Starting with polynomial:
P : t
Extension levels are: 1 2 28
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Trying to find an order 2 Kronrod extension for:
P1 : t
Solvable: 1
-------------------------------------------------
Trying to find an order 28 Kronrod extension for:
P2 : t^3 - 3*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^31 - 56735685319/94518463*t^29 + 14112617924629/94518463*t^27 - 150371025565509/7270651*t^25 + 13029636735701775/7270651*t^23 - 747941195631912975/7270651*t^21 + 29280397035306064725/7270651*t^19 - 791066818602524997225/7270651*t^17 + 14736541235109459883425/7270651*t^15 - 186957709796386606163625/7270651*t^13 + 1575515020428670206760875/7270651*t^11 - 8463799522227624427227375/7270651*t^9 + 27150071826935693461951125/7270651*t^7 - 46698742063919906652817125/7270651*t^5 + 35385482708586154410564375/7270651*t^3 - 7482944217160189385251875/7270651*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:
| (6.0846428993783326861 + 8.3334978857129006944e-323j)  +/-  (3.03e-120, 3.03e-120j)
| (-14.14395940886043552 - 1.8147302491732170792e-334j)  +/-  (2e-123, 2e-123j)
| (14.14395940886043552 + 1.7321547162180988184e-331j)  +/-  (1.74e-123, 1.74e-123j)
| (3.5115556101009978131 + 4.4686248513778028001e-330j)  +/-  (1.4e-121, 1.4e-121j)
| (9.4387303811369805663 - 2.4517664133975826705e-334j)  +/-  (1.75e-121, 1.75e-121j)
| (-4.1257956377373614969 - 3.559507524467838992e-339j)  +/-  (4.51e-121, 4.51e-121j)
| (-5.4067163029078072369 - 3.0090154738925583409e-340j)  +/-  (2.2e-120, 2.2e-120j)
| (-3.5115556101009978131 - 3.6058481676341705559e-345j)  +/-  (1.31e-121, 1.31e-121j)
| (-2.9096623305612518781 + 5.6580847244481208806e-350j)  +/-  (2.79e-122, 2.79e-122j)
| (5.4067163029078072369 + 4.8881212675132981382e-360j)  +/-  (2.42e-120, 2.42e-120j)
| (7.5675480796659053863 + 2.3763256543465113409e-372j)  +/-  (2.29e-120, 2.29e-120j)
| (4.1257956377373614969 + 1.679703487015627126e-379j)  +/-  (4.42e-121, 4.42e-121j)
| (-9.4387303811369805663 - 3.2466068540802560677e-378j)  +/-  (1.79e-121, 1.79e-121j)
| (-1.7320508075688772935 - 1.0036662905622454267e-385j)  +/-  (7.07e-124, 7.07e-124j)
| (-2.3172784105939238793 + 4.1745111086260391189e-385j)  +/-  (5.24e-123, 5.24e-123j)
| (2.3172784105939238793 + 2.6104545154203006347e-384j)  +/-  (5.34e-123, 5.34e-123j)
| (-2.9697142541504807843e-388 + 5.7033678372964822067e-388j)  +/-  (1.99e-386, 1.99e-386j)
| (-1.151950859075392626 - 6.1961058317949151107e-388j)  +/-  (5.45e-125, 5.45e-125j)
| (-6.0846428993783326861 + 1.1005007801522605012e-381j)  +/-  (2.87e-120, 2.87e-120j)
| (8.4199982493644851111 - 1.0852651685242518338e-386j)  +/-  (9.13e-121, 9.13e-121j)
| (4.7559494243855141612 + 8.6153268302368665727e-391j)  +/-  (1.14e-120, 1.14e-120j)
| (1.7320508075688772935 + 4.5431885118932450352e-395j)  +/-  (6.72e-124, 6.72e-124j)
| (-8.4199982493644851111 + 4.2765666728914965996e-393j)  +/-  (8.4e-121, 8.4e-121j)
| (-4.7559494243855141612 - 2.3190077175345747559e-398j)  +/-  (1.43e-120, 1.43e-120j)
| (-7.5675480796659053863 - 4.5914143003815246805e-407j)  +/-  (2.07e-120, 2.07e-120j)
| (6.7995240917322319305 + 1.7179561480163386625e-421j)  +/-  (3.46e-120, 3.46e-120j)
