Starting with polynomial:
P : 2*t^2 - 1
Extension levels are: 2 72
-------------------------------------------------
Trying to find an order 72 Kronrod extension for:
P1 : 2*t^2 - 1
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 2*t^74 - 37*t^72 + 2627/8*t^70 - 29785/16*t^68 + 969289/128*t^66 - 6026449/256*t^64 + 7444437/128*t^62 - 30015843/256*t^60 + 804970335/4096*t^58 - 2274557203/8192*t^56 + 175140904631/524288*t^54 - 361654595277/1048576*t^52 + 2578247276007/8388608*t^50 - 3982790558775/16777216*t^48 + 5348318750355/33554432*t^46 - 6254813453805/67108864*t^44 + 102018164263785/2147483648*t^42 - 90647718711165/4294967296*t^40 + 280576272201225/34359738368*t^38 - 188751310389915/68719476736*t^36 + 440419724243135/549755813888*t^34 - 221990534861095/1099511627776*t^32 + 48123822242615/1099511627776*t^30 - 17846430243425/2199023255552*t^28 + 44973004213431/35184372088832*t^26 - 11931613362747/70368744177664*t^24 + 21109777487937/1125899906842624*t^22 - 3842678171563/2251799813685248*t^20 + 2267418796885/18014398509481984*t^18 - 265835307221/36028797018963968*t^16 + 24166846111/72057594037927936*t^14 - 1649799697/144115188075855872*t^12 + 2592542381/9223372036854775808*t^10 - 86226465/18446744073709551616*t^8 + 7101003/147573952589676412928*t^6 - 78033/295147905179352825856*t^4 + 1369/2361183241434822606848*t^2 - 1/4722366482869645213696
-------------------------------------------------
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:   74 out of 74
Indefinite weights: 0 out of 74
Negative weights:   0 out of 74
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (-0.9818067598301891217 - 5.2428660847756858471e-791j)  +/-  (6.8e-229, 6.8e-229j)
| (-0.99797305456081250033 + 1.9288547625948092403e-812j)  +/-  (5.31e-229, 5.31e-229j)
| (-0.9355940105763622179 - 2.2432875718850558273e-831j)  +/-  (1.05e-229, 1.05e-229j)
| (-0.99437297804890248193 + 3.4531011024265037007e-837j)  +/-  (8.05e-229, 8.05e-229j)
| (0.94973605027053188743 - 3.1450819770909911767e-850j)  +/-  (2.09e-229, 2.09e-229j)
| (0.9355940105763622179 - 3.5333100690646761157e-850j)  +/-  (1.23e-229, 1.23e-229j)
| (0.99977471617476941283 - 7.3858012868052325157e-849j)  +/-  (2.15e-229, 2.15e-229j)
| (-0.91976596723773874368 - 2.8853341433473163171e-851j)  +/-  (5.41e-230, 5.41e-230j)
| (0.98898097422024528437 + 7.5917728645735179937e-853j)  +/-  (7.47e-229, 7.47e-229j)
| (0.99797305456081250033 + 1.0208368263814125245e-850j)  +/-  (5.79e-229, 5.79e-229j)
| (0.84020867891375434048 - 2.7975312022488095179e-856j)  +/-  (8.74e-232, 8.74e-232j)
| (-0.98898097422024528437 - 1.550282896184669423e-849j)  +/-  (8.8e-229, 8.8e-229j)
| (-0.97286326329797459614 + 1.2103977029306578339e-856j)  +/-  (5.21e-229, 5.21e-229j)
| (-0.8624659250699805315 + 1.6017373036607064236e-864j)  +/-  (2.65e-231, 2.65e-231j)
| (0.91976596723773874368 - 6.8980896295132639867e-865j)  +/-  (4.89e-230, 4.89e-230j)
