Starting with polynomial:
P : 4*t^2 - 2
Extension levels are: 2 58
-------------------------------------------------
Trying to find an order 58 Kronrod extension for:
P1 : 4*t^2 - 2
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 4*t^60 - 7100056248952808251326215218100848843/2031870062999831360924751535500812*t^58 + 5791527230493455445334986465437072379759/4063740125999662721849503071001624*t^56 - 209544792278338545268124721947505750328545/580534303714237531692786153000232*t^54 + 73958940429153327335161553593069567418585265/1161068607428475063385572306000464*t^52 - 38694393945555743669385549187155812489343638235/4644274429713900253542289224001856*t^50 + 7791197202028914847874454612828453310723387265775/9288548859427800507084578448003712*t^48 - 309486498646990861776617058169250251882004349502425/4644274429713900253542289224001856*t^46 + 39472189964977110901679716161182062178025142554078375/9288548859427800507084578448003712*t^44 - 16357207867757684885206703110642059944799959947622830125/74308390875422404056676627584029696*t^42 + 1387807392178377928695548102693462423100128802484999751625/148616781750844808113353255168059392*t^40 - 48475552991609043965651966940786450830151146441552072136375/148616781750844808113353255168059392*t^38 + 2797179923141512100472082555990429212104206947634333073925375/297233563501689616226706510336118784*t^36 - 266974650941614531758849853950902288190384202573488703195801875/1188934254006758464906826041344475136*t^34 + 10532294825069122620301580737365197707016287119407151363621294375/2377868508013516929813652082688950272*t^32 - 42848340510803620120034421618789046816868243358951098536619934375/594467127003379232453413020672237568*t^30 + 573155942153902094785240770080120164170627733799793674220882988125/594467127003379232453413020672237568*t^28 - 200595174188110594726684845970611295397593555310949395128681924689375/19022948064108135438509216661511602176*t^26 + 3562030571506248739281040164397943200815761152382733235697279955421875/38045896128216270877018433323023204352*t^24 - 25437059406158723869170737412125921704884884354799234922288603790109375/38045896128216270877018433323023204352*t^22 + 288779202391539686349420354323588703604933370659923458053398614870109375/76091792256432541754036866646046408704*t^20 - 5134711432568548693512814418290797351286171631825142192698012631737765625/304367169025730167016147466584185634816*t^18 + 35077993157232416753588844267452849679164746181689207530417388967529703125/608734338051460334032294933168371269632*t^16 - 44930089905251287769789439235341900660264697963937453113966552287476015625/304367169025730167016147466584185634816*t^14 + 167236295333582233454784506864121225615485993842446815538087891293511796875/608734338051460334032294933168371269632*t^12 - 1733029757638995208262679637987150582562065683476421121481195510528429484375/4869874704411682672258359465346970157056*t^10 + 2942384255576588130997214221423582539157960278421045161138778077110840296875/9739749408823365344516718930693940314112*t^8 - 1496078334397705381994991141402369261385888464530449531019768188751825015625/9739749408823365344516718930693940314112*t^6 + 785612112686584460193819891583289376321955023546619889268345022084261640625/19479498817646730689033437861387880628224*t^4 - 318518767898765749373335667107812800294204251487497105917203917321792265625/77917995270586922756133751445551522512896*t^2 + 10398555386079770047503022980751344714023432533006199393077801080060703125/155835990541173845512267502891103045025792
-------------------------------------------------
Computing nodes and weights
  current precision for roots: 53
  current precision for roots: 106
 current precision for weights: 53
Linear system for weights solvable: 0
  current precision for roots: 106
  current precision for roots: 212
 current precision for weights: 106
Linear system for weights solvable: 0
  current precision for roots: 212
  current precision for roots: 424
 current precision for weights: 212
Linear system for weights solvable: 0
  current precision for roots: 424
  current precision for roots: 848
 current precision for weights: 424
Linear system for weights solvable: 1
Sufficient bits for target precision reached
-------------------------------------------------
The nodes are:
| (-8.9430168819726570181 + 7.4266841219459390083e-912j)  +/-  (7.42e-243, 7.42e-243j)
| (-6.8666129390656305957 + 1.4023618914473997666e-909j)  +/-  (8.38e-241, 8.38e-241j)
| (7.2396493591957207392 - 2.2171385130969069049e-907j)  +/-  (5.8e-241, 5.8e-241j)
| (8.4717843510538516393 - 2.2798995325091375298e-915j)  +/-  (3.73e-242, 3.73e-242j)
| (-10.108673669078215453 - 6.0742693572334529311e-923j)  +/-  (4.44e-245, 4.44e-245j)
| (-9.470977357844282626 + 1.5115175340347884173e-922j)  +/-  (9.43e-244, 9.43e-244j)
| (-3.9075993527348546888 - 1.0926370082425922848e-920j)  +/-  (1.16e-242, 1.16e-242j)
| (9.470977357844282626 - 5.9219454007403233205e-918j)  +/-  (9.79e-244, 9.79e-244j)
| (4.8383351844435399865 - 3.4771257243612558301e-924j)  +/-  (2.37e-241, 2.37e-241j)
| (5.8165826588167862553 + 1.333284719003361988e-936j)  +/-  (9.97e-241, 9.97e-241j)
| (5.4840120606913354557 - 2.8786297746012252343e-949j)  +/-  (6.94e-241, 6.94e-241j)
| (3.3060638313543792842 - 1.2194190262652868869e-964j)  +/-  (9.28e-244, 9.28e-244j)
| (6.5064268202538565646 - 2.5364879267584900093e-968j)  +/-  (1.08e-240, 1.08e-240j)
| (-8.0370579910464019999 + 6.8440295440702428764e-980j)  +/-  (1.2e-241, 1.2e-241j)
| (6.1569599142481210405 + 1.3908921946007167809e-980j)  +/-  (1.14e-240, 1.14e-240j)
| (8.0370579910464019999 - 3.2021434995111468932e-990j)  +/-  (1.24e-241, 1.24e-241j)
| (8.9430168819726570181 - 3.0582415996129161149e-998j)  +/-  (7.21e-243, 7.21e-243j)
| (-2.7159681408676619381 + 2.9843433676856686337e-1004j)  +/-  (4.48e-245, 4.48e-245j)
| (-5.4840120606913354557 + 1.5019656530539814448e-999j)  +/-  (7.11e-241, 7.11e-241j)
