Starting with polynomial:
P : t
Extension levels are: 1 40
-------------------------------------------------
Trying to find an order 40 Kronrod extension for:
P1 : t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^41 - 820/81*t^39 + 101270/2133*t^37 - 7493980/54747*t^35 + 6369883/23463*t^33 - 101918128/259515*t^31 + 1579730984/3685113*t^29 - 91624397072/254272797*t^27 + 148889645242/630973237*t^25 - 229060992680/1892919711*t^23 + 251967091948/5184953991*t^21 - 229060992680/15061056831*t^19 + 1088039715230/296200784343*t^17 - 599082596240/888602353029*t^15 + 299541298120/3258208627773*t^13 - 1557614750224/172685057271969*t^11 + 28632624085/47095924710537*t^9 - 6737088020/256411145646257*t^7 + 3368544010/5164853076588891*t^5 - 354583580/46483677689300019*t^3 + 17729179/666266046879966939*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:
| (0.97833867356108338447 + 1.6121086940683579952e-863j)  +/-  (2.57e-241, 2.57e-241j)
| (-0.99832158857477144152 - 8.5716334225944013112e-878j)  +/-  (6.94e-242, 6.94e-242j)
| (-0.9599068917303462261 + 3.6032718828700652132e-880j)  +/-  (2.26e-241, 2.26e-241j)
| (0.99832158857477144152 + 6.8558984185424228905e-895j)  +/-  (6.23e-242, 6.23e-242j)
| (0.93597698749785382568 - 7.3268945496407388629e-922j)  +/-  (1.68e-241, 1.68e-241j)
| (0.9599068917303462261 + 4.0877280577383403816e-940j)  +/-  (2.42e-241, 2.42e-241j)
| (-0.87220151169244140883 + 8.7746289548565562661e-945j)  +/-  (3.6e-242, 3.6e-242j)
| (-0.90668594475810117296 - 8.8454119776992738094e-945j)  +/-  (8.23e-242, 8.23e-242j)
| (-0.97833867356108338447 - 2.3112972593218074035e-943j)  +/-  (2.57e-241, 2.57e-241j)
| (0.78847114504740937274 + 4.0362090043438259407e-946j)  +/-  (3.87e-243, 3.87e-243j)
| (0.90668594475810117296 + 5.735392679497001379e-945j)  +/-  (8.48e-242, 8.48e-242j)
| (-0.99116710969901630825 - 3.9975158947393488271e-951j)  +/-  (1.84e-241, 1.84e-241j)
| (-0.93597698749785382568 - 4.7248023117902004878e-955j)  +/-  (1.57e-241, 1.57e-241j)
| (-0.78847114504740937274 + 6.9315088163213053005e-958j)  +/-  (3.3e-243, 3.3e-243j)
| (0.99116710969901630825 + 5.0920654833046468993e-953j)  +/-  (2.04e-241, 2.04e-241j)
| (0.87220151169244140883 - 3.1752287770145915374e-963j)  +/-  (3.62e-242, 3.62e-242j)
| (0.83272120040136133124 + 2.8980799154567716879e-974j)  +/-  (1.27e-242, 1.27e-242j)
| (-0.83272120040136133124 + 1.0960896471024334355e-978j)  +/-  (1.24e-242, 1.24e-242j)
| (-0.73970480306992618106 + 3.692394026838326064e-982j)  +/-  (8.2e-244, 8.2e-244j)
| (-0.22513960563342277561 - 1.3474905021841610372e-987j)  +/-  (9.32e-252, 9.32e-252j)
| (0.50541659919940603271 + 6.4845016025507328945e-983j)  +/-  (3.32e-247, 3.32e-247j)
| (0.73970480306992618106 - 2.5918968656183906418e-979j)  +/-  (8.74e-244, 8.74e-244j)
| (0.15081335486399216357 + 2.7026370933582389584e-991j)  +/-  (4.94e-253, 4.94e-253j)
| (-0.56922094161021586965 + 3.9605688666192256443e-985j)  +/-  (3.14e-246, 3.14e-246j)
| (-0.62976483907219632049 + 3.0956841535359216006e-985j)  +/-  (2.26e-245, 2.26e-245j)
| (0.075623258989162996924 - 1.7020127794813685173e-991j)  +/-  (1.95e-254, 1.95e-254j)
| (0.68670150203495128958 + 4.1929316163177626362e-985j)  +/-  (1.61e-244, 1.61e-244j)
| (0.43871727705140708852 - 4.9884511571919292854e-991j)  +/-  (3e-248, 3e-248j)
| (-0.15081335486399216357 - 1.2961732190435521002e-994j)  +/-  (4.27e-253, 4.27e-253j)
| (-0.68670150203495128958 - 2.7524844641026570776e-990j)  +/-  (1.68e-244, 1.68e-244j)
| (-0.075623258989162996924 - 1.9170492625024659438e-995j)  +/-  (1.95e-254, 1.95e-254j)
| (0.36950502264048144143 - 2.1101063679529295412e-992j)  +/-  (2.44e-249, 2.44e-249j)
| (0.62976483907219632049 - 4.070818416034781688e-991j)  +/-  (2.56e-245, 2.56e-245j)
| (-1.7250059941143725445e-998 - 9.7890157702268875236e-999j)  +/-  (8.13e-997, 8.13e-997j)
| (-0.43871727705140708852 + 6.6172794583172367997e-999j)  +/-  (2.68e-248, 2.68e-248j)
| (-0.36950502264048144143 + 5.6865214961531987149e-998j)  +/-  (2.14e-249, 2.14e-249j)
