Starting with polynomial:
P : 8*t^4 - 8*t^2 + 1
Extension levels are: 4 8 72
-------------------------------------------------
Trying to find an order 8 Kronrod extension for:
P1 : 8*t^4 - 8*t^2 + 1
Solvable: 1
-------------------------------------------------
Trying to find an order 72 Kronrod extension for:
P2 : 8*t^12 - 24*t^10 + 27*t^8 - 14*t^6 + 105/32*t^4 - 9/32*t^2 + 1/256
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 8*t^84 - 168*t^82 + 1701*t^80 - 11060*t^78 + 1660659/32*t^76 - 5990985/32*t^74 + 138304705/256*t^72 - 163964205/128*t^70 + 20840713425/8192*t^68 - 35166774209/8192*t^66 + 407744490153/65536*t^64 - 31989916413/4096*t^62 + 2240478960629/262144*t^60 - 2148238223355/262144*t^58 + 14494031768187/2097152*t^56 - 5391499739857/1048576*t^54 + 453837419278551/134217728*t^52 - 264174020177067/134217728*t^50 + 1089606648878475/1073741824*t^48 - 124400435216085/268435456*t^46 + 25750890089729595/137438953472*t^44 - 9206478467454345/137438953472*t^42 + 23245683168557745/1099511627776*t^40 - 3230868294988425/549755813888*t^38 + 50473342475041395/35184372088832*t^36 - 10779052799754603/35184372088832*t^34 + 16039916765682579/281474976710656*t^32 - 323091240894191/35184372088832*t^30 + 2868258975285165/2251799813685248*t^28 - 339875201460123/2251799813685248*t^26 + 272739359196395/18014398509481984*t^24 - 11454057081285/9007199254740992*t^22 + 203529783521295/2305843009213693952*t^20 - 11488609289675/2305843009213693952*t^18 + 4135899344283/18446744073709551616*t^16 - 36174046743/4611686018427387904*t^14 + 121919935319/590295810358705651712*t^12 - 2313604293/590295810358705651712*t^10 + 238243005/4722366482869645213696*t^8 - 950257/2361183241434822606848*t^6 + 259161/151115727451828646838272*t^4 - 441/151115727451828646838272*t^2 + 1/1208925819614629174706176
-------------------------------------------------
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
  current precision for roots: 848
  current precision for roots: 1696
 current precision for weights: 848
Linear system for weights solvable: 1
Sufficient bits for target precision reached
-------------------------------------------------
The nodes are:
| (0.97059656745339095328 - 2.592197360633182745e-1846j)  +/-  (5.01e-480, 5.01e-480j)
| (-0.96091732194509954321 + 1.5017935092046071995e-1845j)  +/-  (3.3e-480, 3.3e-480j)
| (-0.92387953251128675613 - 1.0292623826142879621e-1853j)  +/-  (5.06e-481, 5.06e-481j)
| (-0.99144486137381041114 - 3.3447595745024890007e-1863j)  +/-  (8.57e-480, 8.57e-480j)
| (0.92387953251128675613 - 1.3560468088970191939e-1885j)  +/-  (5.17e-481, 5.17e-481j)
| (0.93754245854399921726 + 4.1089868011408968964e-1884j)  +/-  (1.06e-480, 1.06e-480j)
| (0.98587101851823587392 - 2.5277556399957042091e-1883j)  +/-  (8.29e-480, 8.29e-480j)
| (-0.90892447741221084203 - 1.0733464484136315357e-1885j)  +/-  (2.18e-481, 2.18e-481j)
