Starting with polynomial:
P : t
Extension levels are: 1 4 60
-------------------------------------------------
Trying to find an order 4 Kronrod extension for:
P1 : t
Solvable: 1
-------------------------------------------------
Trying to find an order 60 Kronrod extension for:
P2 : t^5 - 5/4*t^3 + 5/16*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^65 - 65/4*t^63 + 2015/16*t^61 - 19825/32*t^59 + 556075/256*t^57 - 2958319/512*t^55 + 24819795/2048*t^53 - 84240585/4096*t^51 + 1884328875/65536*t^49 - 4396767375/131072*t^47 + 17283292845/524288*t^45 - 28805488075/1048576*t^43 + 163593432275/8388608*t^41 - 198441737375/16777216*t^39 + 411891673375/67108864*t^37 - 365759805957/134217728*t^35 + 4441369072335/4294967296*t^33 - 2873827046805/8589934592*t^31 + 3159171576275/34359738368*t^29 - 1467532791725/68719476736*t^27 + 2289351155091/549755813888*t^25 - 743295829575/1099511627776*t^23 + 397576839075/4398046511104*t^21 - 86429747625/8796093022208*t^19 + 120158429625/140737488355328*t^17 - 16341546429/281474976710656*t^15 + 3384343935/1125899906842624*t^13 - 257289305/2251799813685248*t^11 + 54636725/18014398509481984*t^9 - 1884025/36028797018963968*t^7 + 75361/144115188075855872*t^5 - 715/288230376151711744*t^3 + 65/18446744073709551616*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: 0
  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:
| (0.99737314969149111899 - 1.3352668769684407716e-803j)  +/-  (1.8e-232, 1.8e-232j)
| (-0.93501624268541482344 - 4.2392425084336979137e-804j)  +/-  (5.4e-233, 5.4e-233j)
| (-0.91679219531658239802 + 1.0394640748624698291e-808j)  +/-  (2.48e-233, 2.48e-233j)
| (0.99970801408019296428 + 4.8654735399233249701e-811j)  +/-  (8.02e-233, 8.02e-233j)
| (0.91679219531658239802 + 1.5378926139495005995e-813j)  +/-  (2.42e-233, 2.42e-233j)
| (0.93501624268541482344 + 9.0972825245549023621e-814j)  +/-  (6.4e-233, 6.4e-233j)
| (-0.9927088740980539928 + 1.1688712090865987741e-810j)  +/-  (2.8e-232, 2.8e-232j)
| (-0.89642693729570375935 + 2.9751104500091028875e-825j)  +/-  (1.2e-233, 1.2e-233j)
| (-0.7945776797137542687 + 8.8203684041568858882e-833j)  +/-  (1.04e-235, 1.04e-235j)
| (-0.99970801408019296428 + 1.0109606375671289326e-834j)  +/-  (8.06e-233, 8.06e-233j)
| (0.87396803262651796304 + 3.1452802358860591447e-855j)  +/-  (4.08e-234, 4.08e-234j)
| (0.50695985381359040966 - 6.336551160510896686e-870j)  +/-  (2.23e-242, 2.23e-242j)
| (-0.96487555334355145835 - 9.7226789948678143439e-858j)  +/-  (1.97e-232, 1.97e-232j)
| (-0.87396803262651796304 + 3.5213665281268111254e-866j)  +/-  (3.59e-234, 3.59e-234j)
| (0.97644107882927207448 + 4.6260532730737796037e-864j)  +/-  (2.48e-232, 2.48e-232j)
| (0.84946793512152102964 - 6.0561883588301305974e-873j)  +/-  (1.14e-234, 1.14e-234j)
| (0.89642693729570375935 + 2.5640561602002769024e-872j)  +/-  (9.95e-234, 9.95e-234j)
| (-0.97644107882927207448 - 1.0247394474013059243e-868j)  +/-  (2.32e-232, 2.32e-232j)
| (-0.73226866659777351242 + 4.0694011557224810516e-882j)  +/-  (4.98e-237, 4.98e-237j)
| (-0.99737314969149111899 - 1.6550887036869117035e-876j)  +/-  (2.3e-232, 2.3e-232j)
| (0.9927088740980539928 - 4.1398636329199351219e-876j)  +/-  (2.56e-232, 2.56e-232j)
