Starting with polynomial:
P : 32768*t^16 - 131072*t^14 + 212992*t^12 - 180224*t^10 + 84480*t^8 - 21504*t^6 + 2688*t^4 - 128*t^2 + 1
Extension levels are: 16 64
-------------------------------------------------
Trying to find an order 64 Kronrod extension for:
P1 : 32768*t^16 - 131072*t^14 + 212992*t^12 - 180224*t^10 + 84480*t^8 - 21504*t^6 + 2688*t^4 - 128*t^2 + 1
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 32768*t^80 - 655360*t^78 + 6307840*t^76 - 38912000*t^74 + 172864000*t^72 - 589120512*t^70 + 1602168960*t^68 - 3571175040*t^66 + 6649453525*t^64 - 10489278800*t^62 + 14168018722*t^60 - 16520021830*t^58 + 267721530245/16*t^56 - 118338449075/8*t^54 + 733083639075/64*t^52 - 498496874571/64*t^50 + 610658671349475/131072*t^48 - 80394839085225/32768*t^46 + 298238919187125/262144*t^44 - 121714416544875/262144*t^42 + 1397281501935165/8388608*t^40 - 219911132265825/4194304*t^38 + 484631742893025/33554432*t^36 - 116444697949125/33554432*t^34 + 3110736930926625/4294967296*t^32 - 70132978079073/536870912*t^30 + 86916938645005/4294967296*t^28 - 11479595670095/4294967296*t^26 + 40998555964625/137438953472*t^24 - 1912711535875/68719476736*t^22 + 1178230306099/549755813888*t^20 - 73687872995/549755813888*t^18 + 3758081522745/562949953421312*t^16 - 36345082425/140737488355328*t^14 + 8458829925/1125899906842624*t^12 - 177232627/1125899906842624*t^10 + 80560285/36028797018963968*t^8 - 354445/18014398509481984*t^6 + 13325/144115188075855872*t^4 - 25/144115188075855872*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
  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:
| (0.99518472667219688624 + 3.561541206502071365e-1814j)  +/-  (2.35e-481, 2.35e-481j)
| (-0.94480604646687801758 + 2.5555381315610470576e-1813j)  +/-  (5.05e-482, 5.05e-482j)
| (-0.93121493475880355847 + 1.0810606514499757848e-1822j)  +/-  (2.59e-482, 2.59e-482j)
| (-0.99826561018471589329 + 1.4249298276579785747e-1832j)  +/-  (1.74e-481, 1.74e-481j)
| (0.91618795711713591084 - 2.8228269914008486154e-1845j)  +/-  (1.23e-482, 1.23e-482j)
| (0.93121493475880355847 + 2.9521138570801639843e-1846j)  +/-  (2.57e-482, 2.57e-482j)
| (0.99980724048206485639 + 6.4541821286360879122e-1843j)  +/-  (6.49e-482, 6.49e-482j)
| (-0.91618795711713591084 - 3.4086200175630686368e-1847j)  +/-  (1.22e-482, 1.22e-482j)
| (-0.984426568089891643 - 4.1130778942974510855e-1849j)  +/-  (2.53e-481, 2.53e-481j)
| (-0.99980724048206485639 + 5.8390189784686042259e-1870j)  +/-  (6.56e-482, 6.56e-482j)
| (0.86273438597779181929 - 1.9848851469383256509e-1901j)  +/-  (6.69e-484, 6.69e-484j)
| (-0.99518472667219688624 + 5.680096626267750617e-1895j)  +/-  (2.56e-481, 2.56e-481j)
| (-0.88192126434835502971 + 4.8486449495625268771e-1912j)  +/-  (1.99e-483, 1.99e-483j)
| (-0.86273438597779181929 - 1.1910253861400678451e-1921j)  +/-  (6.75e-484, 6.75e-484j)
| (0.984426568089891643 + 4.0155536303685255991e-1932j)  +/-  (2.4e-481, 2.4e-481j)
