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 - 41/4*t^39 + 779/16*t^37 - 4551/32*t^35 + 73185/256*t^33 - 53669/128*t^31 + 237677/512*t^29 - 405449/1024*t^27 + 4312503/16384*t^25 - 35937525/262144*t^23 + 58659315/1048576*t^21 - 37328655/2097152*t^19 + 73370115/16777216*t^17 - 13706505/16777216*t^15 + 7614725/67108864*t^13 - 1522945/134217728*t^11 + 3350479/4294967296*t^9 - 591261/17179869184*t^7 + 59983/68719476736*t^5 - 1435/137438953472*t^3 + 41/1099511627776*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
Positive weights:   41 out of 41
Indefinite weights: 0 out of 41
Negative weights:   0 out of 41
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (0.98170831999685493768 + 9.6811360560231892805e-878j)  +/-  (2.03e-241, 2.03e-241j)
| (-0.99926618105081002039 + 2.821167534794575096e-896j)  +/-  (9.01e-242, 9.01e-242j)
| (-0.94114004797956157414 + 2.194947908295715731e-898j)  +/-  (1.16e-241, 1.16e-241j)
| (0.99926618105081002039 - 9.8655591567414520002e-906j)  +/-  (6.85e-242, 6.85e-242j)
| (0.94114004797956157414 + 7.3265398112015213603e-927j)  +/-  (1.21e-241, 1.21e-241j)
| (0.96425349545314098385 - 8.5089554797756715451e-940j)  +/-  (1.77e-241, 1.77e-241j)
| (-0.87851225091094237703 - 4.5493146171720457387e-951j)  +/-  (2.4e-242, 2.4e-242j)
| (-0.91250361647655001597 + 6.0544373166481312379e-950j)  +/-  (6.24e-242, 6.24e-242j)
| (-0.98170831999685493768 - 8.9366824353050137642e-949j)  +/-  (2.29e-241, 2.29e-241j)
| (0.79529287127342644197 - 1.122648499177619224e-955j)  +/-  (2.88e-243, 2.88e-243j)
| (0.91250361647655001597 + 1.4386474394631625078e-956j)  +/-  (6.88e-242, 6.88e-242j)
| (-0.99340208975967506879 - 2.5980008117941648733e-967j)  +/-  (1.97e-241, 1.97e-241j)
| (-0.96425349545314098385 + 3.2612250905555136873e-972j)  +/-  (2.06e-241, 2.06e-241j)
| (-0.79529287127342644197 - 5.6739770191431893263e-975j)  +/-  (2.71e-243, 2.71e-243j)
| (0.99340208975967506879 - 1.0363665006942265875e-972j)  +/-  (1.82e-241, 1.82e-241j)
| (0.87851225091094237703 - 1.237120360389063446e-989j)  +/-  (2.82e-242, 2.82e-242j)
| (0.83936542613194995964 - 6.5827528166998269422e-997j)  +/-  (8.74e-243, 8.74e-243j)
| (-0.83936542613194995964 - 4.3501773487302798808e-1001j)  +/-  (1.1e-242, 1.1e-242j)
| (-0.74655322161196265054 + 4.2371906900776698864e-1003j)  +/-  (7.28e-244, 7.28e-244j)
| (-0.2278535089031375756 + 1.1013239511819747022e-1012j)  +/-  (4.3e-252, 4.3e-252j)
| (0.63624244232655983326 - 2.3381499274226131156e-1004j)  +/-  (1.82e-245, 1.82e-245j)
| (0.74655322161196265054 + 2.7671321267033990274e-1005j)  +/-  (6.29e-244, 6.29e-244j)
| (0.15264928421887449854 - 2.4766539978624736199e-1013j)  +/-  (2.73e-253, 2.73e-253j)
| (-0.69343250079224172863 + 6.4870776793892498995e-1007j)  +/-  (1.36e-244, 1.36e-244j)
| (-0.57531866021862059959 - 1.3663995656144359172e-1010j)  +/-  (2.07e-246, 2.07e-246j)
| (0.076549252836495646867 - 1.0791793056226094442e-1017j)  +/-  (1.8e-254, 1.8e-254j)
| (0.69343250079224172863 - 1.0770376255793167588e-1009j)  +/-  (1.18e-244, 1.18e-244j)
| (0.443719837866959686 - 2.3654875457576699548e-1013j)  +/-  (2.32e-248, 2.32e-248j)
| (-0.15264928421887449854 - 2.5967542985284278683e-1018j)  +/-  (2.16e-253, 2.16e-253j)
| (-0.63624244232655983326 - 8.8942388749251077028e-1012j)  +/-  (1.45e-245, 1.45e-245j)
| (-0.076549252836495646867 - 4.0750409192568848681e-1022j)  +/-  (1.28e-254, 1.28e-254j)
| (0.37381707184076879139 + 4.0041749550622569683e-1016j)  +/-  (1.31e-249, 1.31e-249j)
| (0.57531866021862059959 - 8.7224397813780487323e-1012j)  +/-  (2.15e-246, 2.15e-246j)
| (-1.2327010033737969871e-1023 - 4.279831191427797384e-1024j)  +/-  (5.35e-1022, 5.35e-1022j)
| (-0.443719837866959686 + 2.1488005418792513603e-1015j)  +/-  (2.25e-248, 2.25e-248j)
| (-0.37381707184076879139 - 2.59327181077568984e-1017j)  +/-  (1.42e-249, 1.42e-249j)
| (0.2278535089031375756 + 5.545405034058751617e-1020j)  +/-  (4.68e-252, 4.68e-252j)
