Starting with polynomial:
P : t^2 - 1
Extension levels are: 2 5 24
-------------------------------------------------
Trying to find an order 5 Kronrod extension for:
P1 : t^2 - 1
Solvable: 1
-------------------------------------------------
Trying to find an order 24 Kronrod extension for:
P2 : t^7 - 53/3*t^5 + 215/3*t^3 - 55*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^31 - 96657541582151448787367676751/245453218400091920776940445*t^29 + 16525784320411178110137554287243/245453218400091920776940445*t^27 - 540039099972192259946823127602279/81817739466697306925646815*t^25 + 6756917853779025669084479334295455/16363547893339461385129363*t^23 - 40595088809386224908564905755364635/2337649699048494483589909*t^21 + 1178205960512932611330713531009743215/2337649699048494483589909*t^19 - 23852244649500030519836924678879492745/2337649699048494483589909*t^17 + 336467457528962278004654997588483422655/2337649699048494483589909*t^15 - 3267362881668834906997293857098828883925/2337649699048494483589909*t^13 + 21302598534616197849725834520688607676825/2337649699048494483589909*t^11 - 89362716720645198654683411072553147547575/2337649699048494483589909*t^9 + 32138068803752257768465039917519303629925/333949957006927783369987*t^7 - 43202649335807960445596863464308613916575/333949957006927783369987*t^5 + 25031976048061962234911105259205584205875/333949957006927783369987*t^3 - 3822577331156843962680063363436679359125/333949957006927783369987*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
  current precision for roots: 424
  current precision for roots: 848
 current precision for weights: 424
Linear system for weights solvable: 1
Sufficient bits for target precision reached
-------------------------------------------------
The nodes are:
| (3.2756077652061586678 + 4.5188225508265501899e-519j)  +/-  (2.36e-248, 2.36e-248j)
| (-8.3021737953134137937 - 1.3740334240664464894e-519j)  +/-  (1.12e-248, 1.12e-248j)
| (-9.33883013958302842 + 3.9259493284663212336e-527j)  +/-  (1.41e-249, 1.41e-249j)
| (1.5549035425686693724 - 5.2280881931274447723e-542j)  +/-  (1.32e-251, 1.32e-251j)
| (2.7141280536775387018 - 3.4604290831698587887e-540j)  +/-  (1.69e-249, 1.69e-249j)
| (8.3021737953134137937 - 5.3711528348044367163e-538j)  +/-  (1.03e-248, 1.03e-248j)
| (-4.5939649452143797635 + 2.9731840632566884856e-546j)  +/-  (5.29e-248, 5.29e-248j)
| (-5.2492491401051431851 - 1.6891025131331059229e-573j)  +/-  (7.71e-248, 7.71e-248j)
| (5.9342536240565421264 + 4.6538109379844704981e-583j)  +/-  (7.13e-248, 7.13e-248j)
| (9.33883013958302842 + 5.6817295754804290451e-588j)  +/-  (1.35e-249, 1.35e-249j)
| (3.9669263033739472364 - 1.9359209299851906898e-586j)  +/-  (4.26e-248, 4.26e-248j)
| (6.6579581321455528226 + 9.2509384547574422922e-595j)  +/-  (5.66e-248, 5.66e-248j)
| (-7.4366023253307604629 + 4.4951427393814527031e-608j)  +/-  (3.37e-248, 3.37e-248j)
| (-3.2756077652061586678 + 1.1738892866887570442e-626j)  +/-  (2.26e-248, 2.26e-248j)
| (-2.1290252659381178426 - 8.1236367072042780881e-638j)  +/-  (1.42e-250, 1.42e-250j)
| (3.4833773961004847262 + 3.9524811639893503251e-639j)  +/-  (4.09e-248, 4.09e-248j)
| (0.478878574708922334 + 6.1129506740073646514e-647j)  +/-  (6.99e-254, 6.99e-254j)
| (-3.4833773961004847262 - 7.5435317951754679445e-649j)  +/-  (4.31e-248, 4.31e-248j)
| (-1 + 7.915998418987644793e-662j)  +/-  (8.52e-253, 8.52e-253j)
| (5.0424988012421540447e-663 - 4.7320257735258501857e-663j)  +/-  (2.14e-661, 2.14e-661j)
| (2.1290252659381178426 - 5.6165440766157358376e-660j)  +/-  (1.39e-250, 1.39e-250j)
| (4.5939649452143797635 + 1.4188594156419183772e-656j)  +/-  (5.6e-248, 5.6e-248j)
