Starting with polynomial:
P : 4*t^3 - 3*t
Extension levels are: 3 54
-------------------------------------------------
Trying to find an order 54 Kronrod extension for:
P1 : 4*t^3 - 3*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 4*t^57 - 57*t^55 + 1539/4*t^53 - 13091/8*t^51 + 314925/64*t^49 - 712215/64*t^47 + 5032055/256*t^45 - 14233527/512*t^43 + 262303569/8192*t^41 - 1991564135/65536*t^39 + 6279783081/262144*t^37 - 8265485241/524288*t^35 + 36429360877/4194304*t^33 - 8406775587/2097152*t^31 + 12987211455/8388608*t^29 - 8369536271/16777216*t^27 + 71651395881/536870912*t^25 - 63221819895/2147483648*t^23 + 45570143685/8589934592*t^21 - 13254473925/17179869184*t^19 + 12251432655/137438953472*t^17 - 1101980715/137438953472*t^15 + 300540195/549755813888*t^13 - 29977155/1099511627776*t^11 + 16653975/17592186044416*t^9 - 5995431/281474976710656*t^7 + 312417/1125899906842624*t^5 - 3857/2251799813685248*t^3 + 57/18014398509481984*t
-------------------------------------------------
Computing nodes and weights
  current precision for roots: 53
  current precision for roots: 106
  current precision for roots: 212
 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:   57 out of 57
Indefinite weights: 0 out of 57
Negative weights:   0 out of 57
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (0.99052208463750327553 - 5.5180321603946387146e-850j)  +/-  (2.41e-235, 2.41e-235j)
| (-0.83716647826252857481 - 3.0033854946033019552e-862j)  +/-  (1.87e-237, 1.87e-237j)
| (-0.93651124119705478803 - 1.5318870193134903913e-860j)  +/-  (8.54e-236, 8.54e-236j)
| (-0.98145149325241789412 + 2.1943349641452700857e-859j)  +/-  (2.35e-235, 2.35e-235j)
| (0.93651124119705478803 + 7.0846008550015035771e-860j)  +/-  (9.03e-236, 9.03e-236j)
| (0.91577332665505743992 + 1.3871869601554046962e-867j)  +/-  (3.39e-236, 3.39e-236j)
| (-0.96940026593933041674 - 1.2672811190640593067e-865j)  +/-  (1.94e-235, 1.94e-235j)
| (-0.91577332665505743992 - 8.4429448431470423028e-869j)  +/-  (3.39e-236, 3.39e-236j)
| (-0.99658449300666984982 - 5.8178764899044378008e-867j)  +/-  (2.11e-235, 2.11e-235j)
| (0.99658449300666984982 - 1.4201798032011210293e-877j)  +/-  (1.67e-235, 1.67e-235j)
| (0.86602540378443864676 + 1.6034897626902083041e-891j)  +/-  (4.85e-237, 4.85e-237j)
| (0.96940026593933041674 - 1.4661071791495900748e-891j)  +/-  (1.97e-235, 1.97e-235j)
| (-0.73572391067313162477 - 5.1721127218276657695e-917j)  +/-  (2.33e-239, 2.33e-239j)
| (-0.80576510566097814488 + 9.7711062917945462567e-914j)  +/-  (5.57e-238, 5.57e-238j)
| (0.99962030702495140574 - 4.7389570286300884692e-909j)  +/-  (6.85e-236, 6.85e-236j)
| (0.83716647826252857481 + 2.7752327522122977418e-921j)  +/-  (2.03e-237, 2.03e-237j)
| (0.80576510566097814488 - 3.6933422378510408689e-922j)  +/-  (4.7e-238, 4.7e-238j)
