Starting with polynomial:
P : t^2 - 1
Extension levels are: 2 12 23
-------------------------------------------------
Trying to find an order 12 Kronrod extension for:
P1 : t^2 - 1
Solvable: 1
-------------------------------------------------
Trying to find an order 23 Kronrod extension for:
P2 : t^14 - 124249/1555*t^12 + 3530769/1555*t^10 - 8883963/311*t^8 + 50229333/311*t^6 - 114812775/311*t^4 + 78937551/311*t^2 - 6151761/311
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^37 - 5206884703785885069401677643109785203839199881736405351984973/11066327465203363561144655495935600117998477897742339287660*t^35 + 2156429944282243047560762390617286453826152091146369834371071307/22132654930406727122289310991871200235996955795484678575320*t^33 - 86671141549637352704475679652555623951611997891451497886174682427/7377551643468909040763103663957066745332318598494892858440*t^31 + 123518601412956111184936671657539022617506177131307392658484794715885/134271439911134144541888486684018614765048198492607050023608*t^29 - 6634894636616140976129239001203571630003689171698638172481741732529783/134271439911134144541888486684018614765048198492607050023608*t^27 + 27984193286268544860406840523333155528054351995643712525407140010370871/14919048879014904949098720742668734973894244276956338891512*t^25 - 762319826189697387389954799944129656121308992952344429367894845400093273/14919048879014904949098720742668734973894244276956338891512*t^23 + 2141154568056680646228102431828154896676041637403169249211150215822469967/2131292697002129278442674391809819281984892039565191270216*t^21 - 2332727986225237200396896324418045137505390260409204757726171557292053045/163945592077086867572513414754601483229607079966553174632*t^19 + 306647904980060519990721883441138932051996577804641660311663146649331107295/2131292697002129278442674391809819281984892039565191270216*t^17 - 2177945703339572817190900580135097263659178954192712199266029099102007723105/2131292697002129278442674391809819281984892039565191270216*t^15 + 10594131628712078808649316189348036060554190415129309632821986435893666840505/2131292697002129278442674391809819281984892039565191270216*t^13 - 2615777001630548106955338323855385492351061247026664881831433485591159869255/163945592077086867572513414754601483229607079966553174632*t^11 + 5243227607723868206507210155028908789967102821968911098249588328935428433575/163945592077086867572513414754601483229607079966553174632*t^9 - 6025327761610584106536736008289786718370542873480159816510125947967967444025/163945592077086867572513414754601483229607079966553174632*t^7 + 3440106866321040850522941439207881228368189838811425201201348807406843590225/163945592077086867572513414754601483229607079966553174632*t^5 - 754916267618211034491302104174238743065302564319660875949733949124139476225/163945592077086867572513414754601483229607079966553174632*t^3 + 10968860114584057416273968979414201488964692856321689645227909669688919075/40986398019271716893128353688650370807401769991638293658*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:
| (-7.1808185362715664143 - 9.0340990833277497131e-873j)  +/-  (2.77e-247, 2.77e-247j)