| (0.84221723371628655087 - 1.7503046909973014445e-1935j)  +/-  (2.29e-484, 2.29e-484j)
| (0.89974828405222145968 - 1.2820302011209887942e-1934j)  +/-  (5.16e-483, 5.16e-483j)
| (0.99826561018471589329 - 3.1226285394261540471e-1932j)  +/-  (1.71e-481, 1.71e-481j)
| (-0.79732065377270713636 - 4.4920633054635756904e-1933j)  +/-  (1.56e-485, 1.56e-485j)
| (-0.96759909236025979091 + 4.0957536688922377982e-1949j)  +/-  (1.4e-481, 1.4e-481j)
| (0.88192126434835502971 + 1.2884523773882684139e-1975j)  +/-  (2.01e-483, 2.01e-483j)
| (0.77301045336273696081 - 3.1633865799714972643e-1978j)  +/-  (3.63e-486, 3.63e-486j)
| (0.99056934044357724802 + 3.0580167004260948274e-1972j)  +/-  (2.6e-481, 2.6e-481j)
| (-0.82040144352551360454 + 1.6582620293894818619e-1972j)  +/-  (5.76e-485, 5.76e-485j)
| (-0.77301045336273696081 - 5.9241596783721948447e-1978j)  +/-  (3.65e-486, 3.65e-486j)
| (0.82040144352551360454 + 7.1608686103152322129e-1986j)  +/-  (5.84e-485, 5.84e-485j)
| (0.69308736254563586978 + 8.8900473707076634895e-1989j)  +/-  (1.84e-488, 1.84e-488j)
| (0.97676588132087243254 + 7.4957410079187683754e-1982j)  +/-  (2e-481, 2e-481j)
| (-0.97676588132087243254 + 1.4967290122941661965e-1979j)  +/-  (2.01e-481, 2.01e-481j)
| (-0.60355594195357142 - 8.7811007718250064831e-2012j)  +/-  (6.29e-491, 6.29e-491j)
| (-0.89974828405222145968 + 9.5637282562557763718e-2003j)  +/-  (5.16e-483, 5.16e-483j)
| (0.79732065377270713636 + 3.4880762351632866099e-2024j)  +/-  (1.61e-485, 1.61e-485j)
| (0.72085359670291879907 - 6.7454476564517461244e-2026j)  +/-  (1.57e-487, 1.57e-487j)
| (-0.99056934044357724802 + 1.5974029212195721666e-2017j)  +/-  (2.54e-481, 2.54e-481j)
| (-0.69308736254563586978 + 2.8399979214924290749e-2046j)  +/-  (1.89e-488, 1.89e-488j)
| (-0.72085359670291879907 + 2.4551251265498570621e-2045j)  +/-  (1.6e-487, 1.6e-487j)
| (0.1370123416819680379 - 2.6644617068643667674e-2064j)  +/-  (6.4e-506, 6.4e-506j)
| (0.63439328416364549822 - 2.8489801408770070885e-2048j)  +/-  (4.59e-490, 4.59e-490j)
| (0.95694033573220886494 + 6.339063273254122491e-2039j)  +/-  (8.83e-482, 8.83e-482j)
| (-0.95694033573220886494 + 3.3144440377232794257e-2041j)  +/-  (9.05e-482, 9.05e-482j)
| (-0.57178796022761227056 + 4.212228852344154341e-2058j)  +/-  (6.89e-492, 6.89e-492j)
| (0.96759909236025979091 + 1.4457405289208552571e-2046j)  +/-  (1.42e-481, 1.42e-481j)
| (0.60355594195357142 + 2.1731356512223505817e-2058j)  +/-  (6.25e-491, 6.25e-491j)
| (0.66425243791128172114 - 5.105396021690108583e-2056j)  +/-  (3.25e-489, 3.25e-489j)
| (-0.32763017956169351687 + 8.0534267877693555288e-2069j)  +/-  (1.34e-499, 1.34e-499j)
| (-0.63439328416364549822 + 2.7499102770444359925e-2058j)  +/-  (4.59e-490, 4.59e-490j)
| (-0.84221723371628655087 + 9.0084000356606470047e-2053j)  +/-  (2.27e-484, 2.27e-484j)
| (0.94480604646687801758 - 6.5276578099788009992e-2059j)  +/-  (5.1e-482, 5.1e-482j)
