Starting with polynomial:
P : 4*t^2 - 2
Extension levels are: 2 3 28
-------------------------------------------------
Trying to find an order 3 Kronrod extension for:
P1 : 4*t^2 - 2
Solvable: 1
-------------------------------------------------
Trying to find an order 28 Kronrod extension for:
P2 : 4*t^5 - 14*t^3 + 6*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 4*t^33 - 698492568358167251449774126/731920585313098339748759*t^31 + 657240022528862881909056388207/6587285267817885057738831*t^29 - 79573517733554730166815688400197/13174570535635770115477662*t^27 + 53086809779399742747204235893153/225206333942491796845772*t^25 - 2815792603462840072802797930921575/450412667884983593691544*t^23 + 104259628011825322249806556571921775/900825335769967187383088*t^21 - 2726722453179241400708773447915895325/1801650671539934374766176*t^19 + 50418890049627922435926888445784835075/3603301343079868749532352*t^17 - 653738087220368272409176338360331953225/7206602686159737499064704*t^15 + 5841037283776106711891660906763634025625/14413205372319474998129408*t^13 - 34959311577941753940030323657853442891875/28826410744638949996258816*t^11 + 134277521292479385225611437351493801302875/57652821489277899992517632*t^9 - 310086668501896173612636021864409855324125/115305642978555799985035264*t^7 + 387657021039988449995973810264977526241125/230611285957111599970070528*t^5 - 216899480153462061317271227602400628579375/461222571914223199940141056*t^3 + 17387912520216136647422070388280314554375/461222571914223199940141056*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:
| (5.1692569587478459436 + 6.9683516571152355821e-442j)  +/-  (5.21e-120, 5.21e-120j)
| (-5.7060365738632554994 + 7.145443032662720093e-446j)  +/-  (2.62e-120, 2.62e-120j)
| (-4.2010586361820591109 - 3.6622220221413974368e-446j)  +/-  (6.65e-120, 6.65e-120j)
| (-3.7516590594429690222 + 2.0605529932817260192e-446j)  +/-  (4.94e-120, 4.94e-120j)
| (6.3039388755077678548 + 3.5367183184666444449e-446j)  +/-  (8.35e-121, 8.35e-121j)
| (-7.0214551035782853345 - 1.9460896668109149086e-448j)  +/-  (1.01e-121, 1.01e-121j)
| (7.0214551035782853345 + 6.4274603498727826564e-447j)  +/-  (1.13e-121, 1.13e-121j)
| (5.7060365738632554994 - 2.4869280201576424217e-445j)  +/-  (2.81e-120, 2.81e-120j)
| (3.3190607979305594646 + 9.2678982616142833898e-446j)  +/-  (2.44e-120, 2.44e-120j)
| (-6.3039388755077678548 + 1.9077360879202939033e-457j)  +/-  (8.38e-121, 8.38e-121j)
| (2.9008250598286869754 - 4.7998341919427155164e-458j)  +/-  (9.52e-121, 9.52e-121j)
| (-4.6713771005287162426 + 3.1432206285745038862e-464j)  +/-  (7.76e-120, 7.76e-120j)
| (-5.1692569587478459436 - 1.3601765570691944628e-467j)  +/-  (5.62e-120, 5.62e-120j)
| (4.6713771005287162426 - 6.2194575893219168155e-467j)  +/-  (7.28e-120, 7.28e-120j)
| (-2.4959898162010776492 + 9.9008303783216096424e-480j)  +/-  (3.35e-121, 3.35e-121j)
| (1.7320508075688772935 - 9.0022659970855498429e-479j)  +/-  (1.98e-122, 1.98e-122j)
| (2.1053623052915647114 + 1.4728028791178265588e-479j)  +/-  (9.33e-122, 9.33e-122j)
| (4.2010586361820591109 + 5.1076735373593566148e-484j)  +/-  (7.04e-120, 7.04e-120j)
| (-0.35769751003905112946 + 4.7680993953113279087e-503j)  +/-  (2.95e-126, 2.95e-126j)
| (-1.7320508075688772935 + 1.0313580172161257245e-497j)  +/-  (2e-122, 2e-122j)
| (3.7516590594429690222 + 2.2541739396563466046e-498j)  +/-  (4.78e-120, 4.78e-120j)
| (1.0442288392983726161 + 4.5645702345614973789e-507j)  +/-  (6.02e-124, 6.02e-124j)
| (-2.1053623052915647114 + 2.1958727313112112925e-503j)  +/-  (9.67e-122, 9.67e-122j)
| (-0.7071067811865475244 + 5.7602168191377408425e-507j)  +/-  (4.74e-125, 4.74e-125j)
