Starting with polynomial:
P : 4*t^2 - 1
Extension levels are: 2 54
-------------------------------------------------
Trying to find an order 54 Kronrod extension for:
P1 : 4*t^2 - 1
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 4*t^56 - 55*t^54 + 1431/4*t^52 - 11713/8*t^50 + 270725/64*t^48 - 587265/64*t^46 + 3972675/256*t^44 - 10737573/512*t^42 + 188674497/8192*t^40 - 1362649145/65536*t^38 + 4076350421/262144*t^36 - 5075297955/524288*t^34 + 21090682613/4194304*t^32 - 4572106021/2097152*t^30 + 6607528635/8388608*t^28 - 3964517181/16777216*t^26 + 31426050825/536870912*t^24 - 25510558905/2147483648*t^22 + 16789000305/8589934592*t^20 - 4418157975/17179869184*t^18 + 3653936055/137438953472*t^16 - 289994925/137438953472*t^14 + 68544255/549755813888*t^12 - 5785065/1099511627776*t^10 + 2629575/17592186044416*t^8 - 736281/281474976710656*t^6 + 27405/1125899906842624*t^4 - 203/2251799813685248*t^2 + 1/18014398509481984
-------------------------------------------------
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
-------------------------------------------------
The nodes are:
| (-0.82177781522524516716 - 2.0940298205176572002e-813j)  +/-  (3.81e-238, 3.81e-238j)
| (0.9863613034027223736 - 3.0161839011886235072e-809j)  +/-  (2.95e-236, 2.95e-236j)
| (-0.94581724170063467902 - 8.4417895628817043921e-822j)  +/-  (2.85e-236, 2.85e-236j)
| (0.99848151643331622548 + 1.4058684340108544046e-819j)  +/-  (5.86e-237, 5.86e-237j)
| (0.94581724170063467902 - 2.3691477611819905994e-841j)  +/-  (2.52e-236, 2.52e-236j)
| (0.92649406721480177432 - 1.2081351926133136772e-861j)  +/-  (1.61e-236, 1.61e-236j)
| (-0.97579638262743562288 - 4.1253563792385119125e-869j)  +/-  (4e-236, 4e-236j)
| (-0.92649406721480177432 + 9.464943026187604348e-878j)  +/-  (1.51e-236, 1.51e-236j)
| (-0.29851481100169454812 - 5.6436036339933692801e-894j)  +/-  (8.59e-249, 8.59e-249j)
| (0.96226800030925040495 - 1.371186409984900535e-879j)  +/-  (3.39e-236, 3.39e-236j)
| (0.82177781522524516716 - 5.300884054619147851e-890j)  +/-  (3.81e-238, 3.81e-238j)
| (-0.99393067731794947926 + 1.6288399539411738683e-886j)  +/-  (1.98e-236, 1.98e-236j)
| (-0.96226800030925040495 - 4.5497985840896199514e-888j)  +/-  (3.5e-236, 3.5e-236j)
| (-0.85191940883832707488 - 1.9471663225726674978e-891j)  +/-  (1.26e-237, 1.26e-237j)
| (0.90435716069757749176 - 1.6461481552923468387e-890j)  +/-  (8.1e-237, 8.1e-237j)
| (0.85191940883832707488 - 5.3543436853939824801e-894j)  +/-  (1.13e-237, 1.13e-237j)
| (0.87947375120648907139 + 3.3143136346253179951e-898j)  +/-  (3.54e-237, 3.54e-237j)
| (-0.99848151643331622548 + 1.02237925431772938e-896j)  +/-  (7.56e-237, 7.56e-237j)
| (-0.75410660977689625841 - 1.9445044092162071441e-907j)  +/-  (2.75e-239, 2.75e-239j)
