Starting with polynomial:
P : 128*t^8 - 256*t^6 + 160*t^4 - 32*t^2 + 1
Extension levels are: 8 16 48
-------------------------------------------------
Trying to find an order 16 Kronrod extension for:
P1 : 128*t^8 - 256*t^6 + 160*t^4 - 32*t^2 + 1
Solvable: 1
-------------------------------------------------
Trying to find an order 48 Kronrod extension for:
P2 : 128*t^24 - 768*t^22 + 2016*t^20 - 3040*t^18 + 2907*t^16 - 1836*t^14 + 1547/2*t^12 - 429/2*t^10 + 19305/512*t^8 - 1001/256*t^6 + 429/2048*t^4 - 9/2048*t^2 + 1/65536
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 128*t^72 - 2304*t^70 + 19872*t^68 - 109344*t^66 + 431145*t^64 - 1297296*t^62 + 3097458*t^60 - 6024726*t^58 + 4979436039/512*t^56 - 3381098545/256*t^54 + 31215174309/2048*t^52 - 30843011277/2048*t^50 + 839615306985/65536*t^48 - 154349098155/16384*t^46 + 786952298475/131072*t^44 - 435354897285/131072*t^42 + 53548652366055/33554432*t^40 - 11167900760835/16777216*t^38 + 32308782859535/134217728*t^36 - 10106520954075/134217728*t^34 + 87227050080555/4294967296*t^32 - 2524779227355/536870912*t^30 + 3993741686907/4294967296*t^28 - 669757922649/4294967296*t^26 + 24185702762325/1099511627776*t^24 - 1420266800511/549755813888*t^22 + 1097262979659/4398046511104*t^20 - 85794224747/4398046511104*t^18 + 170474238783/140737488355328*t^16 - 2050612335/35184372088832*t^14 + 592399119/281474976710656*t^12 - 15380937/281474976710656*t^10 + 138428433/144115188075855872*t^8 - 752913/72057594037927936*t^6 + 34965/576460752303423488*t^4 - 81/576460752303423488*t^2 + 1/18446744073709551616
-------------------------------------------------
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:   72 out of 72
Indefinite weights: 0 out of 72
Negative weights:   0 out of 72
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (0.9883615104677607085 - 7.0338478346108055734e-847j)  +/-  (1.21e-229, 1.21e-229j)
| (-0.96004985438592867412 + 4.3529656114148320425e-846j)  +/-  (5.21e-230, 5.21e-230j)
| (-0.91531147911944714241 + 3.1414790187478227391e-852j)  +/-  (8.43e-231, 8.43e-231j)
| (-0.99785892323860350674 - 2.4701894159978536695e-858j)  +/-  (9.34e-230, 9.34e-230j)
| (0.91531147911944714241 + 1.7033905868313283199e-878j)  +/-  (7.27e-231, 7.27e-231j)
| (0.93200786928279850264 - 6.8089278375682402993e-878j)  +/-  (1.6e-230, 1.6e-230j)
| (0.9997620270799090923 - 9.555117465286326494e-876j)  +/-  (2.94e-230, 2.94e-230j)
| (-0.89687274153268830389 + 2.0399656593880719784e-878j)  +/-  (3.01e-231, 3.01e-231j)
| (-0.9940563382223196121 - 6.8568255454402970169e-878j)  +/-  (1.16e-229, 1.16e-229j)
| (-0.9997620270799090923 + 1.4628458379840867358e-890j)  +/-  (2.78e-230, 2.78e-230j)
| (0.8767267557075077174 - 6.3761068140523304413e-902j)  +/-  (1.1e-231, 1.1e-231j)
| (0.94693012949510566426 - 9.0913728304456186415e-901j)  +/-  (2.9e-230, 2.9e-230j)