| (-0.99982516091274642234 + 2.615884874449470216e-1893j)  +/-  (2.09e-480, 2.09e-480j)
| (0.99842681501781656213 - 7.9905125445750394373e-1911j)  +/-  (5.73e-480, 5.73e-480j)
| (0.8752234219087536975 + 2.2594427818650145556e-1915j)  +/-  (3.51e-482, 3.51e-482j)
| (0.99144486137381041114 - 5.7331334229888693668e-1914j)  +/-  (8.49e-480, 8.49e-480j)
| (-0.93754245854399921726 - 2.6417859561239297403e-1912j)  +/-  (1.03e-480, 1.03e-480j)
| (-0.85652455547785143144 - 2.1185669009901655654e-1923j)  +/-  (1.09e-482, 1.09e-482j)
| (0.97891834589764844845 - 8.2194929105242061986e-1929j)  +/-  (6.8e-480, 6.8e-480j)
| (0.85652455547785143144 + 8.1042188190979973416e-1933j)  +/-  (1.1e-482, 1.1e-482j)
| (0.83662776200641972597 - 5.1555412953291555557e-1933j)  +/-  (2.98e-483, 2.98e-483j)
| (0.99982516091274642234 - 9.4358217260084889502e-1928j)  +/-  (2.01e-480, 2.01e-480j)
| (-0.79335334029123516458 + 1.7418834739348028893e-1932j)  +/-  (2.09e-484, 2.09e-484j)
| (-0.94989414667284594426 - 8.7081632307580521874e-1939j)  +/-  (1.95e-480, 1.95e-480j)
| (0.94989414667284594426 + 9.6487177203688744066e-1962j)  +/-  (1.86e-480, 1.86e-480j)
| (0.77003623523926280917 + 1.1082822342378406199e-1979j)  +/-  (4.87e-485, 4.87e-485j)
| (-0.99842681501781656213 + 4.1128683435709100198e-1976j)  +/-  (5.85e-480, 5.85e-480j)
| (-0.83662776200641972597 - 2.7392379410537363019e-2005j)  +/-  (3.04e-483, 3.04e-483j)
| (-0.81556086895926017135 - 1.1202702963398949447e-2005j)  +/-  (8.49e-484, 8.49e-484j)
| (0.99563207894113381569 - 3.0478347091857736625e-2002j)  +/-  (8.11e-480, 8.11e-480j)
| (0.74564216488316560949 - 1.2037334045401571404e-2009j)  +/-  (1.07e-485, 1.07e-485j)
| (0.66634657795200394558 + 4.0058609742586475229e-2012j)  +/-  (4.48e-488, 4.48e-488j)
| (-0.8752234219087536975 - 5.5362068042404132494e-2002j)  +/-  (3.38e-482, 3.38e-482j)
| (-0.66634657795200394558 - 3.2388171499332257931e-2016j)  +/-  (4.5e-488, 4.5e-488j)
| (-0.89269820924361151416 + 2.2725381108161868196e-2007j)  +/-  (9.14e-482, 9.14e-482j)
| (0.81556086895926017135 - 2.8127467269204240899e-2030j)  +/-  (8.52e-484, 8.52e-484j)
| (0.7202052465361265407 - 7.0893373841594532952e-2032j)  +/-  (2.17e-486, 2.17e-486j)
| (-0.99563207894113381569 + 1.338734260410890246e-2022j)  +/-  (7.97e-480, 7.97e-480j)
| (-0.69376105602854156565 + 1.5913202194818733628e-2054j)  +/-  (2.54e-487, 2.54e-487j)
| (-0.77003623523926280917 + 1.0828491486071946329e-2051j)  +/-  (5.01e-485, 5.01e-485j)
| (-0.98587101851823587392 + 2.5632306354858979104e-2045j)  +/-  (8.2e-480, 8.2e-480j)
| (0.63800015393300863172 + 2.1229561373179416005e-2072j)  +/-  (6.24e-489, 6.24e-489j)
| (0.79335334029123516458 - 8.0575374744234545081e-2067j)  +/-  (2.04e-484, 2.04e-484j)
| (-0.97891834589764844845 - 1.5663086514813538119e-2060j)  +/-  (6.69e-480, 6.69e-480j)