| (-0.40169542465296945752 - 9.6136813082089945548e-915j)  +/-  (2.06e-246, 2.06e-246j)
| (0.99393067731794947926 - 8.4599637156187503673e-903j)  +/-  (1.84e-236, 1.84e-236j)
| (0.71678251316845125603 - 2.7466968212812651543e-917j)  +/-  (5.41e-240, 5.41e-240j)
| (-0.71678251316845125603 + 3.822740311475381121e-916j)  +/-  (4.81e-240, 4.81e-240j)
| (-0.87947375120648907139 + 1.3527327256073835398e-913j)  +/-  (3.69e-237, 3.69e-237j)
| (-0.78914050939639359922 + 2.106027422623136267e-915j)  +/-  (1e-238, 1e-238j)
| (0.97579638262743562288 - 4.1960833565813008796e-913j)  +/-  (4e-236, 4e-236j)
| (0.78914050939639359922 + 3.2227898985305641894e-926j)  +/-  (1e-238, 1e-238j)
| (0.75410660977689625841 - 4.9323561067239026033e-927j)  +/-  (2.49e-239, 2.49e-239j)
| (-0.9863613034027223736 + 2.3833897740274220954e-922j)  +/-  (3.71e-236, 3.71e-236j)
| (-0.63572374820996799828 + 7.3845014162286277975e-934j)  +/-  (1.62e-241, 1.62e-241j)
| (-0.90435716069757749176 + 1.1811690762601399853e-931j)  +/-  (8.38e-237, 8.38e-237j)
| (0.67728157162574107476 - 3.2741093635964542642e-937j)  +/-  (1.05e-240, 1.05e-240j)
| (0.63572374820996799828 + 1.3974924847764522962e-939j)  +/-  (1.53e-241, 1.53e-241j)
| (0.0825793454723323246 - 1.0513625837521052824e-951j)  +/-  (4.88e-254, 4.88e-254j)
| (-0.67728157162574107476 - 2.9200199097781733196e-939j)  +/-  (8.35e-241, 8.35e-241j)
| (-0.0825793454723323246 - 2.372345531737516104e-955j)  +/-  (6.23e-254, 6.23e-254j)
| (0.1373535578184081751 + 4.940021782457566234e-954j)  +/-  (1.1e-252, 1.1e-252j)
| (0.59223525266498002174 + 9.8475645443183570435e-945j)  +/-  (2.08e-242, 2.08e-242j)
| (0.29851481100169454812 - 5.6222593243175414395e-950j)  +/-  (8.78e-249, 8.78e-249j)
| (-0.35063755519275437533 + 1.5774076134076912948e-948j)  +/-  (1.31e-247, 1.31e-247j)
| (-0.54694815812242687471 + 5.5956416378829952838e-942j)  +/-  (2.42e-243, 2.42e-243j)
| (-0.59223525266498002174 - 7.1173407383138930156e-946j)  +/-  (1.87e-242, 1.87e-242j)
| (0.54694815812242687471 + 7.3343290724758897046e-946j)  +/-  (2.47e-243, 2.47e-243j)
| (0.5 - 3.9050036138131336423e-948j)  +/-  (2.09e-244, 2.09e-244j)
| (-0.027554342368161996514 - 1.457279330712985786e-958j)  +/-  (3.38e-255, 3.38e-255j)
| (-0.5 + 1.4653329084759400328e-949j)  +/-  (2.41e-244, 2.41e-244j)
| (-0.19171063192373842061 - 1.9291060053074549313e-956j)  +/-  (2.68e-251, 2.68e-251j)
| (0.24548548714079914892 + 5.6411767202417879143e-955j)  +/-  (5.39e-250, 5.39e-250j)
| (0.45153335831088935076 + 1.5025300455221038256e-949j)  +/-  (1.9e-245, 1.9e-245j)
| (0.19171063192373842061 - 1.0607133031656961679e-956j)  +/-  (2.52e-251, 2.52e-251j)