| (0.8624659250699805315 + 5.071996637639422658e-865j)  +/-  (2.71e-231, 2.71e-231j)
| (0.88316894933460930366 - 1.1970743705427023394e-864j)  +/-  (9.23e-231, 9.23e-231j)
| (0.9818067598301891217 - 1.5227021828521764548e-861j)  +/-  (6.65e-229, 6.65e-229j)
| (-0.76452626518709253371 - 4.9964964553962322245e-870j)  +/-  (1.16e-233, 1.16e-233j)
| (-0.90228044345858519688 - 7.5053922526811923192e-864j)  +/-  (2.04e-230, 2.04e-230j)
| (-0.94973605027053188743 - 2.0312292053173935516e-863j)  +/-  (2.1e-229, 2.1e-229j)
| (0.7911946857079884338 + 1.308505451585058444e-872j)  +/-  (6.04e-233, 6.04e-233j)
| (0.7071067811865475244 + 2.945312573910642028e-875j)  +/-  (4.61e-235, 4.61e-235j)
| (-0.88316894933460930366 - 1.9991465751877958327e-869j)  +/-  (7.52e-231, 7.52e-231j)
| (-0.7911946857079884338 - 6.4841135362312225244e-874j)  +/-  (5.28e-233, 5.28e-233j)
| (0.96216660140884938635 + 6.6852340838116331481e-868j)  +/-  (4e-229, 4e-229j)
| (0.76452626518709253371 - 7.0262040827029459776e-874j)  +/-  (1.28e-233, 1.28e-233j)
| (0.90228044345858519688 - 7.9008853106060840192e-871j)  +/-  (1.93e-230, 1.93e-230j)
| (-0.99977471617476941283 + 1.9089907266631232234e-867j)  +/-  (1.91e-229, 1.91e-229j)
| (-0.61156436235889138243 - 2.4428573401634521747e-888j)  +/-  (1.29e-237, 1.29e-237j)
| (-0.96216660140884938635 - 2.6277240127357678797e-879j)  +/-  (3.67e-229, 3.67e-229j)
| (0.97286326329797459614 - 1.0097086131720454299e-886j)  +/-  (5.7e-229, 5.7e-229j)
| (0.67645919149808690027 + 1.0454943645545909565e-896j)  +/-  (7.47e-236, 7.47e-236j)
| (0.99437297804890248193 + 1.8270436477977724115e-894j)  +/-  (8.27e-229, 8.27e-229j)
| (-0.7071067811865475244 + 1.3357560730421232767e-901j)  +/-  (4.4e-235, 4.4e-235j)
| (-0.73648011666151218338 - 3.2664552573757254755e-901j)  +/-  (2.7e-234, 2.7e-234j)
| (-0.67645919149808690027 - 5.9173447060816891258e-903j)  +/-  (7.68e-236, 7.68e-236j)
| (0.57743406777654816216 - 1.2743731687392960584e-906j)  +/-  (1.67e-238, 1.67e-238j)
| (0.73648011666151218338 + 6.9164090924914761417e-902j)  +/-  (2.68e-234, 2.68e-234j)
| (-0.54226319797493510366 - 3.2553736155594770071e-907j)  +/-  (1.7e-239, 1.7e-239j)
| (-0.57743406777654816216 + 1.1650544621346020851e-905j)  +/-  (1.6e-238, 1.6e-238j)
| (0.10593573771941602347 + 1.2503187446828668504e-920j)  +/-  (1.35e-252, 1.35e-252j)
| (0.81643731992788569697 - 1.638313602836210443e-900j)  +/-  (2.35e-232, 2.35e-232j)
| (0.54226319797493510366 - 4.316786037841472813e-908j)  +/-  (1.49e-239, 1.49e-239j)
| (-0.021225383333623537202 - 1.0621131631258727061e-922j)  +/-  (2.48e-255, 2.48e-255j)
| (-0.64459257662423902828 - 3.95424665417030764e-903j)  +/-  (1.06e-236, 1.06e-236j)
| (-0.84020867891375434048 - 2.292912917633554245e-904j)  +/-  (7.95e-232, 7.95e-232j)
| (0.64459257662423902828 + 6.341071295020985767e-914j)  +/-  (1.07e-236, 1.07e-236j)
| (0.50611513323865620934 - 1.1587534042116853677e-917j)  +/-  (1.44e-240, 1.44e-240j)
