Starting with polynomial:
P : t^2 - 1
Extension levels are: 2 31
-------------------------------------------------
Trying to find an order 31 Kronrod extension for:
P1 : t^2 - 1
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^33 - 54243334727750161/107745194932861*t^31 + 11996350518445808505/107745194932861*t^29 - 53111919992551954695/3715351549409*t^27 + 4408636421389309466175/3715351549409*t^25 - 249402111805931094471825/3715351549409*t^23 + 9879061282851902684367825/3715351549409*t^21 - 277250005536611326555210875/3715351549409*t^19 + 5517489689061351613884397125/3715351549409*t^17 - 77199047703306501408950889375/3715351549409*t^15 + 745738304438368740184977666375/3715351549409*t^13 - 4828105038488863528629612505125/3715351549409*t^11 + 20021134625234264956426340473125/3715351549409*t^9 - 49606489358938814972216188516875/3715351549409*t^7 + 65654755018151036636108382046875/3715351549409*t^5 - 37933183998595900542594987545625/3715351549409*t^3 + 6018099622204583123959572573750/3715351549409*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
Sufficient bits for target precision reached
-------------------------------------------------
The nodes are:
| (-6.1312840430870032236 + 1.5847584077772771042e-263j)  +/-  (1.38e-119, 1.38e-119j)
| (6.7942584950465594094 - 1.751333152311025829e-267j)  +/-  (1.47e-119, 1.47e-119j)
| (7.4955958438382717143 + 1.9111231818405777756e-271j)  +/-  (1.3e-119, 1.3e-119j)
| (-4.8851425421012608192 - 1.5616032519800053379e-270j)  +/-  (5.22e-120, 5.22e-120j)
| (-9.0932395854589439688 - 1.088035075039076334e-273j)  +/-  (1.65e-120, 1.65e-120j)
| (-10.103423989252543735 + 2.2257457740598712594e-277j)  +/-  (1.88e-121, 1.88e-121j)
| (-7.4955958438382717143 + 1.7204822859875529431e-279j)  +/-  (1.17e-119, 1.17e-119j)
| (6.1312840430870032236 - 2.8236399215294853497e-288j)  +/-  (1.44e-119, 1.44e-119j)
| (10.103423989252543735 - 3.7754341207515470764e-302j)  +/-  (2.05e-121, 2.05e-121j)
| (4.2913151897707412228 + 2.2030147966845966136e-299j)  +/-  (2.23e-120, 2.23e-120j)
| (-6.7942584950465594094 - 2.170930032462911158e-305j)  +/-  (1.47e-119, 1.47e-119j)
| (5.4970159746652161132 + 2.7888833656761445654e-309j)  +/-  (1.05e-119, 1.05e-119j)
| (4.8851425421012608192 + 2.1987018460921755456e-315j)  +/-  (5.82e-120, 5.82e-120j)
| (-3.7124778636227872469 + 2.0484451249073213108e-327j)  +/-  (6.74e-121, 6.74e-121j)
| (3.1465417308841895347 + 3.0312755365027185425e-335j)  +/-  (1.47e-121, 1.47e-121j)
| (-5.4970159746652161132 - 3.3193880750040670317e-338j)  +/-  (1.01e-119, 1.01e-119j)
| (2.592264781496141571 + 4.9892498984125973085e-348j)  +/-  (2.96e-122, 2.96e-122j)
| (-2.0492714125479250214 - 2.4898602540962626838e-345j)  +/-  (4.32e-123, 4.32e-123j)
| (-3.1465417308841895347 - 5.066772865536990959e-345j)  +/-  (1.53e-121, 1.53e-121j)
| (8.2514502114239605578 + 1.3373828363374912717e-350j)  +/-  (5.83e-120, 5.83e-120j)
| (-2.592264781496141571 - 2.6801289853039470727e-349j)  +/-  (2.87e-122, 2.87e-122j)
| (2.0492714125479250214 + 5.3340221029760130799e-359j)  +/-  (5.17e-123, 5.17e-123j)
| (3.7124778636227872469 + 5.7971576556942022495e-355j)  +/-  (6.49e-121, 6.49e-121j)
| (-0.49526517183664030908 - 2.0580731148879210896e-360j)  +/-  (3.6e-126, 3.6e-126j)
| (-1.5768187435684951689e-361 + 1.5983264969961378084e-361j)  +/-  (7.41e-360, 7.41e-360j)
| (1.5181123669345370139 - 1.2235913349114020998e-362j)  +/-  (5.57e-124, 5.57e-124j)
| (1 + 2.4118888961878392714e-363j)  +/-  (4.6e-125, 4.6e-125j)