| (-8.7799770917055470222 - 6.252462630146707312e-873j)  +/-  (3.54e-248, 3.54e-248j)
| (8.7799770917055470222 + 9.4700282695488248622e-872j)  +/-  (3.49e-248, 3.49e-248j)
| (6.482648563943994848 - 2.4845952941322014539e-877j)  +/-  (3.77e-247, 3.77e-247j)
| (7.9363651550047812848 + 1.4151264446247103172e-886j)  +/-  (1.33e-247, 1.33e-247j)
| (7.1808185362715664143 - 7.8834419261576778467e-902j)  +/-  (2.65e-247, 2.65e-247j)
| (4.6254356317132469284 - 1.8861208072858673095e-920j)  +/-  (2.6e-247, 2.6e-247j)
| (9.7940328246276516726 + 2.7653239002116506421e-934j)  +/-  (4.34e-249, 4.34e-249j)
| (-2.2114563993234611912 + 7.8508922801432151427e-934j)  +/-  (1.27e-249, 1.27e-249j)
| (-7.9363651550047812848 + 5.9432762334335816828e-931j)  +/-  (1.28e-247, 1.28e-247j)
| (-9.7940328246276516726 + 3.7414140980793797298e-934j)  +/-  (4.3e-249, 4.3e-249j)
| (1.440535754319341614 - 2.9694498574687555907e-935j)  +/-  (5.33e-251, 5.33e-251j)
| (-0.54169306817476850375 + 1.1386350530852327232e-937j)  +/-  (3.06e-253, 3.06e-253j)
| (-3.6069468897368460303 + 2.5150408123214458516e-931j)  +/-  (6.52e-248, 6.52e-248j)
| (-5.2080501705948494711 - 4.5157267071599252266e-931j)  +/-  (3.49e-247, 3.49e-247j)
| (2.6788642116343808239 - 3.6196107415165700618e-936j)  +/-  (5.47e-249, 5.47e-249j)
| (5.2080501705948494711 - 4.402407561777615281e-954j)  +/-  (3.36e-247, 3.36e-247j)
| (5.8272369191325365786 + 9.241095003609292057e-976j)  +/-  (3.73e-247, 3.73e-247j)
| (-1.440535754319341614 - 1.8104847916191291991e-986j)  +/-  (4.27e-251, 4.27e-251j)
| (-5.8272369191325365786 + 1.1424900505273971052e-981j)  +/-  (4.18e-247, 4.18e-247j)
| (-6.482648563943994848 - 2.8814925680369568371e-983j)  +/-  (4.19e-247, 4.19e-247j)
| (2.2114563993234611912 + 2.0915594299327656607e-984j)  +/-  (1.38e-249, 1.38e-249j)
| (4.0884980817682484434 - 1.3828680993659171592e-983j)  +/-  (1.3e-247, 1.3e-247j)
| (-3.1509656636637971181 + 1.2924862371994477848e-988j)  +/-  (2.21e-248, 2.21e-248j)
| (-1 - 5.8304880518299390937e-993j)  +/-  (3.35e-252, 3.35e-252j)
| (0.54169306817476850375 + 3.8747610823783985802e-994j)  +/-  (3.06e-253, 3.06e-253j)
| (1.8100151044187559318 - 7.4885724939582562605e-991j)  +/-  (2.92e-250, 2.92e-250j)
| (3.1509656636637971181 - 4.8605148837704324935e-988j)  +/-  (2.17e-248, 2.17e-248j)
| (-0.2983537964726121739 + 3.4457899395425180366e-997j)  +/-  (4.71e-254, 4.71e-254j)
| (-2.6788642116343808239 + 2.0402379017996523112e-992j)  +/-  (6.06e-249, 6.06e-249j)
| (-4.6254356317132469284 + 8.3921988330535159745e-991j)  +/-  (2.45e-247, 2.45e-247j)
| (1 + 1.1034879703987347596e-998j)  +/-  (3.86e-252, 3.86e-252j)
| (0.2983537964726121739 - 4.3563533897609216381e-1000j)  +/-  (4.71e-254, 4.71e-254j)
| (-4.0884980817682484434 + 3.2738798800049439165e-997j)  +/-  (1.33e-247, 1.33e-247j)
| (-1.8100151044187559318 - 1.1045198330488380836e-1001j)  +/-  (3.14e-250, 3.14e-250j)
| (2.900735854521490145e-1010 + 5.2241873843753605824e-1010j)  +/-  (2.21e-1008, 2.21e-1008j)
| (3.6069468897368460303 + 1.1887551667382045623e-1000j)  +/-  (6.39e-248, 6.39e-248j)
-------------------------------------------------
The weights are:
| (1.8337971102649639799e-12 - 7.7046224521947890159e-884j)  +/-  (1.64e-91, 5.64e-216j)