| (0.53913832291100023106 - 4.1962045915986548475e-2070j)  +/-  (7.96e-493, 7.96e-493j)
| (0.058870803651189034718 - 2.4258297631477213792e-2087j)  +/-  (9.06e-509, 9.06e-509j)
| (-0.74750832686259677682 - 4.9650790674289800877e-2066j)  +/-  (7.63e-487, 7.63e-487j)
| (-0.50565737337798459744 - 6.9779810142373450968e-2073j)  +/-  (8.72e-494, 8.72e-494j)
| (0.019633692460628302085 + 9.6610170552321608391e-2088j)  +/-  (9.96e-511, 9.96e-511j)
| (0.32763017956169351687 + 8.9003551514317346385e-2078j)  +/-  (1.37e-499, 1.37e-499j)
| (0.57178796022761227056 - 1.1152789716819162432e-2068j)  +/-  (6.79e-492, 6.79e-492j)
| (-0.17579627993435450616 - 4.4998516425800541923e-2083j)  +/-  (8.6e-505, 8.6e-505j)
| (-0.47139673682599764856 + 3.5396509149908118543e-2074j)  +/-  (5.03e-495, 5.03e-495j)
| (-0.66425243791128172114 - 3.8413766986395663944e-2068j)  +/-  (3.23e-489, 3.23e-489j)
| (0.50565737337798459744 + 2.7320708812329755011e-2071j)  +/-  (8.77e-494, 8.77e-494j)
| (0.4364092406733420746 - 6.8736869987067851429e-2074j)  +/-  (4.68e-496, 4.68e-496j)
| (0.74750832686259677682 - 2.8547217544723780147e-2078j)  +/-  (7.57e-487, 7.57e-487j)
| (-0.53913832291100023106 + 1.1776458172878109658e-2085j)  +/-  (7.73e-493, 7.73e-493j)
| (-0.4364092406733420746 + 1.9722982080529846535e-2087j)  +/-  (4.57e-496, 4.57e-496j)
| (-0.058870803651189034718 + 7.420325009273873683e-2100j)  +/-  (9.4e-509, 9.4e-509j)
| (0.40074883310314096198 - 3.0594232590661167822e-2088j)  +/-  (3.74e-497, 3.74e-497j)
| (0.3644704998791496598 + 2.377235551957615878e-2089j)  +/-  (2.86e-498, 2.86e-498j)
| (-0.019633692460628302085 + 1.0257388918373950971e-2100j)  +/-  (9.96e-511, 9.96e-511j)
| (-0.40074883310314096198 + 3.8013452950352881183e-2088j)  +/-  (3.78e-497, 3.78e-497j)
| (-0.21430915306505074789 + 2.1227375204612123464e-2094j)  +/-  (2.59e-503, 2.59e-503j)
| (0.21430915306505074789 + 1.726777135759950553e-2094j)  +/-  (2.8e-503, 2.8e-503j)
| (0.29028467725446236764 - 3.1590783217373654456e-2092j)  +/-  (8.17e-501, 8.17e-501j)
| (0.25249157701515795859 - 4.8383878517287428129e-2093j)  +/-  (6.75e-502, 6.75e-502j)
| (-0.25249157701515795859 - 3.0315959817485704304e-2093j)  +/-  (6.55e-502, 6.55e-502j)
| (-0.3644704998791496598 + 2.667050679231803457e-2089j)  +/-  (2.81e-498, 2.81e-498j)
| (0.098017140329560601994 - 7.7298974187038265926e-2100j)  +/-  (3.28e-507, 3.28e-507j)
| (0.47139673682599764856 + 2.6951138436536411904e-2086j)  +/-  (5.04e-495, 5.04e-495j)
| (0.17579627993435450616 + 1.3470330373589834702e-2095j)  +/-  (8.42e-505, 8.42e-505j)
| (-0.098017140329560601994 - 1.874832844616982294e-2098j)  +/-  (3.28e-507, 3.28e-507j)
| (-0.29028467725446236764 - 6.7799006573289474936e-2092j)  +/-  (8.24e-501, 8.24e-501j)
| (-0.1370123416819680379 + 4.1496799671874746344e-2097j)  +/-  (6.29e-506, 6.29e-506j)
-------------------------------------------------
