Starting with polynomial:
P : t
Extension levels are: 1 2 38
-------------------------------------------------
Trying to find an order 2 Kronrod extension for:
P1 : t
Solvable: 1
-------------------------------------------------
Trying to find an order 38 Kronrod extension for:
P2 : t^3 - 3*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^41 - 797765011935897511/1022870211820812*t^39 + 93461891597073053977/340956737273604*t^37 - 6541585512284644635567/113652245757868*t^35 + 917339918149900137429355/113652245757868*t^33 - 22746741371572927772398335/28413061439467*t^31 + 1648867440059108123541281595/28413061439467*t^29 - 89022020581636231993858149195/28413061439467*t^27 + 3615726887948163960079376252985/28413061439467*t^25 - 221707508191802549428548414002625/56826122878934*t^23 + 5119873896832639121750668468498125/56826122878934*t^21 - 88401367786060135092854821197569625/56826122878934*t^19 + 1126600560423470889070101004859767125/56826122878934*t^17 - 5196673140992290000658262686191027875/28413061439467*t^15 + 33752690513655876669431516256059169375/28413061439467*t^13 - 148357728843321807336415524301565274375/28413061439467*t^11 + 416630042866238629971768376496203608750/28413061439467*t^9 - 2738375092237201811784918111860695794375/113652245757868*t^7 + 2272256752385151884247725363869336876875/113652245757868*t^5 - 710390823066790344603357682755015084375/113652245757868*t^3 + 33728555942261954624607933994714771875/113652245757868*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:
| (5.8945001395220588506 - 5.3925640199871543976e-644j)  +/-  (1.1e-245, 1.1e-245j)
| (9.6733701875051215503 - 1.1207717058879793256e-645j)  +/-  (3.36e-246, 3.36e-246j)
| (-10.481388707952421994 - 4.1260413169789404328e-644j)  +/-  (7.78e-247, 7.78e-247j)
| (8.2787230801794203541 - 1.1099983792265062792e-644j)  +/-  (1.8e-245, 1.8e-245j)
| (-11.453220594705903324 - 3.9757187304338425416e-647j)  +/-  (7.19e-248, 7.19e-248j)
| (-8.9493033011068555168 - 3.3217324020780842761e-643j)  +/-  (1e-245, 1e-245j)
| (10.481388707952421994 + 1.2993386664806121965e-649j)  +/-  (7.76e-247, 7.76e-247j)
| (-9.6733701875051215503 - 3.9401731003120648827e-647j)  +/-  (3.97e-246, 3.97e-246j)
| (-3.7570804205013913893 + 1.011392827647915281e-657j)  +/-  (1.8e-247, 1.8e-247j)
| (1.7320508075688772935 + 1.0662426144852028043e-672j)  +/-  (7.6e-251, 7.6e-251j)
| (11.453220594705903324 + 6.7554813919888620063e-668j)  +/-  (7.01e-248, 7.01e-248j)
| (6.4591445509565751686 - 1.4130199631371447501e-692j)  +/-  (1.87e-245, 1.87e-245j)
| (-7.645928216681227861 + 1.1106400424104354622e-730j)  +/-  (2.45e-245, 2.45e-245j)
| (-5.3442684528024026854 + 1.4202172401659907994e-761j)  +/-  (5.18e-246, 5.18e-246j)
| (-8.2787230801794203541 + 2.6943886506646497202e-781j)  +/-  (1.66e-245, 1.66e-245j)
| (-4.8059124495274055399 + 7.3882782206520618384e-795j)  +/-  (2.16e-246, 2.16e-246j)
