Starting with polynomial:
P : t^2 - 1
Extension levels are: 2 3 26
-------------------------------------------------
Trying to find an order 3 Kronrod extension for:
P1 : t^2 - 1
Solvable: 1
-------------------------------------------------
Trying to find an order 26 Kronrod extension for:
P2 : t^5 - 7*t^3 + 6*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^31 - 465321135547626582930907/1125069771993873607576*t^29 + 83451340490287791822560481/1125069771993873607576*t^27 - 1070175761602162102629723150/140633721499234200947*t^25 + 279174002128220793921997459725/562534885996936803788*t^23 - 24339265627198042613297436241725/1125069771993873607576*t^21 + 726288708519777768435429617533275/1125069771993873607576*t^19 - 47618408139822641942622016139925/3583024751572845884*t^17 + 52870109639147194416021740041426125/281267442998468401894*t^15 - 2024136949495866312172628827326187125/1125069771993873607576*t^13 + 12761667593438502307307959750293138375/1125069771993873607576*t^11 - 12706147588452267480645347583157182375/281267442998468401894*t^9 + 59985147285282691999285948513815616125/562534885996936803788*t^7 - 151708174846833323334165697016636641875/1125069771993873607576*t^5 + 85738431503892957321157157245256668125/1125069771993873607576*t^3 - 7055361137735873206993013403969455625/562534885996936803788*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:
| (3.6030553035125436861 - 5.4504683294186152977e-259j)  +/-  (2.41e-121, 2.41e-121j)
| (-9.5394527188747089607 + 2.0160685035115185961e-260j)  +/-  (7.5e-122, 7.5e-122j)
| (7.651858774467953772 + 7.1423415871610309535e-265j)  +/-  (1.39e-120, 1.39e-120j)
| (2.4494897427831780982 + 2.9091368220514436891e-275j)  +/-  (1.54e-122, 1.54e-122j)
| (4.2095396951037462178 - 1.2844522107520720193e-272j)  +/-  (7.05e-121, 7.05e-121j)
| (9.5394527188747089607 + 4.0524085271959986632e-279j)  +/-  (6.87e-122, 6.87e-122j)
| (-4.2095396951037462178 - 1.7139162430272045524e-290j)  +/-  (6.59e-121, 6.59e-121j)
| (-5.4848571633456785035 - 2.2215266816780709038e-289j)  +/-  (2.54e-120, 2.54e-120j)
| (-8.5104432663060364719 + 6.1143418848198742633e-289j)  +/-  (4.62e-121, 4.62e-121j)
| (3.0152654278468987884 - 4.9927602672724139125e-294j)  +/-  (7.12e-122, 7.12e-122j)
| (1.4442953696694810756 + 6.0277182625349019411e-295j)  +/-  (5.03e-124, 5.03e-124j)
| (8.5104432663060364719 + 1.1960414889856470897e-297j)  +/-  (4.49e-121, 4.49e-121j)
| (-6.163122129410129881 + 9.3920923836053597181e-304j)  +/-  (3.23e-120, 3.23e-120j)
| (-4.8356507902065295259 + 1.1572991572665385319e-307j)  +/-  (1.51e-120, 1.51e-120j)
| (-3.6030553035125436861 + 3.1024639461807763883e-310j)  +/-  (2.34e-121, 2.34e-121j)
| (1.9184917030337658659 + 2.5347446949231639256e-311j)  +/-  (3.53e-123, 3.53e-123j)
| (-7.651858774467953772 - 1.7002041412001559787e-307j)  +/-  (1.35e-120, 1.35e-120j)
| (-2.4494897427831780982 - 3.4236836234617688205e-316j)  +/-  (1.6e-122, 1.6e-122j)
| (-1 + 3.67878191983105669e-321j)  +/-  (5.92e-125, 5.92e-125j)
| (-1.4442953696694810756 + 1.0824385421606702287e-318j)  +/-  (5.34e-124, 5.34e-124j)
| (5.4848571633456785035 - 2.296363083440100051e-321j)  +/-  (2.36e-120, 2.36e-120j)
| (0.51642637505063061732 - 2.5672802593202960496e-347j)  +/-  (4.92e-126, 4.92e-126j)
| (6.8800280871148546845 - 7.0233456467752923654e-341j)  +/-  (2.8e-120, 2.8e-120j)
| (-6.8800280871148546845 - 1.2116857155039016638e-353j)  +/-  (2.61e-120, 2.61e-120j)
