Starting with polynomial:
P : 4*t^2 - 2
Extension levels are: 2 3 26
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Trying to find an order 3 Kronrod extension for:
P1 : 4*t^2 - 2
Solvable: 1
-------------------------------------------------
Trying to find an order 26 Kronrod extension for:
P2 : 4*t^5 - 14*t^3 + 6*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 4*t^31 - 465321135547626582930907/562534885996936803788*t^29 + 83451340490287791822560481/1125069771993873607576*t^27 - 535087880801081051314861575/140633721499234200947*t^25 + 279174002128220793921997459725/2250139543987747215152*t^23 - 24339265627198042613297436241725/9000558175950988860608*t^21 + 726288708519777768435429617533275/18001116351901977721216*t^19 - 47618408139822641942622016139925/114656792050331068288*t^17 + 52870109639147194416021740041426125/18001116351901977721216*t^15 - 2024136949495866312172628827326187125/144008930815215821769728*t^13 + 12761667593438502307307959750293138375/288017861630431643539456*t^11 - 12706147588452267480645347583157182375/144008930815215821769728*t^9 + 59985147285282691999285948513815616125/576035723260863287078912*t^7 - 151708174846833323334165697016636641875/2304142893043453148315648*t^5 + 85738431503892957321157157245256668125/4608285786086906296631296*t^3 - 7055361137735873206993013403969455625/4608285786086906296631296*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: 1
  current precision for roots: 212
  current precision for roots: 424
 current precision for weights: 212
Linear system for weights solvable: 1
Sufficient bits for target precision reached
-------------------------------------------------
The nodes are:
| (-3.8783796940413404424 + 1.988671758639056307e-299j)  +/-  (1.88e-120, 1.88e-120j)
| (6.0177921445083893334 - 5.942410268378855084e-299j)  +/-  (3.57e-121, 3.57e-121j)
| (-5.4106812281080750908 + 2.4664856804604729394e-306j)  +/-  (1.06e-120, 1.06e-120j)
| (3.8783796940413404424 - 1.0044918000639696624e-309j)  +/-  (1.84e-120, 1.84e-120j)
| (6.7454117063247546844 + 1.9989876731297544504e-322j)  +/-  (4.92e-122, 4.92e-122j)
| (-6.7454117063247546844 - 8.1846882421204420079e-328j)  +/-  (5.23e-122, 5.23e-122j)
| (-3.419321465205124102 - 6.0021783324066143677e-327j)  +/-  (1.05e-120, 1.05e-120j)
| (-1.7320508075688772935 - 4.721247644928513737e-335j)  +/-  (1.03e-122, 1.03e-122j)
| (4.3579854509867775448 - 2.6103989787220522024e-348j)  +/-  (2.48e-120, 2.48e-120j)
| (-6.0177921445083893334 + 1.2808854612200141096e-356j)  +/-  (3.63e-121, 3.63e-121j)
| (1.7320508075688772935 + 2.3507212375772788058e-362j)  +/-  (1e-122, 1e-122j)
| (2.1321146311078986641 - 8.8429256714837467502e-363j)  +/-  (4.43e-122, 4.43e-122j)
| (5.4106812281080750908 - 4.7401218525688477591e-368j)  +/-  (1.04e-120, 1.04e-120j)
| (4.8649145151528246807 + 5.100033225352077328e-380j)  +/-  (1.79e-120, 1.79e-120j)
| (-2.5477448381038738062 - 1.2704989189246808505e-386j)  +/-  (1.63e-121, 1.63e-121j)
| (1.3565784928653039935 + 2.9184732824422668326e-389j)  +/-  (2.15e-123, 2.15e-123j)
| (2.5477448381038738062 + 3.6973812945056374675e-386j)  +/-  (1.75e-121, 1.75e-121j)
| (-2.1321146311078986641 - 1.0131023033327612093e-387j)  +/-  (4.48e-122, 4.48e-122j)
| (-1.3565784928653039935 - 1.3679292097963962056e-388j)  +/-  (2.25e-123, 2.25e-123j)
| (-4.8649145151528246807 - 2.46505525303480081e-386j)  +/-  (1.91e-120, 1.91e-120j)
| (3.419321465205124102 - 9.7236416453182670896e-385j)  +/-  (1.04e-120, 1.04e-120j)
| (1.021271049929621523 - 4.5107875520589992099e-391j)  +/-  (3.51e-124, 3.51e-124j)
