Starting with polynomial:
P : 3/2*t^2 - 1/2
Extension levels are: 2 20 23
-------------------------------------------------
Trying to find an order 20 Kronrod extension for:
P1 : 3/2*t^2 - 1/2
Solvable: 1
-------------------------------------------------
Trying to find an order 23 Kronrod extension for:
P2 : 3/2*t^22 - 30461783/3830466*t^20 + 66155815/3643614*t^18 - 14341808855/614151382*t^16 + 39940250075/2149529837*t^14 - 670092247/70863621*t^12 + 2251326473/732257417*t^10 - 13150594545/21235465093*t^8 + 27599544115/382238371674*t^6 - 544763725/127412790558*t^4 + 4285838227/43957412742510*t^2 - 333527539/923105667592710
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 3/2*t^45 - 2472630009368782708631892228831660071856653075110383462705143788111517569747228439103919524175/148458272315597919555072864418835773531783637061312834617362325283761978563739592482847168762*t^43 + 12803591469084327665453165411130460342978452682546171907832994461940166046038704189314048648695/148458272315597919555072864418835773531783637061312834617362325283761978563739592482847168762*t^41 - 203768673348221334029932961796192750259476609213855442867711461089740195448088997622298486214384745/736725986832890231864238785689014219270665710912338860237863189980733254744247529398476426776166*t^39 + 1595457029938531246191733811401759066224549068176855005006730305233730671290803761538250617299405/2592801361402831384137592508709451752083790837801092016925612031103636391759543844036870280258*t^37 - 457688311994096815488945929200171644036113919066072654574658444515030361568160764109286956400386851443/454026917985211680959011307698562985455684336839986893973907583249061908462749586054180808134786094*t^35 + 7599181757836996637607159873361271587615590717865682588617726029764712419107054825067766881515016406065/6032071910374955189884007373709479663911234760874111591367629320308965355290815929005545022362158106*t^33 - 4922574229907279680455893467582414089322026697208024428533338695445463442834231313184694026928171624489370455/4009455867416492173512270899895162801311937329460492942295619077039726079019800676245386052398895417424438*t^31 + 1546641571496362503647304258452873641400700077444852456584087526307769435428060747629215673427895678291220485/1635192830720550955556847809404248423576527436208542052503052019898690129001162948606989242568213108027939*t^29 - 4785977780060574188422035022918725828075890981689951791160659439216496090399006792256010293010677488702318755765/8244585866533337898919159177505551439658245246210496320373750248052647399729760098498901588986083310914522647*t^27 + 33384874819464219257154347232661480997339473183012066701338104915403233212289412215840199975608498700341163059087817/117251751998548287152461975436091450724339677809856941836248684777722067103156738200818545431363748153389369578085*t^25 - 860473842953193989648128719504845219406116295635931023308829933902209266500943556691372142614482877784892970858523990/7715165281504477294631997983694817457661550799888586772825163458374112015387713373613860289383734628493020518237993*t^23 + 19066616804490385524512363261194664055367746579393448072827491438949629953877049211043618930360789461815009418497593/548905039790832376693185627298445510821770412640294711110090680832940775798335338834187688572755823371044938056458*t^21 - 19463712122867585301785981333495054866357078775815777177788601443068847420303889294351153052115324157794654085/2281429277134928435072696780502024176618039346460241445695876011891007684211920093908850436924632573851897314*t^19 + 12633737356418823882445572985509597833691857691430469097348541408681951899884752337132129905570361391513705708065/7741694747651918625531685833930604039797931516426585192815176441056268251713707909254109126757134075752611785454*t^17 - 1471740479453429974093979744970596123605711854909323877533568788583389253255609693267973742412190163184751296257/6161757044049486252974198929046807296982027125319118826934528187779478812588461397161433794765882223558201216994*t^15 + 97104840701752019962976413230296451222978734004746781585983509800307329074983354393536226567065474898454941955/3720035138482090768112628257862757785357447611789398079664435432715349679394898605745481008961220270166839429374*t^13 - 84263502435970256601281068770772807325953951727424515773197263032708536628642285537893226299984235767959684497/40920386523302998449238910836490335638931923729683378876308789759868846473343884663200291098573422971835233723114*t^11 + 1056614248796214411293566055990002992018171675354602063947136534897884335811797593135818590414626893579164650815/9452609286882992641774188403229267532593274381556860520427330434529703535342437357199267243770460706493938990039334*t^9 - 380055595826622505413123881785401469943640852820055335506702961835699090137707214194599454288560117163254123845/97676962631124257298333280166702431170130501942754225377749081156806936531871852691059094852294760633770702897073118*t^7 + 15716628750271364689555984769158375496781628329071617386940884617339952441928832252558195994281563326507096088/202330851164471675832261794631026464566698896881419466853908810967671511387448837717193839336896289884239313143937173*t^5 - 27854534684632669928755596331766808994963998017674691445864779358171561226429162257865381646573010875674431460/38240530870085146732297479185264001803106091510588279235388765272889915652227830328549635634673398788121230184204125697*t^3 + 6152740244067124820523167602414272291309728799596742212466402137059440105016550117517921522487313778747691/3034962767467075137483926919465396968500483453221292002808632164515072670811732565757907590053444348263589697159057595*t
-------------------------------------------------
Computing nodes and weights
  current precision for roots: 53
  current precision for roots: 106
  current precision for roots: 212
 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: 1
  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:
| (0.3965044793486969045 - 5.4165633781323036052e-881j)  +/-  (3.03e-248, 3.03e-248j)
| (0.98403402179106086377 - 4.6764261905098884709e-882j)  +/-  (9.6e-240, 9.6e-240j)
| (-0.94888574829235089511 - 4.0014053171884680067e-901j)  +/-  (5.53e-240, 5.53e-240j)
| (0.99901334269512857612 + 4.72971317897398621e-907j)  +/-  (3e-240, 3e-240j)
| (0.96888548864291551998 - 7.5967181291794553665e-926j)  +/-  (8.24e-240, 8.24e-240j)
| (0.92419486526088066841 + 1.2725667933034237367e-935j)  +/-  (2.92e-240, 2.92e-240j)
| (-0.99406617535715816159 - 1.4202693395680081196e-935j)  +/-  (7.52e-240, 7.52e-240j)
| (-0.92419486526088066841 + 9.8787619304929866995e-942j)  +/-  (3.21e-240, 3.21e-240j)
| (-0.98403402179106086377 - 1.0242707794640315109e-940j)  +/-  (9.28e-240, 9.28e-240j)
| (-0.99901334269512857612 + 1.999964889892136971e-942j)  +/-  (2.83e-240, 2.83e-240j)
| (0.86102168810005007167 + 1.2213853933242460303e-944j)  +/-  (5.28e-241, 5.28e-241j)
