", "im": "-0.004045593317855264653880241104642972256002443411153161046720601169445549559026" }, "dm": { "re": "-0.08922283354339970478021223329256364533270072199934229813680071695018259141497", "im": "-0.2437562208220403631435220414006078550304009221358303550689135871020920993371" } }, "metadata": { "metadata": { "classification": "diagnostic, not a certificate", "bits": 256, "lattice_cutoff": 32, "gauss_legendre_order_per_segment": 96, "positive_half_segments": [ "0.0", "0.125", "0.25", "0.5", "1.0", "2.0", "4.0", "4.5" ], "normalization": "B=exp(2*pi*exp(2*z)-9*z)/(4*pi^4), analytic and nonzero", "derivative": "dm=(B*M)' includes B' contribution", "majorants": { "status": "analytic majorants evaluated as floating numbers; NOT interval bounds", "quadrature_error": "NOT bounded: fixed Gauss-Legendre approximation and replay only", "roundoff_error": "NOT bounded: ordinary mpmath arithmetic", "normalized_lattice_m": "3.029118639336333780212354501578763904771789948337324768623522184962491798975e-944", "normalized_lattice_c": "2.044655081552025301643339288565665635720958215127694218820877474849681964308e-943", "normalized_lattice_dm": "2.086215813266272963599325179053876337175283278034443309263913001813869194201e-940", "normalized_real_tail_m": "5.215256562020952822199607094930177046017479132663963530276452055748528578084e-3546", "normalized_real_tail_c": "1.056118219431045195094233634416396377656678789151537657701273987250110344433e-3544", "normalized_real_tail_dm": "3.215527755388779049400736238506870865408220657286191448169514274891077557083e-3544", "phi_lattice_tail": "9.668485024315516543729351451933772910895142596853698295286408702407495304973e-946", "phi_derivative_lattice_tail": "6.619903334684820062799263524195967568453333077130561488370770814423777087211e-942", "envelope_K0": "16.75849503075523727939509627319001396789447037356131252371512192091490976134", "envelope_K1": "357.6272578805098800372820405573579721803672157671081907399443467458496851584", "envelope_d": "1.006862122079054519691405883662508250621262585512181486716053309486018806617" } } }, "elapsed_seconds": 0.5725289999973029 } ], "all_cells": [ { "i": 0, "j": 0, "sampled_winding": "6.5772329241784788113771413707924794895e-41", "rounded_winding": 0, "corner_ratio": "0.78853332067824912550014555490921398529", "m_scale": "0.21145279596299382021497632368476542076", "c_scale": "0.00474475228589292592538526416070992913", "winding_unresolved": false }, { "i": 0, "j": 1, "sampled_winding": "1.2606363104675417721806187627352252355e-40", "rounded_winding": 0, "corner_ratio": "0.82684957838837956836299018734699887932", "m_scale": "0.22186457057686522214967320405994332892", "c_scale": "0.0058548909562062062011020745068405402655", "winding_unresolved": false }, { "i": 0, "j": 2, "sampled_winding": "4.384821949452319207584760913861652993e-41", "rounded_winding": 0, "corner_ratio": "0.8560010879623426605512962380512133123", "m_scale": "0.24364516703571729151752873533702256283", "c_scale": "0.0076688254791845566831493305962490335247", "winding_unresolved": false }, { "i": 0, "j": 3, "sampled_winding": "1.3154465848356957622754282741584958979e-40", "rounded_winding": 0, "corner_ratio": "0.80805634845100122508858799248872312131", "m_scale": "0.29020964124996359594029838770911106386", "c_scale": "0.010695357612201237123472321150379442716", "winding_unresolved": false }, { "i": 0, "j": 4, "sampled_winding": "2.1924109747261596037923804569308264965e-40", "rounded_winding": 0, "corner_ratio": "0.71372849690105447620265108296656509164", "m_scale": "0.3484805565491223666551342101904642492", "c_scale": "0.016054899522175089312802822241677377868", "winding_unresolved": false }, { "i": 0, "j": 5, "sampled_winding": "1.0231251215388744817697775465677190317e-40", "rounded_winding": 0, "corner_ratio": "0.63725313393568587041863517134941325659", "m_scale": "0.41472982711030505309050612037852721725", "c_scale": "0.026656312276944997136524664350642936495", "winding_unresolved": false }, { "i": 0, "j": 6, "sampled_winding": "-4.384821949452319207584760913861652993e-41", "rounded_winding": 0, "corner_ratio": "0.58795676604066541479253265032922155138", "m_scale": "0.48319511432902079130588590022688640197", "c_scale": "0.050876437364814437493857774812792119476", "winding_unresolved": false }, { "i": 0, "j": 7, "sampled_winding": "-4.0925004861554979270791101862708761268e-40", "rounded_winding": 0, "corner_ratio": "0.53310094920153785039684178172002840202", "m_scale": "0.60828670295972911642551373684317772015", "c_scale": "0.109409126196452569602506367391405789", "winding_unresolved": false }, { "i": 1, "j": 0, "sampled_winding": "3.6540182912102660063206340948847108275e-41", "rounded_winding": 0, "corner_ratio": "0.95194413474328827556810876841130305781", "m_scale": "0.21145279596299382021497632368476542076", "c_scale": "0.0038392944128148231693051560576466194075", "winding_unresolved": false }, { "i": 1, "j": 1, "sampled_winding": "-9.1350457280256650158015852372117770687e-42", "rounded_winding": 0, "corner_ratio": "0.92296375473186385300910036397151543161", "m_scale": "0.22186457057686522214967320405994332892", "c_scale": "0.0041145394601384971141475843042472305372", "winding_unresolved": false }, { "i": 1, "j": 2, "sampled_winding": "1.461607316484106402528253637953884331e-41", "rounded_winding": 0, "corner_ratio": "0.89350346552478856874348196150930424286", "m_scale": "0.23450574299372064220471834369619877905", "c_scale": "0.0044340046238660281715119085045868634263", "winding_unresolved": false }, { "i": 1, "j": 3, "sampled_winding": "5.846429265936425610113014551815537324e-41", "rounded_winding": 0, "corner_ratio": "0.86628093980416982510676727191085656303", "m_scale": "0.24872050382504802222090727504118072542", "c_scale": "0.0047395033590023131829692256621332204765", "winding_unresolved": false }, { "i": 1, "j": 4, "sampled_winding": "-8.7696438989046384151695218277233059859e-41", "rounded_winding": 0, "corner_ratio": "0.84164722871005189174230313526909979574", "m_scale": "0.26428788206264707093593221956931311436", "c_scale": "0.0049327494299087644577655188133127295344", "winding_unresolved": false }, { "i": 1, "j": 5, "sampled_winding": "-1.3154465848356957622754282741584958979e-40", "rounded_winding": 0, "corner_ratio": "0.81067150032427249580002685708480783227", "m_scale": "0.28409783678754065415288445794077031072", "c_scale": "0.0049993330777706144449263535184695222287", "winding_unresolved": false }, { "i": 1, "j": 6, "sampled_winding": "4.384821949452319207584760913861652993e-41", "rounded_winding": 0, "corner_ratio": "0.73696010915997215744670922438307734132", "m_scale": "0.324278218734505495288858882629572607", "c_scale": "0.0064705811807290547600650464759401966607", "winding_unresolved": false }, { "i": 1, "j": 7, "sampled_winding": "0.0", "rounded_winding": 0, "corner_ratio": "0.54306820794881006012433779799600160623", "m_scale": "0.45855394841007548341583114652923333612", "c_scale": "0.021451241356443265241381645076779195894", "winding_unresolved": false }, { "i": 2, "j": 0, "sampled_winding": "-1.461607316484106402528253637953884331e-41", "rounded_winding": 0, "corner_ratio": "0.88149726268295151178730121506075813413", "m_scale": "0.20477295710159613045590039278116755667", "c_scale": "0.0024023264993690119824616809982085115599", "winding_unresolved": false }, { "i": 2, "j": 1, "sampled_winding": "-1.461607316484106402528253637953884331e-41", "rounded_winding": 0, "corner_ratio": "0.86935833873061286940492580482766503525", "m_scale": "0.20953169405035480027974255804243722248", "c_scale": "0.002472547499323624209749965346600027801", "winding_unresolved": false }, { "i": 2, "j": 2, "sampled_winding": "0.0", "rounded_winding": 0, "corner_ratio": "0.85595261654387314135885559238250152493", "m_scale": "0.21546183180212921647107632796228255925", "c_scale": "0.0025589218564790602729101830116743438898", "winding_unresolved": false }, { "i": 2, "j": 3, "sampled_winding": "2.923214632968212805056507275907768662e-41", "rounded_winding": 0, "corner_ratio": "0.8418779503581276494341220939521676964", "m_scale": "0.22243716351967594021869597484880255116", "c_scale": "0.0026590656750066057939625172971899238545", "winding_unresolved": false }, { "i": 2, "j": 4, "sampled_winding": "-2.923214632968212805056507275907768662e-41", "rounded_winding": 0, "corner_ratio": "0.82768937004228466723585874131634827437", "m_scale": "0.23031001958743587799958456515134798156", "c_scale": "0.0027690984596439718184405805427215014127", "winding_unresolved": false }, { "i": 2, "j": 5, "sampled_winding": "-2.923214632968212805056507275907768662e-41", "rounded_winding": 0, "corner_ratio": "0.81364634894041569996183392703539191115", "m_scale": "0.2389801114767824981331111546132369783", "c_scale": "0.0028832418137653515171319717629183298662", "winding_unresolved": false }, { "i": 2, "j": 6, "sampled_winding": "2.923214632968212805056507275907768662e-41", "rounded_winding": 0, "corner_ratio": "0.7977414227820406323069549161222034077", "m_scale": "0.24902607101091079287450986839236968339", "c_scale": "0.0030577824278517128765739415186469739754", "winding_unresolved": false }, { "i": 2, "j": 7, "sampled_winding": "2.923214632968212805056507275907768662e-41", "rounded_winding": 0, "corner_ratio": "0.76977716706286079511787170953695039677", "m_scale": "0.26396324386588450462875488038393092339", "c_scale": "0.0042263440581005008560339533635972495762", "winding_unresolved": false }, { "i": 3, "j": 0, "sampled_winding": "2.923214632968212805056507275907768662e-41", "rounded_winding": 