Starting with polynomial:
P : t
Extension levels are: 1 22 46
-------------------------------------------------
Trying to find an order 22 Kronrod extension for:
P1 : t
Solvable: 1
-------------------------------------------------
Trying to find an order 46 Kronrod extension for:
P2 : t^23 - 23/4*t^21 + 115/8*t^19 - 1311/64*t^17 + 1173/64*t^15 - 2737/256*t^13 + 2093/512*t^11 - 16445/16384*t^9 + 9867/65536*t^7 - 3289/262144*t^5 + 253/524288*t^3 - 23/4194304*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^69 - 69/4*t^67 + 2277/16*t^65 - 1495/2*t^63 + 44919/16*t^61 - 8220177/1024*t^59 + 74416523/4096*t^57 - 136830381/4096*t^55 + 3331034685/65536*t^53 - 17000614059/262144*t^51 + 73477230255/1048576*t^49 - 33859413315/524288*t^47 + 214046934465/4194304*t^45 - 1164321236925/33554432*t^43 + 2730862537515/134217728*t^41 - 1382288444915/134217728*t^39 + 19325957314755/4294967296*t^37 - 29120107628115/17179869184*t^35 + 37748287666075/68719476736*t^33 - 2622512616801/17179869184*t^31 + 4977421905357/137438953472*t^29 - 16038359472817/2199023255552*t^27 + 10888712137251/8796093022208*t^25 - 1543768261425/8796093022208*t^23 + 2893136075115/140737488355328*t^21 - 1104651955953/562949953421312*t^19 + 337916787957/2251799813685248*t^17 - 10131543907/1125899906842624*t^15 + 3706662405/9007199254740992*t^13 - 996964371/72057594037927936*t^11 + 93731693/288230376151711744*t^9 - 1432233/288230376151711744*t^7 + 812889/18446744073709551616*t^5 - 13685/73786976294838206464*t^3 + 69/295147905179352825856*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
Positive weights:   69 out of 69
Indefinite weights: 0 out of 69
Negative weights:   0 out of 69
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (0.97908408768232287563 - 8.9653057131523206389e-788j)  +/-  (8.31e-231, 8.31e-231j)
| (0.99974088484134917149 + 9.5369603753634102915e-787j)  +/-  (2.61e-231, 2.61e-231j)
| (-0.9260425209878052307 - 4.8941466759753944774e-791j)  +/-  (1.09e-231, 1.09e-231j)
| (-0.99766876919053919845 + 6.0984748089044243281e-794j)  +/-  (8.01e-231, 8.01e-231j)
| (0.9260425209878052307 + 2.3772509227197108657e-800j)  +/-  (1.18e-231, 1.18e-231j)
| (0.90790475531928896828 + 5.850715398579246709e-801j)  +/-  (5.79e-232, 5.79e-232j)
| (0.99766876919053919845 - 2.7419190626347580534e-798j)  +/-  (7.29e-231, 7.29e-231j)
| (-0.94226092211882049562 - 7.4671947258916632437e-803j)  +/-  (2.13e-231, 2.13e-231j)
| (0.99352883266503117762 - 6.9458362471582745997e-804j)  +/-  (9.01e-231, 9.01e-231j)
| (-0.88788521840237523498 + 1.2121269318355563822e-806j)  +/-  (1.71e-232, 1.71e-232j)
| (0.88788521840237523498 - 2.5377720756816970845e-807j)  +/-  (2.16e-232, 2.16e-232j)
| (-0.31334396798488224017 - 7.8635293246451745174e-821j)  +/-  (8.39e-247, 8.39e-247j)