| (-0.57867129617980574163 - 8.5903990543273831257e-2084j)  +/-  (9.71e-491, 9.71e-491j)
| (-0.97059656745339095328 + 3.5710330987538292189e-2071j)  +/-  (4.85e-480, 4.85e-480j)
| (0.69376105602854156565 - 3.7940952409570163875e-2085j)  +/-  (2.48e-487, 2.48e-487j)
| (0.60876142900872063942 - 2.9803275460948502425e-2087j)  +/-  (8.51e-490, 8.51e-490j)
| (0.90892447741221084203 - 1.8843849246815629922e-2075j)  +/-  (2.23e-481, 2.23e-481j)
| (-0.54777183921787136178 + 4.6555265808197900129e-2090j)  +/-  (1.17e-491, 1.17e-491j)
| (-0.7202052465361265407 + 3.3426810394446755214e-2084j)  +/-  (2.21e-486, 2.21e-486j)
| (0.89269820924361151416 - 2.5746870186686219546e-2076j)  +/-  (8.93e-482, 8.93e-482j)
| (0.45065497579994520036 + 1.8294499811563384422e-2092j)  +/-  (7.27e-495, 7.27e-495j)
| (0.96091732194509954321 - 3.1753376804087738551e-2090j)  +/-  (3.37e-480, 3.37e-480j)
| (-0.63800015393300863172 - 3.2627453894626704477e-2097j)  +/-  (6.37e-489, 6.37e-489j)
| (-0.51610627380750663127 + 1.3447818350272775146e-2101j)  +/-  (1.31e-492, 1.31e-492j)
| (-0.60876142900872063942 - 1.4142998969975293537e-2098j)  +/-  (8.37e-490, 8.37e-490j)
| (0.51610627380750663127 - 7.0233158083187508611e-2104j)  +/-  (1.25e-492, 1.25e-492j)
| (0.54777183921787136178 - 1.0202210050556180319e-2102j)  +/-  (1.14e-491, 1.14e-491j)
| (-0.74564216488316560949 + 1.970511724486141726e-2106j)  +/-  (1.07e-485, 1.07e-485j)
| (-0.41696078276132807406 + 2.5878351187374096093e-2116j)  +/-  (5.58e-496, 5.58e-496j)
| (-0.24071207540897300251 + 2.3105581872994782159e-2122j)  +/-  (4.34e-502, 4.34e-502j)
| (0.57867129617980574163 - 8.3707498917994940051e-2116j)  +/-  (9.72e-491, 9.72e-491j)
| (0.41696078276132807406 - 1.9788864690469960214e-2121j)  +/-  (5.45e-496, 5.45e-496j)
| (0.24071207540897300251 + 8.0426405220511646271e-2127j)  +/-  (4.56e-502, 4.56e-502j)
| (-0.48371888710523979107 - 2.4143686155409433547e-2118j)  +/-  (7.49e-494, 7.49e-494j)
| (-0.45065497579994520036 + 9.3476346533571509837e-2120j)  +/-  (7.34e-495, 7.34e-495j)
| (-0.018698866430902266063 - 5.6137344420756904876e-2135j)  +/-  (1.19e-510, 1.19e-510j)
| (0.38268343236508977173 - 3.1023109962467462009e-2122j)  +/-  (4.58e-497, 4.58e-497j)
| (0.48371888710523979107 + 3.8834210407149941079e-2120j)  +/-  (7.72e-494, 7.72e-494j)
| (-0.056070447237191788191 - 1.257904538988480107e-2134j)  +/-  (9.73e-509, 9.73e-509j)
| (-0.38268343236508977173 - 2.9087102760051874617e-2122j)  +/-  (4.43e-497, 4.43e-497j)
| (-0.16750622330473640809 - 5.8958133126497732321e-2130j)  +/-  (1.01e-504, 1.01e-504j)
| (0.13052619222005159155 - 3.124787069689061394e-2131j)  +/-  (7.25e-506, 7.25e-506j)
| (0.3478708645852272422 - 2.9925444903449721105e-2124j)  +/-  (2.41e-498, 2.41e-498j)
| (0.093363608452950670683 - 1.6435340040512600361e-2133j)  +/-  (3.77e-507, 3.77e-507j)