0, "corner_ratio": "0.84404842563810826709224635367174030997", "m_scale": "0.18215812545102748970292366627819046105", "c_scale": "0.001358180056526549984105807154007242195", "winding_unresolved": false }, { "i": 3, "j": 1, "sampled_winding": "-1.461607316484106402528253637953884331e-41", "rounded_winding": 0, "corner_ratio": "0.83800428166619398644900181117095354204", "m_scale": "0.18442511869636840051360546199215491012", "c_scale": "0.0013781390262194665444930183705619985426", "winding_unresolved": false }, { "i": 3, "j": 2, "sampled_winding": "2.923214632968212805056507275907768662e-41", "rounded_winding": 0, "corner_ratio": "0.83116260172079290186301281460810861165", "m_scale": "0.18726494330742046373373331589129003447", "c_scale": "0.0014029804815747754655953152474148962851", "winding_unresolved": false }, { "i": 3, "j": 3, "sampled_winding": "2.923214632968212805056507275907768662e-41", "rounded_winding": 0, "corner_ratio": "0.82374720624536210824731545315243613884", "m_scale": "0.19062515502675104431621184380934436785", "c_scale": "0.0014321531111150401553033990785959913018", "winding_unresolved": false }, { "i": 3, "j": 4, "sampled_winding": "-5.846429265936425610113014551815537324e-41", "rounded_winding": 0, "corner_ratio": "0.81597914469353696918585391722864069581", "m_scale": "0.19444529517245761520771822318700898374", "c_scale": "0.0014650428450486734220490022450310407812", "winding_unresolved": false }, { "i": 3, "j": 5, "sampled_winding": "2.923214632968212805056507275907768662e-41", "rounded_winding": 0, "corner_ratio": "0.80806519031760945202806404115678912787", "m_scale": "0.19865841219806545945714830205896063134", "c_scale": "0.0015009926475405898538262130488836734263", "winding_unresolved": false }, { "i": 3, "j": 6, "sampled_winding": "0.0", "rounded_winding": 0, "corner_ratio": "0.80018862116920742415697514428394185075", "m_scale": "0.20319287807180364131362349070790167206", "c_scale": "0.0015389739788683840659880670694985884007", "winding_unresolved": false }, { "i": 3, "j": 7, "sampled_winding": "0.0", "rounded_winding": 0, "corner_ratio": "0.79193841261249882649722579426807994518", "m_scale": "0.20812260430203123658247213341717083605", "c_scale": "0.0015845846202042779331586989346481818942", "winding_unresolved": false }, { "i": 4, "j": 0, "sampled_winding": "7.3080365824205320126412681897694216549e-42", "rounded_winding": 0, "corner_ratio": "0.82291846724433510863978959127274640465", "m_scale": "0.15454903911435276380918797667709937129", "c_scale": "0.00072681727721389078259373533416977480681", "winding_unresolved": false }, { "i": 4, "j": 1, "sampled_winding": "1.461607316484106402528253637953884331e-41", "rounded_winding": 0, "corner_ratio": "0.81961734472418302095511082708061471998", "m_scale": "0.15564761749049237714132413095912701279", "c_scale": "0.00073270534435659034055290348845189032263", "winding_unresolved": false }, { "i": 4, "j": 2, "sampled_winding": "0.0", "rounded_winding": 0, "corner_ratio": "0.81583874956664620966660071910976850357", "m_scale": "0.15702693889337521793539666606437730053", "c_scale": "0.00074007287871376872965500866876418682362", "winding_unresolved": false }, { "i": 4, "j": 3, "sampled_winding": "-2.923214632968212805056507275907768662e-41", "rounded_winding": 0, "corner_ratio": "0.81168020921536423054626100974061192744", "m_scale": "0.15866330564450429791983030447594629028", "c_scale": "0.00074877787343340744959984480153590654803", "winding_unresolved": false }, { "i": 4, "j": 4, "sampled_winding": "2.923214632968212805056507275907768662e-41", "rounded_winding": 0, "corner_ratio": "0.80724350059583589232592433604997430963", "m_scale": "0.16052894766102387256767068345583339183", "c_scale": "0.00075865688030386677747156679561134462223", "winding_unresolved": false }, { "i": 4, "j": 5, "sampled_winding": "-2.923214632968212805056507275907768662e-41", "rounded_winding": 0, "corner_ratio": "0.80263020682396032306743062155762425638", "m_scale": "0.16259262893567943823109922207605114053", "c_scale": "0.00076952972618889648199046667900095417832", "winding_unresolved": false }, { "i": 4, "j": 6, "sampled_winding": "-2.923214632968212805056507275907768662e-41", "rounded_winding": 0, "corner_ratio": "0.79793796672306693074133770346427213774", "m_scale": "0.16482028487972983677605989742395763311", "c_scale": "0.00078120411314699352389862010447962477596", "winding_unresolved": false }, { "i": 4, "j": 7, "sampled_winding": "2.923214632968212805056507275907768662e-41", "rounded_winding": 0, "corner_ratio": "0.79325648399815037181961830134671729955", "m_scale": "0.16717590347233361240412678080904519255", "c_scale": "0.00079348215806731599422842223069458149916", "winding_unresolved": false }, { "i": 5, "j": 0, "sampled_winding": "-7.3080365824205320126412681897694216549e-42", "rounded_winding": 0, "corner_ratio": "0.81051463416150723003680766954843066445", "m_scale": "0.12757148696020266924354871249948225881", "c_scale": "0.00037704851096011291333875600728851271047", "winding_unresolved": false }, { "i": 5, "j": 1, "sampled_winding": "-1.461607316484106402528253637953884331e-41", "rounded_winding": 0, "corner_ratio": "0.80861226202155937165404838719560363208", "m_scale": "0.12810866147504940192749637170430325478", "c_scale": "0.00037882110836189269200179962512564816026", "winding_unresolved": false }, { "i": 5, "j": 2, "sampled_winding": "-2.1924109747261596037923804569308264965e-41", "rounded_winding": 0, "corner_ratio": "0.80642254836639312814024263755656849046", "m_scale": "0.12878386512033252897302102618491482532", "c_scale": "0.00038104488756287773444271612057397466034", "winding_unresolved": false }, { "i": 5, "j": 3, "sampled_winding": "0.0", "rounded_winding": 0, "corner_ratio": "0.80399316766721168657166490727308584897", "m_scale": "0.12958594965685063324882823278815171676", "c_scale": "0.0003836804244150355389785620151413312318", "winding_unresolved": false }, { "i": 5, "j": 4, "sampled_winding": "1.461607316484106402528253637953884331e-41", "rounded_winding": 0, "corner_ratio": "0.80137536420568900586180050397979073542", "m_scale": "0.13050175539069582332361674240051676564", "c_scale": "0.00038668164383209259548480811893391917449", "winding_unresolved": false }, { "i": 5, "j": 5, "sampled_winding": "4.384821949452319207584760913861652993e-41", "rounded_winding": 0, "corner_ratio": "0.7986221822842365732550235279313285616", "m_scale": "0.13151636299164827809850039582877413542", "c_scale": "0.00038999689997393828191884378660579549164", "winding_unresolved": false }, { "i": 5, "j": 6, "sampled_winding": "-2.923214632968212805056507275907768662e-41", "rounded_winding": 0, "corner_ratio": "0.79578681741792258758532107781443560668", "m_scale": "0.13261336939767753938857319831774128593", "c_scale": "0.0003935701134946239994217227566313741977", "winding_unresolved": false }, { "i": 5, "j": 7, "sampled_winding": "2.923214632968212805056507275907768662e-41", "rounded_winding": 0, "corner_ratio": "0.79292117015387721341927856761375421308", "m_scale": "0.13377518032796355770915788614137681636", "c_scale": "0.00039734192269331293278654117370091319622", "winding_unresolved": false }, { "i": 6, "j": 0, "sampled_winding": "-1.461607316484106402528253637953884331e-41", "rounded_winding": 0, "corner_ratio": "0.80305312879667789153757147535619042707", "m_scale": "0.10359023453989389569918326184363608092", "c_scale": "0.00019206450725172636278399932476421611786", "winding_unresolved": false }, { "i": 6, "j": 1, "sampled_winding": "2.923214632968212805056507275907768662e-41", "rounded_winding": 0, "corner_ratio": "0.80192128909237600736835428045781138396", "m_scale": "0.10385421269881240781713715980339433157", "c_scale": "0.00019260429904380061304051924175367973504", "winding_unresolved": false }, { "i": 6, "j": 2, "sampled_winding": "7.3080365824205320126412681897694216549e-42", "rounded_winding": 0, "corner_ratio": "0.80061456250637661907638581905746146225", "m_scale": "0.1041862181497751638982190822729559698", "c_scale": "0.00019328242763207535035270800185245886769", "winding_unresolved": false }, { "i": 6, "j": 3, "sampled_winding": "3.6540182912102660063206340948847108275e-41", "rounded_winding": 0, "corner_ratio": "0.79915826656726043140788000947324964492", "m_scale": "0.10458089175570060395877514546074791054", "c_scale": "0.00019408745442624444274156901106438589244", "winding_unresolved": false }, { "i": 6, "j": 4, "sampled_winding": "-1.461607316484106402528253637953884331e-41", "rounded_winding": 0, "corner_ratio": "0.79758007845159112445657628951923743712", "m_scale": "0.10503188481847595597527709810353536796", "c_scale": "0.00019500590647451858009244702962577824064", "winding_unresolved": false }, { "i": 6, "j": 5, "sampled_winding": "0.0", "rounded_winding": 0, "corner_ratio": "0.79590926085587472378542188550721114389", "m_scale": "0.10553197118004513874951022102230451045", "c_scale": "0.00019602254966340241008053445896327375779", "winding_unresolved": false }, { "i": 6, "j": 6, "sampled_winding": "1.461607316484106402528253637953884331e-41", "rounded_winding": 0, "corner_ratio": "0.79417589903702181640269498526771150892", "m_scale": "0.10607317252319479986963651500997740177", "c_scale": "0.00019712068666826606899222280586122039269", "winding_unresolved": false }, { "i": 6, "j": 7, "sampled_winding": "0.0", "rounded_winding": 0, "corner_ratio": "0.79241018204866369442624817484550601913", "m_scale": "0.10664689402953942630872666743074364795", "c_scale": "0.00019828247072345877755576767335733800279", "winding_unresolved": false }, { "i": 7, "j": 0, "sampled_winding": "-9.1350457280256650158015852372117770687e-42", "rounded_winding": 0, "corner_ratio": "0.7984967891168875636259264879938681553", "m_scale": "0.083282904125105452363412435146723228127", "c_scale": "0.000096768331474566722990398278902906682415", "winding_unresolved": false }, { "i": 7, "j": 1, "sampled_winding": "1.0962054873630798018961902284654132482e-41", "rounded_winding": 0, "corner_ratio": "0.79781025507427007234398998393800609257", "m_scale": "0.083413003463176158143888815846825580213", "c_scale": "0.000096933815240034798166007367032254371352", "winding_unresolved": false }, { "i": 7, "j": 2, "sampled_winding": "3.6540182912102660063206340948847108275e-42", "rounded_winding": 0, "corner_ratio": "0.79701628310251101536701222508933595685", "m_scale": "0.083576684171543992049207007158960224532", "c_scale": "0.000097141872302481277718570668365683156233", "winding_unresolved": false }, { "i": 7, "j": 3, "sampled_winding": "2.923214632968212805056507275907768662e-41", "rounded_winding": 0, "corner_ratio": "0.79612910784276392043071027113413695755", "m_scale": "0.083771338933438535776855235154512969099", "c_scale": "0.000097389096781083751329920243344019731595", "winding_unresolved": false }, { "i": 7, "j": 4, "sampled_winding": "3.2886164620892394056885706853962397447e-41", "rounded_winding": 0, "corner_ratio": "0.79516444744680376827575192262687518807", "m_scale": "0.083993873178573199832972241416556172294", "c_scale": "0.000097671460065941807356599328403650082412", "winding_unresolved": false }, { "i": 7, "j": 5, "sampled_winding": "-7.3080365824205320126412681897694216549e-42", "rounded_winding": 0, "corner_ratio": "0.79413913345692337350838854380725107076", "m_scale": "0.084240757152317350056998770370733655226", "c_scale": "0.000097984385052407017458023844852960834235", "winding_unresolved": false }, { "i": 7, "j": 6, "sampled_winding": "-7.3080365824205320126412681897694216549e-42", "rounded_winding": 0, "corner_ratio": "0.79307073282531693305146644707972245799", "m_scale": "0.08450808471287188204003566426290574389", "c_scale": "0.000098322828708803194929988064241556855308", "winding_unresolved": false }, { "i": 7, "j": 7, "sampled_winding": "0.0", "rounded_winding": 0, "corner_ratio": "0.79197717574929983716502358756317548732", "m_scale": "0.084791637685968627963314200641283183432", "c_scale": "0.000098681370926596444080574721621438740224", "winding_unresolved": false } ], "selected_cells": [ { "i": 0, "j": 7, "sampled_winding": "-4.0925004861554979270791101862708761268e-40", "rounded_winding": 0, "corner_ratio": "0.53310094920153785039684178172002840202", "m_scale": "0.60828670295972911642551373684317772015", "c_scale": "0.109409126196452569602506367391405789", "winding_unresolved": false }, { "i": 1, "j": 7, "sampled_winding": "0.0", "rounded_winding": 0, "corner_ratio": "0.54306820794881006012433779799600160623", "m_scale": "0.45855394841007548341583114652923333612", "c_scale": "0.021451241356443265241381645076779195894", "winding_unresolved": false }, { "i": 0, "j": 6, "sampled_winding": "-4.384821949452319207584760913861652993e-41", "rounded_winding": 0, "corner_ratio": "0.58795676604066541479253265032922155138", "m_scale": "0.48319511432902079130588590022688640197", "c_scale": "0.050876437364814437493857774812792119476", "winding_unresolved": false }, { "i": 0, "j": 5, "sampled_winding": "1.0231251215388744817697775465677190317e-40", "rounded_winding": 0, "corner_ratio": "0.63725313393568587041863517134941325659", "m_scale": "0.41472982711030505309050612037852721725", "c_scale": "0.026656312276944997136524664350642936495", "winding_unresolved": false } ], "first_refinements": [ { "i": 0, "j": 7, "bits": 128, "stop": "newton_step_leaves_cell_after_16_halvings", "steps": [ { "iteration": 0, "z": { "re": "0.2421875", "im": "0.59375" }, "m": { "re": "0.19333576060874026365519907272340131948", "im": "0.057979299093506573992428430424645359394" }, "c": { "re": "-0.012519745081136390792848864521385382645", "im": "-0.00094569379303306057482543007510119339126" }, "relative_m_residual": "0.3318210022460202865896268966544739284" }, { "iteration": 1, "z": { "re": "0.20971052195016394915473619513351983776", "im": "0.61343637785919879282635807295505602743" }, "m": { "re": "0.080564127128848554513802498383617071786", "im": "-0.011878756280444612222886074428500447844" }, "c": { "re": "-0.024302986289613173893399359485275902", "im": "-0.005471697287064923918289281914188583187" }, "relative_m_residual": "0.13387625970454445973078790816033405216" }, { "iteration": 2, "z": { "re": "0.20856621186873558427018883738799649583", "im": "0.6224134417632680006649664128418227517" }, "m": { "re": "0.037378557708846397677597901547922038405", "im": "-0.0048635469801233748660110609369981362376" }, "c": { "re": "-0.027032270638813440229840833423691709043", "im": "-0.0034632002373904931674316837000350966413" }, "relative_m_residual": "0.06196690156242352789660304484467404069" }, { "iteration": 3, "z": { "re": "0.20825677961382788685529139842652398396", "im": "0.62420532024261016314515117684667960121" }, "m": { "re": "0.02790366959261160853086275895503921767", "im": "-0.0036151219499676757602047439358200845602" }, "c": { "re": "-0.027556407820519689674986752174452556449", "im": "-0.0030503489656217110115411605366526330717" }, "relative_m_residual": "0.046255947245270536108021434115027757248" }, { "iteration": 4, "z": { "re": "0.20814206876233783640486859749652997952", "im": "0.62485520909587472103498939154256419831" }, "m": { "re": "0.024398216895282276615989540702472896155", "im": "-0.003159133379244850417288761156559114133" }, "c": { "re": "-0.027742884711151328747460290692880501033", "im": "-0.0028984719988006128034322517204185572284" }, "relative_m_residual": "0.040444567200250723369298114121682553904" }, { "iteration": 5, "z": { "re": "0.20811709312702776346794591730574104551", "im": "0.6249958104595712872330239390812473354" }, "m": { "re": "0.023634948008475734098275822619122638583", "im": "-0.0030602214944233928353822501779159820733" }, "c": { "re": "-0.027782954699225456604026262454698017031", "im": "-0.0028654607936006101933005289348701016944" }, "relative_m_residual": "0.039179290182084209054858966484857205136" }, { "iteration": 6, "z": { "re": "0.20811671546167514755066653646371395198", "im": "0.62499793389363215154130364854802648275" }, "m": { "re": "0.023623407318174955585346630792895936339", "im": "-0.0030587272026777349966312713619069838789" }, "c": { "re": "-0.027783559107645680958090029902378375551", "im": "-0.0028649618337091961380015058948264929398" }, "relative_m_residual": "0.039160159353163124258327043009868410375" }, { "iteration": 7, "z": { "re": "0.20811652672407991959256788931691875277", "im": "0.62499899505656741409541631388857035529" }, "m": { "re": "0.023617639837709727804795039986987787752", "im": "-0.0030579804323762484072235714303816476379" }, "c": { "re": "-0.027783861145266613605065483687101203479", "im": "-0.0028647124789998652147831647242090700136" }, "relative_m_residual": "0.039150598688429966643414488399511986324" }, { "iteration": 8, "z": { "re": "0.2081164323790404598947492267077536198", "im": "0.62499952549958709610192458963196426634" }, "m": { "re": "0.023614756813280728394270240533341831967", "im": "-0.003057607141068086639486910834647270124" }, "c": { "re": "-0.027784012122453804261798045201024284007", "im": "-0.0028645878329379249752114597404299527456" }, "relative_m_residual": "0.039145819542885184402809912164927975808" }, { "iteration": 9, "z": { "re": "0.20811638521245875492481972995005715754", "im": "0.62499979068649442467742219746864044644" }, "m": { "re": "0.023613315479971197654174853675010842735", "im": "-0.0030574205188683730851175970633377969321" }, "c": { "re": "-0.027784087600644581268162063639136778046", "im": "-0.0028645255177280911976270813750587674737" }, "relative_m_residual": "0.039143430266742027486644114037219019084" }, { "iteration": 10, "z": { "re": "0.20811636163065221949650578544218539785", "im": "0.62499992327129864487584747661140845087" }, "m": { "re": "0.023612594858036934244641360770231120096", "im": "-0.0030573272136313236151683913333133963437" }, "c": { "re": "-0.027784125337139640152294778570209631264", "im": "-0.0028644943620782028450042534585476032409" }, "relative_m_residual": "0.039142235702818233290038684367646513978" }, { "iteration": 11, "z": { "re": "0.20811634984012000740414410514067041294", "im": "0.62499998956153854193346158813727035093" }, "m": { "re": "0.023612234558249210591819892185238525555", "im": "-0.0030572805624784026558174143576979454954" }, "c": { "re": "-0.027784144204737134052727144138323722065", "im": "-0.0028644787847419838635007541952038962038" }, "relative_m_residual": "0.039141638439392091881966823637420943916" } ], "endpoint": { "re": "0.20811634984012000740414410514067041294", "im": "0.62499998956153854193346158813727035093" }, "m": { "re": "0.023612234558249210591819892185238525555", "im": "-0.0030572805624784026558174143576979454954" }, "c": { "re": "-0.027784144204737134052727144138323722065", "im": "-0.0028644787847419838635007541952038962038" }, "m_scale": "0.60828670295972911642551373684317772015", "c_scale": "0.109409126196452569602506367391405789", "cell_diagonal": "0.24256522962906287076347596511207782348" }, { "i": 1, "j": 7, "bits": 128, "stop": "newton_step_leaves_cell_after_16_halvings", "steps": [ { "iteration": 