| (-0.24548548714079914892 + 1.3908645320702107326e-955j)  +/-  (4.06e-250, 4.06e-250j)
| (-0.45153335831088935076 + 1.3687878971810981962e-951j)  +/-  (1.89e-245, 1.89e-245j)
| (0.027554342368161996514 + 8.07761603830241018e-960j)  +/-  (3.38e-255, 3.38e-255j)
| (0.35063755519275437533 - 6.8864860097210220577e-952j)  +/-  (1.26e-247, 1.26e-247j)
| (0.40169542465296945752 - 3.9964358204112290203e-952j)  +/-  (2.03e-246, 2.03e-246j)
| (-0.1373535578184081751 - 7.35542457815824962e-958j)  +/-  (9.41e-253, 9.41e-253j)
-------------------------------------------------
The weights are:
| (0.0056961617965547861814 - 9.5063811607757165187e-812j)  +/-  (6.92e-53, 1.85e-166j)
| (0.00047528735350320457 + 7.8290767777057242054e-811j)  +/-  (2.85e-53, 7.61e-167j)
| (0.0018496446544176000069 + 2.8842236610676620064e-812j)  +/-  (1.23e-53, 3.3e-167j)
| (5.3239672649565971436e-05 - 1.3248989019987824611e-811j)  +/-  (1.34e-53, 3.59e-167j)
| (0.0018496446544176000069 - 1.3760035574411864176e-810j)  +/-  (7.57e-54, 2.03e-167j)
| (0.0024843639195749889822 + 1.2516556217487582722e-810j)  +/-  (3.98e-54, 1.06e-167j)
| (0.00083897227458265358107 + 1.2885083218364024625e-812j)  +/-  (1.37e-55, 3.66e-169j)
| (0.0024843639195749889822 - 3.9123686272088552933e-812j)  +/-  (2.85e-55, 7.62e-169j)
| (0.015980507151098641817 - 3.751985493774003325e-811j)  +/-  (6.2e-57, 1.66e-170j)
| (0.0012989525540497625011 + 1.6261296510473626746e-810j)  +/-  (2.79e-54, 7.47e-168j)
| (0.0056961617965547861814 + 1.0438951770667327126e-810j)  +/-  (2.17e-56, 5.81e-170j)
| (0.00021231243309266997475 + 3.2311494170984257706e-813j)  +/-  (9.29e-57, 2.48e-170j)
| (0.0012989525540497625011 - 2.0086462892400337361e-812j)  +/-  (1.34e-55, 3.58e-169j)
| (0.0048111108920097425372 + 7.8604708840169725681e-812j)  +/-  (1.7e-56, 4.55e-170j)
| (0.0031954057174564210677 - 1.1753019729151792516e-810j)  +/-  (3.64e-56, 9.75e-170j)
| (0.0048111108920097425372 - 1.0793715895863908098e-810j)  +/-  (2.78e-57, 7.44e-171j)
| (0.0039741389638383607481 + 1.1214389330571704479e-810j)  +/-  (6.73e-57, 1.8e-170j)
| (5.3239672649565971436e-05 - 8.0840364148009415575e-814j)  +/-  (4.55e-58, 1.22e-171j)
| (0.0075670740542244896921 - 1.3136950714133606317e-811j)  +/-  (1.03e-59, 2.77e-173j)
| (0.014712996242331062059 - 3.1978003286782738207e-811j)  +/-  (2.36e-61, 6.31e-175j)
| (0.00021231243309266997475 + 8.4600544853050304683e-811j)  +/-  (1.1e-57, 2.95e-171j)
| (0.008530225066945947399 - 9.5441634987147464195e-811j)  +/-  (2.28e-61, 6.09e-175j)
| (0.008530225066945947399 + 1.5123621598754946138e-811j)  +/-  (2e-60, 5.36e-174j)
| (0.0039741389638383607481 - 6.4099028690853505724e-812j)  +/-  (2.7e-59, 7.23e-173j)
| (0.0066185483584140425533 + 1.1285911159311513121e-811j)  +/-  (1.13e-59, 3.01e-173j)