| (-0.20139298243596146919 + 2.1614469865959852266e-962j)  +/-  (8.17e-252, 8.17e-252j)
| (-0.86102168810005007167 + 2.1247585152816287082e-950j)  +/-  (4.71e-241, 4.71e-241j)
| (-0.780839931409340531 - 2.9405101081057301006e-951j)  +/-  (4.3e-242, 4.3e-242j)
| (0.99406617535715816159 + 1.9893718823155552523e-949j)  +/-  (7.63e-240, 7.63e-240j)
| (0.89486329886735047101 + 1.5762571684572821966e-960j)  +/-  (1.35e-240, 1.35e-240j)
| (0.780839931409340531 - 2.622172541987662105e-968j)  +/-  (3.97e-242, 3.97e-242j)
| (-0.96888548864291551998 + 3.1956785278776698932e-965j)  +/-  (8.24e-240, 8.24e-240j)
| (-0.82292771859227532435 + 2.4145647422251550586e-968j)  +/-  (1.55e-241, 1.55e-241j)
| (-0.89486329886735047101 + 3.220006761442571477e-967j)  +/-  (1.26e-240, 1.26e-240j)
| (0.82292771859227532435 + 3.8776266373520171668e-968j)  +/-  (1.54e-241, 1.54e-241j)
| (0.73496197869585485798 + 5.8043792853466688107e-975j)  +/-  (9.55e-243, 9.55e-243j)
| (0.20139298243596146919 + 5.0862055632378367749e-985j)  +/-  (8.22e-252, 8.22e-252j)
| (-0.73496197869585485798 - 1.1895961029861846972e-976j)  +/-  (1.02e-242, 1.02e-242j)
| (-0.68553363455588642792 - 1.4963671249146491216e-976j)  +/-  (1.88e-243, 1.88e-243j)
| (-5.8344118366987533523e-985 - 4.2918685810320276236e-985j)  +/-  (3.26e-983, 3.26e-983j)
| (0.68553363455588642792 + 2.6265160739939482343e-977j)  +/-  (1.77e-243, 1.77e-243j)
| (0.94888574829235089511 + 2.7473113232289585777e-986j)  +/-  (5.81e-240, 5.81e-240j)
| (-0.4588223560349795942 - 6.9429581397097509775e-1009j)  +/-  (4.11e-247, 4.11e-247j)
| (-0.63288340507353386874 - 9.6279202023712366658e-1007j)  +/-  (2.98e-244, 2.98e-244j)
| (-0.26749860075872435362 + 1.0021781417583652936e-1012j)  +/-  (1.53e-250, 1.53e-250j)
| (0.26749860075872435362 + 2.6296221012862262694e-1011j)  +/-  (1.55e-250, 1.55e-250j)
| (0.63288340507353386874 + 6.7180553119295691464e-1006j)  +/-  (2.82e-244, 2.82e-244j)
| (0.06741352924250103978 - 1.1789035521354697419e-1016j)  +/-  (2.42e-254, 2.42e-254j)
| (-0.57735026918962576451 + 2.9989291802903489697e-1012j)  +/-  (3.61e-245, 3.61e-245j)
| (-0.3965044793486969045 - 7.9563291126110171485e-1014j)  +/-  (3.1e-248, 3.1e-248j)
| (0.13461338896681897232 + 6.358794586662920466e-1016j)  +/-  (4.03e-253, 4.03e-253j)
| (0.57735026918962576451 - 9.4882519522797485734e-1011j)  +/-  (3.55e-245, 3.55e-245j)
| (0.33263121197918282965 + 8.7907338705306866743e-1017j)  +/-  (2e-249, 2e-249j)
| (-0.33263121197918282965 - 1.6035016628286323924e-1017j)  +/-  (2.18e-249, 2.18e-249j)
| (-0.51922703896308681875 - 5.2409113182184175126e-1014j)  +/-  (3.91e-246, 3.91e-246j)
| (-0.13461338896681897232 + 3.2096166662975218751e-1019j)  +/-  (4.43e-253, 4.43e-253j)
| (0.4588223560349795942 - 3.0034288407682372407e-1014j)  +/-  (3.94e-247, 3.94e-247j)
| (0.51922703896308681875 + 4.6867978782245880911e-1016j)  +/-  (3.97e-246, 3.97e-246j)
| (-0.06741352924250103978 - 1.5166569664307878732e-1025j)  +/-  (2.42e-254, 2.42e-254j)
-------------------------------------------------
The weights are:
| (0.063149684060381810366 + 6.2851261919809184085e-882j)  +/-  (4.09e-72, 1.64e-187j)
| (0.012630853802229355335 + 3.932966637998425907e-883j)  +/-  (2.01e-72, 8.07e-188j)
| (0.022357278067738573968 + 4.6466843272290100878e-883j)  +/-  (7.37e-74, 2.96e-189j)
| (0.0026560942648756319432 - 9.13250420836273331e-883j)  +/-  (7.06e-73, 2.83e-188j)
| (0.017615760913568980125 - 4.7736250058148088859e-882j)  +/-  (1.13e-72, 4.53e-188j)