| (-0.93200786928279850264 - 2.1393396040009254382e-899j)  +/-  (1.59e-230, 1.59e-230j)
| (-0.8767267557075077174 - 2.535152283863141376e-903j)  +/-  (1.21e-231, 1.21e-231j)
| (0.98078528040323044913 - 3.2181647135096973164e-900j)  +/-  (9.49e-230, 9.49e-230j)
| (0.77988448309288180111 - 3.6548188772338390669e-908j)  +/-  (6.45e-234, 6.45e-234j)
| (0.89687274153268830389 + 2.6063938753801368929e-903j)  +/-  (2.87e-231, 2.87e-231j)
| (0.9940563382223196121 - 1.8438285664237550364e-901j)  +/-  (1.15e-229, 1.15e-229j)
| (-0.75183980747897739641 - 6.616033895517195558e-906j)  +/-  (1.57e-234, 1.57e-234j)
| (-0.97134206981326143451 + 1.8875668365915327254e-900j)  +/-  (7.85e-230, 7.85e-230j)
| (0.96004985438592867412 + 9.3336378977667887076e-912j)  +/-  (5.42e-230, 5.42e-230j)
| (0.72236396205975558059 + 1.8979020249939674652e-916j)  +/-  (3.08e-235, 3.08e-235j)
| (0.97134206981326143451 - 1.4303178979844475897e-911j)  +/-  (7.32e-230, 7.32e-230j)
| (-0.80644460426748256644 + 4.4936151018952409856e-914j)  +/-  (3.07e-233, 3.07e-233j)
| (-0.77988448309288180111 - 1.6657110229148726211e-914j)  +/-  (7.02e-234, 7.02e-234j)
| (-0.3214394653031615807 + 4.9677138121277289002e-928j)  +/-  (3.3e-246, 3.3e-246j)
| (0.75183980747897739641 + 6.3517639237899269285e-916j)  +/-  (1.66e-234, 1.66e-234j)
| (0.83146961230254523708 + 6.950519588497974253e-914j)  +/-  (9.81e-233, 9.81e-233j)
| (0.99785892323860350674 + 1.53078980489881272e-911j)  +/-  (7.54e-230, 7.54e-230j)
| (-0.65934581510006886843 + 2.0486258856732795345e-918j)  +/-  (7.45e-237, 7.45e-237j)
| (0.27982901403099205675 - 3.1013809601625786549e-929j)  +/-  (1.9e-247, 1.9e-247j)
| (-0.94693012949510566426 - 7.8476329734696717518e-910j)  +/-  (2.88e-230, 2.88e-230j)
| (0.65934581510006886843 - 3.9215137521198020668e-935j)  +/-  (7.47e-237, 7.47e-237j)
| (0.15212338618991670154 + 1.7635957544557812644e-948j)  +/-  (2.62e-251, 2.62e-251j)
| (-0.69151305578226937776 + 1.5351806965890864456e-932j)  +/-  (5.2e-236, 5.2e-236j)
| (-0.72236396205975558059 - 3.9559821761916902776e-932j)  +/-  (2.89e-235, 2.89e-235j)
| (0.85491187067294659555 - 7.3791639330827533471e-929j)  +/-  (3.24e-232, 3.24e-232j)
| (0.62592347218405906344 - 2.9948343779365192215e-935j)  +/-  (1.08e-237, 1.08e-237j)
| (-0.98078528040323044913 - 3.0884002103712742136e-925j)  +/-  (1.08e-229, 1.08e-229j)
| (-0.85491187067294659555 + 2.3895621388402270677e-945j)  +/-  (3.65e-232, 3.65e-232j)
| (-0.55557023301960222474 + 1.1478579657032699893e-955j)  +/-  (1.51e-239, 1.51e-239j)
| (-0.9883615104677607085 - 4.5461055659874971763e-953j)  +/-  (1.23e-229, 1.23e-229j)
| (0.80644460426748256644 + 2.8414138754687134411e-965j)  +/-  (2.79e-233, 2.79e-233j)
| (0.59130964836358237728 + 2.1783622984703878003e-971j)  +/-  (1.3e-238, 1.3e-238j)
| (-0.15212338618991670154 + 8.2543168078485042342e-983j)  +/-  (2.52e-251, 2.52e-251j)
| (-0.51877325816052144952 - 2.674244673826976925e-971j)  +/-  (1.66e-240, 1.66e-240j)