| (0.00083897227458265358107 - 2.3951866317363168718e-810j)  +/-  (7.28e-58, 1.95e-171j)
| (0.0066185483584140425533 - 1.0122121648124573335e-810j)  +/-  (1.33e-60, 3.55e-174j)
| (0.0075670740542244896921 + 9.8271083863120252052e-811j)  +/-  (2.4e-61, 6.43e-175j)
| (0.00047528735350320457 - 7.2608339272892419575e-813j)  +/-  (7.38e-60, 1.98e-173j)
| (0.010453602034418758076 + 1.9449701939063999282e-811j)  +/-  (7.14e-64, 1.91e-177j)
| (0.0031954057174564210677 + 5.0893939365845307112e-812j)  +/-  (7.13e-60, 1.91e-173j)
| (0.0094963100480029151281 + 9.267196954904452978e-811j)  +/-  (4.72e-64, 1.26e-177j)
| (0.010453602034418758076 - 8.9923376199544131254e-811j)  +/-  (4.11e-65, 1.1e-178j)
| (0.017424221959673003277 + 5.8153743461283665226e-811j)  +/-  (3.12e-69, 8.34e-183j)
| (0.0094963100480029151281 - 1.7230568501505436725e-811j)  +/-  (1.42e-64, 3.8e-178j)
| (0.017424221959673003277 - 4.9170114458632888131e-811j)  +/-  (2.3e-69, 6.16e-183j)
| (0.017212877195695178991 - 6.1154204941314881827e-811j)  +/-  (1.72e-69, 4.61e-183j)
| (0.011390480798260478492 + 8.71712224263419489e-811j)  +/-  (1.02e-67, 2.72e-181j)
| (0.015980507151098641817 + 7.007697729294956364e-811j)  +/-  (3.19e-70, 8.52e-184j)
| (0.015386900085762247881 + 3.4718701199080413018e-811j)  +/-  (4.58e-69, 1.22e-182j)
| (0.012295573900464644364 + 2.4196078956980813084e-811j)  +/-  (9.02e-69, 2.41e-182j)
| (0.011390480798260478492 - 2.1773890255741656067e-811j)  +/-  (4.3e-68, 1.15e-181j)
| (0.012295573900464644364 - 8.4400157431371150843e-811j)  +/-  (2.46e-70, 6.58e-184j)
| (0.013157894736842105263 + 8.160115502665253206e-811j)  +/-  (3.81e-71, 1.02e-184j)
| (0.017530539617836107241 + 5.2154257575476879052e-811j)  +/-  (1.56e-72, 4.18e-186j)
| (0.013157894736842105263 - 2.6709089858272514629e-811j)  +/-  (8.69e-71, 2.32e-184j)
| (0.016899070765042120827 - 4.3271824233218522011e-811j)  +/-  (9.63e-73, 2.58e-186j)
| (0.016486611852688500626 - 6.7121977422344220845e-811j)  +/-  (1.62e-73, 4.34e-187j)
| (0.013966975900570000191 - 7.8769624352905457567e-811j)  +/-  (1.67e-73, 4.47e-187j)
| (0.016899070765042120827 + 6.4145770753531184403e-811j)  +/-  (1.57e-73, 4.21e-187j)
| (0.016486611852688500626 + 4.0373553882698569386e-811j)  +/-  (1.2e-73, 3.19e-187j)
| (0.013966975900570000191 + 2.930557262089370635e-811j)  +/-  (4.41e-73, 1.18e-186j)
| (0.017530539617836107241 - 5.5151326216453432424e-811j)  +/-  (4.05e-74, 1.09e-187j)
| (0.015386900085762247881 - 7.3005716034921721685e-811j)  +/-  (6.1e-75, 1.64e-188j)
| (0.014712996242331062059 + 7.590416393111485951e-811j)  +/-  (5.69e-75, 1.54e-188j)
| (0.017212877195695178991 + 4.6206669300732895954e-811j)  +/-  (6.48e-75, 1.64e-188j)