| (-0.97908408768232287563 - 1.5720194974986251066e-802j)  +/-  (8.85e-231, 8.85e-231j)
| (-0.86602540378443864676 - 1.3282935928507608578e-816j)  +/-  (6.39e-233, 6.39e-233j)
| (-0.95652634359933473408 + 9.2374725896608155502e-814j)  +/-  (5.05e-231, 5.05e-231j)
| (0.86602540378443864676 + 4.3226738928415587232e-829j)  +/-  (6.41e-233, 6.41e-233j)
| (0.78987587189155863993 + 4.8403357842992407687e-830j)  +/-  (1.66e-234, 1.66e-234j)
| (0.96880921816490635508 + 5.7325381915920602026e-826j)  +/-  (7.24e-231, 7.24e-231j)
| (-0.78987587189155863993 + 6.2543920375895777336e-833j)  +/-  (1.39e-234, 1.39e-234j)
| (-0.090934862308846951302 - 2.0633364507742822396e-858j)  +/-  (2.7e-253, 2.7e-253j)
| (-0.98732965591546962712 - 2.203915464342350273e-833j)  +/-  (1.17e-230, 1.17e-230j)
| (0.73083596427812410165 - 6.4251122002981834588e-860j)  +/-  (6.32e-236, 6.32e-236j)
| (0.045514599132963596262 + 5.9723383668435589301e-880j)  +/-  (9.59e-255, 9.59e-255j)
| (-0.84237061926941163872 - 2.475350886210914094e-855j)  +/-  (1.95e-233, 1.95e-233j)
| (-0.81696989301044201697 - 2.5551686927314577176e-859j)  +/-  (7.22e-234, 7.22e-234j)
| (0.95652634359933473408 - 2.6998069215085937756e-855j)  +/-  (4.24e-231, 4.24e-231j)
| (0.76114471240896474477 + 9.4324036376801786264e-866j)  +/-  (3.11e-235, 3.11e-235j)
| (0.63108794432605278937 - 1.905056128317722484e-868j)  +/-  (2.24e-238, 2.24e-238j)
| (-0.99352883266503117762 + 3.2309222432172728525e-858j)  +/-  (9.37e-231, 9.37e-231j)
| (-0.63108794432605278937 - 7.2955201793363627899e-889j)  +/-  (2.24e-238, 2.24e-238j)
| (-0.18111620970985575085 + 1.2243636001833807945e-901j)  +/-  (1.31e-250, 1.31e-250j)
| (0.81696989301044201697 + 3.3179208766649313054e-884j)  +/-  (5.42e-234, 5.42e-234j)
| (0.66574011969744063546 + 5.805595666393954128e-888j)  +/-  (1.66e-237, 1.66e-237j)
| (0.84237061926941163872 + 1.1993125478974004241e-883j)  +/-  (2.28e-233, 2.28e-233j)
| (-0.69901244700788208384 - 9.6995744393932167004e-888j)  +/-  (1.17e-236, 1.17e-236j)
| (-0.66574011969744063546 + 2.2313790661317794993e-887j)  +/-  (1.62e-237, 1.62e-237j)
| (0.26979677115702427125 + 2.8103209903792910585e-899j)  +/-  (4.49e-248, 4.49e-248j)
| (0.59512774281878971963 - 3.5036558747367954667e-890j)  +/-  (3.02e-239, 3.02e-239j)
| (-0.99974088484134917149 - 3.736919136263054034e-880j)  +/-  (2.5e-231, 2.5e-231j)
| (-0.96880921816490635508 - 2.6854163362915775473e-890j)  +/-  (6.51e-231, 6.51e-231j)
| (-0.5579340481846333535 + 3.9149426440922662086e-906j)  +/-  (3.07e-240, 3.07e-240j)
| (-2.9439858112184793747e-946 - 1.9637798670611144043e-947j)  +/-  (2.04e-944, 2.04e-944j)
| (0.69901244700788208384 + 4.4708285481427400198e-901j)  +/-  (1.06e-236, 1.06e-236j)
| (0.5579340481846333535 - 1.1980709229232090984e-904j)  +/-  (3.38e-240, 3.38e-240j)