| (-0.62592347218405906344 + 3.9111807219390619174e-969j)  +/-  (1.03e-237, 1.03e-237j)
| (0.021814885034561121843 + 9.3874108776477452478e-987j)  +/-  (2.29e-255, 2.29e-255j)
| (0.48098876891938764278 + 2.7323487500652744489e-974j)  +/-  (1.47e-241, 1.47e-241j)
| (0.69151305578226937776 - 1.4618125529159644281e-968j)  +/-  (4.86e-236, 4.86e-236j)
| (-0.59130964836358237728 + 4.7338609857344932775e-969j)  +/-  (1.37e-238, 1.37e-238j)
| (-0.48098876891938764278 - 2.6697909123378331683e-973j)  +/-  (1.35e-241, 1.35e-241j)
| (-0.83146961230254523708 - 1.0417372125572875804e-976j)  +/-  (1.06e-232, 1.06e-232j)
| (0.55557023301960222474 + 3.6456498584777393062e-984j)  +/-  (1.47e-239, 1.47e-239j)
| (0.51877325816052144952 + 2.2941261394766315424e-989j)  +/-  (1.59e-240, 1.59e-240j)
| (-0.021814885034561121843 - 8.3808478651109957084e-1004j)  +/-  (2.29e-255, 2.29e-255j)
| (-0.442288690219001282 + 4.9980667460716413103e-991j)  +/-  (1.16e-242, 1.16e-242j)
| (-0.27982901403099205675 + 5.0660786023779328058e-996j)  +/-  (1.99e-247, 1.99e-247j)
| (0.19509032201612826785 + 6.3270492841116520328e-999j)  +/-  (5.73e-250, 5.73e-250j)
| (0.442288690219001282 + 3.2734236870486588251e-992j)  +/-  (1.05e-242, 1.05e-242j)
| (0.23768589232617309353 + 5.311311587375601677e-998j)  +/-  (1.15e-248, 1.15e-248j)
| (-0.23768589232617309353 - 1.0423417175986326145e-997j)  +/-  (1.09e-248, 1.09e-248j)
| (-0.40274668985873723482 + 1.2189818960706447628e-992j)  +/-  (7.68e-244, 7.68e-244j)
| (-0.065403129230143066815 + 1.4727349799010514503e-1002j)  +/-  (5.77e-254, 5.77e-254j)
| (0.40274668985873723482 + 3.6838296442901985751e-993j)  +/-  (7.93e-244, 7.93e-244j)
| (0.36243803828370164506 - 1.2543951398678038266e-995j)  +/-  (4.99e-245, 4.99e-245j)
| (-0.10886687485196457597 + 4.8000649890872139055e-1001j)  +/-  (9.5e-253, 9.5e-253j)
| (-0.36243803828370164506 + 1.9159380945586178488e-993j)  +/-  (5.39e-245, 5.39e-245j)
| (-0.19509032201612826785 + 7.6887834734262325797e-999j)  +/-  (4.85e-250, 4.85e-250j)
| (0.10886687485196457597 - 2.1753111884054399131e-1001j)  +/-  (1.21e-252, 1.21e-252j)
| (0.3214394653031615807 + 3.9945691944744366362e-995j)  +/-  (3.31e-246, 3.31e-246j)
| (0.065403129230143066815 - 1.220523522272265625e-1002j)  +/-  (5.54e-254, 5.54e-254j)
-------------------------------------------------
The weights are:
| (0.013888888888888888889 + 2.2548767475318450609e-847j)  +/-  (4.69e-25, 2.24e-133j)
| (0.013888888888888888889 + 3.798456427026277983e-847j)  +/-  (2.14e-25, 1.03e-133j)
| (0.013888888888888888889 - 1.9585511725570022248e-846j)  +/-  (1.57e-25, 7.53e-134j)
| (0.013888888888888888889 + 3.7161922194197065264e-847j)  +/-  (3.59e-26, 1.72e-134j)
| (0.013888888888888888889 + 4.0045815000972496235e-847j)  +/-  (1.73e-26, 8.26e-135j)
| (0.013888888888888888889 - 4.5441148445072733999e-847j)  +/-  (1.88e-26, 9.02e-135j)