| (7.4366023253307604629 - 1.3025568962103679217e-667j)  +/-  (3.46e-248, 3.46e-248j)
| (-6.6579581321455528226 + 2.5024748481008606128e-694j)  +/-  (5.75e-248, 5.75e-248j)
| (-1.5549035425686693724 - 2.3067663073828930693e-714j)  +/-  (1.22e-251, 1.22e-251j)
| (-3.9669263033739472364 + 1.0344076325006450266e-726j)  +/-  (4.14e-248, 4.14e-248j)
| (1 + 3.4247766522785541625e-743j)  +/-  (9.18e-253, 9.18e-253j)
| (5.2492491401051431851 + 1.6500483234310498352e-745j)  +/-  (6.36e-248, 6.36e-248j)
| (-5.9342536240565421264 + 7.2090391389177727093e-756j)  +/-  (7.57e-248, 7.57e-248j)
| (-2.7141280536775387018 + 5.7574112378508505022e-767j)  +/-  (1.75e-249, 1.75e-249j)
| (-0.478878574708922334 + 1.2536201893366820273e-775j)  +/-  (7.96e-254, 7.96e-254j)
-------------------------------------------------
The weights are:
| (0.00086002575368211658016 + 8.7580983728945929406e-522j)  +/-  (1.96e-87, 3.41e-211j)
| (3.9946778316436988942e-16 - 2.0983383260891579401e-531j)  +/-  (7.14e-100, 1.25e-223j)
| (5.4842555550131140184e-20 + 1.5189962184660776457e-533j)  +/-  (2.06e-101, 3.59e-225j)
| (0.067435715679031119586 + 5.2829947450644810866e-522j)  +/-  (2.87e-80, 5.01e-204j)
| (0.0058891845520775767337 + 6.2136741897304775374e-522j)  +/-  (1.24e-86, 2.16e-210j)
| (3.9946778316436988942e-16 + 4.8273418135942566085e-531j)  +/-  (2.19e-101, 3.83e-225j)
| (6.6934464076465601738e-06 + 4.3667498940472428916e-525j)  +/-  (1.84e-94, 3.21e-218j)
| (2.7732875752126613316e-07 - 4.265627237270898738e-526j)  +/-  (7.16e-96, 1.25e-219j)
| (6.3177689136264169159e-09 - 1.2325764375794026203e-526j)  +/-  (5.13e-98, 8.95e-222j)
| (5.4842555550131140184e-20 - 3.1610930466826074934e-533j)  +/-  (7.45e-104, 1.3e-227j)
| (9.2743858390955478085e-05 + 4.9663885046538052714e-523j)  +/-  (3.98e-94, 6.94e-218j)
| (7.059904041318889451e-11 + 6.5855391500333253479e-528j)  +/-  (1.63e-99, 2.84e-223j)
| (3.1838102561754028429e-13 + 9.3657189366443722906e-530j)  +/-  (7.28e-102, 1.27e-225j)
| (0.00086002575368211658016 - 5.9323622088287338688e-523j)  +/-  (4.15e-95, 7.24e-219j)
| (0.024027106625354611443 - 9.9667093521585394427e-523j)  +/-  (8.51e-93, 1.48e-216j)
| (0.00018435102875898057251 - 1.312633471272768265e-521j)  +/-  (3.98e-94, 6.94e-218j)
| (0.17730370630380159269 + 7.9260443202942116821e-522j)  +/-  (3.49e-89, 6.09e-213j)
| (0.00018435102875898057251 + 4.0351343736482100156e-523j)  +/-  (1.35e-95, 2.35e-219j)
| (0.13093417475324305957 - 3.5019652822697071708e-522j)  +/-  (8.5e-90, 1.48e-213j)
| (0.18653202856361616987 - 7.8858775719126835515e-522j)  +/-  (2.55e-89, 4.45e-213j)
| (0.024027106625354611443 - 4.6979152205427629661e-522j)  +/-  (2.03e-92, 3.55e-216j)
| (6.6934464076465601738e-06 - 2.6064807992129727133e-524j)  +/-  (1.64e-97, 2.86e-221j)
| (3.1838102561754028429e-13 - 2.4104542625147409551e-529j)  +/-  (2.08e-102, 3.63e-226j)
| (7.059904041318889451e-11 - 2.2426748845853699022e-528j)  +/-  (9.92e-103, 1.73e-226j)
| (0.067435715679031119586 + 1.8819089956333985663e-522j)  +/-  (1.83e-95, 3.2e-219j)
| (9.2743858390955478085e-05 - 4.7407309792001427043e-524j)  +/-  (1.59e-98, 2.79e-222j)
| (0.13093417475324305957 - 6.5797431027188290458e-522j)  +/-  (4.57e-95, 7.98e-219j)
| (2.7732875752126613316e-07 + 1.8423532131812475895e-525j)  +/-  (4.92e-100, 8.62e-224j)
| (6.3177689136264169159e-09 + 3.5584535482968912134e-527j)  +/-  (8.72e-102, 1.52e-225j)
| (0.0058891845520775767337 + 5.8248521574138817957e-523j)  +/-  (1.53e-97, 2.72e-221j)
| (0.17730370630380159269 + 5.9041579714019348367e-522j)  +/-  (3.21e-96, 4.7e-220j)