| (-2.4244035376244508095 + 1.2506584511025244891e-1004j)  +/-  (7.17e-246, 7.17e-246j)
| (-7.6284269114276458454 + 1.9313555264372543945e-999j)  +/-  (2.96e-241, 2.96e-241j)
| (1.5603366881635462822 + 6.9450109530308205099e-1009j)  +/-  (1.39e-248, 1.39e-248j)
| (-6.5064268202538565646 + 1.3685052154660456436e-999j)  +/-  (1.11e-240, 1.11e-240j)
| (-7.2396493591957207392 - 1.5428474988737286434e-1000j)  +/-  (5.53e-241, 5.53e-241j)
| (3.6052245286321654588 - 2.1696736884281502774e-1005j)  +/-  (3.54e-243, 3.54e-243j)
| (3.0097545596835917052 - 8.8393544714443418015e-1007j)  +/-  (2.13e-244, 2.13e-244j)
| (-3.0097545596835917052 + 2.5225682664168998499e-1006j)  +/-  (2.05e-244, 2.05e-244j)
| (10.108673669078215453 - 1.3617608760799902291e-1005j)  +/-  (4.68e-245, 4.68e-245j)
| (-4.5236640808463846979 - 3.4246803331786896926e-1003j)  +/-  (8.87e-242, 8.87e-242j)
| (-0.99069373567916181374 - 3.7456667484994358972e-1013j)  +/-  (1.14e-250, 1.14e-250j)
| (4.2135933189855834198 - 6.2213842429830901138e-1004j)  +/-  (3.58e-242, 3.58e-242j)
| (6.8666129390656305957 - 1.8956007065439791553e-1003j)  +/-  (9.42e-241, 9.42e-241j)
| (0.99069373567916181374 - 7.2734055559095180225e-1019j)  +/-  (1.08e-250, 1.08e-250j)
| (-5.8165826588167862553 + 1.052561857763465896e-1007j)  +/-  (9.15e-241, 9.15e-241j)
| (7.6284269114276458454 - 1.1604632538455600905e-1010j)  +/-  (2.97e-241, 2.97e-241j)
| (-2.1347818669185493109 - 1.6544226192829851052e-1018j)  +/-  (9.59e-247, 9.59e-247j)
| (-5.1582134234141102616 + 1.2452207330579525571e-1012j)  +/-  (3.94e-241, 3.94e-241j)
| (-6.1569599142481210405 - 6.0487172653589750081e-1012j)  +/-  (1.04e-240, 1.04e-240j)
| (2.4244035376244508095 + 1.1078953129291689645e-1017j)  +/-  (6.37e-246, 6.37e-246j)
| (-8.4717843510538516393 - 7.0758794853866189954e-1014j)  +/-  (3.62e-242, 3.62e-242j)
| (-4.2135933189855834198 - 1.0942015673908903661e-1013j)  +/-  (3.46e-242, 3.46e-242j)
| (4.5236640808463846979 - 5.5297699306203702547e-1013j)  +/-  (8.98e-242, 8.98e-242j)
| (0.14131537646782573227 - 1.5293263312879583077e-1034j)  +/-  (2.28e-254, 2.28e-254j)
| (1.8468419621840626234 - 1.2268498595454928425e-1028j)  +/-  (1.17e-247, 1.17e-247j)
| (-1.2750298703641554577 - 3.9791779339129823291e-1031j)  +/-  (1.24e-249, 1.24e-249j)
| (5.1582134234141102616 - 2.8157906698888865344e-1022j)  +/-  (3.83e-241, 3.83e-241j)
| (-1.5603366881635462822 + 1.3501409523496393635e-1036j)  +/-  (1.31e-248, 1.31e-248j)
| (2.7159681408676619381 + 6.7501140526989101848e-1034j)  +/-  (4.17e-245, 4.17e-245j)
| (1.2750298703641554577 - 3.8402117266492056679e-1037j)  +/-  (1.38e-249, 1.38e-249j)
| (3.9075993527348546888 - 5.0863223633258533185e-1031j)  +/-  (1.17e-242, 1.17e-242j)
| (-1.8468419621840626234 - 2.6164876947492755663e-1034j)  +/-  (1.21e-247, 1.21e-247j)
| (-0.7071067811865475244 - 5.7256233810588158841e-1039j)  +/-  (7.15e-252, 7.15e-252j)
| (-3.6052245286321654588 + 1.7297895478979165692e-1028j)  +/-  (3.4e-243, 3.4e-243j)