| (0.027020403973171891551 - 9.9795078772901837026e-883j)  +/-  (1.21e-73, 4.84e-189j)
| (0.0074226100516476613752 - 1.4728795884430397042e-883j)  +/-  (1.63e-74, 6.55e-190j)
| (0.027020403973171891551 - 5.9403956455018806396e-883j)  +/-  (1.1e-74, 4.42e-190j)
| (0.012630853802229355335 + 2.4388448295626215693e-883j)  +/-  (9.86e-75, 3.95e-190j)
| (0.0026560942648756319432 + 4.9720072213875891717e-884j)  +/-  (7.33e-75, 2.94e-190j)
| (0.036015612837360993572 + 5.2602525317311430277e-883j)  +/-  (1.06e-76, 4.27e-192j)
| (0.066490697425402272233 - 8.1783234971862922482e-882j)  +/-  (4.75e-78, 1.9e-193j)
| (0.036015612837360993572 - 9.0284277708437933244e-883j)  +/-  (9.62e-77, 3.86e-192j)
| (0.044015740172183673281 - 1.3248338819419742588e-882j)  +/-  (9.69e-78, 3.89e-193j)
| (0.0074226100516476613752 + 3.8811658013010896057e-882j)  +/-  (1.31e-75, 5.25e-191j)
| (0.031621741615636868629 + 1.9840715192704246295e-883j)  +/-  (1.21e-76, 4.87e-192j)
| (0.044015740172183673281 + 2.2256934009676841123e-882j)  +/-  (2.33e-78, 9.35e-194j)
| (0.017615760913568980125 - 3.477755441271557317e-883j)  +/-  (4.32e-76, 1.73e-191j)
| (0.040128068008405023368 + 1.0968663491526233361e-882j)  +/-  (5.07e-78, 2.03e-193j)
| (0.031621741615636868629 + 7.3773289732611576042e-883j)  +/-  (3.76e-77, 1.51e-192j)
| (0.040128068008405023368 - 1.3002402364591896114e-882j)  +/-  (5.08e-79, 2.04e-194j)
| (0.047701383924733346024 - 3.4273287873074185193e-882j)  +/-  (2.82e-80, 1.13e-195j)
| (0.066490697425402272233 - 2.3899922480206963047e-881j)  +/-  (8.97e-83, 3.6e-198j)
| (0.047701383924733346024 + 1.5933755608980148974e-882j)  +/-  (1.68e-80, 6.72e-196j)
| (0.051098704734905193159 - 1.9144463892167011999e-882j)  +/-  (1.74e-81, 6.98e-197j)
| (0.067450532222104456902 + 1.3370556366014985955e-881j)  +/-  (3.59e-84, 1.44e-199j)
| (0.051098704734905193159 + 5.1155541487043750597e-882j)  +/-  (2.64e-82, 1.06e-197j)
| (0.022357278067738573968 + 2.12988607600225947e-882j)  +/-  (3.62e-80, 1.45e-195j)
| (0.06142526218828800363 - 4.0019051569302840353e-882j)  +/-  (2.39e-84, 9.57e-200j)
| (0.054143971645002954733 + 2.3021919244994592295e-882j)  +/-  (6.19e-83, 2.48e-198j)
| (0.065669174165434287318 + 6.8829369305698836595e-882j)  +/-  (1.22e-84, 4.91e-200j)
| (0.065669174165434287318 + 3.3181199513167512802e-881j)  +/-  (2.32e-85, 9.28e-201j)
| (0.054143971645002954733 - 7.6954185305243969862e-882j)  +/-  (1e-84, 4.02e-200j)
| (0.067340509459790468051 - 1.5797956256063839155e-881j)  +/-  (1.05e-85, 4.21e-201j)
| (0.056875029411384650373 - 2.769028379739335248e-882j)  +/-  (5.08e-85, 2.04e-200j)
| (0.063149684060381810366 + 4.8090407268395981689e-882j)  +/-  (5.51e-86, 2.21e-201j)
| (0.067026188642210363669 + 1.9012119579845881227e-881j)  +/-  (6.04e-86, 2.42e-201j)
| (0.056875029411384650373 + 1.2077710165215888371e-881j)  +/-  (1.03e-86, 4.13e-202j)
| (0.064548896643377116283 - 6.0411006071699009781e-881j)  +/-  (1.43e-86, 5.75e-202j)
| (0.064548896643377116283 - 5.7652724297798606774e-882j)  +/-  (1.1e-86, 4.45e-202j)
| (0.059321067881218652562 + 3.3289397908535672625e-882j)  +/-  (1.78e-86, 7.14e-202j)
| (0.067026188642210363669 + 9.6688293754117066574e-882j)  +/-  (1.46e-87, 5.87e-203j)
| (0.06142526218828800363 + 4.7938183420653675901e-881j)  +/-  (5.52e-88, 2.14e-203j)
| (0.059321067881218652562 - 2.0972091029963857467e-881j)  +/-  (4.93e-88, 1.9e-203j)
| (0.067340509459790468051 - 1.1378565090193028378e-881j)  +/-  (5.1e-88, 2.19e-203j)