| (0.013888888888888888889 + 1.2047839835288656166e-847j)  +/-  (2.27e-27, 1.09e-135j)
| (0.013888888888888888889 + 1.5276008173924677593e-846j)  +/-  (1.27e-26, 6.09e-135j)
| (0.013888888888888888889 - 6.8813535043816500725e-847j)  +/-  (4.33e-27, 2.08e-135j)
| (0.013888888888888888889 - 1.1797852931839037109e-847j)  +/-  (5.19e-27, 2.49e-135j)
| (0.013888888888888888889 + 3.332709641373736707e-847j)  +/-  (3.96e-29, 1.89e-137j)
| (0.013888888888888888889 + 5.3465277704010599051e-847j)  +/-  (1.67e-28, 8.02e-137j)
| (0.013888888888888888889 + 2.8045701393072254442e-846j)  +/-  (5.53e-28, 2.65e-136j)
| (0.013888888888888888889 - 1.2637412634109443642e-846j)  +/-  (8.35e-29, 4e-137j)
| (0.013888888888888888889 - 1.6753805429875959735e-846j)  +/-  (2.87e-29, 1.37e-137j)
| (0.013888888888888888889 + 2.7053184591596340669e-847j)  +/-  (5.41e-32, 2.59e-140j)
| (0.013888888888888888889 - 3.6191801367542801003e-847j)  +/-  (1.55e-29, 7.4e-138j)
| (0.013888888888888888889 + 1.2156276716749240852e-846j)  +/-  (1.12e-29, 5.36e-138j)
| (0.013888888888888888889 + 7.0851347017794031134e-847j)  +/-  (1.91e-34, 9.16e-143j)
| (0.013888888888888888889 + 4.5398314554160141774e-846j)  +/-  (2.24e-31, 1.07e-139j)
| (0.013888888888888888889 - 6.6622109927405983454e-847j)  +/-  (6.4e-30, 3.07e-138j)
| (0.013888888888888888889 + 2.557532507574907756e-847j)  +/-  (2.93e-35, 1.4e-143j)
| (0.013888888888888888889 + 9.2344421336666284545e-847j)  +/-  (7.04e-30, 3.37e-138j)
| (0.013888888888888888889 + 8.5286100919902653732e-847j)  +/-  (7.53e-36, 3.61e-144j)
| (0.013888888888888888889 - 7.7333412253016875661e-847j)  +/-  (4.84e-36, 2.32e-144j)
| (0.013888888888888888889 + 3.6679022724945261208e-847j)  +/-  (2.08e-40, 9.97e-149j)
| (0.013888888888888888889 - 2.6223630516237969351e-847j)  +/-  (2.71e-36, 1.3e-144j)
| (0.013888888888888888889 + 2.9440690588562000629e-847j)  +/-  (1.97e-35, 9.45e-144j)
| (0.013888888888888888889 - 4.3502252356090951807e-847j)  +/-  (3.12e-32, 1.5e-140j)
| (0.013888888888888888889 - 5.6949191585386780336e-847j)  +/-  (3.29e-40, 1.58e-148j)
| (0.013888888888888888889 + 2.5430754023605815394e-847j)  +/-  (2e-42, 9.56e-151j)
| (0.013888888888888888889 - 5.3040644775685334226e-846j)  +/-  (1.16e-36, 5.57e-145j)
| (0.013888888888888888889 + 2.4705553921428694949e-847j)  +/-  (1.59e-39, 7.61e-148j)
| (0.013888888888888888889 - 2.6790234937608851736e-847j)  +/-  (4.48e-43, 2.14e-151j)
| (0.013888888888888888889 + 6.0879670769490737911e-847j)  +/-  (3.15e-40, 1.51e-148j)
| (0.013888888888888888889 - 6.5453322313132922248e-847j)  +/-  (1.03e-39, 4.95e-148j)
| (0.013888888888888888889 - 3.1140071085038687943e-847j)  +/-  (1.3e-36, 6.22e-145j)
| (0.013888888888888888889 - 2.4442652506958692915e-847j)  +/-  (4.98e-41, 2.38e-149j)
| (0.013888888888888888889 - 2.0263816007712455557e-846j)  +/-  (3.11e-38, 1.49e-146j)