0, "z": { "re": "0.4765625", "im": "0.59375" }, "m": { "re": "0.25931656163177871818690457609486358615", "im": "-0.063579312949005699511988326532405486647" }, "c": { "re": "-0.00092032972335829699576249552576219090562", "im": "-0.0044577546119330775535714711730615193899" }, "relative_m_residual": "0.5822586850621144882907352017148048978" }, { "iteration": 1, "z": { "re": "0.49248587882772789735474457048318192554", "im": "0.61053052883086246979188866964546056996" }, "m": { "re": "0.25420860616864853518552113973934182932", "im": "-0.058136561635618569126330551120501396038" }, "c": { "re": "-0.0014617506854332383111818562414574613313", "im": "-0.0028155146226595013738262643070921705526" }, "relative_m_residual": "0.56868268763868925661895818411854422161" }, { "iteration": 2, "z": { "re": "0.48748233901214250662786266482616159919", "im": "0.62031984712668993131887523744349247668" }, "m": { "re": "0.24877975026869851452742703765795681914", "im": "-0.056911088583531567182983404946686200029" }, "c": { "re": "-0.0025076548128952588509870129267108489566", "im": "-0.0024639153377716729529632684013257956453" }, "relative_m_residual": "0.55654577362718301407162126008513654439" }, { "iteration": 3, "z": { "re": "0.48613160227975949750314030964813164178", "im": "0.62303193887843511344948995659022703211" }, "m": { "re": "0.24669263088193023938985251159280606243", "im": "-0.056440501793464312361671877711756638577" }, "c": { "re": "-0.0028609194601813763037783957158913764685", "im": "-0.0023459380563869704583385183749233965779" }, "relative_m_residual": "0.55188001239008677225908263526963272018" }, { "iteration": 4, "z": { "re": "0.48555596654018882291302298886041990586", "im": "0.62420656107687421300772421352681055755" }, "m": { "re": "0.24570017475659077870270477381890053601", "im": "-0.056214934267601473609572375120916051935" }, "c": { "re": "-0.0030231486684761609114655017873379515079", "im": "-0.0022914526989731991845042032313221645452" }, "relative_m_residual": "0.54966050025779412147491848417323799173" }, { "iteration": 5, "z": { "re": "0.48528700483745377703847215903078804066", "im": "0.62475943371450393023905276192004946463" }, "m": { "re": "0.24521371737668273827301714923946599839", "im": "-0.056103986604419314190122552893435211441" }, "c": { "re": "-0.0031015026175881760612923784867645096317", "im": "-0.0022650706923463475317356433847232640338" }, "relative_m_residual": "0.54857240812391826353892928519977727529" }, { "iteration": 6, "z": { "re": "0.48522185733606836659091292232771230847", "im": "0.6248938201901790392252124541081879884" }, "m": { "re": "0.24509359086420007685659938263022467109", "im": "-0.056076523251527812245050181594562319627" }, "c": { "re": "-0.0031207401953228757770173079168469689985", "im": "-0.0022585820368207168655266952380598774644" }, "relative_m_residual": "0.54830368103618952400382784830544787493" }, { "iteration": 7, "z": { "re": "0.48518953204646093839857094904733561352", "im": "0.62496055783080188153572014487564210985" }, "m": { "re": "0.24503365624829668099115327644487998015", "im": "-0.056062815678255740675888316234266624123" }, "c": { "re": "-0.0031303223768156588091678837627833492439", "im": "-0.0022553491349732358213806683766274994666" }, "relative_m_residual": "0.54816960268408076306157845016023757169" }, { "iteration": 8, "z": { "re": "0.48517343068586377081265014770242030693", "im": "0.62499381424133787424947503868363831717" }, "m": { "re": "0.24500372070788526632279215436255544921", "im": "-0.05605596784236070393202632547833235336" }, "c": { "re": "-0.0031351044287776368215446133169741729367", "im": "-0.002253735505168423559781636794426431772" }, "relative_m_residual": "0.54810263393497585339285328843793785543" }, { "iteration": 9, "z": { "re": "0.48517142182053746703914053753054876594", "im": "0.62499796431277187627193381276144721368" }, "m": { "re": "0.24499998187058813757329452845631908348", "im": "-0.056055112430250040321385696962788510792" }, "c": { "re": "-0.0031357015031878970019692340251431540599", "im": "-0.0022535340071435361712487825246244868397" }, "relative_m_residual": "0.54809426971856412204227693932094367204" } ], "endpoint": { "re": "0.48517142182053746703914053753054876594", "im": "0.62499796431277187627193381276144721368" }, "m": { "re": "0.24499998187058813757329452845631908348", "im": "-0.056055112430250040321385696962788510792" }, "c": { "re": "-0.0031357015031878970019692340251431540599", "im": "-0.0022535340071435361712487825246244868397" }, "m_scale": "0.45855394841007548341583114652923333612", "c_scale": "0.021451241356443265241381645076779195894", "cell_diagonal": "0.24256522962906287076347596511207782348" }, { "i": 0, "j": 6, "bits": 128, "stop": "newton_step_leaves_cell_after_16_halvings", "steps": [ { "iteration": 0, "z": { "re": "0.2421875", "im": "0.53125" }, "m": { "re": "0.2697247124805976359467257024546990676", "im": "0.011120050797520824744791108657355120062" }, "c": { "re": "-0.0014615082693746377413461112433944748851", "im": "-0.0074867993102034398712350080200193383137" }, "relative_m_residual": "0.5586849547739596810850967462488427896" }, { "iteration": 1, "z": { "re": "0.23827038030432312208413625177168416359", "im": "0.55823659156148061650237768148629437405" }, "m": { "re": "0.2448799948953459937615917481171721811", "im": "0.014302925004887338507130217592989879076" }, "c": { "re": "-0.005885570953555815137689990798291813643", "im": "-0.0066312582115753762309520682994691291953" }, "relative_m_residual": "0.50765691508893457133208979818235711092" }, { "iteration": 2, "z": { "re": "0.23700940097229086064503881993138272917", "im": "0.56094817439280887202734267155433065337" }, "m": { "re": "0.24090689332628002389760123264000165612", "im": "0.014070037509074137007303884498001946101" }, "c": { "re": "-0.0064979464212758641490508864551545677709", "im": "-0.0066288430582608742674532098409582035136" }, "relative_m_residual": "0.49942024012456413491515463065456132986" }, { "iteration": 3, "z": { "re": "0.23643429368081381441350896320707363253", "im": "0.56218639238886315501152574942793309998" }, "m": { "re": "0.23899294825188044180052227873717818817", "im": "0.013957967978534381311762457621876816231" }, "c": { "re": "-0.0067867791386990557916357640891535427226", "im": "-0.0066258278964012074103234446503523159907" }, "relative_m_residual": "0.49545243651986408623138772604248251453" }, { "iteration": 4, "z": { "re": "0.23629644111537569145666399286726293045", "im": "0.56248343226219903671834932859184071108" }, "m": { "re": "0.2385243016242476549906971522693672133", "im": "0.013930578456597019041947720769952244134" }, "c": { "re": "-0.0068569293017458121923296285197144071659", "im": "-0.0066249109148947635159781394081755197696" }, "relative_m_residual": "0.49448089043869564750529104469218007746" }, { "iteration": 5, "z": { "re": "0.23629217652694226550583286362987240139", "im": "0.56249262341061182575845400773695562459" }, "m": { "re": "0.23850974146574874391721109688232660819", "im": "0.013929728078282764612540270236589339281" }, "c": { "re": "-0.0068591052315213281014263298476814297426", "im": "-0.0066248812866354064733659326577726712746" }, "relative_m_residual": "0.49445070600621229679362134404202061255" }, { "iteration": 6, "z": { "re": "0.23629004489931548986395037608482544232", "im": "0.56249721757899703068090570271831277551" }, "m": { "re": "0.23850246227867389672484406000374316705", "im": "0.013929302945907654483780093157806599845" }, "c": { "re": "-0.006860192983719348753210582351236037976", "im": "-0.0066248664499271274571017102933688521732" }, "relative_m_residual": "0.4944356156400876841651300009645633737" }, { "iteration": 7, "z": { "re": "0.23628897925206121968335256031003708843", "im": "0.56249951431192514707485625588666797336" }, "m": { "re": "0.23849882290808629237677759583432488032", "im": "0.013929090393910928763799568353381421628" }, "c": { "re": "-0.0068607368066702985995811158074063648802", "im": "-0.0066248590259310732131875097709910718836" }, "relative_m_residual": "0.49442807091936021734549951636636496928" } ], "endpoint": { "re": "0.23628897925206121968335256031003708843", "im": "0.56249951431192514707485625588666797336" }, "m": { "re": "0.23849882290808629237677759583432488032", "im": "0.013929090393910928763799568353381421628" }, "c": { "re": "-0.0068607368066702985995811158074063648802", "im": "-0.0066248590259310732131875097709910718836" }, "m_scale": "0.48319511432902079130588590022688640197", "c_scale": "0.050876437364814437493857774812792119476", "cell_diagonal": "0.24256522962906287076347596511207782348" }, { "i": 0, "j": 5, "bits": 128, "stop": "newton_step_leaves_cell_after_16_halvings", "steps": [ { "iteration": 0, "z": { "re": "0.2421875", "im": "0.46875" }, "m": { "re": "0.28397486666669995372153992006634205833", "im": "0.021717836494381494066484435638345982756" }, "c": { "re": "0.0041341631418207781352000186686367978895", "im": "-0.0067697141183706178546287117499397100385" }, "relative_m_residual": "0.68672206786674268251858704493918913739" }, { "iteration": 1, "z": { "re": "0.304210931605665319422852495180841582", "im": "0.45785608540004263193088440193342373827" }, "m": { "re": "0.27392681143513542936383803142696344172", "im": "0.014357514892977283122337162222534204729" }, "c": { "re": "0.0035255229763382625619424733531486775499", "im": "-0.0043520287214149680134811653189711369024" }, "relative_m_residual": "0.6614012318513045948521566774509486387" }, { "iteration": 