| (-0.99962030702495140574 + 1.4416924913793302862e-916j)  +/-  (7.21e-236, 7.21e-236j)
| (-0.77191665091632089389 - 1.4172141045943172272e-932j)  +/-  (1.2e-238, 1.2e-238j)
| (0.98145149325241789412 + 8.9236602567463367334e-930j)  +/-  (2.52e-235, 2.52e-235j)
| (0.89225423861839401792 + 1.3853574485494520174e-940j)  +/-  (1.5e-236, 1.5e-236j)
| (0.73572391067313162477 - 7.592966107308917367e-945j)  +/-  (2.19e-239, 2.19e-239j)
| (-0.99052208463750327553 - 2.0478446291242710582e-938j)  +/-  (2.29e-235, 2.29e-235j)
| (-0.86602540378443864676 + 1.4880888869589932434e-948j)  +/-  (5.84e-237, 5.84e-237j)
| (-0.69729680109399541239 + 5.0834501092406997975e-952j)  +/-  (3.78e-240, 3.78e-240j)
| (0.52367291398787786131 + 4.1477297208018655713e-956j)  +/-  (1.08e-243, 1.08e-243j)
| (0.77191665091632089389 + 1.1856461783330793417e-950j)  +/-  (1.06e-238, 1.06e-238j)
| (0.95440500187950743136 - 8.3312128227527514861e-948j)  +/-  (1.16e-235, 1.16e-235j)
| (-0.95440500187950743136 - 1.3940316195032024468e-963j)  +/-  (1.21e-235, 1.21e-235j)
| (-0.65675202404773440672 + 8.8092403265395401892e-972j)  +/-  (7.28e-241, 7.28e-241j)
| (-0.89225423861839401792 - 5.3008889016182552899e-975j)  +/-  (1.62e-236, 1.62e-236j)
| (0.69729680109399541239 - 9.7504085451499289165e-979j)  +/-  (4.44e-240, 4.44e-240j)
| (0.65675202404773440672 + 3.259205083985770798e-981j)  +/-  (5.75e-241, 5.75e-241j)
| (0.11000822099407929504 + 1.7875545632867439183e-995j)  +/-  (2.9e-253, 2.9e-253j)
| (-0.61421271268966781744 - 2.1786292432103116018e-983j)  +/-  (9.29e-242, 9.29e-242j)
| (-0.47594739303707354443 + 1.0922339764755904529e-986j)  +/-  (9.26e-245, 9.26e-245j)
| (0.055087760355865443115 + 1.4218886776781026882e-997j)  +/-  (1.31e-254, 1.31e-254j)
| (0.61421271268966781744 - 3.7167832389566111202e-984j)  +/-  (7.94e-242, 7.94e-242j)
| (0.56980805751026618168 - 4.3436826308081404031e-989j)  +/-  (1.09e-242, 1.09e-242j)
| (-0.32469946920468348741 + 8.2909806759145208033e-992j)  +/-  (3.73e-248, 3.73e-248j)
| (-0.56980805751026618168 + 2.5554800366983999038e-988j)  +/-  (9.76e-243, 9.76e-243j)
| (-0.16459459028073389414 + 3.3570747424513379728e-998j)  +/-  (5.94e-252, 5.94e-252j)
| (0.27210346484533500435 - 2.4022686745851494518e-996j)  +/-  (2.09e-249, 2.09e-249j)
| (0.42677643549640366813 + 2.9296728224054608256e-991j)  +/-  (7.4e-246, 7.4e-246j)
| (-0.11000822099407929504 - 3.0953295238803128034e-1000j)  +/-  (2.25e-253, 2.25e-253j)
| (-0.52367291398787786131 - 1.247829597061148471e-991j)  +/-  (1.15e-243, 1.15e-243j)
| (-0.27210346484533500435 - 7.1699854632638099547e-997j)  +/-  (2.17e-249, 2.17e-249j)
| (0.16459459028073389414 - 2.004053565207049717e-998j)  +/-  (5.4e-252, 5.4e-252j)
| (0.47594739303707354443 + 1.6293779007383423555e-992j)  +/-  (1.06e-244, 1.06e-244j)
| (0.21868109120637580658 - 6.5034004508203560609e-999j)  +/-  (9.84e-251, 9.84e-251j)