| (8.9493033011068555168 + 2.0712798905096937803e-808j)  +/-  (9.78e-246, 9.78e-246j)
| (-6.4591445509565751686 - 3.3004398157259156537e-810j)  +/-  (1.67e-245, 1.67e-245j)
| (-1.7320508075688772935 - 1.3348190812955637731e-824j)  +/-  (8e-251, 8e-251j)
| (2.2320523524566528202 - 1.1364674956412403322e-823j)  +/-  (7.68e-250, 7.68e-250j)
| (7.645928216681227861 - 9.5370023874526635761e-818j)  +/-  (2.28e-245, 2.28e-245j)
| (4.2774051115884738374 - 1.2069040804181853011e-821j)  +/-  (6.94e-247, 6.94e-247j)
| (5.3442684528024026854 - 1.5879741278197794026e-820j)  +/-  (4.99e-246, 4.99e-246j)
| (-3.2435334817918385549 + 1.4572802839581937685e-821j)  +/-  (3.42e-248, 3.42e-248j)
| (-4.2774051115884738374 + 1.3069193371602022411e-838j)  +/-  (6.46e-247, 6.46e-247j)
| (-5.8945001395220588506 + 1.2676288026431119491e-864j)  +/-  (1.04e-245, 1.04e-245j)
| (0.73843199186576855747 + 8.8267166162006519103e-892j)  +/-  (4.63e-253, 4.63e-253j)
| (-7.0414826390420884799 + 9.0731530234123516313e-883j)  +/-  (2.37e-245, 2.37e-245j)
| (-7.0243335469962126353e-909 + 8.6107447939798267742e-909j)  +/-  (4.56e-907, 4.56e-907j)
| (-0.73843199186576855747 + 1.4022160149201456132e-899j)  +/-  (4.63e-253, 4.63e-253j)
| (7.0414826390420884799 + 1.708300728379866743e-891j)  +/-  (2.36e-245, 2.36e-245j)
| (2.7355499818707681235 + 1.076295823696395886e-895j)  +/-  (5.53e-249, 5.53e-249j)
| (0.23931300252813243724 - 3.3075777788358997774e-900j)  +/-  (3.22e-254, 3.22e-254j)
| (3.7570804205013913893 - 2.2982282259699939377e-894j)  +/-  (1.68e-247, 1.68e-247j)
| (-2.2320523524566528202 - 2.3096978291771785176e-897j)  +/-  (8.07e-250, 8.07e-250j)
| (-2.7355499818707681235 + 2.2533815795725560122e-894j)  +/-  (5.63e-249, 5.63e-249j)
| (4.8059124495274055399 + 3.5841657422237896815e-893j)  +/-  (1.98e-246, 1.98e-246j)
| (1.2345732564964127544 - 3.2458746369833133316e-898j)  +/-  (6.88e-252, 6.88e-252j)
| (3.2435334817918385549 - 1.8458587840989224824e-895j)  +/-  (3.61e-248, 3.61e-248j)
| (-0.23931300252813243724 + 3.6322186353504080895e-900j)  +/-  (3.22e-254, 3.22e-254j)
| (-1.2345732564964127544 - 4.7496578790793631602e-898j)  +/-  (7.29e-252, 7.29e-252j)
-------------------------------------------------
The weights are:
| (6.3376290751725506788e-09 + 1.0652491017778272838e-651j)  +/-  (1.47e-78, 8.52e-201j)
| (1.4512486592811960648e-21 - 2.6375331431163538243e-659j)  +/-  (2.46e-87, 1.43e-209j)
| (4.8292365811171187105e-25 - 1.0232019069311432227e-661j)  +/-  (9.94e-90, 5.78e-212j)
| (3.3960533296803533045e-16 - 2.3608846831861945859e-656j)  +/-  (3.31e-85, 1.92e-207j)
| (1.4644951193576220945e-29 + 4.8699271909675060174e-664j)  +/-  (1.77e-91, 1.03e-213j)
| (1.1243235312536758281e-18 - 2.0370578546074628893e-658j)  +/-  (5.8e-88, 3.37e-210j)
| (4.8292365811171187105e-25 + 3.658041090092866225e-661j)  +/-  (1.4e-90, 8.12e-213j)
| (1.4512486592811960648e-21 + 6.3844529766650586954e-660j)  +/-  (5.87e-89, 3.42e-211j)