| (0.76431572054584830198 - 1.1990856044537800562e-891j)  +/-  (2.24e-236, 2.24e-236j)
| (-0.84946793512152102964 - 5.6548939105682118312e-890j)  +/-  (1.22e-234, 1.22e-234j)
| (-0.82298386589365639458 - 8.2418498571702779037e-891j)  +/-  (3.57e-235, 3.57e-235j)
| (-0.76431572054584830198 - 8.7819878669509088862e-893j)  +/-  (2.16e-236, 2.16e-236j)
| (0.95105651629515357212 - 5.4424317730494747784e-886j)  +/-  (1.11e-232, 1.11e-232j)
| (0.73226866659777351242 - 7.635656856839138172e-894j)  +/-  (4.96e-237, 4.96e-237j)
| (0.82298386589365639458 - 1.1131641851461530328e-890j)  +/-  (4.34e-235, 4.34e-235j)
| (0.98572608093165088542 - 1.9107843028717951687e-887j)  +/-  (3.13e-232, 3.13e-232j)
| (-0.62618519753831368341 - 7.5322894196310771031e-903j)  +/-  (1.8e-239, 1.8e-239j)
| (-0.98572608093165088542 - 4.8035224843274042578e-896j)  +/-  (2.72e-232, 2.72e-232j)
| (0.7945776797137542687 - 7.2800740495804207723e-907j)  +/-  (1.04e-235, 1.04e-235j)
| (0.69851136524893698805 - 7.2023620921170044234e-910j)  +/-  (8.55e-238, 8.55e-238j)
| (0.96487555334355145835 + 3.1460122232335915466e-912j)  +/-  (1.95e-232, 1.95e-232j)
| (-0.69851136524893698805 - 5.2064345391424964634e-919j)  +/-  (8.3e-238, 8.3e-238j)
| (-0.66312265824079520238 + 6.8224043213951893065e-922j)  +/-  (1.17e-238, 1.17e-238j)
| (8.5010805415954010455e-946 + 7.0841858727992716691e-946j)  +/-  (7.19e-944, 7.19e-944j)
| (0.58778525229247312917 - 3.1352714427607985718e-922j)  +/-  (1.97e-240, 1.97e-240j)
| (0.62618519753831368341 - 4.196111741018661836e-923j)  +/-  (1.64e-239, 1.64e-239j)
| (-0.46472317204376854566 - 1.4654779105746940595e-927j)  +/-  (1.87e-243, 1.87e-243j)
| (-0.58778525229247312917 + 4.2956541678809383756e-924j)  +/-  (2.06e-240, 2.06e-240j)
| (-0.95105651629515357212 + 6.3419253074302569097e-929j)  +/-  (9.6e-233, 9.6e-233j)
| (0.66312265824079520238 + 6.5169119000720443044e-940j)  +/-  (1.15e-238, 1.15e-238j)
| (0.54801250735466998123 + 1.2434576455546153202e-945j)  +/-  (2.04e-241, 2.04e-241j)
| (0.04831337952550706727 + 2.2571178420945213813e-956j)  +/-  (1.06e-254, 1.06e-254j)
| (-0.54801250735466998123 + 2.160662935703661391e-943j)  +/-  (2.28e-241, 2.28e-241j)
| (-0.50695985381359040966 - 4.9264361678352697295e-947j)  +/-  (1.91e-242, 1.91e-242j)
| (0.19212671735370837601 - 6.242772389617876049e-955j)  +/-  (1.17e-250, 1.17e-250j)
| (0.46472317204376854566 - 5.9890126284846152133e-948j)  +/-  (1.8e-243, 1.8e-243j)
| (0.23931566428755776715 + 1.4874780397811373191e-954j)  +/-  (2.12e-249, 2.12e-249j)
| (-0.19212671735370837601 + 1.3857004036791536778e-955j)  +/-  (1.19e-250, 1.19e-250j)
| (-0.42140110777252910665 + 7.7230716765041163058e-950j)  +/-  (1.67e-244, 1.67e-244j)
| (-0.14448904956922131632 + 1.0106612402851381135e-957j)  +/-  (4.81e-252, 4.81e-252j)
| (0.37709484168832044548 + 7.9510780556509870478e-950j)  +/-  (1.14e-245, 1.14e-245j)
| (0.33190785312852843693 + 5.2821851442235528226e-952j)  +/-  (7.18e-247, 7.18e-247j)
| (-0.04831337952550706727 + 1.3800008427518758725e-960j)  +/-  (1.06e-254, 1.06e-254j)
| (-0.37709484168832044548 - 1.7809931815373651011e-950j)  +/-  (1.04e-245, 1.04e-245j)