| (9.0932395854589439688 + 4.7899754423095943794e-358j)  +/-  (1.75e-120, 1.75e-120j)
| (-8.2514502114239605578 + 4.7151119064121343612e-362j)  +/-  (5.93e-120, 5.93e-120j)
| (-1 + 5.3552551779733446423e-372j)  +/-  (4.3e-125, 4.3e-125j)
| (-4.2913151897707412228 + 8.7310539596506421826e-375j)  +/-  (2.23e-120, 2.23e-120j)
| (-1.5181123669345370139 + 1.2291533677266231309e-388j)  +/-  (4.9e-124, 4.9e-124j)
| (0.49526517183664030908 + 9.7171857911407844763e-392j)  +/-  (3.6e-126, 3.6e-126j)
-------------------------------------------------
The weights are:
| (1.7738350010639430359e-09 + 9.0471093422391567067e-272j)  +/-  (5.09e-33, 3.33e-92j)
| (2.5679114882924647723e-11 - 2.3738931432241834712e-274j)  +/-  (8.27e-35, 5.41e-94j)
| (1.8243626802259243966e-13 + 1.7301043143699092804e-275j)  +/-  (3.56e-36, 2.33e-95j)
| (1.5796100667128964611e-06 + 8.2981871410601727095e-271j)  +/-  (3.7e-31, 2.42e-90j)
| (3.9961683471027803655e-19 - 9.7762779502242023661e-278j)  +/-  (6.32e-40, 4.14e-99j)
| (3.1647497330877845593e-23 + 5.8555374878261220688e-280j)  +/-  (1.24e-41, 8.14e-101j)
| (1.8243626802259243966e-13 - 1.7275583032326069653e-274j)  +/-  (1.76e-37, 1.15e-96j)
| (1.7738350010639430359e-09 + 2.291796365878817675e-273j)  +/-  (1.66e-36, 1.08e-95j)
| (3.1647497330877845593e-23 - 1.4327690850080264801e-280j)  +/-  (6.66e-44, 4.36e-103j)
| (2.343640692864656392e-05 - 4.2892015393006192636e-271j)  +/-  (4.29e-34, 2.81e-93j)
| (2.5679114882924647723e-11 + 4.6313236368795815406e-273j)  +/-  (6.89e-38, 4.51e-97j)
| (6.8119377809733200858e-08 - 1.6578873486243850814e-272j)  +/-  (3.49e-36, 2.28e-95j)
| (1.5796100667128964611e-06 + 9.3859024141797066519e-272j)  +/-  (2.4e-35, 1.57e-94j)
| (0.0002320384041750508841 + 6.5889072234718404161e-270j)  +/-  (5.46e-35, 3.58e-94j)
| (0.0015818277363499173543 - 5.1363238396875017134e-270j)  +/-  (1.66e-33, 1.09e-92j)
| (6.8119377809733200858e-08 - 3.0398862154401875834e-271j)  +/-  (2.74e-37, 1.79e-96j)
| (0.0076034478471017272155 + 1.3878774268639039925e-269j)  +/-  (1.1e-32, 7.23e-92j)
| (0.026252392571733857364 - 6.4579442117214656754e-269j)  +/-  (2.19e-32, 1.43e-91j)
| (0.0015818277363499173543 - 1.596634304625123634e-269j)  +/-  (1.25e-34, 8.16e-94j)
| (5.1827068095070961593e-16 - 7.9657022761700377294e-277j)  +/-  (7.14e-43, 4.67e-102j)
| (0.0076034478471017272155 + 3.4211475052669811802e-269j)  +/-  (3.5e-34, 2.29e-93j)
| (0.026252392571733857364 - 3.2223898306208892541e-269j)  +/-  (6.74e-34, 4.41e-93j)
| (0.0002320384041750508841 + 1.6189575338488231671e-270j)  +/-  (5.71e-36, 3.73e-95j)
| (0.17603179101979988716 + 1.8805829059225586438e-268j)  +/-  (1.22e-32, 7.99e-92j)
| (0.19684021564332060711 - 1.9136481933276301828e-268j)  +/-  (9.45e-33, 6.18e-92j)
| (0.066144446749521115681 + 6.4485417539774035759e-269j)  +/-  (1.21e-33, 7.94e-93j)
| (0.1237088619135879007 - 1.1059108930066071124e-268j)  +/-  (1.65e-33, 1.08e-92j)
| (3.9961683471027803655e-19 + 1.9021681354160230613e-278j)  +/-  (1.1e-44, 7.2e-104j)
| (5.1827068095070961593e-16 + 5.4029907329707302198e-276j)  +/-  (1.01e-43, 6.63e-103j)
| (0.1237088619135879007 - 1.5369698326290442637e-268j)  +/-  (5.83e-35, 3.81e-94j)
| (2.343640692864656392e-05 - 2.4297714281156018619e-270j)  +/-  (3.56e-38, 2.33e-97j)
| (0.066144446749521115681 + 1.0692877154530637452e-268j)  +/-  (8.09e-36, 5.29e-95j)
| (0.17603179101979988716 + 1.5994688089110743329e-268j)  +/-  (1.75e-35, 1.11e-94j)
