Starting with polynomial:
P : t^2 - 1
Extension levels are: 2 3 12 20
-------------------------------------------------
Trying to find an order 3 Kronrod extension for:
P1 : t^2 - 1
Solvable: 1
-------------------------------------------------
Trying to find an order 12 Kronrod extension for:
P2 : t^5 - 7*t^3 + 6*t
Solvable: 1
-------------------------------------------------
Trying to find an order 20 Kronrod extension for:
P3 : t^17 - 1927729267/18122395*t^15 + 76689404679/18122395*t^13 - 1451963624397/18122395*t^11 + 2765036333631/3624479*t^9 - 12957851045997/3624479*t^7 + 27641768331177/3624479*t^5 - 23638263740091/3624479*t^3 + 6464746886598/3624479*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^37 - 137885427060691155603188011852832155018157808492382636008901500330210326626896760426867851611919971059045419/296246896185710938304554200393915299263986747233743795083330865212148833473368091501155397420631665875015*t^35 + 28401865784716907268077654505005876097810837471748400964181150772250851140807280076221697317810624865462795563/296246896185710938304554200393915299263986747233743795083330865212148833473368091501155397420631665875015*t^33 - 3429045819264892772698962900221791065307139422256570722901911899410360071343163074391597045572010496169312593329/296246896185710938304554200393915299263986747233743795083330865212148833473368091501155397420631665875015*t^31 + 54191795693746139715063552146702609120600365696976827935532647393032468854229089011799596564796372640135068605237/59249379237142187660910840078783059852797349446748759016666173042429766694673618300231079484126333175003*t^29 - 2964381279369501701809614173664502854362094572701530434214881236744562824941150458294545548979806479039860459956747/59249379237142187660910840078783059852797349446748759016666173042429766694673618300231079484126333175003*t^27 + 115813400216063060540306092187747016522028385895236684244477115973650558395235893704582765081533984435177483891468251/59249379237142187660910840078783059852797349446748759016666173042429766694673618300231079484126333175003*t^25 - 3287202806406687286268138519862366893951135669346210638778578946679197500624803911213277240215680990033086664771003769/59249379237142187660910840078783059852797349446748759016666173042429766694673618300231079484126333175003*t^23 + 68306496467102120852281737301604522784094306835252244244320161215213867080985316241915022378589191543568194466569428567/59249379237142187660910840078783059852797349446748759016666173042429766694673618300231079484126333175003*t^21 - 1039493849531555969960377470180425722399144022787714873318254047561873426704197696529357090918994447510354158188036475285/59249379237142187660910840078783059852797349446748759016666173042429766694673618300231079484126333175003*t^19 + 11514023597923209516375958316968114306303072432688887822303613002551747106248655677113953252165599823398609778992272726445/59249379237142187660910840078783059852797349446748759016666173042429766694673618300231079484126333175003*t^17 - 91638700727372879598684525814340388215359457769385669078923474187943867527577112601072928850984355228880973370320231719655/59249379237142187660910840078783059852797349446748759016666173042429766694673618300231079484126333175003*t^15 + 513292406290775689709898294056809060361284241014944920166560319543435028218719892044852013150619956767040482138922313800855/59249379237142187660910840078783059852797349446748759016666173042429766694673618300231079484126333175003*t^13 - 1961709479044381440148093600801797722990561355937816179577321889743194724618569617777320335732421664803744592311233461713065/59249379237142187660910840078783059852797349446748759016666173042429766694673618300231079484126333175003*t^11 + 4889399494554241310261405047869067703214016505518883005993457070423397086230265565886769244982985401313532697692047075345225/59249379237142187660910840078783059852797349446748759016666173042429766694673618300231079484126333175003*t^9 - 7447055826185708139971679984325950995709190795250496319355685363719159173238792939229441119467985844518011222418309742039075/59249379237142187660910840078783059852797349446748759016666173042429766694673618300231079484126333175003*t^7 + 6341401182847613248823218430372918700172896104613411387804297605376892662990804668284419880731614568243749344493309405866050/59249379237142187660910840078783059852797349446748759016666173042429766694673618300231079484126333175003*t^5 - 2696809572103540545499318078388479322687922108200790168563080579858541524180007618336374798568657113498737582221371059313800/59249379237142187660910840078783059852797349446748759016666173042429766694673618300231079484126333175003*t^3 + 442580832423789831364499912448837078911661405168780064891696086924254708390365818929956440391966485862625809364719813574400/59249379237142187660910840078783059852797349446748759016666173042429766694673618300231079484126333175003*t
-------------------------------------------------
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: 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:
| (9.6205892293917661361 + 7.6505127646088924234e-631j)  +/-  (5.25e-249, 5.25e-249j)
| (5.1972139741334507794 - 3.6289650361385836915e-627j)  +/-  (1.03e-246, 1.03e-246j)
| (7.7764375000524462017 - 2.8970612922271833175e-630j)  +/-  (2.03e-247, 2.03e-247j)
| (3.7769507101607374279 - 4.4485420390442634494e-629j)  +/-  (2.35e-247, 2.35e-247j)
| (7.0383239062881268111 - 5.907139291239378743e-633j)  +/-  (4.56e-247, 4.56e-247j)
| (5.7592663526291469682 + 5.233641483923887351e-632j)  +/-  (1.12e-246, 1.12e-246j)
| (8.6106397401162822493 - 2.2192276848201087172e-634j)  +/-  (4.64e-248, 4.64e-248j)
| (4.2051618777898870634 - 1.4929840758864847507e-632j)  +/-  (5.64e-247, 5.64e-247j)
| (4.6748420265746822739 - 1.3580697224037472782e-633j)  +/-  (8.75e-247, 8.75e-247j)
| (6.3696949628033208131 + 7.0483398667557836507e-636j)  +/-  (7.89e-247, 7.89e-247j)
| (3.3008613454059083377 - 4.1835270631741429829e-653j)  +/-  (7.99e-248, 7.99e-248j)
| (-5.1972139741334507794 - 1.295745393212333344e-692j)  +/-  (1.03e-246, 1.03e-246j)
| (-6.3696949628033208131 - 2.2798632655225529777e-728j)  +/-  (8.01e-247, 8.01e-247j)
| (-9.6205892293917661361 + 3.6853213532826726244e-745j)  +/-  (5.73e-249, 5.73e-249j)
| (-7.7764375000524462017 + 1.1021498822153570675e-757j)  +/-  (1.91e-247, 1.91e-247j)
| (-5.7592663526291469682 + 1.1688130898133139201e-772j)  +/-  (1.11e-246, 1.11e-246j)
| (-2.7732162444963326412 - 6.3104028882777606523e-782j)  +/-  (2.34e-248, 2.34e-248j)
| (-7.0383239062881268111 - 8.760707194658918812e-787j)  +/-  (4.59e-247, 4.59e-247j)
| (2.2024673943900419838 + 2.3092188406085546007e-797j)  +/-  (2.94e-249, 2.94e-249j)
| (1 - 1.1290608807930328392e-800j)  +/-  (7.98e-252, 7.98e-252j)
| (-2.4494897427831780982 + 1.7413962218742378813e-794j)  +/-  (1.13e-248, 1.13e-248j)
| (-4.6748420265746822739 - 1.3932594045411336072e-800j)  +/-  (9.05e-247, 9.05e-247j)
| (-8.6106397401162822493 - 6.5781043301552837695e-808j)  +/-  (5e-248, 5e-248j)
| (-0.72668426889066405757 + 4.8220111204286765727e-814j)  +/-  (1.64e-250, 1.64e-250j)
| (-3.3008613454059083377 - 3.0366734214064975637e-811j)  +/-  (7.91e-248, 7.91e-248j)
| (-1 - 4.7246170406655439067e-828j)  +/-  (9.83e-252, 9.83e-252j)
| (0.72406087233068678388 - 3.3984569365104972878e-826j)  +/-  (1.56e-250, 1.56e-250j)
| (1.638713499982732431 + 1.6899299079202005366e-828j)  +/-  (8.36e-251, 8.36e-251j)
| (-3.7769507101607374279 + 4.0811241099650075768e-825j)  +/-  (2.65e-247, 2.65e-247j)
| (5.3920917664420246834e-843 - 8.1614045321978600532e-843j)  +/-  (3.62e-841, 3.62e-841j)
| (2.7732162444963326412 - 1.4473039267848399094e-837j)  +/-  (2.35e-248, 2.35e-248j)