| (-1.9184917030337658659 - 1.5065175454055412921e-365j)  +/-  (2.97e-123, 2.97e-123j)
| (-5.7568809373482346104e-368 + 5.9685023864089818353e-368j)  +/-  (2.57e-366, 2.57e-366j)
| (1 + 2.4384848849317518949e-365j)  +/-  (5.56e-125, 5.56e-125j)
| (4.8356507902065295259 - 1.0909881036582020628e-359j)  +/-  (1.4e-120, 1.4e-120j)
| (-3.0152654278468987884 + 2.2864618639148752353e-372j)  +/-  (6.59e-122, 6.59e-122j)
| (-0.51642637505063061732 - 8.7652531063536225305e-378j)  +/-  (4.92e-126, 4.92e-126j)
| (6.163122129410129881 + 1.155652084708209218e-371j)  +/-  (3.1e-120, 3.1e-120j)
-------------------------------------------------
The weights are:
| (0.00036145166678094234241 + 4.7287785757116823803e-262j)  +/-  (3.34e-29, 1.08e-88j)
| (8.196475426965743158e-21 + 9.4593453175566850925e-273j)  +/-  (1.63e-42, 5.29e-102j)
| (6.2230813230412240429e-14 - 1.3245238730586807651e-268j)  +/-  (1.66e-39, 5.38e-99j)
| (0.01095808548685092467 + 2.1926369134716151662e-261j)  +/-  (1.02e-25, 3.31e-85j)
| (3.4876227013796299766e-05 + 7.2333451067040283658e-263j)  +/-  (7.7e-32, 2.5e-91j)
| (8.196475426965743158e-21 - 2.0941911756933528895e-272j)  +/-  (1.02e-42, 3.31e-102j)
| (3.4876227013796299766e-05 - 5.6151776912618620813e-264j)  +/-  (1.37e-34, 4.44e-94j)
| (7.7537571433198635172e-08 - 1.3063566105707529849e-265j)  +/-  (9.99e-38, 3.24e-97j)
| (6.8826330559092399167e-17 - 1.1855916177767376224e-270j)  +/-  (5.95e-43, 1.93e-102j)
| (0.0024461117656768395574 - 1.285047783692804563e-261j)  +/-  (7.4e-31, 2.4e-90j)
| (0.062725841146888318121 + 7.2393673170426301849e-261j)  +/-  (7.35e-26, 2.38e-85j)
| (6.8826330559092399167e-17 + 2.9265389733579179041e-270j)  +/-  (2.51e-42, 8.14e-102j)
| (1.5671906676624689502e-09 + 1.3578916502748112531e-266j)  +/-  (1.22e-39, 3.96e-99j)
| (2.1247505566334812284e-06 + 9.5778494777380247354e-265j)  +/-  (2.65e-37, 8.59e-97j)
| (0.00036145166678094234241 + 2.7339031731745600667e-263j)  +/-  (8.67e-36, 2.82e-95j)
| (0.032027473073200077792 - 4.3126760959705194534e-261j)  +/-  (9.63e-32, 3.13e-91j)
| (6.2230813230412240429e-14 + 4.7647959406322550851e-269j)  +/-  (1.93e-42, 6.28e-102j)
| (0.01095808548685092467 + 4.1789865481137926095e-262j)  +/-  (2.33e-34, 7.57e-94j)
| (0.11083503848190479556 - 4.9920890197104307351e-261j)  +/-  (2.68e-30, 8.73e-90j)
| (0.062725841146888318121 + 3.0962889505660302065e-261j)  +/-  (4.1e-32, 1.33e-91j)
| (7.7537571433198635172e-08 + 6.3088759475505570409e-265j)  +/-  (1.11e-40, 3.62e-100j)
| (0.1765615491432642334 + 8.3476461852866582589e-261j)  +/-  (1.23e-32, 3.99e-92j)
| (1.5559898778831833929e-11 + 3.2161758232602420159e-267j)  +/-  (5.62e-43, 1.82e-102j)
| (1.5559898778831833929e-11 - 1.0053645765333576754e-267j)  +/-  (2.76e-42, 8.81e-102j)
| (0.032027473073200077792 - 1.3157503085131362094e-261j)  +/-  (1.07e-35, 3.44e-95j)
| (0.20809473827495827897 - 7.2629873236033853772e-261j)  +/-  (1.82e-34, 5.85e-94j)
| (0.11083503848190479556 - 8.827650260878041199e-261j)  +/-  (1.02e-34, 3.29e-94j)
| (2.1247505566334812284e-06 - 6.5572734470094533887e-264j)  +/-  (3.52e-40, 1.14e-99j)
| (0.0024461117656768395574 - 1.1412835802332421772e-262j)  +/-  (6.7e-38, 2.01e-97j)
| (0.1765615491432642334 + 6.2546912974808838868e-261j)  +/-  (6.96e-36, 1.97e-95j)
| (1.5671906676624689502e-09 - 5.1801033496163694998e-266j)  +/-  (3.69e-42, 1.21e-101j)