The weights are:
| (0.0125 - 2.3550406410731704275e-1814j)  +/-  (4.42e-139, 5.24e-372j)
| (0.0125 + 1.4825505341199565375e-1814j)  +/-  (2.14e-139, 2.54e-372j)
| (0.0125 - 2.6232572891414721577e-1813j)  +/-  (1.92e-139, 2.27e-372j)
| (0.0125 + 1.0602867468316937394e-1814j)  +/-  (1.17e-140, 1.39e-373j)
| (0.0125 - 2.5140997753506275891e-1814j)  +/-  (6.23e-141, 7.39e-374j)
| (0.0125 + 2.7772392564765486568e-1814j)  +/-  (5.36e-141, 6.35e-374j)
| (0.0125 + 1.919322433331105635e-1814j)  +/-  (1.67e-141, 1.98e-374j)
| (0.0125 + 1.3748607653869227182e-1813j)  +/-  (9e-141, 1.07e-373j)
| (0.0125 - 4.2857796952878034353e-1814j)  +/-  (6.55e-142, 7.76e-375j)
| (0.0125 - 3.4357736830679354114e-1815j)  +/-  (6.87e-142, 8.14e-375j)
| (0.0125 + 2.0067580833992288257e-1814j)  +/-  (2.26e-146, 2.68e-379j)
| (0.0125 - 1.8746168919924158659e-1814j)  +/-  (6.78e-142, 8.03e-375j)
| (0.0125 + 7.4229201425356824381e-1814j)  +/-  (5.09e-144, 6.03e-377j)
| (0.0125 - 6.1308094723322979286e-1814j)  +/-  (1.5e-144, 1.78e-377j)
| (0.0125 - 7.510789533566371266e-1814j)  +/-  (2.02e-146, 2.39e-379j)
| (0.0125 - 1.8949931448568239298e-1814j)  +/-  (5.65e-147, 6.7e-380j)
| (0.0125 + 2.3076286890135216081e-1814j)  +/-  (2.08e-146, 2.46e-379j)
| (0.0125 - 8.6494784982292893281e-1814j)  +/-  (4.69e-146, 5.56e-379j)
| (0.0125 + 4.142971341371566945e-1814j)  +/-  (5.01e-149, 5.94e-382j)
| (0.0125 - 1.0742299571303157387e-1813j)  +/-  (8.66e-147, 1.03e-379j)
| (0.0125 - 2.1419582642898638704e-1814j)  +/-  (6.28e-147, 7.44e-380j)
| (0.0125 + 1.6569855465878170721e-1814j)  +/-  (3.91e-150, 4.64e-383j)
| (0.0125 + 1.3552367920937369021e-1813j)  +/-  (1.82e-146, 2.16e-379j)
| (0.0125 - 4.6243733025723716408e-1814j)  +/-  (3.54e-149, 4.19e-382j)
| (0.0125 - 3.7633930006970770535e-1814j)  +/-  (2.69e-150, 3.19e-383j)
| (0.0125 + 1.8016967687191395227e-1814j)  +/-  (1.99e-149, 2.35e-382j)
| (0.0125 - 1.5129036403156311165e-1814j)  +/-  (9.06e-153, 1.07e-385j)
| (0.0125 + 5.393488736340309217e-1814j)  +/-  (2.86e-148, 3.39e-381j)
| (0.0125 + 6.4886345625049051587e-1814j)  +/-  (2.33e-148, 2.76e-381j)
| (0.0125 - 2.5045956529742708707e-1814j)  +/-  (3.94e-155, 4.67e-388j)
| (0.0125 - 9.5480993465871747072e-1814j)  +/-  (6.47e-149, 7.66e-382j)
| (0.0125 - 1.723257740481903574e-1814j)  +/-  (6.75e-151, 7.99e-384j)
| (0.0125 + 1.5532211019018309316e-1814j)  +/-  (5.79e-153, 6.86e-386j)
| (0.0125 + 2.8877742470975766589e-1814j)  +/-  (2.32e-148, 2.75e-381j)
| (0.0125 + 2.986091175801397035e-1814j)  +/-  (6.47e-155, 7.67e-388j)
| (0.0125 - 3.2008993374410419814e-1814j)  +/-  (2.86e-154, 3.39e-387j)
| (0.0125 - 1.4170403607012724714e-1814j)  +/-  (7.59e-161, 8.99e-394j)
| (0.0125 - 1.4504015330318335616e-1814j)  +/-  (2.73e-157, 3.24e-390j)
| (0.0125 + 3.5963109019778873548e-1814j)  +/-  (6.59e-153, 7.8e-386j)
| (0.0125 + 2.3257276886927355661e-1813j)  +/-  (1.18e-151, 1.4e-384j)