| (-0.21868109120637580658 - 2.9602501829646728954e-999j)  +/-  (1.04e-250, 1.04e-250j)
| (-0.37630937194783545809 + 1.4399226889984765623e-995j)  +/-  (5.44e-247, 5.44e-247j)
| (-0.055087760355865443115 - 1.8372149832057661543e-1002j)  +/-  (1.52e-254, 1.52e-254j)
| (0.37630937194783545809 + 9.0503514289298230112e-996j)  +/-  (6.14e-247, 6.14e-247j)
| (0.32469946920468348741 + 3.2341727627189308747e-996j)  +/-  (3.38e-248, 3.38e-248j)
| (-2.08165461408619784e-1013 - 1.2878361333187961767e-1014j)  +/-  (1.19e-1011, 1.19e-1011j)
| (-0.42677643549640366813 + 3.7798007211102054111e-995j)  +/-  (8.67e-246, 8.67e-246j)
-------------------------------------------------
The weights are:
| (0.017543859649122807018 + 2.5413455020590642143e-850j)  +/-  (3.58e-51, 4.45e-163j)
| (0.017543859649122807018 + 2.1091789420002583291e-851j)  +/-  (1.82e-51, 2.26e-163j)
| (0.017543859649122807018 + 1.2824447299653188376e-851j)  +/-  (1.06e-51, 1.31e-163j)
| (0.017543859649122807018 - 6.8519559519132008257e-852j)  +/-  (2.63e-52, 3.27e-164j)
| (0.017543859649122807018 + 4.5755881712409390518e-850j)  +/-  (2.34e-53, 2.91e-165j)
| (0.017543859649122807018 - 3.7875847784070029204e-850j)  +/-  (1.67e-53, 2.07e-165j)
| (0.017543859649122807018 + 8.8278794732746787357e-852j)  +/-  (2.36e-52, 2.94e-164j)
| (0.017543859649122807018 - 1.4851698938089278218e-851j)  +/-  (1.37e-52, 1.7e-164j)
| (0.017543859649122807018 - 2.929002552383244323e-852j)  +/-  (2.53e-53, 3.14e-165j)
| (0.017543859649122807018 + 9.6005410123911307478e-850j)  +/-  (2.8e-54, 3.48e-166j)
| (0.017543859649122807018 - 2.8306207737083286058e-850j)  +/-  (3.21e-55, 3.99e-167j)
| (0.017543859649122807018 + 8.1915100811006360624e-850j)  +/-  (7.57e-55, 9.41e-167j)
| (0.017543859649122807018 - 2.7652603867323186373e-851j)  +/-  (5.34e-56, 6.64e-168j)
| (0.017543859649122807018 - 2.3237421692608057208e-851j)  +/-  (3.62e-55, 4.49e-167j)
| (0.017543859649122807018 - 2.1345334285860956668e-850j)  +/-  (1.12e-54, 1.39e-166j)
| (0.017543859649122807018 + 2.513714584693503846e-850j)  +/-  (2.06e-56, 2.55e-168j)
| (0.017543859649122807018 - 2.259242561731668417e-850j)  +/-  (3.74e-57, 4.64e-169j)
| (0.017543859649122807018 + 9.758327102603911765e-853j)  +/-  (8.51e-57, 1.06e-168j)
| (0.017543859649122807018 + 2.5422828235357504025e-851j)  +/-  (2.5e-57, 3.11e-169j)
| (0.017543859649122807018 - 1.4896356385276009298e-849j)  +/-  (2.38e-55, 2.96e-167j)
| (0.017543859649122807018 + 3.2385295359814023142e-850j)  +/-  (3.26e-56, 4.05e-168j)
| (0.017543859649122807018 - 1.8734512905105700754e-850j)  +/-  (1.87e-59, 2.32e-171j)
| (0.017543859649122807018 + 4.8866950732580110401e-852j)  +/-  (6.3e-57, 7.83e-169j)
| (0.017543859649122807018 - 1.8981625387200405884e-851j)  +/-  (2.79e-58, 3.47e-170j)