| (0.36516859178188818963 + 2.2612555460193352508e-393j)  +/-  (3.25e-126, 3.25e-126j)
| (-2.9765940640818106581 + 2.1794779642289354618e-387j)  +/-  (4.73e-121, 4.73e-121j)
| (-1.021271049929621523 + 3.2363122231300106226e-392j)  +/-  (3.52e-124, 3.52e-124j)
| (2.713078528422054353e-402 - 1.0710869758095406707e-402j)  +/-  (9.04e-401, 9.04e-401j)
| (0.7071067811865475244 + 1.9271398996845619645e-393j)  +/-  (4.03e-125, 4.03e-125j)
| (2.9765940640818106581 + 5.1424517183849409378e-388j)  +/-  (5.22e-121, 5.22e-121j)
| (-0.36516859178188818963 + 3.0279913142559991734e-394j)  +/-  (3.25e-126, 3.25e-126j)
| (-0.7071067811865475244 - 1.1909232603827534284e-393j)  +/-  (4.03e-125, 4.03e-125j)
| (-4.3579854509867775448 - 1.5315347405571871586e-390j)  +/-  (2.14e-120, 2.14e-120j)
-------------------------------------------------
The weights are:
| (7.7537571433198635172e-08 + 6.805866585881125884e-306j)  +/-  (5.97e-39, 4.53e-98j)
| (6.8826330559092399167e-17 + 1.9108878823477819729e-312j)  +/-  (3.72e-45, 2.82e-104j)
| (6.2230813230412240429e-14 + 4.5454711182589496706e-310j)  +/-  (7.92e-44, 6e-103j)
| (7.7537571433198635172e-08 + 1.9894823644871837304e-307j)  +/-  (2.02e-40, 1.53e-99j)
| (8.196475426965743158e-21 - 1.5150138459252199203e-314j)  +/-  (7.59e-47, 5.75e-106j)
| (8.196475426965743158e-21 + 5.6316386231612153945e-314j)  +/-  (2.05e-47, 1.55e-106j)
| (2.1247505566334812284e-06 - 2.2868103147585566499e-305j)  +/-  (1.65e-39, 1.25e-98j)
| (0.01095808548685092467 - 1.5306945058041293471e-303j)  +/-  (1.57e-33, 1.19e-92j)
| (1.5671906676624689502e-09 - 2.0935137717137904711e-308j)  +/-  (8.19e-43, 6.21e-102j)
| (6.8826330559092399167e-17 - 8.7185182031824416791e-312j)  +/-  (7.65e-46, 5.8e-105j)
| (0.01095808548685092467 - 5.8571571263053511372e-304j)  +/-  (1.67e-35, 1.27e-94j)
| (0.0024461117656768395574 + 1.6327807706964491711e-304j)  +/-  (2.35e-37, 1.78e-96j)
| (6.2230813230412240429e-14 - 7.5234775239373718331e-311j)  +/-  (1.05e-45, 7.99e-105j)
| (1.5559898778831833929e-11 + 1.5682255086648849563e-309j)  +/-  (1.61e-44, 1.22e-103j)
| (0.00036145166678094234241 - 1.9230446520940058018e-304j)  +/-  (4.97e-41, 3.8e-100j)
| (0.032027473073200077792 + 1.8029238675112895955e-303j)  +/-  (1.17e-36, 8.82e-96j)
| (0.00036145166678094234241 - 3.9834616680870455634e-305j)  +/-  (1.93e-40, 1.47e-99j)
| (0.0024461117656768395574 + 5.6182496732087350483e-304j)  +/-  (3.87e-40, 2.99e-99j)
| (0.032027473073200077792 + 3.7420138303766817469e-303j)  +/-  (1.28e-38, 9.88e-98j)
| (1.5559898778831833929e-11 - 1.3875255389056938301e-308j)  +/-  (1.27e-46, 9.62e-106j)
| (2.1247505566334812284e-06 - 1.4393770157116782838e-306j)  +/-  (4.67e-43, 3.35e-102j)
| (0.062725841146888318121 - 4.1436458039629929362e-303j)  +/-  (1.72e-38, 1.22e-97j)
| (0.1765615491432642334 - 7.8875151644649530955e-303j)  +/-  (1.59e-38, 1.11e-97j)
| (3.4876227013796299766e-05 + 6.3185069903269577971e-305j)  +/-  (6.15e-43, 4.62e-102j)
| (0.062725841146888318121 - 7.1050358720442634573e-303j)  +/-  (1.38e-39, 9.47e-99j)
| (0.20809473827495827897 + 8.7648941428771686607e-303j)  +/-  (3.95e-39, 2.76e-98j)
| (0.11083503848190479556 + 6.5099061724760508232e-303j)  +/-  (5.75e-39, 4.1e-98j)
| (3.4876227013796299766e-05 + 8.3160486834218811831e-306j)  +/-  (1.4e-42, 9.97e-102j)
| (0.1765615491432642334 - 9.5267778136293746129e-303j)  +/-  (6.85e-40, 4.69e-99j)
| (0.11083503848190479556 + 9.4121581842696799178e-303j)  +/-  (3.87e-40, 2.5e-99j)
| (1.5671906676624689502e-09 + 3.5912890113139041585e-307j)  +/-  (3.41e-46, 3.02e-105j)