| (0.00017741477666304566114 + 9.2980264450436922494e-651j)  +/-  (1.71e-77, 9.94e-200j)
| (0.044381029596550142278 + 7.3968159830145094556e-649j)  +/-  (2.63e-67, 1.53e-189j)
| (1.4644951193576220945e-29 - 1.5211628390285597553e-663j)  +/-  (9.65e-93, 5.61e-215j)
| (1.9927902210147469691e-10 + 9.7943068660117021035e-653j)  +/-  (4.34e-84, 2.52e-206j)
| (4.9771974994945986476e-14 - 5.460314325748103025e-656j)  +/-  (3.01e-87, 1.75e-209j)
| (1.3628805955155298852e-07 - 1.5560461486974190377e-652j)  +/-  (8.92e-84, 5.19e-206j)
| (3.3960533296803533045e-16 + 3.9849472786129346688e-657j)  +/-  (4.14e-88, 2.41e-210j)
| (2.0527509915754884069e-06 + 7.0528749302270911305e-652j)  +/-  (6.84e-83, 3.97e-205j)
| (1.1243235312536758281e-18 + 9.8173913488306668601e-658j)  +/-  (8.9e-91, 5.18e-213j)
| (1.9927902210147469691e-10 - 4.4797863572750473716e-654j)  +/-  (2.95e-86, 1.71e-208j)
| (0.044381029596550142278 + 4.0374331472543880468e-649j)  +/-  (2.77e-75, 1.61e-197j)
| (0.016573651608199172071 - 3.9859941895506523727e-649j)  +/-  (3.16e-78, 1.84e-200j)
| (4.9771974994945986476e-14 + 4.2148799915055280884e-655j)  +/-  (2.9e-89, 1.69e-211j)
| (2.2254002938153069698e-05 - 1.7259236883726851289e-650j)  +/-  (3.53e-85, 2.05e-207j)
| (1.3628805955155298852e-07 - 3.1769511361634874533e-651j)  +/-  (1.98e-86, 1.15e-208j)
| (0.0010579636142684522996 - 2.7778171010733564729e-650j)  +/-  (4.95e-83, 2.88e-205j)
| (2.2254002938153069698e-05 - 2.7445919424903265906e-651j)  +/-  (1.33e-84, 7.71e-207j)
| (6.3376290751725506788e-09 + 2.900534624750288452e-653j)  +/-  (2.13e-87, 1.24e-209j)
| (0.1506893697232180627 + 2.5841754947979441402e-648j)  +/-  (3.56e-81, 2.07e-203j)
| (4.0450639079895293564e-12 + 5.5923318241770260734e-655j)  +/-  (3.16e-89, 1.84e-211j)
| (-0.015495501861619533058 + 1.3079721583499074501e-647j)  +/-  (1.91e-81, 1.11e-203j)
| (0.1506893697232180627 + 2.008868518581863118e-648j)  +/-  (5.39e-82, 3.13e-204j)
| (4.0450639079895293564e-12 - 6.3010588921095379736e-654j)  +/-  (7.79e-91, 4.53e-213j)
| (0.0047833018619577235136 + 2.0255892255026672521e-649j)  +/-  (6.32e-86, 3.68e-208j)
| (0.19760850613198259898 - 8.436516964682816514e-648j)  +/-  (2.08e-82, 1.21e-204j)
| (0.00017741477666304566114 + 4.1975742314737615377e-650j)  +/-  (9.97e-88, 5.8e-210j)
| (0.016573651608199172071 - 1.7966122285866702927e-649j)  +/-  (1.46e-85, 8.46e-208j)
| (0.0047833018619577235136 + 7.4156214062582493648e-650j)  +/-  (4.29e-86, 2.49e-208j)
| (2.0527509915754884069e-06 + 6.9303188894580658348e-651j)  +/-  (3.47e-89, 2.02e-211j)
| (0.092452064034978015029 - 1.3382571999103068533e-648j)  +/-  (8.72e-86, 5.12e-208j)
| (0.0010579636142684522996 - 9.573472897675693276e-650j)  +/-  (1.12e-87, 6.5e-210j)
| (0.19760850613198259898 - 7.7783039484100094563e-648j)  +/-  (3.02e-85, 2.11e-207j)
| (0.092452064034978015029 - 8.7480930620315655676e-649j)  +/-  (3.79e-86, 1.93e-208j)