| (-0.27683551142484938763 - 2.0643928339689230658e-2126j)  +/-  (9.29e-501, 9.29e-501j)
| (-0.3478708645852272422 - 1.2852178079802969157e-2123j)  +/-  (2.36e-498, 2.36e-498j)
| (0.056070447237191788191 + 1.1048136321118300801e-2134j)  +/-  (1.02e-508, 1.02e-508j)
| (0.27683551142484938763 + 2.2604249919862896507e-2127j)  +/-  (9.34e-501, 9.34e-501j)
| (0.16750622330473640809 + 3.0943402175364929918e-2130j)  +/-  (1.07e-504, 1.07e-504j)
| (-0.13052619222005159155 - 1.4083386520886867152e-2132j)  +/-  (7.02e-506, 7.02e-506j)
| (-0.31257176794564450287 - 5.5065692356165111393e-2125j)  +/-  (1.48e-499, 1.48e-499j)
| (-0.093363608452950670683 - 1.6198415279825562524e-2132j)  +/-  (3.69e-507, 3.69e-507j)
| (0.20425198178968033477 - 7.9055775168053783919e-2129j)  +/-  (2.81e-503, 2.81e-503j)
| (0.31257176794564450287 + 4.174402417676808429e-2125j)  +/-  (1.51e-499, 1.51e-499j)
| (0.018698866430902266063 + 5.2442856080059424526e-2135j)  +/-  (1.19e-510, 1.19e-510j)
| (-0.20425198178968033477 - 1.0361920898843240517e-2128j)  +/-  (2.8e-503, 2.8e-503j)
-------------------------------------------------
The weights are:
| (0.011904761904761904762 + 3.3894895350809601881e-1847j)  +/-  (4.29e-127, 4e-359j)
| (0.011904761904761904762 + 1.139213787143235666e-1846j)  +/-  (1.75e-127, 1.63e-359j)
| (0.011904761904761904762 - 6.6986294118103179909e-1846j)  +/-  (1.42e-127, 1.33e-359j)
| (0.011904761904761904762 - 2.7527803372744423724e-1846j)  +/-  (3.13e-128, 2.92e-360j)
| (0.011904761904761904762 + 1.1812841829135279152e-1846j)  +/-  (3.4e-128, 3.18e-360j)
| (0.011904761904761904762 - 1.4675607059530084163e-1846j)  +/-  (4.03e-128, 3.76e-360j)
| (0.011904761904761904762 - 1.3503382806423800276e-1846j)  +/-  (2.7e-129, 2.52e-361j)
| (0.011904761904761904762 + 5.2076178837279804878e-1846j)  +/-  (1.7e-129, 1.58e-361j)
| (0.011904761904761904762 + 3.0915881398195490736e-1847j)  +/-  (2.53e-130, 2.36e-362j)
| (0.011904761904761904762 + 2.3980885733757118346e-1847j)  +/-  (1.91e-130, 1.78e-362j)
| (0.011904761904761904762 - 8.2035227983511738313e-1847j)  +/-  (2.59e-131, 2.41e-363j)
| (0.011904761904761904762 + 7.5945851647794118148e-1847j)  +/-  (3.92e-130, 3.66e-362j)
| (0.011904761904761904762 + 9.6345831096570704332e-1846j)  +/-  (8.9e-132, 8.3e-364j)
| (0.011904761904761904762 - 3.22905812196464532e-1846j)  +/-  (2.46e-133, 2.3e-365j)
| (0.011904761904761904762 + 3.0785960760021432412e-1846j)  +/-  (4.08e-130, 3.81e-362j)
| (0.011904761904761904762 + 7.6342575071454680315e-1847j)  +/-  (1.22e-132, 1.14e-364j)
| (0.011904761904761904762 - 7.2098960268407201114e-1847j)  +/-  (2.66e-133, 2.48e-365j)
| (0.011904761904761904762 - 7.5857029306244023143e-1848j)  +/-  (4.46e-131, 4.16e-363j)
| (0.011904761904761904762 + 2.3905008191503266251e-1846j)  +/-  (2.55e-136, 2.37e-368j)
| (0.011904761904761904762 - 1.8333556729845446992e-1845j)  +/-  (3.71e-134, 3.46e-366j)