2, "z": { "re": "0.31057865606611512777169043973268955338", "im": "0.44031563350894778003315997006244609012" }, "m": { "re": "0.26936804647074164978464877178884014775", "im": "0.014263280182800773413763986812757932648" }, "c": { "re": "0.0037882967904835743198514641314731894772", "im": "-0.0040931544609745977145302926052752736067" }, "relative_m_residual": "0.65041236791803316762149608880815705691" }, { "iteration": 3, "z": { "re": "0.31137999080695178901577205629098701453", "im": "0.43842460210714959513459929026967462538" }, "m": { "re": "0.26883973165856775438262745022060889025", "im": "0.014235879472847615077343735080565765509" }, "c": { "re": "0.0038088131359849324174950715324452814348", "im": "-0.0040612236593342699507104224577783311498" }, "relative_m_residual": "0.64913677945206510240129135975828738045" }, { "iteration": 4, "z": { "re": "0.31157929610332558594958747482094065727", "im": "0.43795700762019360429246480630550255129" }, "m": { "re": "0.26870833532302467657253692727520284297", "im": "0.014228951917451255753523204487971657197" }, "c": { "re": "0.0038136869681275128607141803417705194996", "im": "-0.0040532791504655473630808170918049864747" }, "relative_m_residual": "0.64881951549834100943596701840802228052" }, { "iteration": 5, "z": { "re": "0.31167881714487651187799395116094813262", "im": "0.4377238138545392647400299243775646456" }, "m": { "re": "0.26864270166859389750737674798437310512", "im": "0.014225483628086689767838455479183032311" }, "c": { "re": "0.0038160889684253681189489532181838674189", "im": "-0.004049310982175244813421931225886699602" }, "relative_m_residual": "0.64866103828370184472610206004181881402" }, { "iteration": 6, "z": { "re": "0.31172854458326531406091100511812604465", "im": "0.43760736495292179473029795997224809012" }, "m": { "re": "0.26860990069785043756040724135263277397", "im": "0.014223748474561171252697702544833073714" }, "c": { "re": "0.0038172813583362903643794515294316502142", "im": "-0.0040473279267547888662858983517988017857" }, "relative_m_residual": "0.64858183772751773845456047112536253942" }, { "iteration": 7, "z": { "re": "0.31175340001089588367694274036787401294", "im": "0.43754917714262862298733361406334052217" }, "m": { "re": "0.26859350414322920548404370229747370599", "im": "0.014222880660052231242740210472989716318" }, "c": { "re": "0.0038178754153184326247278953835191375905", "im": "-0.0040463366570586496787128651370727952198" }, "relative_m_residual": "0.64854224688371040736837771219365060451" }, { "iteration": 8, "z": { "re": "0.31176582564929686618436081229292875834", "im": "0.4375200923536450703644608123395124695" }, "m": { "re": "0.2685853068444730122190619527369397188", "im": "0.014222446695143841534088615504943225776" }, "c": { "re": "0.0038181719111240019878588114707880700244", "im": "-0.0040458410868142613321949307439148132807" }, "relative_m_residual": "0.648522453810653142660007615324572423" }, { "iteration": 9, "z": { "re": "0.31177203794933434178190940429754046885", "im": "0.437505552232721989337429371579857033" }, "m": { "re": "0.26858120843921920703670246351350388967", "im": "0.014222229698497427450524792519891457657" }, "c": { "re": "0.0038183200260804337349626082018647541774", "im": "-0.0040455933178552646538802411046858488925" }, "relative_m_residual": "0.64851255786012593794698022090709352075" } ], "endpoint": { "re": "0.31177203794933434178190940429754046885", "im": "0.437505552232721989337429371579857033" }, "m": { "re": "0.26858120843921920703670246351350388967", "im": "0.014222229698497427450524792519891457657" }, "c": { "re": "0.0038183200260804337349626082018647541774", "im": "-0.0040455933178552646538802411046858488925" }, "m_scale": "0.41472982711030505309050612037852721725", "c_scale": "0.026656312276944997136524664350642936495", "cell_diagonal": "0.24256522962906287076347596511207782348" } ], "replay_cells": [ { "i": 0, "j": 7, "sampled_winding": "8.590555718237951894356880680944724666645999928481111115573370275543590674852e-79", "rounded_winding": 0, "corner_ratio": "0.5331009492015378503891489822908884816080885172098606194955850133271072142879", "m_scale": "0.6082867029597291164357471824402855332929151296481002675002953623324572346674", "c_scale": "0.1094091261964525695896007178497216631540869452256403578475874399920707490254", "winding_unresolved": false }, { "i": 1, "j": 7, "sampled_winding": "0.0", "rounded_winding": 0, "corner_ratio": "0.5430682079488109675002856961489065272326797845423867808272275043652461181854", "m_scale": "0.4585539484100747172230662363735258736936669710774068406209861320258109016812", "c_scale": "0.0214512413564424018809832611140382189247981243027188200795217631659653377419", "winding_unresolved": false }, { "i": 0, "j": 6, "sampled_winding": "8.590555718237951894356880680944724666645999928481111115573370275543590674852e-80", "rounded_winding": 0, "corner_ratio": "0.5879567660406654147925326410782655770694942125168536944642532256585535673842", "m_scale": "0.4831951143290207913058859001904531625265789693811280893779476486094240296972", "c_scale": "0.05087643736481443749385777476773070443102177336412778041293392129744570533189", "winding_unresolved": false }, { "i": 0, "j": 5, "sampled_winding": "3.436222287295180757742752272377889866658399971392444446229348110217436269941e-79", "rounded_winding": 0, "corner_ratio": "0.6372531339356858704186351713496671872140274669719951871963633829763816730155", "m_scale": "0.4147298271103050530905061203785272174753102513820104073172841416288033825803", "c_scale": "0.02665631227694499713652466435064293648721240752045817472063482145140090199288", "winding_unresolved": false } ], "second_refinements": [ { "i": 0, "j": 7, "bits": 256, "stop": "newton_step_leaves_cell_after_16_halvings", "steps": [ { "iteration": 0, "z": { "re": "0.2421875", "im": "0.59375" }, "m": { "re": "0.1933357606087402636551724844074496543667504373791615252503463754366290365585", "im": "0.05797929909350657399243285862558084676701059445365958823010965826740233774581" }, "c": { "re": "-0.01251974508113639079291057459496232813697340041433678532406572327934930412904", "im": "-0.0009456937930330605748432228929919592589129125681065828410533847287010319458137" }, "relative_m_residual": "0.3318210022460202865840047649858805191440835082733245170713977047514170502477" }, { "iteration": 1, "z": { "re": "0.2097105219501639491548216649211800177596422383770527720221005334709142505361", "im": "0.6134363778591987928264051037475765506039547622505328473607422570554653525157" }, "m": { "re": "0.08056412712884855451371375115490022239849690612622300704163723038831864702623", "im": "-0.01187875628044461222244996493924086333926796714523846324476642420159594263493" }, "c": { "re": "-0.02430298628961317389336948058247403703827491201848412590864947869181992039331", "im": "-0.005471697287064923918213403834397781372050694726640705242044687581273810153275" }, "relative_m_residual": "0.1338762597045444597282867394007724933062214765447186802436288057578559753068" }, { "iteration": 2, "z": { "re": "0.2085662118687355842702066618726665597282954385350474977317882757020641989562", "im": "0.6224134417632680006649833309801167886089278290964207163986691899263918656414" }, "m": { "re": "0.03737855770884639767731345089145585754761754675025720380225715876162741347556", "im": "-0.00486354698012337486577763983201040672080050793973991335240783114491310918394" }, "c": { "re": "-0.02703227063881344023032189092288455841938400760522377684624506239357806807019", "im": "-0.003463200237390493167268628958724245520872225256403962004829877857202359908592" }, "relative_m_residual": "0.06196690156242352789504732161396459125456570643602421501737180399332918064405" }, { "iteration": 3, "z": { "re": "0.2082567796138278868553077860928407597685053954532763638622493802924112007668", "im": "0.6242053202426101631451200261467148026122830097996875556597206391306865960767" }, "m": { "re": "0.02790366959261160853060259535037264573722721853431712946794334652289639989434", "im": "-0.003615121949967675760043364406925739708117994434472300079472962676878752615081" }, "c": { "re": "-0.02755640782051968967580662539248120939094600851209733907246420335001400359194", "im": "-0.003050348965621711011496372155317578922481675755465494401844436497384344058732" }, "relative_m_residual": "0.04625594724527053610678501124426270738827680784758445999252361362981078218889" }, { "iteration": 4, "z": { "re": "0.2081420687623378364048891570314145602832215280645709508238859094657142447174", "im": "0.6248552090958747210349336236722631747386862090887371027504874959171388726176" }, "m": { "re": "0.02439821689528227661575311661220162086602486517201744026511934532090112813428", "im": "-0.00315913337924485041715038606511208416402682691230839573335194092215120300822" }, "c": { "re": "-0.02774288471115132874843693572614383671965898645316420221345817277639298704114", "im": "-0.002898471998800612803463408177888113820601449295668405290113753001045946240143" }, "relative_m_residual": "0.04044456720025072336820303376876089514162239981528957502801090152096765723043" }, { "iteration": 5, "z": { "re": "0.2081170931270277634679678545195606694452440791500713633850984307856272838969", "im": "0.6249958104595712872329621604309444450314627344139543672894489604744180208714" }, "m": { "re": "0.02363494800847573409804632131769647768764278210590140599894705493475464582469", "im": "-0.003060221494423392835248350721543502415058980442923400965534342330698503588054" }, "c": { "re": "-0.02778295469922545660503948375334287024939134817575417166273835870139806194171", "im": "-0.002865460793600610193350986425939877524482776688335101380443375244380165689455" }, "relative_m_residual": "0.03917929018208420905379740435613428877619825557348597349258029039302711245861" }, { "iteration": 