| (0.42405199772148581809 - 8.7284168137526832348e-1041j)  +/-  (3.73e-253, 3.73e-253j)
| (2.1347818669185493109 - 2.5877140144855264598e-1034j)  +/-  (9.65e-247, 9.65e-247j)
| (0.7071067811865475244 + 7.482544216041049633e-1039j)  +/-  (7.34e-252, 7.34e-252j)
| (-0.42405199772148581809 + 5.7250545508804016977e-1040j)  +/-  (3.53e-253, 3.53e-253j)
| (-4.8383351844435399865 + 1.3971392871336084221e-1034j)  +/-  (2.09e-241, 2.09e-241j)
| (-0.14131537646782573227 - 3.3670194999795848198e-1048j)  +/-  (2.28e-254, 2.28e-254j)
| (-3.3060638313543792842 - 1.243788786520484123e-1042j)  +/-  (1.01e-243, 1.01e-243j)
-------------------------------------------------
The weights are:
| (5.1534310098637738118e-36 - 1.8137453964766905051e-938j)  +/-  (4.13e-65, 4.16e-184j)
| (6.8865380007423514399e-22 + 7.5389867041885546859e-930j)  +/-  (1.3e-58, 1.31e-177j)
| (3.7079323598082713395e-24 + 6.0292766038722192684e-930j)  +/-  (3.16e-61, 3.19e-180j)
| (1.7199985069606263743e-32 + 4.0593257266555976255e-935j)  +/-  (3.11e-65, 3.13e-184j)
| (1.7387339200018362547e-45 - 4.4816304528280752145e-943j)  +/-  (3.76e-69, 3.79e-188j)
| (3.5494911965018798159e-40 + 1.8551367446047163995e-940j)  +/-  (3.86e-67, 3.89e-186j)
| (4.0093406822393543229e-08 - 1.3636638380649663175e-923j)  +/-  (2.83e-48, 2.86e-167j)
| (3.5494911965018798159e-40 + 2.9539475527378778635e-939j)  +/-  (1.86e-69, 1.88e-188j)
| (1.2192700413315395882e-11 - 7.8578478957163390863e-925j)  +/-  (1.39e-54, 1.4e-173j)
| (3.8441852102570564331e-16 + 6.7527122784913872967e-927j)  +/-  (1.08e-58, 1.09e-177j)
| (1.612570174455528539e-14 - 3.6643191042599121754e-926j)  +/-  (1.38e-57, 1.39e-176j)
| (3.0082044503836238592e-06 + 2.7666749572404283018e-922j)  +/-  (3.37e-49, 3.4e-168j)
| (8.2379801552026701234e-20 + 1.792847418887886991e-928j)  +/-  (7.41e-62, 7.47e-181j)
| (2.0995609811764439806e-29 + 1.0552749906289898547e-935j)  +/-  (1.06e-69, 1.07e-188j)
| (6.6917958786921302007e-18 - 1.1323282614239617572e-927j)  +/-  (1.84e-60, 1.86e-179j)
| (2.0995609811764439806e-29 - 2.2786484133886737405e-933j)  +/-  (1.17e-67, 1.18e-186j)
| (5.1534310098637738118e-36 - 4.8770829577099833493e-937j)  +/-  (1.25e-70, 1.26e-189j)
| (0.00010331755855941275776 - 7.7987251253140507004e-922j)  +/-  (4.07e-52, 4.1e-171j)
| (1.612570174455528539e-14 + 8.8310447882966371613e-927j)  +/-  (3.31e-65, 3.34e-184j)
| (0.00045917322576623160306 + 1.702427850510500015e-921j)  +/-  (1.23e-50, 1.24e-169j)
| (1.1976401236464140107e-26 - 1.905339737880832328e-933j)  +/-  (7.34e-71, 7.4e-190j)
| (0.014133003807973406996 + 1.5123996543307594e-920j)  +/-  (6.61e-46, 6.66e-165j)
| (8.2379801552026701234e-20 - 3.9812704145284451282e-929j)  +/-  (1.41e-68, 1.42e-187j)
| (3.7079323598082713395e-24 + 1.2698232382392264407e-931j)  +/-  (5.23e-70, 5.28e-189j)
| (3.8437875155632205841e-07 - 1.040644436656493329e-922j)  +/-  (1.59e-59, 1.61e-178j)
| (1.9370052406144784588e-05 - 6.707949975172342145e-922j)  +/-  (2.83e-57, 2.85e-176j)