| (0.013888888888888888889 + 1.0841238712796988809e-846j)  +/-  (1.1e-39, 5.29e-148j)
| (0.013888888888888888889 + 4.7871396612736985696e-847j)  +/-  (9.44e-45, 4.52e-153j)
| (0.013888888888888888889 + 1.1559466695233255524e-846j)  +/-  (2.66e-38, 1.27e-146j)
| (0.013888888888888888889 - 2.8106101597891219279e-847j)  +/-  (4.61e-40, 2.21e-148j)
| (0.013888888888888888889 + 2.427451826199431437e-847j)  +/-  (1.49e-44, 7.11e-153j)
| (0.013888888888888888889 + 3.1995729305334734625e-847j)  +/-  (2.08e-48, 9.98e-157j)
| (0.013888888888888888889 - 4.5499990093531483641e-847j)  +/-  (8.9e-46, 4.26e-154j)
| (0.013888888888888888889 + 5.3531392189425030705e-847j)  +/-  (5.34e-44, 2.56e-152j)
| (0.013888888888888888889 + 2.8641694632837085092e-847j)  +/-  (1.98e-49, 9.48e-158j)
| (0.013888888888888888889 - 2.4241530000003062043e-847j)  +/-  (5.91e-48, 2.83e-156j)
| (0.013888888888888888889 - 2.5077124221424564364e-847j)  +/-  (9.79e-44, 4.69e-152j)
| (0.013888888888888888889 - 5.0529782273145215909e-847j)  +/-  (2.51e-45, 1.2e-153j)
| (0.013888888888888888889 + 4.3371482660139282027e-847j)  +/-  (1.5e-47, 7.17e-156j)
| (0.013888888888888888889 - 9.5312689627083404498e-847j)  +/-  (1.77e-43, 8.48e-152j)
| (0.013888888888888888889 - 2.419030720290965197e-847j)  +/-  (2.11e-47, 1.01e-155j)
| (0.013888888888888888889 + 2.4181526871668917992e-847j)  +/-  (3.64e-48, 1.74e-156j)
| (0.013888888888888888889 - 2.9377799899016957252e-847j)  +/-  (8.27e-52, 3.96e-160j)
| (0.013888888888888888889 - 4.1450829449337709007e-847j)  +/-  (2.23e-49, 1.07e-157j)
| (0.013888888888888888889 - 3.5354782122940642291e-847j)  +/-  (2.8e-51, 1.34e-159j)
| (0.013888888888888888889 + 2.6284141665388720998e-847j)  +/-  (2.06e-52, 9.87e-161j)
| (0.013888888888888888889 + 2.436514644690715485e-847j)  +/-  (1.45e-51, 6.96e-160j)
| (0.013888888888888888889 - 2.5831168401131181902e-847j)  +/-  (1.62e-52, 7.74e-161j)
| (0.013888888888888888889 + 3.4139783369943257388e-847j)  +/-  (5.02e-53, 2.41e-161j)
| (0.013888888888888888889 + 3.970982035908110078e-847j)  +/-  (5.54e-52, 2.65e-160j)
| (0.013888888888888888889 + 3.0179006912450603793e-847j)  +/-  (7.77e-54, 3.72e-162j)
| (0.013888888888888888889 - 2.4548413010413909418e-847j)  +/-  (1.83e-53, 8.74e-162j)
| (0.013888888888888888889 + 2.4788374087252670861e-847j)  +/-  (5.92e-54, 2.83e-162j)
| (0.013888888888888888889 - 3.1049840329931932915e-847j)  +/-  (1.25e-54, 5.96e-163j)
| (0.013888888888888888889 - 3.8125501544056754613e-847j)  +/-  (4.43e-54, 2.12e-162j)
| (0.013888888888888888889 - 3.3023146035207264968e-847j)  +/-  (1.23e-54, 5.87e-163j)
| (0.013888888888888888889 + 2.7350595657885534545e-847j)  +/-  (3.9e-56, 1.87e-164j)
| (0.013888888888888888889 - 2.5082934808849795465e-847j)  +/-  (3.63e-56, 1.83e-164j)
| (0.013888888888888888889 - 2.7966963740383603721e-847j)  +/-  (3.89e-56, 1.85e-164j)