6, "z": { "re": "0.2081167154616751475506884961151864687499800810325239035610795612692283826445", "im": "0.6249979338936321515412417767863457340877808756829600716114345282571420301567" }, "m": { "re": "0.02362340731817495558511724144383931120052918613827422861973297205235777823008", "im": "-0.003058727202677734996497437321535713410405947748526572004272910540992288069597" }, "c": { "re": "-0.02778355910764568095910381099590968117122327199360084423174213871362406535637", "im": "-0.002864961833709196138052263252194378931187117845175353173500189022402907142485" }, "relative_m_residual": "0.03916015935316312425726599905754963433432303034918427238296562990685265315918" }, { "iteration": 7, "z": { "re": "0.2081165267240799195925898601937006677720280969020139499811300309093608888403", "im": "0.6249989950565674140953543955778627417422161703537683140477894923036583543764" }, "m": { "re": "0.02361763983770972780456570661400231611758330663417181610451256420392113634262", "im": "-0.003057980432376248407089770073183376941299770971408756122625601789668850173984" }, "c": { "re": "-0.02778386114526661360607954461902494934560310596142635826198366709112832474431", "im": "-0.002864712478999865214834072029369815562682366182986377268674647255792375183354" }, "relative_m_residual": "0.03915059868842996664235370345002961238787145707301032761766334434081426549806" }, { "iteration": 8, "z": { "re": "0.2081164323790404598947712031988086336900811120457349441475892393004080551285", "im": "0.6249995254995870961018626480484099381212668476846968970389189059388709857916" }, "m": { "re": "0.02361475681328072839404093514835780660698704175817110295224241142929225756309", "im": "-0.003057607141068086639353125812833534699814551651006586280830959949261602032544" }, "c": { "re": "-0.02778401212245380426281224603737969361211789258065529922010944510067615541684", "im": "-0.002864587832937924975262442023136812029341676440022664695746203162537533781903" }, "relative_m_residual": "0.03914581954288518440174925669552437299507283329795907108374474534699493069724" }, { "iteration": 9, "z": { "re": "0.2081163852124587549248417092486530287348101857725001721032584847829507337025", "im": "0.6249997906864944246773602442490795903852093304811764833559108024183695819037" }, "m": { "re": "0.0236133154799711976539455622840182926859744496068000393839345488846135819061", "im": "-0.00305742051886837308498382020766645471977109989760057342023243213161176996293" }, "c": { "re": "-0.02778408760064458126917633442401664856417434770118120721877471629245582465211", "im": "-0.002864525517728091197678101147449697167430357230660477819633753946619268881774" }, "relative_m_residual": "0.03914343026674202748558352330252019303044892861164940510129358313623888714247" }, { "iteration": 10, "z": { "re": "0.2081163616306522194965277661446527381650434918381000720677595784458972501384", "im": "0.6249999232712986448757855175739485570148252007490377910949665563510613110589" }, "m": { "re": "0.02361259485803693424441207637623190638438653008234601014165988666494564651368", "im": "-0.003057327213631323615034618560325859199566951770806790642585261816791432363514" }, "c": { "re": "-0.02778412533713964015330908432842886055462763316183560757452154402691641905043", "im": "-0.002864494362078202845055291976008145652245252497033307773750093100368405248472" }, "relative_m_residual": "0.03914223570281823328897812599896645520490637294955147446091684599774378840948" }, { "iteration": 11, "z": { "re": "0.2081163498401200074041660865450987433769233540804510788824981553524498780692", "im": "0.6249999895615385419333996261908869970346372779413140303522101934113284522996" }, "m": { "re": "0.02361223455824921059159061128973536852595528569148084911773043718819571028044", "im": "-0.003057280562478402655683643625955472637732640403978799783693627681009657342925" }, "c": { "re": "-0.02778414420473713405374146738298190920693137125909545803893323509061730089833", "im": "-0.002864478784741983863551802085256117372387694896775320192811956753930676391959" }, "relative_m_residual": "0.03914163843939209188090628145141686741443788188142344791504787031273268353157" } ], "endpoint": { "re": "0.2081163498401200074041660865450987433769233540804510788824981553524498780692", "im": "0.6249999895615385419333996261908869970346372779413140303522101934113284522996" }, "m": { "re": "0.02361223455824921059159061128973536852595528569148084911773043718819571028044", "im": "-0.003057280562478402655683643625955472637732640403978799783693627681009657342925" }, "c": { "re": "-0.02778414420473713405374146738298190920693137125909545803893323509061730089833", "im": "-0.002864478784741983863551802085256117372387694896775320192811956753930676391959" }, "m_scale": "0.6082867029597291164357471824402855332929151296481002675002953623324572346674", "c_scale": "0.1094091261964525695896007178497216631540869452256403578475874399920707490254", "cell_diagonal": "0.2425652296290628707634759651120778234836316051057918425888564152259776575775" }, { "i": 1, "j": 7, "bits": 256, "stop": "newton_step_leaves_cell_after_16_halvings", "steps": [ { "iteration": 0, "z": { "re": "0.4765625", "im": "0.59375" }, "m": { "re": "0.2593165616317787174712183172231062549086477729852209917558786467057302955807", "im": "-0.06357931294900568000200385641902776151175680549432533863319024520491857831451" }, "c": { "re": "-0.0009203297233583062525239317326944812817521491327675165581786522723597334110402", "im": "-0.004457754611933045362391141158646310265018221463728138745592859051270896326333" }, "relative_m_residual": "0.5822586850621154495329885295444982353329813435133137474269916148924792979137" }, { "iteration": 1, "z": { "re": "0.4924858788277277980103217808324627340482857752009607847824485245893683927109", "im": "0.6105305288308627206014858329642470933734738140832391972780051660584790481705" }, "m": { "re": "0.2542086061686483209857262183173111330370930070430212699673921687000075801096", "im": "-0.05813656163561934536309236400558906586465707983711637184058780107013614971908" }, "c": { "re": "-0.001461750685433165486092172352595339349517362701727685955248271603607310007551", "im": "-0.002815514622660873056234706257677769755411323155896173800096485757705104075432" }, "relative_m_residual": "0.5686826876386901288528952625791488498962625255084647342043415197127385446095" }, { "iteration": 2, "z": { "re": "0.4874823390121451545036626997095388612292968819034232102915736488474955705852", "im": "0.620319847126694588730167884033894289911548219330350700556818374882535823905" }, "m": { "re": "0.2487797502687029587991329289045571757064664995830565716085463874880346416403", "im": "-0.05691108858353198115388656958012019061239359885321595945540999872304936209943" }, "c": { "re": "-0.002507654812884555617867122111606935003579840936333646670389397427246186436277", "im": "-0.002463915337775299650412829613369294831169065495026328892627548428450959980914" }, "relative_m_residual": "0.5565457736271935931860036170820171953556314305892164079599274819532395727132" }, { "iteration": 3, "z": { "re": "0.4861316022797578893311352775247352325264208155297943771609685858766637764472", "im": "0.6230319388784448556348324783782016534327698827416895498688218161699026617974" }, "m": { "re": "0.2466926308819356266046811035814658106226789411524493896320520381070400126163", "im": "-0.05644050179346383193528145217393426750750237591063386193553446584357964310926" }, "c": { "re": "-0.002860919460161307487713467778152917876151415705879903849697933903989355580997", "im": "-0.0023459380563875590284049467715200895184862321100295749521632306910879348707" }, "relative_m_residual": "0.5518800123900989130835504972500698320734266813235022047201088302941531653391" }, { "iteration": 4, "z": { "re": "0.4855559665401836409818469108658818742968680982788746702847837092693809454119", "im": "0.6242065610768863544867394662599014347542733757532309572227154362174768082984" }, "m": { "re": "0.2457001747565963718467626996719916917749069270779835334128399648458035275741", "im": "-0.0562149342676006793409967200654076261577004368753024812967714800995941335834" }, "c": { "re": "-0.003023148668450491435846349294392864153176222213763161551439854121998516538542", "im": "-0.002291452698970653288442970633758503916517013771836695473504536496214625153062" }, "relative_m_residual": "0.5496605002578065436950735852627144268094694745871745956395644773353487968356" }, { "iteration": 5, "z": { "re": "0.4852870048374464316837169243551370368987268865058633870002371157170765631872", "im": "0.6247594337145171692330820895290675746733679950686951345063532371247921306593" }, "m": { "re": "0.2452137173766883737434675127759100480341910948017932590656410136949605246714", "im": "-0.05610398660441843060557301076896679828885532795390780246680632937389002836699" }, "c": { "re": "-0.003101502617559507152743471359717516672533731428592084027055583165132936490252", "im": "-0.002265070692341749904625003896405821992834084810185138426232868640933533431569" }, "relative_m_residual": "0.5485724081239307304721838955567188506228539598834607349455921406137850701155" }, { "iteration": 