| (2.4494897427831780982 + 1.2884756376046783521e-838j)  +/-  (1.12e-248, 1.12e-248j)
| (0.72668426889066405757 - 1.6231667932607026215e-840j)  +/-  (1.65e-250, 1.65e-250j)
| (-1.638713499982732431 - 7.4169068762925560674e-838j)  +/-  (8.39e-251, 8.39e-251j)
| (-0.72406087233068678388 - 3.9506017286272060559e-845j)  +/-  (1.52e-250, 1.52e-250j)
| (-2.2024673943900419838 - 1.3287594916730996266e-844j)  +/-  (3.05e-249, 3.05e-249j)
| (-4.2051618777898870634 - 1.797563105479202844e-865j)  +/-  (5.94e-247, 5.94e-247j)
-------------------------------------------------
The weights are:
| (3.7112612025153023163e-21 - 6.7962930070680857974e-644j)  +/-  (4.34e-85, 6.02e-209j)
| (2.9468941100980440268e-07 + 4.7108136062547924366e-633j)  +/-  (4.94e-76, 6.85e-200j)
| (2.2969780265081665293e-14 - 2.1434575636602961417e-639j)  +/-  (3.62e-82, 5.02e-206j)
| (0.00014036397789546449403 - 1.5707286453131738689e-631j)  +/-  (1.22e-72, 1.7e-196j)
| (4.891688558466824596e-12 + 1.1709211234366619753e-637j)  +/-  (6.06e-81, 8.41e-205j)
| (1.4620105501409031624e-08 + 1.5749597145814886749e-634j)  +/-  (2.24e-78, 3.11e-202j)
| (2.8521422904039545853e-17 + 2.1557250084976156242e-641j)  +/-  (1.69e-84, 2.35e-208j)
| (2.5219392745758652604e-05 + 6.5731644971919175065e-632j)  +/-  (2.52e-75, 3.49e-199j)
| (3.587507358127395944e-06 - 1.89471741832831276e-632j)  +/-  (1.98e-76, 2.75e-200j)
| (3.9400032069822203011e-10 - 4.5098976413782352508e-636j)  +/-  (3.2e-80, 4.44e-204j)
| (0.00087466127946270921673 + 4.4070642005598493775e-631j)  +/-  (2.6e-74, 3.61e-198j)
| (2.9468941100980440268e-07 + 9.9878290452279229662e-635j)  +/-  (2.78e-86, 3.86e-210j)
| (3.9400032069822203011e-10 + 4.4912528512538117234e-637j)  +/-  (3.42e-89, 4.74e-213j)
| (3.7112612025153023163e-21 + 2.0105526321804150404e-644j)  +/-  (9.63e-96, 1.34e-219j)
| (2.2969780265081665293e-14 + 4.2097396406721058389e-640j)  +/-  (1.29e-92, 1.8e-216j)
| (1.4620105501409031624e-08 - 7.9019528743091078678e-636j)  +/-  (9.73e-89, 1.35e-212j)
| (0.0045746627746214707619 - 7.0607572659948650687e-631j)  +/-  (2.55e-83, 3.53e-207j)
| (4.891688558466824596e-12 - 1.7364055872118545883e-638j)  +/-  (2.36e-91, 3.28e-215j)
| (0.019172352762454920146 - 6.785949862489679624e-630j)  +/-  (8.11e-81, 1.13e-204j)
| (0.23726464622749018391 - 3.5636606660680635409e-629j)  +/-  (7.83e-80, 1.09e-203j)
| (0.00073473839254811076669 + 2.344466216281074336e-630j)  +/-  (7.47e-83, 1.04e-206j)
| (3.587507358127395944e-06 - 9.5895942272717933335e-634j)  +/-  (8.3e-88, 1.15e-211j)
| (2.8521422904039545853e-17 - 5.2729974983642420093e-642j)  +/-  (5.09e-95, 7.07e-219j)
| (-19.31011757351190177 + 2.9061277819514083998e-627j)  +/-  (2.84e-80, 3.97e-204j)
| (0.00087466127946270921673 + 1.0602291789238089465e-631j)  +/-  (6.79e-86, 9.44e-210j)
| (0.23726464622749018391 - 2.4271397052538509381e-629j)  +/-  (1.97e-80, 2.76e-204j)
| (19.367280302627233046 - 3.8095087263546659626e-627j)  +/-  (1.5e-80, 2.09e-204j)
| (0.060177808135462837501 + 5.8940030672253417598e-630j)  +/-  (1.5e-82, 2.09e-206j)
| (0.00014036397789546449403 - 2.6739868903767666176e-632j)  +/-  (4.11e-87, 5.71e-211j)
| (0.23973784145239524466 + 1.1020221601475089875e-629j)  +/-  (1.08e-81, 1.5e-205j)
| (0.0045746627746214707619 - 2.2492329527492611083e-630j)  +/-  (8.31e-85, 1.16e-208j)
| (0.00073473839254811076669 + 6.3813959902969845435e-630j)  +/-  (2.87e-84, 4e-208j)
| (-19.31011757351190177 + 3.8358010196015597497e-627j)  +/-  (4.35e-81, 6.1e-205j)
| (0.060177808135462837501 + 3.1006712283674623734e-630j)  +/-  (4.91e-85, 6.89e-209j)
| (19.367280302627233046 - 2.8891368744413391962e-627j)  +/-  (1.78e-81, 2.5e-205j)
| (0.019172352762454920146 - 2.7947524454163047797e-630j)  +/-  (1.59e-85, 2.24e-209j)
| (2.5219392745758652604e-05 + 6.3574008209996463167e-633j)  +/-  (2.24e-88, 3.04e-212j)