| (0.0125 + 2.3821955863560165307e-1814j)  +/-  (8.29e-160, 9.83e-393j)
| (0.0125 - 4.2860144972994015806e-1814j)  +/-  (1.43e-152, 1.7e-385j)
| (0.0125 + 1.4267829305335488634e-1814j)  +/-  (2.91e-159, 3.44e-392j)
| (0.0125 + 1.4788946211742636958e-1814j)  +/-  (1.64e-157, 1.94e-390j)
| (0.0125 - 1.8170022671463588906e-1814j)  +/-  (2.74e-164, 3.25e-397j)
| (0.0125 + 2.6434860749959856705e-1814j)  +/-  (1.28e-159, 1.52e-392j)
| (0.0125 + 5.2572677153730399844e-1814j)  +/-  (1.33e-155, 1.57e-388j)
| (0.0125 - 3.1228652796609659622e-1814j)  +/-  (1.49e-154, 1.76e-387j)
| (0.0125 + 1.3921742694898476667e-1814j)  +/-  (4e-162, 4.74e-395j)
| (0.0125 - 1.4540030625053435991e-1814j)  +/-  (4.62e-166, 5.48e-399j)
| (0.0125 + 3.4557365029958220863e-1814j)  +/-  (5.37e-158, 6.36e-391j)
| (0.0125 + 2.1765527700702046877e-1814j)  +/-  (2.23e-163, 2.64e-396j)
| (0.0125 + 1.4762557754015889379e-1814j)  +/-  (1.21e-166, 1.44e-399j)
| (0.0125 + 1.3667993885430607174e-1814j)  +/-  (1.18e-166, 1.39e-399j)
| (0.0125 - 1.4075163299721037273e-1814j)  +/-  (1.13e-162, 1.34e-395j)
| (0.0125 - 1.6299686181244465603e-1814j)  +/-  (1.25e-167, 1.48e-400j)
| (0.0125 - 2.0894883096978335799e-1814j)  +/-  (7.01e-165, 8.31e-398j)
| (0.0125 - 2.8024155013194823561e-1814j)  +/-  (3.94e-161, 4.66e-394j)
| (0.0125 - 1.3804062358473506397e-1814j)  +/-  (4.62e-165, 5.47e-398j)
| (0.0125 - 1.3664954144671477129e-1814j)  +/-  (1.04e-166, 1.24e-399j)
| (0.0125 - 1.6008342625009005069e-1814j)  +/-  (1.19e-161, 1.41e-394j)
| (0.0125 - 2.2735584679700189131e-1814j)  +/-  (1.53e-164, 1.82e-397j)
| (0.0125 + 2.0110078256285717135e-1814j)  +/-  (7.83e-167, 9.28e-400j)
| (0.0125 + 1.5287914927234261662e-1814j)  +/-  (4.31e-170, 5.11e-403j)
| (0.0125 + 1.363927425072521791e-1814j)  +/-  (2.75e-168, 3.26e-401j)
| (0.0125 - 1.3640685136058939584e-1814j)  +/-  (8.36e-169, 9.91e-402j)
| (0.0125 - 1.5011441945435762397e-1814j)  +/-  (1.5e-170, 1.78e-403j)
| (0.0125 - 1.9400093535942494022e-1814j)  +/-  (1.59e-169, 1.88e-402j)
| (0.0125 + 1.6705116715351228379e-1814j)  +/-  (2.22e-171, 2.63e-404j)
| (0.0125 - 1.3897615655578710157e-1814j)  +/-  (7.18e-172, 8.51e-405j)
| (0.0125 - 1.3720300942797500251e-1814j)  +/-  (1.66e-171, 1.97e-404j)
| (0.0125 + 1.3796971677655224323e-1814j)  +/-  (7.1e-172, 8.41e-405j)
| (0.0125 - 1.7149414941657139065e-1814j)  +/-  (1.85e-173, 2.19e-406j)
| (0.0125 + 1.8755896458134345832e-1814j)  +/-  (1.43e-172, 1.69e-405j)
| (0.0125 + 1.4342889203924145466e-1814j)  +/-  (2.72e-173, 3.22e-406j)
| (0.0125 + 1.3719248793423337548e-1814j)  +/-  (1.8e-172, 2.13e-405j)
| (0.0125 + 1.4022072502290435489e-1814j)  +/-  (3.08e-173, 3.65e-406j)
| (0.0125 - 1.5593494491398509478e-1814j)  +/-  (7.91e-175, 9.38e-408j)
| (0.0125 + 1.7636261183798047397e-1814j)  +/-  (4.96e-175, 6.08e-408j)
| (0.0125 + 1.593001812644478493e-1814j)  +/-  (5.09e-175, 5.99e-408j)