| (-0.43114962756817828615 - 2.4616008051998164032e-919j)  +/-  (1.09e-242, 1.09e-242j)
| (-0.81643731992788569697 + 7.1195964171074956371e-921j)  +/-  (2.28e-232, 2.28e-232j)
| (-0.50611513323865620934 + 1.0458839483788943193e-929j)  +/-  (1.6e-240, 1.6e-240j)
| (-0.063637900425466240729 + 8.1483977397598494059e-942j)  +/-  (6.88e-254, 6.88e-254j)
| (0.43114962756817828615 - 1.2831301018976029327e-929j)  +/-  (1.19e-242, 1.19e-242j)
| (0.46905501482363697761 - 4.5013016108045286897e-929j)  +/-  (1.4e-241, 1.4e-241j)
| (0.14804267165373141916 + 7.7941194978638437591e-940j)  +/-  (2.55e-251, 2.55e-251j)
| (-0.46905501482363697761 - 9.3706682390735560502e-930j)  +/-  (1.22e-241, 1.22e-241j)
| (-0.31305180851822231181 - 8.2234823000511192919e-936j)  +/-  (3.46e-246, 3.46e-246j)
| (0.1898828226874283024 + 4.8014890716677441965e-937j)  +/-  (6.02e-250, 6.02e-250j)
| (0.39246727954216374392 - 3.041771315815954362e-931j)  +/-  (8.81e-244, 8.81e-244j)
| (0.61156436235889138243 + 2.9575492415836885519e-931j)  +/-  (1.28e-237, 1.28e-237j)
| (-0.27246179756682284294 + 2.4183201130836975384e-941j)  +/-  (2.01e-247, 2.01e-247j)
| (-0.39246727954216374392 + 5.3376594503487404809e-938j)  +/-  (8.59e-244, 8.59e-244j)
| (0.063637900425466240729 + 1.9028000067642231217e-947j)  +/-  (6.88e-254, 6.88e-254j)
| (0.31305180851822231181 - 5.8827933577096209737e-940j)  +/-  (3.38e-246, 3.38e-246j)
| (0.27246179756682284294 - 9.8406253446578163651e-942j)  +/-  (2.06e-247, 2.06e-247j)
| (-0.23138079204034148853 - 3.5493698534526144022e-942j)  +/-  (1.21e-248, 1.21e-248j)
| (-0.35307767895130077503 - 1.8455510302371720627e-938j)  +/-  (6.84e-245, 6.84e-245j)
| (-0.14804267165373141916 - 9.7276144629111542831e-946j)  +/-  (2.81e-251, 2.81e-251j)
| (0.23138079204034148853 + 1.4733090011351988343e-942j)  +/-  (1.04e-248, 1.04e-248j)
| (0.35307767895130077503 - 1.6519303828051817404e-938j)  +/-  (5.74e-245, 5.74e-245j)
| (-0.10593573771941602347 - 1.5553621905904024972e-946j)  +/-  (1.15e-252, 1.15e-252j)
| (0.021225383333623537202 - 8.9146841762319679076e-949j)  +/-  (2.48e-255, 2.48e-255j)
| (-0.1898828226874283024 - 1.5583079871221326867e-943j)  +/-  (5.42e-250, 5.42e-250j)
-------------------------------------------------
The weights are:
| (0.013513513513513513514 - 9.6463209897837646549e-792j)  +/-  (1.41e-18, 1.47e-125j)
| (0.013513513513513513514 - 1.4687798864912835631e-791j)  +/-  (5.48e-19, 5.72e-126j)
| (0.013513513513513513514 - 2.850754530063273854e-791j)  +/-  (8.71e-20, 9.09e-127j)
| (0.013513513513513513514 + 3.1454969198952315203e-791j)  +/-  (7.35e-19, 7.67e-126j)
| (0.013513513513513513514 - 6.0473241039510479474e-793j)  +/-  (1.7e-20, 1.77e-127j)
| (0.013513513513513513514 + 6.8708225382683977717e-793j)  +/-  (1.47e-20, 1.53e-127j)
| (0.013513513513513513514 + 3.9966394858426035979e-794j)  +/-  (9.78e-22, 1.02e-128j)