6, "z": { "re": "0.4852218573360604326100740277678531287745981180137647031825758148436797503615", "im": "0.624893820190192535688368405042634508241362448188452359733753958379029707662" }, "m": { "re": "0.2450935908642057127548110492507063953196028572516131512422591534096876052566", "im": "-0.05607652325152692313998829816889658196136195152185828212383171244481165509123" }, "c": { "re": "-0.003120740195293442455537787576080661712857400508747157234005853615103179996492", "im": "-0.002258582036815556001132213326741909028999456744540110858166387676739817326384" }, "relative_m_residual": "0.5483036810362019887119538899953398508991057968853851965722041010303911824495" }, { "iteration": 7, "z": { "re": "0.4851895320464527041679373154249845369632637373425513686739024013458410236349", "im": "0.6249605578308155044242606014360227023467418799429642719675999598157730730773" }, "m": { "re": "0.2450336562483023162998124038430463046708848563186558062503395436624595678909", "im": "-0.05606281567825485027640311221471012138226118002721433385063041053541816917522" }, "c": { "re": "-0.003130322376785840581802894289702206979212804872886711765843673627247780719901", "im": "-0.002255349134967784999183305792235377701280795765758392916234079191193873277455" }, "relative_m_residual": "0.5481696026840932256627011901232401724288103058453422233587580563514454866031" }, { "iteration": 8, "z": { "re": "0.4851734306858553849706949822076274895222242454419047848951811461584708992124", "im": "0.6249938142413515597573367606966991323492411324198746080586916781281336543633" }, "m": { "re": "0.2450037207078909011390667356802198863940155659576122325817143670820197732383", "im": "-0.05605596784235981326041850828620924987972810093621118134477429404112626540213" }, "c": { "re": "-0.003135104428747625476960545080075483062274421711159478613791027821472586165804", "im": "-0.002253735505162825653949775998194661841017089409814624274249152078906058247217" }, "relative_m_residual": "0.5481026339349883147029699744236853119542734201537890294296928532944697180361" }, { "iteration": 9, "z": { "re": "0.4851714218205290621528010034155596368980397644770142282967955453995515065141", "im": "0.6249979643127855695696222097051404137220393959055699584742106874546902578414" }, "m": { "re": "0.2449999818705937723066336459943721434361201323891329419582643691989657182905", "im": "-0.05605511243024914965740477303371984058533605212132864516709262171736872106249" }, "c": { "re": "-0.003135701503157861499210350047878899729671593467752720032381537492938746974128", "im": "-0.002253534007137919793031881327925322634466997885872215319642794849629560242291" }, "relative_m_residual": "0.5480942697185765831658199197367033268283593360591960883742047518175693363479" } ], "endpoint": { "re": "0.4851714218205290621528010034155596368980397644770142282967955453995515065141", "im": "0.6249979643127855695696222097051404137220393959055699584742106874546902578414" }, "m": { "re": "0.2449999818705937723066336459943721434361201323891329419582643691989657182905", "im": "-0.05605511243024914965740477303371984058533605212132864516709262171736872106249" }, "c": { "re": "-0.003135701503157861499210350047878899729671593467752720032381537492938746974128", "im": "-0.002253534007137919793031881327925322634466997885872215319642794849629560242291" }, "m_scale": "0.4585539484100747172230662363735258736936669710774068406209861320258109016812", "c_scale": "0.0214512413564424018809832611140382189247981243027188200795217631659653377419", "cell_diagonal": "0.2425652296290628707634759651120778234836316051057918425888564152259776575775" }, { "i": 0, "j": 6, "bits": 256, "stop": "newton_step_leaves_cell_after_16_halvings", "steps": [ { "iteration": 0, "z": { "re": "0.2421875", "im": "0.53125" }, "m": { "re": "0.269724712480597635946725702430609012094907888158886773742078658777998635579", "im": "0.0111200507975208247447911087889842771952717272965286410608886015131531938777" }, "c": { "re": "-0.001461508269374637741346111434194298516088480344609404154396141050329776228535", "im": "-0.00748679931020343987123500779621583918964191541290984619551112868363535105343" }, "relative_m_residual": "0.558684954773959681085096746252375973159281856893134928646580876298469445324" }, { "iteration": 1, "z": { "re": "0.2382703803043231220841362510914372655914334533286672844611615890730737342279", "im": "0.5582365915614806165023776804546373979494172297336130821007920279159302428946" }, "m": { "re": "0.2448799948953459937615917582840741956050318718495877792351300686153997925494", "im": "0.01430292500488733850713020901403024569165090617748386260687366377793094837517" }, "c": { "re": "-0.005885570953555815137689964135458035878982666437510961827567970177512073895009", "im": "-0.006631258211575376230952073026895674259099933681309475308832524835327330077856" }, "relative_m_residual": "0.5076569150889345713320898181905753540957560080343766277669282683439279075311" }, { "iteration": 2, "z": { "re": "0.2370094009722908606450388152801390030061937533561228988558630694610177754167", "im": "0.5609481743928088720273426754578870560564979601771878375195265245627833565725" }, "m": { "re": "0.2409068933262800238976012421592106896200860329301823706018582243060736939047", "im": "0.01407003750907413700730387894110857395532978546586982186356269658643173612845" }, "c": { "re": "-0.006497946421275864149050851777736213593346697444322091237012570324124786014658", "im": "-0.006628843058260874267453195063744610673120219524120171570221124832962755646896" }, "relative_m_residual": "0.4994202401245641349151546496887258455123172626648092464486993906698068706975" }, { "iteration": 3, "z": { "re": "0.2364342936808138144135089550404041675627371741867522766113869294082902728578", "im": "0.5621863923888631550115257543275401857053443490037179228902414999516030810392" }, "m": { "re": "0.2389929482518804418005222877087114627324251494434602324660731750676593719772", "im": "0.01395796797853438131176245277271405711872020418276113896243241823908139468883" }, "c": { "re": "-0.006786779138699055791635729509973023596845466883007628321943112968836076953591", "im": "-0.006625827896401207410323417207913841574949121751969755497453127671218455271342" }, "relative_m_residual": "0.4954524365198640862313877440302417887508549033799141154400614953574685665135" }, { "iteration": 4, "z": { "re": "0.2362964411153756914566639837122810547716884427736615342986913776244274910186", "im": "0.5624834322621990367183493334845858078742902606422324043978668781423157630567" }, "m": { "re": "0.2385243016242476549906971611852378446089186878635977967447805277646374554184", "im": "0.01393057845659701904194771596654660048134851056218972903458698474546298326665" }, "c": { "re": "-0.006856929301745812192329594488923603370915513447736760939374142388453793588042", "im": "-0.006624910914894763515978108640329305788640232963280830661817728453207217771032" }, "relative_m_residual": "0.4944808904386956475052910625703871066668373215044607335529920644792002824626" }, { "iteration": 5, "z": { "re": "0.2362921765269422655058328544434754078768397523588079158552639345909373811404", "im": "0.5624926234106118257584540126273648833128865530934715709361374497870248820185" }, "m": { "re": "0.2385097414657487439172111057976142143181639150515036819423081512053360997192", "im": "0.01392972807828276461254026543351083548888620863508512304749062193389117298549" }, "c": { "re": "-0.006859105231521328101426295837458130659435913680348434079079076759994430274128", "im": "-0.006624881286635406473365901785555130784473696350276727930457121770683905081361" }, "relative_m_residual": "0.4944507060062122967936213619190602889330168922437872453043635149914784581019" }, { "iteration": 6, "z": { "re": "0.2362900448993154898639503668827136939546904990357494041969411126330295617601", "im": "0.5624972175789970306809057076075208011784234230768740957443339569072518136023" }, "m": { "re": "0.2385024622786738967248440689187489718120786291704048667356559300016181881713", "im": "0.01392930294590765448378008835488315290406585229515768309443939612452679095118" }, "c": { "re": "-0.006860192983719348753210548351378704982768074997616787107806691109162394754728", "im": "-0.006624866449927127457101679368947176507398394046943298976599002767143366517697" }, "relative_m_residual": "0.4944356156400876841651300188410384101176337139137794473555243842813483531334" }, { "iteration": 7, "z": { "re": "0.2362889792520612196833525511000661753380650054068179826690345373970462296323", "im": "0.5624995143119251470748562607752670500094818035697699403555996031264552841846" }, "m": { "re": "0.2384988229080862923767776047491922186091286216666014976055514281217847658293", "im": "0.01392909039391092876379956355053337957130304375248714724652834427982092418261" }, "c": { "re": "-0.006860736806670298599581081812752579443697008005966217326484181195500050365092", "im": "-0.006624859025931073213187478820462732165598517475380652567973418677861630599312" }, "relative_m_residual": "0.4944280709193602173454995342425624586372332147891268063113549660906901549695" } ], "endpoint": { "re": "0.2362889792520612196833525511000661753380650054068179826690345373970462296323", "im": "0.5624995143119251470748562607752670500094818035697699403555996031264552841846" }, "m": { "re": "0.2384988229080862923767776047491922186091286216666014976055514281217847658293", "im": "0.01392909039391092876379956355053337957130304375248714724652834427982092418261" }, "c": { "re": "-0.006860736806670298599581081812752579443697008005966217326484181195500050365092", "im": "-0.006624859025931073213187478820462732165598517475380652567973418677861630599312" }, "m_scale": "0.4831951143290207913058859001904531625265789693811280893779476486094240296972", "c_scale": "0.05087643736481443749385777476773070443102177336412778041293392129744570533189", "cell_diagonal": "0.2425652296290628707634759651120778234836316051057918425888564152259776575775" }, { "i": 