| (-1.3798948673301217096 - 6.3839657178251234438e-505j)  +/-  (3.56e-123, 3.56e-123j)
| (-6.4464647253817947692e-520 - 1.5065478306219968279e-520j)  +/-  (2.18e-518, 2.18e-518j)
| (0.7071067811865475244 - 7.6899999874296068322e-508j)  +/-  (4.78e-125, 4.78e-125j)
| (-2.9008250598286869754 + 1.2395436387997601098e-502j)  +/-  (1.1e-120, 1.1e-120j)
| (0.35769751003905112946 - 3.8164572359920399249e-509j)  +/-  (2.95e-126, 2.95e-126j)
| (-1.0442288392983726161 - 3.8099946411199239332e-507j)  +/-  (5.36e-124, 5.36e-124j)
| (-3.3190607979305594646 + 5.9773656843435398171e-505j)  +/-  (2.33e-120, 2.33e-120j)
| (2.4959898162010776492 + 8.6217314073586975799e-508j)  +/-  (3.28e-121, 3.28e-121j)
| (1.3798948673301217096 + 8.7821097698079316022e-510j)  +/-  (3.56e-123, 3.56e-123j)
-------------------------------------------------
The weights are:
| (7.2149841394574596895e-13 - 2.7644264395360107063e-453j)  +/-  (2.49e-36, 1.37e-95j)
| (2.2968144752571563734e-15 + 2.3135951275030611728e-456j)  +/-  (5.52e-38, 3.05e-97j)
| (5.6030563033844427635e-09 - 8.1341296273123200144e-453j)  +/-  (5e-34, 2.76e-93j)
| (1.9172031651066930097e-07 + 8.5370314162642680394e-452j)  +/-  (1.1e-32, 6.06e-92j)
| (1.9959225720430142957e-18 + 5.1465234454689705174e-457j)  +/-  (8.09e-41, 4.46e-100j)
| (1.8088489901647612703e-22 + 3.8688848822691387713e-460j)  +/-  (2.24e-42, 1.24e-101j)
| (1.8088489901647612703e-22 - 2.4450448104746902305e-459j)  +/-  (1.07e-42, 5.91e-102j)
| (2.2968144752571563734e-15 - 4.4380914460854176793e-455j)  +/-  (1.3e-39, 7.19e-99j)
| (3.9417515385930762654e-06 - 3.0281034025276010819e-450j)  +/-  (3.7e-35, 2.04e-94j)
| (1.9959225720430142957e-18 - 5.3351164598736815825e-458j)  +/-  (1.25e-41, 6.87e-101j)
| (5.1440465623093344548e-05 + 1.0365267513059596469e-449j)  +/-  (2.02e-34, 1.12e-93j)
| (9.0789918861280717237e-11 + 7.0943713505022758447e-454j)  +/-  (2.02e-38, 1.11e-97j)
| (7.2149841394574596895e-13 - 5.1659370106846449489e-455j)  +/-  (1.86e-39, 1.03e-98j)
| (9.0789918861280717237e-11 + 1.3306698394546742549e-452j)  +/-  (1.33e-39, 7.31e-99j)
| (0.00044229899191857281043 - 8.9568129519328493841e-450j)  +/-  (1.24e-35, 6.85e-95j)
| (0.010200222048394422649 - 2.017087369784305404e-448j)  +/-  (2.37e-33, 1.31e-92j)
| (0.002565881292891860923 + 8.1914047470073980825e-449j)  +/-  (1.24e-34, 6.86e-94j)
| (5.6030563033844427635e-09 - 6.0531753550961100935e-452j)  +/-  (2.61e-39, 1.44e-98j)
| (0.17616452354773206301 - 7.9112811822954633144e-448j)  +/-  (9.57e-34, 5.28e-93j)
| (0.010200222048394422649 - 9.4873074006629154582e-449j)  +/-  (1.43e-35, 7.89e-95j)
| (1.9172031651066930097e-07 + 2.0963247119448749299e-451j)  +/-  (1.7e-38, 9.4e-98j)
| (0.063163891977581285508 - 6.6574794139640577229e-448j)  +/-  (2.46e-34, 1.36e-93j)
| (0.002565881292891860923 + 3.1682216740096885759e-449j)  +/-  (1.39e-36, 7.69e-96j)
| (0.11738418496671283079 + 6.3407550530690736533e-448j)  +/-  (2.99e-34, 1.65e-93j)
| (0.028719276567807718149 + 2.2979886275097090544e-448j)  +/-  (2.48e-35, 1.37e-94j)
| (0.20260828194982605919 + 8.885009964765209809e-448j)  +/-  (2.44e-34, 1.35e-93j)
| (0.11738418496671283079 + 8.4987753016525225789e-448j)  +/-  (9.02e-35, 4.97e-94j)
| (5.1440465623093344548e-05 + 2.1769210925516150792e-450j)  +/-  (7.69e-39, 4.24e-98j)
| (0.17616452354773206301 - 9.1659836408601381159e-448j)  +/-  (1.14e-35, 6.24e-95j)
| (0.063163891977581285508 - 4.2993281997805701881e-448j)  +/-  (7.88e-36, 4.36e-95j)
| (3.9417515385930762654e-06 - 4.6343690750843899703e-451j)  +/-  (1.19e-39, 6.57e-99j)
| (0.00044229899191857281043 - 2.9527339897675664259e-449j)  +/-  (5.37e-39, 3.15e-98j)
| (0.028719276567807718149 + 4.13335904975471094e-448j)  +/-  (2.54e-37, 1.31e-96j)