| (0.011904761904761904762 + 2.0412604829051434626e-1846j)  +/-  (4.67e-132, 4.36e-364j)
| (0.011904761904761904762 + 6.4585525974973861314e-1847j)  +/-  (2.52e-136, 2.35e-368j)
| (0.011904761904761904762 - 9.6173746914456100624e-1847j)  +/-  (2.89e-135, 2.7e-367j)
| (0.011904761904761904762 + 2.8851153564571956713e-1846j)  +/-  (5.15e-136, 4.81e-368j)
| (0.011904761904761904762 - 2.6125616904683081612e-1846j)  +/-  (2.06e-136, 1.92e-368j)
| (0.011904761904761904762 - 4.4727524602401272473e-1847j)  +/-  (2.33e-131, 2.17e-363j)
| (0.011904761904761904762 - 6.3191572873248742241e-1847j)  +/-  (1.07e-137, 1e-369j)
| (0.011904761904761904762 + 6.1011383128842675908e-1847j)  +/-  (1.6e-139, 1.49e-371j)
| (0.011904761904761904762 + 3.6790560470727551244e-1846j)  +/-  (9.91e-137, 9.24e-369j)
| (0.011904761904761904762 - 1.6931415129961767802e-1846j)  +/-  (5.05e-142, 4.71e-374j)
| (0.011904761904761904762 - 4.297265841881315054e-1846j)  +/-  (1.17e-136, 1.09e-368j)
| (0.011904761904761904762 + 6.8887886173773438453e-1847j)  +/-  (1.18e-137, 1.1e-369j)
| (0.011904761904761904762 + 6.2172081136339523977e-1847j)  +/-  (1.73e-139, 1.62e-371j)
| (0.011904761904761904762 + 1.7308038552658450361e-1846j)  +/-  (1.11e-137, 1.03e-369j)
| (0.011904761904761904762 + 1.7964805643595853971e-1846j)  +/-  (2.59e-142, 2.42e-374j)
| (0.011904761904761904762 - 2.2055643152147117133e-1846j)  +/-  (1.9e-140, 1.78e-372j)
| (0.011904761904761904762 + 4.3241845185074225768e-1846j)  +/-  (1.93e-138, 1.8e-370j)
| (0.011904761904761904762 - 6.0783833241152234584e-1847j)  +/-  (1.09e-144, 1.02e-376j)
| (0.011904761904761904762 - 6.6442915773839244177e-1847j)  +/-  (7.8e-141, 7.28e-373j)
| (0.011904761904761904762 - 7.3144459328030914246e-1846j)  +/-  (5.87e-139, 5.47e-371j)
| (0.011904761904761904762 + 1.4454024605748706205e-1846j)  +/-  (2.65e-148, 2.48e-380j)
| (0.011904761904761904762 + 1.6044841287464338445e-1845j)  +/-  (5.08e-139, 4.74e-371j)
| (0.011904761904761904762 - 6.1461685205344735675e-1847j)  +/-  (8.95e-145, 8.35e-377j)
| (0.011904761904761904762 + 6.0750209163015918043e-1847j)  +/-  (1.62e-147, 1.51e-379j)
| (0.011904761904761904762 - 1.0107694371671790332e-1846j)  +/-  (4.03e-143, 3.76e-375j)
| (0.011904761904761904762 - 1.3784304173022348777e-1846j)  +/-  (1.39e-150, 1.3e-382j)
| (0.011904761904761904762 - 1.9139232939492207763e-1846j)  +/-  (1.29e-146, 1.2e-378j)
| (0.011904761904761904762 + 8.9867555274574786551e-1847j)  +/-  (2.28e-143, 2.13e-375j)
| (0.011904761904761904762 - 6.2853408094618329183e-1847j)  +/-  (1.43e-153, 1.33e-385j)
| (0.011904761904761904762 - 3.7596929360511551874e-1846j)  +/-  (7.78e-143, 7.26e-375j)
| (0.011904761904761904762 + 1.6013997760637444337e-1846j)  +/-  (1.47e-149, 1.37e-381j)
| (0.011904761904761904762 + 1.3174385688810887851e-1846j)  +/-  (4.75e-153, 4.43e-385j)