0, "j": 5, "bits": 256, "stop": "newton_step_leaves_cell_after_16_halvings", "steps": [ { "iteration": 0, "z": { "re": "0.2421875", "im": "0.46875" }, "m": { "re": "0.283974866666699953721539920066341595701348078967645840979842142389176983437", "im": "0.02171783649438149406648443563835237472495787626028794651820142792692444505815" }, "c": { "re": "0.004134163141820778135200018668628752816377611364832186497764447896956085727706", "im": "-0.006769714118370617854628711749929391747568583076139653020551585542077879342051" }, "relative_m_residual": "0.686722067866742682518587044939189200062001716817603259210092351443220460286" }, { "iteration": 1, "z": { "re": "0.3042109316056653194228524951810813589120902548365269474651320381980166428007", "im": "0.4578560854000426319308844019334784422122227047239406590125377278681087418413" }, "m": { "re": "0.2739268114351354293638380314268542589980883907757106433477247437822033672962", "im": "0.01435751489297728312233716222235226926530821648867200354641327688459176319144" }, "c": { "re": "0.003525522976338262561942473353096502159083422052151024645668956254400920178099", "im": "-0.00435202872141496801348116531927350866572470902839884128030064938772410330666" }, "relative_m_residual": "0.6614012318513045948521566774506627753908798593211069336198113138929142138393" }, { "iteration": 2, "z": { "re": "0.3105786560661151277716904397349854479271381725576965407413276369972745376694", "im": "0.4403156335089477800331599700632719588701403974520746129292907490397485681401" }, "m": { "re": "0.2693680464707416497846487717888322759269853450038543686618620430657457667887", "im": "0.0142632801828007734137639868121475300971513450913008735407690250461908646294" }, "c": { "re": "0.00378829679048357431985146413141197616221109613185704435646535331324487247708", "im": "-0.004093154460974597714530292605229618168975310010823371469949673379424379453677" }, "relative_m_residual": "0.6504123679180331676214960888080602780026515792725500848273988696736667272195" }, { "iteration": 3, "z": { "re": "0.3113799908069517890157720562932557520283576542995464550338593879270235112212", "im": "0.4384246021071495951345992902704757057885237525445834057663584763170709877988" }, "m": { "re": "0.2688397316585677543826274502206003150874619846544411490383255986250498818992", "im": "0.01423587947284761507734373507995660293133689942027713026770070485993435762725" }, "c": { "re": "0.003808813135984932417495071532393514054761118097338474116211736568461990664137", "im": "-0.004061223659334269950710422457734100349977503096979595644572568353012009158767" }, "relative_m_residual": "0.6491367794520651024012913597581890629880334524310294288479117005787354733737" }, { "iteration": 4, "z": { "re": "0.3115792961033255859495874748232023689765761730218617451786708398874739549524", "im": "0.4379570076201936042924648063062987877713308029870688141350205063713141902199" }, "m": { "re": "0.2687083353230246765725369272751942351473754692884632938097945044799501064672", "im": "0.0142289519174512557535232044873628039049709408629769175510998295400972267806" }, "c": { "re": "0.003813686968127512860714180341720745160279335793966434622775501399165926063078", "im": "-0.00405327915046554736308081709176140266245583807193709231483813218570844167378" }, "relative_m_residual": "0.6488195154983410094359670184079239236923224096426541482571652314512134622344" }, { "iteration": 5, "z": { "re": "0.3116788171448765118779939511632063358878197869550861531948539545615341673006", "im": "0.4377238138545392647400299243783586122916128741474866658185937193358742384886" }, "m": { "re": "0.2686427016685938975073767479843644907353567478236364028415315317617715120944", "im": "0.01422548362808668976783845547857433109020704877555132029225067921782222622096" }, "c": { "re": "0.003816088968425368118948953218135037782437663920495997102978370327710862617994", "im": "-0.004049310982175244813421931225843471710489166305649468851733479764301996023749" }, "relative_m_residual": "0.6486610382837018447261020600417204607412297839799592826203894804405159848733" }, { "iteration": 6, "z": { "re": "0.3117285445832653140609110051203824968678877602592411683503248515636574297177", "im": "0.4376073649529217947302979599730409586438770841640287034183986657587424538606" }, "m": { "re": "0.2686099006978504375604072413526241585258955680503287917897907133323158546413", "im": "0.01422374847456117125269770254422444771254186579040109978726554811444066850799" }, "c": { "re": "0.003817281358336290364379451529383280206395308761162406274243642386393551252026", "im": "-0.004047327926754788866285898351755759203375739034309829241811501516603233726896" }, "relative_m_residual": "0.6485818377275177384545604711252641931611084328786202774660999222933127344032" }, { "iteration": 7, "z": { "re": "0.3117534000108958836769427403701295906731303895803141942843578005530601089058", "im": "0.4375491771426286229873336140641328506269319009079430517884462673559392312125" }, "m": { "re": "0.2685935041432292054840437022974650905626734050939409931065836372851059235438", "im": "0.01422288066005223124274021047238112769970597356312171040311504445117113257585" }, "c": { "re": "0.003817875415318432624727895383470994246906883419849716574136216120069723406481", "im": "-0.004046336657058649678712865137029847038913948443983473592428918593852917566806" }, "relative_m_residual": "0.6485422468837104073683777121935522630598193994953026603619058903321178950432" }, { "iteration": 8, "z": { "re": "0.3117658256492968661843608122951838991102977094943900146182014361467292721218", "im": "0.4375200923536450703644608123403045301600628145476101252648398018616177362055" }, "m": { "re": "0.2685853068444730122190619527369311035097070448792560840284227254534703183086", "im": "0.01422244669514384153408861550433465578020949157009456405397133982779518286297" }, "c": { "re": "0.003818171911124001987858811470740039228978530392156231901357153442639807175094", "im": "-0.004045841086814261332194930743871912726075027658920445874922134468518303408949" }, "relative_m_residual": "0.6485224538106531426600076153244740842359993671945235901214754432767200285963" }, { "iteration": 9, "z": { "re": "0.311772037949334341781909404299795391217921851069400598274038658247870136475", "im": "0.4375055522327219893374293715806489603059600767468189913065627176916393593295" }, "m": { "re": "0.2685812084392192070367024635134952744718672758330110680413337088685327893962", "im": "0.01422222969849742745052479251928289696672602632976804226591054580602847781049" }, "c": { "re": "0.003818320026080433734962608201816779460799379421465590419237313657313184888669", "im": "-0.004045593317855264653880241104642972256002443411153161046720601169445549559026" }, "relative_m_residual": "0.6485125578601259379469802209069951834173619528278276752301569341363334454216" } ], "endpoint": { "re": "0.311772037949334341781909404299795391217921851069400598274038658247870136475", "im": "0.4375055522327219893374293715806489603059600767468189913065627176916393593295" }, "m": { "re": "0.2685812084392192070367024635134952744718672758330110680413337088685327893962", "im": "0.01422222969849742745052479251928289696672602632976804226591054580602847781049" }, "c": { "re": "0.003818320026080433734962608201816779460799379421465590419237313657313184888669", "im": "-0.004045593317855264653880241104642972256002443411153161046720601169445549559026" }, "m_scale": "0.4147298271103050530905061203785272174753102513820104073172841416288033825803", "c_scale": "0.02665631227694499713652466435064293648721240752045817472063482145140090199288", "cell_diagonal": "0.2425652296290628707634759651120778234836316051057918425888564152259776575775" } ], "comparisons": [ { "i": 0, "j": 7, "classification": "inconclusive_no_stable_approximate_root", "promising_for_certificate": false, "root_residuals_small": false, "root_agreement": true, "numerator_samples_large": true, "numerator_replay_agreement": true, "endpoint_difference": "0.00000000000000000000006574545566239120542546902018720124025789713049477215255259362301199579783059" }, { "i": 1, "j": 7, "classification": "inconclusive_no_stable_approximate_root", "promising_for_certificate": false, "root_residuals_small": false, "root_agreement": true, "numerator_samples_large": true, "numerator_replay_agreement": true, "endpoint_difference": "0.00000000000001606700083909701724172324546209604492816601375988886942011396613330028939012" }, { "i": 0, "j": 6, "classification": "inconclusive_no_stable_approximate_root", "promising_for_certificate": false, "root_residuals_small": false, "root_agreement": true, "numerator_samples_large": true, "numerator_replay_agreement": true, "endpoint_difference": "1.042698255259965690555759497215047250846802977691442671647757360971482401405e-26" }, { "i": 0, "j": 5, "classification": "inconclusive_no_stable_approximate_root", "promising_for_certificate": false, "root_residuals_small": false, "root_agreement": true, "numerator_samples_large": true, "numerator_replay_agreement": true, "endpoint_difference": "2.389942205008203307795702184930197641064622696307495366054833511316893304844e-30" } ], "elapsed_seconds": 48.45808616699651, "evaluation_count": 171, "warning": "No sampled winding, approximate root, or numerator sample is a certificate. No witness means inconclusive, not zero-free or PD.", "controls_path": "/private/tmp/riemann-theta-pole-locator-20261005/evidence/diag_theta_pole_locator/controls.json", "remaining_budget_seconds_at_start": 4200.0 }