| (0.22513960563342277561 - 6.8164844660959591545e-997j)  +/-  (8.93e-252, 8.93e-252j)
| (0.56922094161021586965 + 9.4639584052569953741e-997j)  +/-  (3.04e-246, 3.04e-246j)
| (0.29817627734182486592 - 1.4098036768380943503e-999j)  +/-  (1.54e-250, 1.54e-250j)
| (-0.29817627734182486592 + 1.0184848000179371025e-1001j)  +/-  (1.62e-250, 1.62e-250j)
| (-0.50541659919940603271 + 3.8537766544815274109e-1002j)  +/-  (3.45e-247, 3.45e-247j)
-------------------------------------------------
The weights are:
| (0.015644938407818588531 - 5.7580006707910067669e-864j)  +/-  (1.35e-74, 4.05e-191j)
| (0.004306140358164887684 - 1.8727610483251669244e-866j)  +/-  (3.77e-75, 1.14e-191j)
| (0.021201063368779553076 + 2.0512141860915915127e-865j)  +/-  (3.35e-75, 1.01e-191j)
| (0.004306140358164887684 + 1.8524886595088016205e-864j)  +/-  (2.01e-75, 6.05e-192j)
| (0.026635899207110445468 - 1.321195229519449709e-863j)  +/-  (1.42e-75, 4.26e-192j)
| (0.021201063368779553076 + 2.1570116422617665899e-863j)  +/-  (2.46e-75, 7.41e-192j)
| (0.037017716703507988435 - 4.9537473423716365474e-865j)  +/-  (1.25e-76, 3.75e-193j)
| (0.031918211731699281787 + 3.8940701277950974549e-865j)  +/-  (1.47e-76, 4.41e-193j)
| (0.015644938407818588531 - 1.2889882566754210209e-865j)  +/-  (8.73e-77, 2.63e-193j)
| (0.046552648369014342061 - 6.80825293877237864e-864j)  +/-  (7.23e-79, 2.18e-195j)
| (0.031918211731699281787 + 1.0244436156139908543e-863j)  +/-  (1.32e-77, 3.98e-194j)
| (0.0099999387739059453385 + 6.5589616009041522785e-866j)  +/-  (4.6e-77, 1.38e-193j)
| (0.026635899207110445468 - 2.9236587611782348104e-865j)  +/-  (2.73e-77, 8.21e-194j)
| (0.046552648369014342061 - 7.3163854160537619091e-865j)  +/-  (6.03e-80, 1.81e-196j)
| (0.0099999387739059453385 - 1.0069748694409216492e-863j)  +/-  (4.8e-78, 1.45e-194j)
| (0.037017716703507988435 - 8.6370394339314151623e-864j)  +/-  (2.69e-79, 8.1e-196j)
| (0.041905195195909689429 + 7.5818903918277366345e-864j)  +/-  (7.12e-80, 2.14e-196j)
| (0.041905195195909689429 + 6.0961856452402643023e-865j)  +/-  (3e-80, 9.04e-197j)
| (0.050933454294617494781 + 8.6104664517454467663e-865j)  +/-  (7.88e-82, 2.37e-198j)
| (0.073751882027223469939 + 2.1416141303181874875e-864j)  +/-  (2.56e-85, 7.72e-202j)
| (0.065314196453527410436 + 4.5420376680279317639e-864j)  +/-  (9.43e-85, 2.84e-201j)
| (0.050933454294617494781 + 6.1991014467992851182e-864j)  +/-  (9.95e-83, 3e-199j)
| (0.074829623176221551891 - 3.1830826702972209807e-864j)  +/-  (8.66e-86, 2.61e-202j)
| (0.062233542580966316472 - 1.2909892253725226223e-864j)  +/-  (5.63e-85, 1.7e-201j)
| (0.058796420949871944991 + 1.140909383616768803e-864j)  +/-  (1.81e-84, 5.44e-201j)
| (0.075478747092715824027 + 2.956000374379285713e-864j)  +/-  (1.56e-86, 4.68e-203j)
| (0.05502251924257874188 - 5.6952662920094432112e-864j)  +/-  (3.48e-85, 1.05e-201j)
| (0.068020736760876766736 - 4.2305660099230353844e-864j)  +/-  (1.41e-86, 4.25e-203j)
| (0.074829623176221551891 - 2.3327961469022818268e-864j)  +/-  (1.91e-87, 5.76e-204j)
| (0.05502251924257874188 - 9.9754430964121999246e-865j)  +/-  (7.93e-86, 2.39e-202j)
| (0.075478747092715824027 + 2.5318059609381031709e-864j)  +/-  (1.2e-87, 3.61e-204j)
| (0.070337660620817497482 + 3.9428145159550854489e-864j)  +/-  (5.34e-88, 1.61e-204j)
| (0.058796420949871944991 + 5.2634483884326441887e-864j)  +/-  (2.43e-87, 7.33e-204j)
| (0.075695535647298372319 - 2.7392666918589434202e-864j)  +/-  (3.84e-88, 1.16e-204j)
| (0.068020736760876766736 - 1.6110189137657922961e-864j)  +/-  (4.48e-89, 1.35e-205j)
| (0.070337660620817497482 + 1.7810063313845354946e-864j)  +/-  (3.54e-89, 1.06e-205j)
| (0.073751882027223469939 + 3.4219188498803166828e-864j)  +/-  (3.51e-89, 1.06e-205j)
| (0.062233542580966316472 - 4.8833932943479978364e-864j)  +/-  (4.16e-89, 1.25e-205j)
| (0.072251696861023073396 - 3.6743512391434159341e-864j)  +/-  (2.3e-89, 6.91e-206j)
| (0.072251696861023073396 - 1.9577957481808654662e-864j)  +/-  (4.17e-90, 1.27e-206j)
| (0.065314196453527410436 + 1.4476982257298721251e-864j)  +/-  (2.84e-90, 8.34e-207j)