| (0.94226092211882049562 + 3.176767576792654551e-895j)  +/-  (2.18e-231, 2.18e-231j)
| (-0.59512774281878971963 - 7.8676425168475784176e-907j)  +/-  (3.22e-239, 3.22e-239j)
| (-0.76114471240896474477 - 2.6757794852711146024e-901j)  +/-  (3.26e-235, 3.26e-235j)
| (0.98732965591546962712 - 7.0755968586160681795e-900j)  +/-  (1.15e-230, 1.15e-230j)
| (0.48015693480591559336 - 4.0904591008777915061e-913j)  +/-  (3.34e-242, 3.34e-242j)
| (0.22569037932121063242 + 6.3880900881024581309e-920j)  +/-  (2.51e-249, 2.51e-249j)
| (-0.73083596427812410165 - 8.5999351233691196381e-905j)  +/-  (6.32e-236, 6.32e-236j)
| (-0.51958395003543357813 + 1.6713451330422842851e-910j)  +/-  (3.28e-241, 3.28e-241j)
| (-0.90790475531928896828 + 1.0534837691023278494e-919j)  +/-  (5.25e-232, 5.25e-232j)
| (0.51958395003543357813 + 2.1595941246063848156e-930j)  +/-  (3.58e-241, 3.58e-241j)
| (0.43973472100590584495 + 7.1120684846002421863e-933j)  +/-  (2.23e-243, 2.23e-243j)
| (-0.045514599132963596262 + 9.3580210433776622867e-944j)  +/-  (9.59e-255, 9.59e-255j)
| (-0.48015693480591559336 + 2.5292087292658148362e-931j)  +/-  (3.59e-242, 3.59e-242j)
| (-0.13616664909624659076 - 5.0467800266869922912e-942j)  +/-  (6.07e-252, 6.07e-252j)
| (0.18111620970985575085 - 4.4472737980720692984e-942j)  +/-  (9.54e-251, 9.54e-251j)
| (0.398401089846241458 + 3.5833820850029935405e-935j)  +/-  (1.89e-244, 1.89e-244j)
| (0.13616664909624659076 - 1.9560028959458163344e-943j)  +/-  (5.02e-252, 5.02e-252j)
| (-0.26979677115702427125 + 3.9572890587093285571e-938j)  +/-  (4.28e-248, 4.28e-248j)
| (-0.43973472100590584495 - 7.4053953041964992109e-933j)  +/-  (2.43e-243, 2.43e-243j)
| (0.090934862308846951302 - 7.9967245736707360871e-944j)  +/-  (2.19e-253, 2.19e-253j)
| (0.35624171158941683775 - 3.7749845011718585958e-936j)  +/-  (1.38e-245, 1.38e-245j)
| (0.31334396798488224017 + 2.1756697867354986896e-937j)  +/-  (7.53e-247, 7.53e-247j)
| (-0.398401089846241458 + 1.1186487569937911246e-934j)  +/-  (1.6e-244, 1.6e-244j)
| (-0.35624171158941683775 + 1.2996774787899676338e-935j)  +/-  (1.37e-245, 1.37e-245j)
| (-0.22569037932121063242 - 1.1434830562665142998e-939j)  +/-  (2.62e-249, 2.62e-249j)
-------------------------------------------------
The weights are:
| (0.014492753623188405797 - 5.9651018923574904742e-786j)  +/-  (2.32e-37, 1.6e-146j)
| (0.014492753623188405797 - 1.3340771831308388861e-785j)  +/-  (7.88e-38, 5.42e-147j)
| (0.014492753623188405797 - 1.1773644543044817214e-787j)  +/-  (2.85e-39, 1.96e-148j)
| (0.014492753623188405797 + 2.052290237999873801e-788j)  +/-  (3.19e-40, 2.19e-149j)
| (0.014492753623188405797 - 3.0640816879191106185e-786j)  +/-  (4.47e-38, 3.08e-147j)