| (0.017543859649122807018 + 2.9931674733460595725e-851j)  +/-  (2.01e-60, 2.49e-172j)
| (0.017543859649122807018 + 1.2861492812009917776e-850j)  +/-  (1.53e-63, 1.9e-175j)
| (0.017543859649122807018 + 2.0496369462119210519e-850j)  +/-  (1.05e-59, 1.3e-171j)
| (0.017543859649122807018 - 5.8253587729521437826e-850j)  +/-  (1.66e-57, 2.06e-169j)
| (0.017543859649122807018 - 1.0817627162670080044e-851j)  +/-  (3.04e-58, 3.77e-170j)
| (0.017543859649122807018 - 3.2265346450926950307e-851j)  +/-  (1.33e-62, 1.65e-174j)
| (0.017543859649122807018 + 1.6902874537118544048e-851j)  +/-  (8.86e-59, 1.1e-170j)
| (0.017543859649122807018 + 1.7228816482860389116e-850j)  +/-  (1.79e-62, 2.22e-174j)
| (0.017543859649122807018 - 1.5924097505664933317e-850j)  +/-  (1.86e-63, 2.31e-175j)
| (0.017543859649122807018 + 7.9559007215766499066e-851j)  +/-  (7.04e-69, 8.75e-181j)
| (0.017543859649122807018 + 3.46593589292611088e-851j)  +/-  (4.42e-65, 5.49e-177j)
| (0.017543859649122807018 - 4.2268740948694901086e-851j)  +/-  (1.7e-67, 2.12e-179j)
| (0.017543859649122807018 - 7.5230887700650592576e-851j)  +/-  (4.79e-69, 5.95e-181j)
| (0.017543859649122807018 + 1.4780147278022611086e-850j)  +/-  (1.35e-65, 1.68e-177j)
| (0.017543859649122807018 - 1.3766922861123050884e-850j)  +/-  (2.36e-66, 2.93e-178j)
| (0.017543859649122807018 + 5.068480352317906059e-851j)  +/-  (2.63e-70, 3.27e-182j)
| (0.017543859649122807018 - 3.7119949141344771947e-851j)  +/-  (1.28e-67, 1.59e-179j)
| (0.017543859649122807018 - 6.018380348760327926e-851j)  +/-  (3.23e-71, 4.01e-183j)
| (0.017543859649122807018 - 9.4403462249381283826e-851j)  +/-  (1.94e-71, 2.42e-183j)
| (0.017543859649122807018 + 1.1306449228080261646e-850j)  +/-  (1.54e-70, 1.91e-182j)
| (0.017543859649122807018 + 6.3653684467645913125e-851j)  +/-  (9.47e-72, 1.18e-183j)
| (0.017543859649122807018 + 3.9653923389866819325e-851j)  +/-  (9.41e-70, 1.17e-181j)
| (0.017543859649122807018 - 5.3714424721096369678e-851j)  +/-  (1.11e-71, 1.38e-183j)
| (0.017543859649122807018 - 8.4171208075484412804e-851j)  +/-  (2.64e-72, 3.28e-184j)
| (0.017543859649122807018 - 1.204602937522824783e-850j)  +/-  (1.43e-71, 1.78e-183j)
| (0.017543859649122807018 + 8.9104742874137312886e-851j)  +/-  (1.6e-72, 1.99e-184j)
| (0.017543859649122807018 + 5.6876044170383901744e-851j)  +/-  (7.01e-73, 8.71e-185j)
| (0.017543859649122807018 - 4.7774608358888712013e-851j)  +/-  (3.95e-73, 4.91e-185j)
| (0.017543859649122807018 - 6.7303837022604626377e-851j)  +/-  (1.23e-73, 1.53e-185j)
| (0.017543859649122807018 - 1.0631469557162017154e-850j)  +/-  (6.74e-74, 8.35e-186j)
| (0.017543859649122807018 + 1.0011937793972776549e-850j)  +/-  (5.17e-74, 6.4e-186j)
| (0.017543859649122807018 + 7.1154979068142308567e-851j)  +/-  (2.59e-74, 3.27e-186j)
| (0.017543859649122807018 + 4.4972611379740010086e-851j)  +/-  (1.69e-74, 1.94e-186j)