| (2.9096623305612518781 - 1.2771419940861677365e-430j)  +/-  (3.13e-122, 3.13e-122j)
| (1.151950859075392626 + 2.0080534019312784753e-431j)  +/-  (5.58e-125, 5.58e-125j)
| (-6.7995240917322319305 - 1.1129423156589193046e-431j)  +/-  (3.57e-120, 3.57e-120j)
| (-0.57516276221658746081 + 3.854058529450255316e-438j)  +/-  (5.06e-126, 5.06e-126j)
| (0.57516276221658746081 - 1.9032490599078422929e-437j)  +/-  (5.06e-126, 5.06e-126j)
-------------------------------------------------
The weights are:
| (2.5298680969126843842e-09 - 6.3367741042291314502e-331j)  +/-  (6.86e-33, 5.68e-93j)
| (9.4835669981857129774e-35 + 1.4809027311502291222e-344j)  +/-  (1.75e-44, 1.45e-104j)
| (9.4835669981857129774e-35 - 3.7169768570354978928e-344j)  +/-  (2.53e-44, 2.1e-104j)
| (0.00050914272891309765751 - 3.43003608371175727e-329j)  +/-  (1.95e-27, 1.62e-87j)
| (2.1065114176090465763e-20 + 2.189028319737187709e-337j)  +/-  (4.78e-39, 3.95e-99j)
| (4.9893874928891735125e-05 + 2.7395745572912132557e-330j)  +/-  (8e-31, 6.62e-91j)
| (1.1876304984643165151e-07 + 1.2285925394454283806e-331j)  +/-  (3.37e-34, 2.79e-94j)
| (0.00050914272891309765751 - 9.1964292096949343931e-330j)  +/-  (2.19e-29, 1.81e-89j)
| (0.003453642263434136493 + 2.5299713640568687076e-329j)  +/-  (6.71e-28, 5.55e-88j)
| (1.1876304984643165151e-07 + 2.0824671970183719603e-330j)  +/-  (1.2e-34, 9.91e-95j)
| (1.1750018958907576053e-13 + 1.0339699117700256745e-333j)  +/-  (1.41e-38, 1.16e-98j)
| (4.9893874928891735125e-05 + 1.4278292290960542952e-329j)  +/-  (1.62e-32, 1.34e-92j)
| (2.1065114176090465763e-20 - 4.7298432732966145863e-338j)  +/-  (3.34e-43, 2.77e-103j)
| (0.05183819212449018945 + 1.1123312638314658993e-328j)  +/-  (2.48e-27, 2.06e-87j)
| (0.016017073434852904946 - 5.7867042665563193556e-329j)  +/-  (4.02e-29, 3.33e-89j)
| (0.016017073434852904946 - 1.2905993373684188149e-328j)  +/-  (1.94e-30, 1.6e-90j)
| (0.22934946967356771219 - 2.9834444732052971695e-328j)  +/-  (3.91e-27, 3.24e-87j)
| (0.11879596213888437904 - 1.8113066324350149475e-328j)  +/-  (3.78e-27, 3.13e-87j)
| (2.5298680969126843842e-09 - 1.7325042795798435999e-332j)  +/-  (4.8e-38, 3.97e-98j)
| (1.4676531380266198679e-16 - 2.4370335171995134721e-335j)  +/-  (7.64e-41, 6.32e-101j)
| (3.1269595731181732663e-06 - 5.3511068478122026869e-330j)  +/-  (4.1e-35, 3.39e-95j)
| (0.05183819212449018945 + 1.9976526013253510561e-328j)  +/-  (4.28e-31, 3.54e-91j)
| (1.4676531380266198679e-16 + 3.9238804776138212363e-336j)  +/-  (1.48e-42, 1.22e-102j)
| (3.1269595731181732663e-06 - 6.5590667320614259204e-331j)  +/-  (1.11e-36, 9.18e-97j)
| (1.1750018958907576053e-13 - 1.1231263897843780945e-334j)  +/-  (1.23e-41, 1.02e-101j)
| (2.6881609235015196618e-11 - 3.1279481183742431388e-332j)  +/-  (2.49e-40, 2.02e-100j)
| (0.003453642263434136493 + 7.1677942632127875486e-329j)  +/-  (4.31e-36, 3.52e-96j)
| (0.11879596213888437904 - 2.6573465790564940935e-328j)  +/-  (4.19e-35, 3.18e-95j)
| (2.6881609235015196618e-11 + 1.7355959327107151769e-333j)  +/-  (1.65e-40, 1.37e-100j)
| (0.19465811031822222685 + 2.5132265733616661555e-328j)  +/-  (6.23e-35, 5.62e-95j)
| (0.19465811031822222685 + 3.0379829997220427302e-328j)  +/-  (4.02e-35, 2.73e-95j)