| (0.014492753623188405797 + 2.733866875793842327e-786j)  +/-  (3.14e-38, 2.16e-147j)
| (0.014492753623188405797 + 2.0020595380679387181e-785j)  +/-  (4.85e-38, 3.34e-147j)
| (0.014492753623188405797 + 1.0355301161461267994e-787j)  +/-  (1.51e-40, 1.04e-149j)
| (0.014492753623188405797 - 1.1152059010092124781e-785j)  +/-  (2.45e-38, 1.69e-147j)
| (0.014492753623188405797 - 1.4643848222307714712e-787j)  +/-  (4.67e-41, 3.21e-150j)
| (0.014492753623188405797 - 2.4651885097635380385e-786j)  +/-  (8.74e-40, 6.01e-149j)
| (0.014492753623188405797 + 4.3444108200223733852e-787j)  +/-  (1.85e-42, 1.27e-151j)
| (0.014492753623188405797 - 6.1759024792457881169e-788j)  +/-  (6e-42, 4.13e-151j)
| (0.014492753623188405797 + 1.6100490982190430619e-787j)  +/-  (7.26e-42, 4.99e-151j)
| (0.014492753623188405797 - 8.9542127615860217977e-788j)  +/-  (1.56e-41, 1.07e-150j)
| (0.014492753623188405797 + 2.2422283141696126781e-786j)  +/-  (2.2e-41, 1.51e-150j)
| (0.014492753623188405797 - 1.7536420146273735628e-786j)  +/-  (4.1e-43, 2.82e-152j)
| (0.014492753623188405797 + 4.7104893315403950841e-786j)  +/-  (8.67e-41, 5.97e-150j)
| (0.014492753623188405797 - 2.0586811295008946317e-787j)  +/-  (5.02e-44, 3.45e-153j)
| (0.014492753623188405797 - 5.4846584723704078618e-787j)  +/-  (6.91e-46, 4.75e-155j)
| (0.014492753623188405797 + 4.7969015240643682527e-788j)  +/-  (9.1e-43, 6.26e-152j)
| (0.014492753623188405797 - 1.5236644164529910039e-786j)  +/-  (7.96e-45, 5.48e-154j)
| (0.014492753623188405797 + 6.288298987844945999e-787j)  +/-  (2.97e-46, 2.04e-155j)
| (0.014492753623188405797 - 1.7575371369745245077e-787j)  +/-  (1.03e-43, 7.07e-153j)
| (0.014492753623188405797 + 1.9070173377584737658e-787j)  +/-  (3.73e-44, 2.57e-153j)
| (0.014492753623188405797 - 4.0152606420409267562e-786j)  +/-  (5.07e-43, 3.49e-152j)
| (0.014492753623188405797 + 1.6315469790791584891e-786j)  +/-  (2.03e-45, 1.39e-154j)
| (0.014492753623188405797 + 1.2634099785036551449e-786j)  +/-  (7.19e-48, 4.95e-157j)
| (0.014492753623188405797 - 3.4228527514410114109e-788j)  +/-  (2.37e-45, 1.63e-154j)
| (0.014492753623188405797 + 2.8574308888368775046e-787j)  +/-  (3.85e-49, 2.65e-158j)
| (0.014492753623188405797 - 5.0028300824465037384e-787j)  +/-  (1.35e-49, 9.26e-159j)
| (0.014492753623188405797 + 1.8931065962887644039e-786j)  +/-  (1.54e-45, 1.06e-154j)
| (0.014492753623188405797 - 1.3413120299857173049e-786j)  +/-  (3.44e-48, 2.36e-157j)
| (0.014492753623188405797 - 2.054102637487973491e-786j)  +/-  (2.23e-45, 1.53e-154j)
| (0.014492753623188405797 + 2.5288978798382470968e-787j)  +/-  (3.71e-50, 2.55e-159j)
| (0.014492753623188405797 - 2.6914883380400032087e-787j)  +/-  (2.36e-50, 1.63e-159j)
| (0.014492753623188405797 - 7.9232146207496014594e-787j)  +/-  (1.75e-53, 1.2e-162j)