| (6.5885990641427932204e-18 + 4.1500587406386260003e-888j)  +/-  (1.08e-94, 3.7e-219j)
| (6.5885990641427932204e-18 - 3.7040245733594694045e-888j)  +/-  (5.64e-96, 1.94e-220j)
| (2.0172067632092924306e-10 + 4.2701509822599036261e-884j)  +/-  (6.78e-92, 2.33e-216j)
| (6.6462901066638945314e-15 + 8.0862027490257636185e-887j)  +/-  (7.66e-95, 2.63e-219j)
| (1.8337971102649639799e-12 - 2.0749116499270251556e-885j)  +/-  (1.64e-93, 5.63e-218j)
| (5.0690967691515691529e-06 - 9.6123923777136442347e-881j)  +/-  (2.46e-89, 8.43e-214j)
| (6.9030027834980081943e-22 - 9.1533472539396438737e-892j)  +/-  (6.42e-99, 2.21e-223j)
| (0.015399045901706882643 + 7.1349254502949519647e-877j)  +/-  (1.34e-82, 4.61e-207j)
| (6.6462901066638945314e-15 - 6.1827617864558102375e-886j)  +/-  (5.74e-98, 1.97e-222j)
| (6.9030027834980081943e-22 - 1.2435214397894330548e-890j)  +/-  (1.42e-101, 4.89e-226j)
| (0.057119876345811745568 + 2.9051974396145809533e-876j)  +/-  (7.58e-80, 2.6e-204j)
| (0.14566939899085658634 + 3.0212965554767231368e-875j)  +/-  (7.58e-80, 2.6e-204j)
| (0.0002739702584504456345 - 1.3386845223451189634e-878j)  +/-  (3.83e-90, 1.32e-214j)
| (3.0929098959748808277e-07 + 4.3072241841708348852e-881j)  +/-  (4.12e-94, 1.41e-218j)
| (0.0052721430068038914905 - 9.6145620251360449314e-878j)  +/-  (1.74e-87, 5.96e-212j)
| (3.0929098959748808277e-07 + 8.8722648567222700763e-882j)  +/-  (2.45e-93, 8.41e-218j)
| (1.0746824492606225642e-08 - 6.8162290180937925368e-883j)  +/-  (2.57e-94, 8.82e-219j)
| (0.057119876345811745568 + 4.1476316977347152154e-876j)  +/-  (1.49e-84, 5.1e-209j)
| (1.0746824492606225642e-08 - 4.7353665514275441898e-882j)  +/-  (1.18e-96, 4.05e-221j)
| (2.0172067632092924306e-10 + 5.4563555838368961719e-883j)  +/-  (1.11e-97, 3.82e-222j)
| (0.015399045901706882643 + 4.0911424997608938678e-877j)  +/-  (2.54e-89, 8.7e-214j)
| (4.764651408606486519e-05 + 8.3341988429225723909e-880j)  +/-  (1.5e-93, 5.16e-218j)
| (0.0012867390658984062125 + 5.2532435008647799911e-878j)  +/-  (5.24e-93, 1.8e-217j)
| (0.11231715631247896367 - 8.3431086090006487521e-876j)  +/-  (2.3e-87, 7.92e-212j)
| (0.14566939899085658634 + 2.646426566346613074e-875j)  +/-  (6.71e-88, 2.31e-212j)
| (0.027938046061644863218 - 1.332614988507045467e-876j)  +/-  (3.09e-89, 1.06e-213j)
| (0.0012867390658984062125 + 2.314508427562288638e-878j)  +/-  (3.27e-92, 1.13e-216j)
| (0.050327021021995919912 - 5.3392280836447355171e-875j)  +/-  (1.91e-87, 6.58e-212j)
| (0.0052721430068038914905 - 1.9050608010507422635e-877j)  +/-  (2.63e-92, 9.07e-217j)
| (5.0690967691515691529e-06 - 3.6029280017296155559e-880j)  +/-  (2.47e-96, 8.49e-221j)
| (0.11231715631247896367 - 6.5264336499575713821e-876j)  +/-  (2.7e-90, 9.17e-215j)
| (0.050327021021995919912 - 4.9639551964156408031e-875j)  +/-  (1.05e-89, 3.71e-214j)
| (4.764651408606486519e-05 + 2.5549763465048682727e-879j)  +/-  (1.99e-95, 6.85e-220j)
| (0.027938046061644863218 - 2.0912947595420607544e-876j)  +/-  (5.94e-92, 2.14e-216j)
| (0.16868713436424372495 + 5.6699127195284812542e-875j)  +/-  (1.19e-90, 5.82e-215j)
| (0.0002739702584504456345 - 5.1275276693934529643e-879j)  +/-  (1.04e-94, 3.1e-219j)