| (0.011904761904761904762 - 1.5193244454861926664e-1846j)  +/-  (2.27e-150, 2.11e-382j)
| (0.011904761904761904762 - 6.1611347191253565909e-1847j)  +/-  (3.29e-154, 3.07e-386j)
| (0.011904761904761904762 + 6.1179708574849325787e-1847j)  +/-  (1.69e-153, 1.58e-385j)
| (0.011904761904761904762 + 2.0487872239939104418e-1846j)  +/-  (3e-149, 2.8e-381j)
| (0.011904761904761904762 - 1.1631058748297106492e-1846j)  +/-  (2.28e-157, 2.13e-389j)
| (0.011904761904761904762 + 9.7307003331388370671e-1847j)  +/-  (4.76e-160, 4.44e-392j)
| (0.011904761904761904762 - 6.088804227382838021e-1847j)  +/-  (1.93e-153, 1.8e-385j)
| (0.011904761904761904762 + 6.3648833146276870758e-1847j)  +/-  (9.23e-158, 8.61e-390j)
| (0.011904761904761904762 - 6.9212857570341325962e-1847j)  +/-  (3.86e-161, 3.6e-393j)
| (0.011904761904761904762 - 1.2616363393567557937e-1846j)  +/-  (1.34e-156, 1.25e-388j)
| (0.011904761904761904762 + 1.2103725446049194802e-1846j)  +/-  (1.81e-157, 1.69e-389j)
| (0.011904761904761904762 + 8.1486673778171853164e-1847j)  +/-  (8.97e-164, 8.37e-396j)
| (0.011904761904761904762 - 6.4553484898027634422e-1847j)  +/-  (3.09e-160, 2.89e-392j)
| (0.011904761904761904762 + 6.2172074897389431951e-1847j)  +/-  (7.9e-158, 7.37e-390j)
| (0.011904761904761904762 - 8.3728180026207852185e-1847j)  +/-  (3.87e-164, 3.61e-396j)
| (0.011904761904761904762 + 1.1193826692060650967e-1846j)  +/-  (2.98e-161, 2.78e-393j)
| (0.011904761904761904762 + 9.1352679702579067054e-1847j)  +/-  (3.35e-164, 3.13e-396j)
| (0.011904761904761904762 + 7.3794813939329724491e-1847j)  +/-  (3.32e-165, 3.1e-397j)
| (0.011904761904761904762 + 6.5563905637794819263e-1847j)  +/-  (4.9e-163, 4.57e-395j)
| (0.011904761904761904762 - 7.5539419041345661383e-1847j)  +/-  (1.97e-165, 1.84e-397j)
| (0.011904761904761904762 - 1.0059219505791630651e-1846j)  +/-  (8.32e-165, 7.76e-397j)
| (0.011904761904761904762 - 1.0788199595689214888e-1846j)  +/-  (5.66e-164, 5.28e-396j)
| (0.011904761904761904762 + 7.7399204969011094289e-1847j)  +/-  (3.91e-166, 3.65e-398j)
| (0.011904761904761904762 + 6.7894227691454272571e-1847j)  +/-  (7.65e-166, 7.13e-398j)
| (0.011904761904761904762 - 7.216101370484490313e-1847j)  +/-  (2.59e-166, 2.42e-398j)
| (0.011904761904761904762 - 8.8650346538048228556e-1847j)  +/-  (3.74e-167, 3.49e-399j)
| (0.011904761904761904762 + 1.0410923797004055868e-1846j)  +/-  (2.82e-166, 2.63e-398j)
| (0.011904761904761904762 + 8.6112716708699503487e-1847j)  +/-  (2.85e-167, 2.66e-399j)
| (0.011904761904761904762 + 7.0634554131134983679e-1847j)  +/-  (1.84e-167, 1.71e-399j)
| (0.011904761904761904762 - 6.6677865083380400156e-1847j)  +/-  (2.33e-167, 2.17e-399j)
| (0.011904761904761904762 - 7.9379504600337266257e-1847j)  +/-  (7.37e-168, 6.97e-400j)
| (0.011904761904761904762 - 9.423309359711098565e-1847j)  +/-  (6.56e-168, 5.87e-400j)