| (1.9370052406144784588e-05 + 3.2652771173281800651e-922j)  +/-  (1.75e-58, 1.77e-177j)
| (1.7387339200018362547e-45 - 4.8243182000412785073e-942j)  +/-  (6.1e-80, 6.15e-199j)
| (2.284359966384415009e-10 - 9.9653049948290499022e-925j)  +/-  (4.28e-65, 4.31e-184j)
| (0.060031612279458387483 - 2.3279660711303761151e-920j)  +/-  (1.54e-51, 1.55e-170j)
| (3.3828479834464532881e-09 - 1.1052199296708277563e-923j)  +/-  (1.18e-62, 1.19e-181j)
| (6.8865380007423514399e-22 - 3.1118394584189855059e-929j)  +/-  (3.92e-69, 3.96e-188j)
| (0.060031612279458387483 + 2.9275044398531967062e-920j)  +/-  (5.61e-54, 5.65e-173j)
| (3.8441852102570564331e-16 - 1.4851905222859899343e-927j)  +/-  (7.34e-69, 7.4e-188j)
| (1.1976401236464140107e-26 + 1.1588653324626452555e-931j)  +/-  (1.1e-71, 1.11e-190j)
| (0.0017089224298964096489 - 3.4035070175821008913e-921j)  +/-  (3.37e-58, 3.4e-177j)
| (5.0686378086712269744e-13 - 4.7552704215823231963e-926j)  +/-  (9.46e-68, 9.54e-187j)
| (6.6917958786921302007e-18 + 2.3393632352359372308e-928j)  +/-  (8.99e-70, 9.06e-189j)
| (0.00045917322576623160306 - 3.0170231377003068036e-921j)  +/-  (6.13e-62, 6.17e-181j)
| (1.7199985069606263743e-32 + 5.8918235116682955211e-937j)  +/-  (6.41e-77, 6.46e-196j)
| (3.3828479834464532881e-09 + 3.8824059853858569838e-924j)  +/-  (3.76e-66, 3.79e-185j)
| (2.284359966384415009e-10 + 3.1030801914756447657e-924j)  +/-  (5.78e-67, 5.82e-186j)
| (0.15631429673134289349 - 4.2979080318480632289e-920j)  +/-  (8.98e-60, 9.05e-179j)
| (0.0053490950724115713305 - 9.6101711479715303218e-921j)  +/-  (1.08e-61, 1.08e-180j)
| (0.031616060661762463528 + 1.6307321528802864015e-920j)  +/-  (1.79e-60, 1.81e-179j)
| (5.0686378086712269744e-13 + 1.7901473774531749354e-925j)  +/-  (2.64e-68, 2.66e-187j)
| (0.014133003807973406996 - 1.0519375948821905364e-920j)  +/-  (4.21e-62, 4.24e-181j)
| (0.00010331755855941275776 + 1.4865368631180085207e-921j)  +/-  (2.8e-64, 2.82e-183j)
| (0.031616060661762463528 - 2.1918097832677810285e-920j)  +/-  (3.93e-62, 3.96e-181j)
| (4.0093406822393543229e-08 + 3.5606602518284420081e-923j)  +/-  (4.37e-66, 4.41e-185j)
| (0.0053490950724115713305 + 6.2424072430067074686e-921j)  +/-  (8.05e-64, 8.11e-183j)
| (0.096939638665822614521 + 3.0628721365610086119e-920j)  +/-  (8.19e-63, 8.07e-182j)
| (3.8437875155632205841e-07 + 4.329629055571806578e-923j)  +/-  (4.35e-68, 4.39e-187j)
| (0.13332207321399164034 + 4.0980002239154490806e-920j)  +/-  (2.88e-63, 2.74e-182j)
| (0.0017089224298964096489 + 5.617580198398075677e-921j)  +/-  (9.58e-65, 9.43e-184j)
| (0.096939638665822614521 - 3.6059803749594368869e-920j)  +/-  (1.83e-63, 1.74e-182j)
| (0.13332207321399164034 - 3.7163065587009866734e-920j)  +/-  (2.53e-64, 2.32e-183j)
| (1.2192700413315395882e-11 + 2.2985897149978987852e-925j)  +/-  (1.6e-70, 1.61e-189j)
| (0.15631429673134289349 + 4.1602199707928485387e-920j)  +/-  (1.68e-64, 1.35e-183j)
| (3.0082044503836238592e-06 - 1.2467096740275594286e-922j)  +/-  (1.15e-67, 1.17e-186j)