| (0.013513513513513513514 + 2.3603558555105853362e-791j)  +/-  (3.28e-21, 3.43e-128j)
| (0.013513513513513513514 - 2.8028407921695328395e-793j)  +/-  (3.39e-22, 3.54e-129j)
| (0.013513513513513513514 - 1.199362088997444259e-793j)  +/-  (9.65e-22, 1.01e-128j)
| (0.013513513513513513514 - 1.1104766843511775309e-792j)  +/-  (7.65e-24, 7.99e-131j)
| (0.013513513513513513514 - 7.6995249282767469634e-791j)  +/-  (3.37e-21, 3.51e-128j)
| (0.013513513513513513514 + 9.6532004973020634014e-791j)  +/-  (6.2e-22, 6.47e-129j)
| (0.013513513513513513514 - 1.5823830348660404617e-791j)  +/-  (1.52e-24, 1.59e-131j)
| (0.013513513513513513514 - 7.7009070435030979353e-793j)  +/-  (4.99e-24, 5.21e-131j)
| (0.013513513513513513514 + 1.0239424670627140814e-792j)  +/-  (4.59e-25, 4.79e-132j)
| (0.013513513513513513514 - 9.384301881536257173e-793j)  +/-  (5.84e-25, 6.1e-132j)
| (0.013513513513513513514 + 3.6081204868874542599e-793j)  +/-  (1.76e-24, 1.84e-131j)
| (0.013513513513513513514 - 1.1069192102791055039e-791j)  +/-  (1.31e-28, 1.37e-135j)
| (0.013513513513513513514 - 2.0228725208066851713e-791j)  +/-  (2.97e-26, 3.1e-133j)
| (0.013513513513513513514 + 3.6421599502210304705e-791j)  +/-  (1.76e-25, 1.84e-132j)
| (0.013513513513513513514 - 1.2870174826576485444e-792j)  +/-  (6.14e-29, 6.4e-136j)
| (0.013513513513513513514 + 1.5621723642540490354e-792j)  +/-  (1.35e-30, 1.41e-137j)
| (0.013513513513513513514 + 1.7743190941286064666e-791j)  +/-  (2.83e-27, 2.95e-134j)
| (0.013513513513513513514 + 1.1971350019107446597e-791j)  +/-  (1.08e-29, 1.13e-136j)
| (0.013513513513513513514 + 5.229578353607832695e-793j)  +/-  (2.76e-27, 2.88e-134j)
| (0.013513513513513513514 + 1.3772399083903815569e-792j)  +/-  (3.6e-30, 3.76e-137j)
| (0.013513513513513513514 + 8.5384370632254421483e-793j)  +/-  (1.8e-27, 1.88e-134j)
| (0.013513513513513513514 + 4.4076614054132590215e-792j)  +/-  (2.17e-27, 2.27e-134j)
| (0.013513513513513513514 + 7.9734922816743470895e-792j)  +/-  (2.76e-35, 2.88e-142j)
| (0.013513513513513513514 - 5.1762113073792916382e-791j)  +/-  (4.39e-27, 4.59e-134j)
| (0.013513513513513513514 - 4.4167743993039092832e-793j)  +/-  (7.46e-28, 7.79e-135j)
| (0.013513513513513513514 - 1.6571362166361237077e-792j)  +/-  (3.8e-34, 3.96e-141j)
| (0.013513513513513513514 + 2.000172349915703552e-793j)  +/-  (6.99e-28, 7.3e-135j)
| (0.013513513513513513514 - 9.6045659428807640499e-792j)  +/-  (7.86e-35, 8.2e-142j)
| (0.013513513513513513514 + 1.0288409742357749935e-791j)  +/-  (2.77e-34, 2.89e-141j)
| (0.013513513513513513514 + 8.9994905797706925663e-792j)  +/-  (1.08e-35, 1.12e-142j)
| (0.013513513513513513514 + 1.9537141260038181337e-792j)  +/-  (7.2e-39, 7.51e-146j)
| (0.013513513513513513514 - 1.468917129129181967e-792j)  +/-  (9.37e-35, 9.78e-142j)
| (0.013513513513513513514 + 7.1324150253431435457e-792j)  +/-  (2.27e-39, 2.37e-146j)
| (0.013513513513513513514 - 7.5334237217311071965e-792j)  +/-  (1.81e-38, 1.88e-145j)