| (-0.23931566428755776715 - 4.5562460187764288389e-955j)  +/-  (2.22e-249, 2.22e-249j)
| (0.096513920914515116255 + 3.8926532172435796755e-958j)  +/-  (2.82e-253, 2.82e-253j)
| (0.42140110777252910665 - 6.3188645362605703212e-949j)  +/-  (1.34e-244, 1.34e-244j)
| (0.14448904956922131632 + 3.9776058990564354425e-957j)  +/-  (6.03e-252, 6.03e-252j)
| (-0.28594567839868926206 + 9.9537236463530998628e-953j)  +/-  (3.64e-248, 3.64e-248j)
| (-0.33190785312852843693 - 4.451636553002096592e-952j)  +/-  (7.44e-247, 7.44e-247j)
| (-0.096513920914515116255 - 2.9594389657224617715e-959j)  +/-  (3.21e-253, 3.21e-253j)
| (0.28594567839868926206 - 6.7371312006297355071e-953j)  +/-  (3.77e-248, 3.77e-248j)
-------------------------------------------------
The weights are:
| (0.015384615384615384615 + 1.9517972341961216077e-803j)  +/-  (9.4e-35, 7.23e-145j)
| (0.015384615384615384615 + 2.7802202693860438381e-805j)  +/-  (3.29e-35, 2.53e-145j)
| (0.015384615384615384615 + 3.4387734377146406226e-804j)  +/-  (3.24e-35, 2.5e-145j)
| (0.015384615384615384615 + 2.9352421436844922138e-803j)  +/-  (2.41e-35, 1.86e-145j)
| (0.015384615384615384615 - 1.4015780749391949648e-803j)  +/-  (1.76e-36, 1.36e-146j)
| (0.015384615384615384615 + 1.6092645533503984596e-803j)  +/-  (2.11e-36, 1.63e-146j)
| (0.015384615384615384615 - 5.5604251939568152223e-805j)  +/-  (4.4e-38, 3.38e-148j)
| (0.015384615384615384615 - 1.4486940971054873849e-804j)  +/-  (5.18e-37, 3.98e-147j)
| (0.015384615384615384615 + 1.6574827419747530793e-805j)  +/-  (3.17e-38, 2.44e-148j)
| (0.015384615384615384615 - 1.0301425782356970619e-805j)  +/-  (1.97e-38, 1.51e-148j)
| (0.015384615384615384615 - 1.1119112553040039162e-803j)  +/-  (4.46e-39, 3.43e-149j)
| (0.015384615384615384615 + 4.8747349548058067063e-804j)  +/-  (8.99e-41, 6.92e-151j)
| (0.015384615384615384615 + 1.997872007149819879e-804j)  +/-  (1.56e-38, 1.2e-148j)
| (0.015384615384615384615 + 7.2766742394589021176e-805j)  +/-  (1.62e-38, 1.25e-148j)
| (0.015384615384615384615 - 2.9215033562139256047e-803j)  +/-  (9.4e-40, 7.23e-150j)
| (0.015384615384615384615 + 1.0062853798578311564e-803j)  +/-  (4.85e-40, 3.73e-150j)
| (0.015384615384615384615 + 1.2406626886925728122e-803j)  +/-  (3.9e-39, 3e-149j)
| (0.015384615384615384615 - 1.268106616020104755e-804j)  +/-  (1.72e-39, 1.32e-149j)
| (0.015384615384615384615 + 4.9883591237488448491e-805j)  +/-  (1.73e-42, 1.33e-152j)
| (0.015384615384615384615 + 3.166343627051282549e-805j)  +/-  (2.48e-39, 1.91e-149j)
| (0.015384615384615384615 - 7.3278125919811771453e-803j)  +/-  (3.48e-41, 2.68e-151j)
| (0.015384615384615384615 - 7.7771044575912850552e-804j)  +/-  (1.36e-43, 1.05e-153j)
| (0.015384615384615384615 - 3.2416290004507832524e-805j)  +/-  (8.82e-41, 6.79e-151j)
| (0.015384615384615384615 + 4.7590067666172681769e-806j)  +/-  (2.15e-41, 1.65e-151j)
| (0.015384615384615384615 - 3.4328247269749243871e-805j)  +/-  (1.2e-42, 9.26e-153j)
| (0.015384615384615384615 - 1.8891248549118788025e-803j)  +/-  (1.71e-42, 1.32e-152j)
| (0.015384615384615384615 + 7.2101780559241473822e-804j)  +/-  (1.02e-45, 7.88e-156j)
| (0.015384615384615384615 - 9.1787295509902142614e-804j)  +/-  (3.12e-44, 2.4e-154j)