| (0.51101867944711036626 - 9.6233780300453043094e-1015j)  +/-  (2.73e-247, 2.73e-247j)
| (0.30172059859519231597 - 5.6323164906819018722e-1019j)  +/-  (8.38e-251, 8.38e-251j)
| (-0.30172059859519231597 - 7.360406362198323292e-1019j)  +/-  (8.02e-251, 8.02e-251j)
| (-0.51101867944711036626 + 4.1300758781272990475e-1015j)  +/-  (2.78e-247, 2.78e-247j)
-------------------------------------------------
The weights are:
| (0.02439024390243902439 - 3.197434193427456621e-878j)  +/-  (1.91e-73, 4.42e-190j)
| (0.02439024390243902439 - 2.39798624995422083e-880j)  +/-  (5.02e-74, 1.16e-190j)
| (0.02439024390243902439 - 2.1801639378296127128e-879j)  +/-  (4.47e-74, 1.03e-190j)
| (0.02439024390243902439 + 2.7055400429610786626e-878j)  +/-  (3.37e-74, 7.79e-191j)
| (0.02439024390243902439 - 1.0333505622299362182e-877j)  +/-  (1.9e-74, 4.38e-191j)
| (0.02439024390243902439 + 1.8827639457240368133e-877j)  +/-  (3.76e-74, 8.67e-191j)
| (0.02439024390243902439 - 3.1849646684057655116e-879j)  +/-  (1.89e-75, 4.37e-192j)
| (0.02439024390243902439 + 2.6783258802217670254e-879j)  +/-  (2.98e-75, 6.88e-192j)
| (0.02439024390243902439 - 1.2026243684063847246e-879j)  +/-  (4.83e-76, 1.12e-192j)
| (0.02439024390243902439 - 4.0331840308318958793e-878j)  +/-  (5.36e-78, 1.24e-194j)
| (0.02439024390243902439 + 7.3308844543972072321e-878j)  +/-  (1.11e-76, 2.57e-193j)
| (0.02439024390243902439 + 7.2012034539302139491e-880j)  +/-  (3.35e-76, 7.72e-193j)
| (0.02439024390243902439 + 1.6887954362169296198e-879j)  +/-  (2.87e-76, 6.62e-193j)
| (0.02439024390243902439 - 4.2309921601923005697e-879j)  +/-  (3.07e-79, 7.08e-196j)
| (0.02439024390243902439 - 1.2163033985716267346e-877j)  +/-  (3.96e-77, 9.15e-194j)
| (0.02439024390243902439 - 5.7412427103696052524e-878j)  +/-  (1.46e-78, 3.36e-195j)
| (0.02439024390243902439 + 4.7360200717208656853e-878j)  +/-  (3.65e-79, 8.43e-196j)
| (0.02439024390243902439 + 3.7018753570199505125e-879j)  +/-  (1.46e-79, 3.38e-196j)
| (0.02439024390243902439 + 4.7744201765364543299e-879j)  +/-  (3.64e-81, 8.41e-198j)
| (0.02439024390243902439 + 9.9836847464006654742e-879j)  +/-  (6.69e-85, 1.55e-201j)
| (0.02439024390243902439 + 2.7696219003733944675e-878j)  +/-  (3.31e-83, 7.65e-200j)
| (0.02439024390243902439 + 3.508938071622629105e-878j)  +/-  (8.62e-82, 1.99e-198j)
| (0.02439024390243902439 - 1.4783951827918417231e-878j)  +/-  (2.27e-85, 5.24e-202j)
| (0.02439024390243902439 - 5.3344725163673471532e-879j)  +/-  (4.01e-83, 9.24e-200j)
| (0.02439024390243902439 - 6.5150156450020147755e-879j)  +/-  (1.41e-84, 3.25e-201j)
| (0.02439024390243902439 + 1.3661384577822020348e-878j)  +/-  (5.46e-86, 1.26e-202j)
| (0.02439024390243902439 - 3.099806530495664731e-878j)  +/-  (6.02e-84, 1.39e-200j)
| (0.02439024390243902439 - 2.0659084565084736289e-878j)  +/-  (2.44e-86, 5.62e-203j)
| (0.02439024390243902439 - 1.0805030796189021862e-878j)  +/-  (7.51e-87, 1.73e-203j)
| (0.02439024390243902439 + 5.9137143286941823864e-879j)  +/-  (9.86e-86, 2.28e-202j)
| (0.02439024390243902439 + 1.1684987131698603061e-878j)  +/-  (4.41e-87, 1.02e-203j)
| (0.02439024390243902439 + 1.8922781650296779429e-878j)  +/-  (1.07e-87, 2.46e-204j)
| (0.02439024390243902439 - 2.4961400694421327683e-878j)  +/-  (5.52e-87, 1.27e-203j)
| (0.02439024390243902439 - 1.2633198826172505739e-878j)  +/-  (1.15e-87, 2.65e-204j)
| (0.02439024390243902439 - 7.7972007821280524713e-879j)  +/-  (1.18e-88, 2.72e-205j)
| (0.02439024390243902439 + 8.486003600707111264e-879j)  +/-  (9.15e-89, 2.11e-205j)
| (0.02439024390243902439 + 1.6018845808647499528e-878j)  +/-  (8.36e-89, 1.93e-205j)
| (0.02439024390243902439 + 2.2648644452256207993e-878j)  +/-  (8.84e-89, 2.04e-205j)
| (0.02439024390243902439 - 1.7388744904473581384e-878j)  +/-  (5.04e-89, 1.16e-205j)
| (0.02439024390243902439 - 9.2129239526557682172e-879j)  +/-  (8e-90, 1.87e-206j)
| (0.02439024390243902439 + 7.1416155265781533005e-879j)  +/-  (6.23e-90, 1.41e-206j)