| (0.013513513513513513514 + 3.4109439543695826112e-792j)  +/-  (3.91e-44, 4.08e-151j)
| (0.013513513513513513514 + 1.198133275834926352e-792j)  +/-  (8.01e-35, 8.36e-142j)
| (0.013513513513513513514 - 2.0569968516301638331e-792j)  +/-  (6.55e-41, 6.84e-148j)
| (0.013513513513513513514 - 3.8834646227566331885e-792j)  +/-  (6.79e-45, 7.09e-152j)
| (0.013513513513513513514 - 8.4593684960438558869e-792j)  +/-  (2.4e-38, 2.5e-145j)
| (0.013513513513513513514 + 1.4289075460331274269e-791j)  +/-  (8.06e-37, 8.41e-144j)
| (0.013513513513513513514 + 1.7539474924100265453e-792j)  +/-  (1.42e-39, 1.48e-146j)
| (0.013513513513513513514 + 2.1627841483426228222e-792j)  +/-  (1.85e-42, 1.93e-149j)
| (0.013513513513513513514 - 6.1138058306044362111e-792j)  +/-  (6.21e-44, 6.48e-151j)
| (0.013513513513513513514 - 1.3028622890082693613e-791j)  +/-  (1.62e-37, 1.69e-144j)
| (0.013513513513513513514 - 6.7650000639269726454e-792j)  +/-  (2.92e-42, 3.05e-149j)
| (0.013513513513513513514 + 4.055530037888257287e-792j)  +/-  (7.42e-47, 7.74e-154j)
| (0.013513513513513513514 + 2.3826714086244626684e-792j)  +/-  (2.48e-45, 2.59e-152j)
| (0.013513513513513513514 - 2.2712718542120708986e-792j)  +/-  (1.95e-44, 2.04e-151j)
| (0.013513513513513513514 - 3.2660191853640558004e-792j)  +/-  (8.19e-48, 8.55e-155j)
| (0.013513513513513513514 + 6.4266997532720297426e-792j)  +/-  (8.13e-45, 8.49e-152j)
| (0.013513513513513513514 + 5.2989189775965327448e-792j)  +/-  (4.32e-48, 4.51e-155j)
| (0.013513513513513513514 + 3.1265459476961554736e-792j)  +/-  (1.65e-48, 1.72e-155j)
| (0.013513513513513513514 - 2.4972116915133022873e-792j)  +/-  (2.15e-47, 2.24e-154j)
| (0.013513513513513513514 - 1.8527541120050992394e-792j)  +/-  (1.46e-44, 1.52e-151j)
| (0.013513513513513513514 - 5.061091104172190482e-792j)  +/-  (2.06e-49, 2.15e-156j)
| (0.013513513513513513514 + 5.82321957589981392e-792j)  +/-  (6.65e-48, 6.94e-155j)
| (0.013513513513513513514 - 3.5617967461413608689e-792j)  +/-  (1.14e-49, 1.19e-156j)
| (0.013513513513513513514 - 2.736730010126571736e-792j)  +/-  (9.84e-50, 1.03e-156j)
| (0.013513513513513513514 + 2.8622733601414234125e-792j)  +/-  (5.64e-50, 5.88e-157j)
| (0.013513513513513513514 + 4.8372141686261363369e-792j)  +/-  (2.81e-51, 2.93e-158j)
| (0.013513513513513513514 - 5.5523297486663890095e-792j)  +/-  (4.16e-50, 4.34e-157j)
| (0.013513513513513513514 + 4.4258441591912045179e-792j)  +/-  (3.12e-52, 3.26e-159j)
| (0.013513513513513513514 - 2.9920939415354437803e-792j)  +/-  (2.09e-51, 2.18e-158j)
| (0.013513513513513513514 + 2.6151411149882785149e-792j)  +/-  (3.61e-51, 3.78e-158j)
| (0.013513513513513513514 - 4.2360445799272674365e-792j)  +/-  (1.24e-52, 1.29e-159j)
| (0.013513513513513513514 + 3.7191069282552849425e-792j)  +/-  (1.28e-52, 1.36e-159j)
| (0.013513513513513513514 - 4.6258752190210196834e-792j)  +/-  (1.17e-52, 1.21e-159j)