| (0.015384615384615384615 + 4.0978052423013687262e-803j)  +/-  (8.28e-43, 6.38e-153j)
| (0.015384615384615384615 - 8.9758741490992505094e-805j)  +/-  (1.5e-48, 1.15e-158j)
| (0.015384615384615384615 + 8.5138923054206539753e-805j)  +/-  (4.44e-43, 3.42e-153j)
| (0.015384615384615384615 + 8.4263436416308132691e-804j)  +/-  (3.64e-45, 2.8e-155j)
| (0.015384615384615384615 - 6.7100073096594116028e-804j)  +/-  (1.42e-47, 1.09e-157j)
| (0.015384615384615384615 + 2.2900580461596822046e-803j)  +/-  (3.26e-43, 2.51e-153j)
| (0.015384615384615384615 - 6.4018137928240389384e-805j)  +/-  (3.06e-48, 2.35e-158j)
| (0.015384615384615384615 + 7.7206589627006664141e-805j)  +/-  (4.59e-49, 3.53e-159j)
| (0.015384615384615384615 - 2.6467701679328523838e-804j)  +/-  (7.05e-55, 5.43e-165j)
| (0.015384615384615384615 + 5.5039630885872444816e-804j)  +/-  (3.53e-51, 2.72e-161j)
| (0.015384615384615384615 - 5.8651368666957250737e-804j)  +/-  (1.29e-50, 9.9e-161j)
| (0.015384615384615384615 - 1.3712179431767674519e-804j)  +/-  (2.42e-54, 1.86e-164j)
| (0.015384615384615384615 + 1.0188846048974595066e-804j)  +/-  (4.51e-52, 3.47e-162j)
| (0.015384615384615384615 - 3.9930618890040409069e-804j)  +/-  (6.48e-48, 4.99e-158j)
| (0.015384615384615384615 + 6.264730136287966454e-804j)  +/-  (1.04e-50, 8.04e-161j)
| (0.015384615384615384615 - 5.1753979814573536572e-804j)  +/-  (1.11e-52, 8.56e-163j)
| (0.015384615384615384615 + 2.7979154442829213589e-804j)  +/-  (1.56e-57, 1.2e-167j)
| (0.015384615384615384615 - 1.1375095313300318041e-804j)  +/-  (6.82e-54, 5.25e-164j)
| (0.015384615384615384615 + 1.2546417625301863651e-804j)  +/-  (1.08e-54, 8.29e-165j)
| (0.015384615384615384615 - 3.2961629013381974161e-804j)  +/-  (6.79e-59, 5.23e-169j)
| (0.015384615384615384615 - 4.5981185680568749713e-804j)  +/-  (1.02e-56, 7.81e-167j)
| (0.015384615384615384615 + 3.480371349053366933e-804j)  +/-  (5.86e-59, 4.51e-169j)
| (0.015384615384615384615 - 2.0968170634512434744e-804j)  +/-  (1.57e-60, 1.21e-170j)
| (0.015384615384615384615 + 1.4880138912825185435e-804j)  +/-  (8.28e-59, 6.37e-169j)
| (0.015384615384615384615 + 2.227387427348948089e-804j)  +/-  (1.25e-60, 9.59e-171j)
| (0.015384615384615384615 - 4.1047874630615295504e-804j)  +/-  (6.87e-60, 5.29e-170j)
| (0.015384615384615384615 + 3.8831601097706426604e-804j)  +/-  (3.11e-60, 2.4e-170j)
| (0.015384615384615384615 + 2.5017514460853059349e-804j)  +/-  (1.8e-61, 1.39e-171j)
| (0.015384615384615384615 - 1.6056988763762618628e-804j)  +/-  (3.04e-61, 2.34e-171j)
| (0.015384615384615384615 + 1.9698988505634590497e-804j)  +/-  (5.1e-62, 3.92e-172j)
| (0.015384615384615384615 - 2.9559478635285775432e-804j)  +/-  (3.4e-62, 2.61e-172j)
| (0.015384615384615384615 + 4.3423580079923795635e-804j)  +/-  (1.37e-61, 1.05e-171j)
| (0.015384615384615384615 + 3.1217136456023770128e-804j)  +/-  (2.49e-62, 1.92e-172j)
| (0.015384615384615384615 - 1.8460943267518894283e-804j)  +/-  (3.35e-63, 2.58e-173j)
| (0.015384615384615384615 + 1.7248730376450529301e-804j)  +/-  (3.59e-63, 2.76e-173j)
| (0.015384615384615384615 - 2.3621686655304791748e-804j)  +/-  (1.93e-63, 1.5e-173j)
| (0.015384615384615384615 - 3.6755665595057328825e-804j)  +/-  (1.55e-63, 1.13e-173j)