| (0.014492753623188405797 - 1.1926262677164415365e-786j)  +/-  (1.05e-50, 7.21e-160j)
| (0.014492753623188405797 - 6.8384458131848104121e-789j)  +/-  (2.87e-48, 1.97e-157j)
| (0.014492753623188405797 + 7.5612446304420199222e-788j)  +/-  (9.02e-48, 6.2e-157j)
| (0.014492753623188405797 + 3.2005207615077341465e-787j)  +/-  (1.11e-52, 7.62e-162j)
| (0.014492753623188405797 - 6.0083094478775705769e-787j)  +/-  (1.66e-53, 1.14e-162j)
| (0.014492753623188405797 + 1.427556703316796172e-786j)  +/-  (1.27e-49, 8.73e-159j)
| (0.014492753623188405797 + 1.1279639926700661056e-786j)  +/-  (2.41e-52, 1.65e-161j)
| (0.014492753623188405797 + 3.4794498105236685411e-786j)  +/-  (1.32e-48, 9.07e-158j)
| (0.014492753623188405797 - 3.0270075866821183253e-787j)  +/-  (3.16e-53, 2.17e-162j)
| (0.014492753623188405797 + 2.2127342775373822383e-787j)  +/-  (4.23e-52, 2.91e-161j)
| (0.014492753623188405797 + 7.8861224770778001517e-786j)  +/-  (3.32e-49, 2.28e-158j)
| (0.014492753623188405797 + 1.0138630477583276042e-786j)  +/-  (6.9e-55, 4.75e-164j)
| (0.014492753623188405797 + 7.5594190751761141071e-787j)  +/-  (1.67e-56, 1.15e-165j)
| (0.014492753623188405797 - 2.3693956717568583075e-787j)  +/-  (8.7e-53, 5.98e-162j)
| (0.014492753623188405797 - 3.3782953574942302346e-787j)  +/-  (7.95e-56, 5.47e-165j)
| (0.014492753623188405797 + 1.320466695355062399e-787j)  +/-  (5.97e-52, 4.11e-161j)
| (0.014492753623188405797 - 1.0686031538986086443e-786j)  +/-  (6.84e-55, 4.71e-164j)
| (0.014492753623188405797 - 9.6317385321564352651e-787j)  +/-  (2.01e-56, 1.38e-165j)
| (0.014492753623188405797 + 5.7407873588427420684e-787j)  +/-  (3.89e-58, 2.68e-167j)
| (0.014492753623188405797 + 3.5606815798145590527e-787j)  +/-  (4.75e-58, 3.26e-167j)
| (0.014492753623188405797 + 5.2389608300149364964e-787j)  +/-  (1.62e-58, 1.11e-167j)
| (0.014492753623188405797 - 7.215888100197672293e-787j)  +/-  (3.81e-59, 2.62e-168j)
| (0.014492753623188405797 + 9.1605489592948149944e-787j)  +/-  (1.03e-58, 7.11e-168j)
| (0.014492753623188405797 + 6.8906464724068845356e-787j)  +/-  (1.5e-59, 1.03e-168j)
| (0.014492753623188405797 - 4.5562270175444903363e-787j)  +/-  (4.86e-61, 3.34e-170j)
| (0.014492753623188405797 - 3.7480578932997339689e-787j)  +/-  (9.3e-61, 6.39e-170j)
| (0.014492753623188405797 - 6.5819599011075406888e-787j)  +/-  (6.52e-60, 4.49e-169j)
| (0.014492753623188405797 - 8.7209782876134286436e-787j)  +/-  (2.08e-60, 1.43e-169j)
| (0.014492753623188405797 + 8.3095347891481424819e-787j)  +/-  (1.73e-60, 1.19e-169j)
| (0.014492753623188405797 + 3.9408344275983538179e-787j)  +/-  (1.04e-62, 7.13e-172j)
| (0.014492753623188405797 - 4.1394568549415866032e-787j)  +/-  (6.62e-63, 4.57e-172j)
| (0.014492753623188405797 + 4.7754870325266558373e-787j)  +/-  (7.11e-63, 4.8e-172j)
