Starting with polynomial:
P : 65536*t^17 - 278528*t^15 + 487424*t^13 - 452608*t^11 + 239360*t^9 - 71808*t^7 + 11424*t^5 - 816*t^3 + 17*t
Extension levels are: 17 52
-------------------------------------------------
Trying to find an order 52 Kronrod extension for:
P1 : 65536*t^17 - 278528*t^15 + 487424*t^13 - 452608*t^11 + 239360*t^9 - 71808*t^7 + 11424*t^5 - 816*t^3 + 17*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 65536*t^69 - 1146880*t^67 + 9601024*t^65 - 51183616*t^63 + 195154176*t^61 - 566634368*t^59 + 1302550080*t^57 - 2433233632*t^55 + 3762299079*t^53 - 9759379773/2*t^51 + 5361157230*t^49 - 20102143425/4*t^47 + 517169301285/128*t^45 - 715773766995/256*t^43 + 854585539115/512*t^41 - 881081313945/1024*t^39 + 25100044895975/65536*t^37 - 19272728236965/131072*t^35 + 6367972006277/131072*t^33 - 1804965057467/131072*t^31 + 27964935632513/8388608*t^29 - 11498361324175/16777216*t^27 + 3986352710613/33554432*t^25 - 1154967365955/67108864*t^23 + 4425469016085/2147483648*t^21 - 864137913639/4294967296*t^19 + 33814999485/2147483648*t^17 - 8305072577/8589934592*t^15 + 12452236891/274877906944*t^13 - 858404477/549755813888*t^11 + 41396377/1099511627776*t^9 - 1298715/2199023255552*t^7 + 1514513/281474976710656*t^5 - 13107/562949953421312*t^3 + 17/562949953421312*t
-------------------------------------------------
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:   69 out of 69
Indefinite weights: 0 out of 69
Negative weights:   0 out of 69
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (-0.99041043087520515835 + 1.2978906098665336971e-785j)  +/-  (4.56e-230, 4.56e-230j)
| (0.82499747459830231554 + 2.0858636391442635058e-801j)  +/-  (8.58e-234, 8.58e-234j)
| (-0.96182564317281907041 - 3.3189305100489737749e-795j)  +/-  (1.31e-230, 1.31e-230j)
| (-0.98297309968390177828 + 3.0606546633473753394e-798j)  +/-  (3.33e-230, 3.33e-230j)
| (0.93247222940435580457 - 4.350993204683560886e-801j)  +/-  (2.56e-231, 2.56e-231j)
| (0.99041043087520515835 - 2.0020866582177917408e-800j)  +/-  (4.61e-230, 4.61e-230j)
| (0.99893297480237244441 + 5.6860401088618610928e-799j)  +/-  (7.24e-230, 7.24e-230j)
| (-0.89516329135506232207 - 7.2451874977865718666e-802j)  +/-  (3.88e-232, 3.88e-232j)
| (0.98297309968390177828 - 2.7718747423649429175e-800j)  +/-  (3.09e-230, 3.09e-230j)
| (-1 - 8.9079484274781489042e-797j)  +/-  (4.04e-230, 4.04e-230j)
| (0.87362239064636953713 - 5.5427036379803304254e-808j)  +/-  (1.11e-232, 1.11e-232j)
| (0.97343805436069282581 - 3.108685225610700322e-806j)  +/-  (2.02e-230, 2.02e-230j)
| (-0.7071067811865475244 - 4.3955841778203872399e-813j)  +/-  (1.44e-236, 1.44e-236j)
| (-0.87362239064636953713 + 3.3370035996929295052e-807j)  +/-  (1.41e-232, 1.41e-232j)
| (0.99573417629503452187 + 5.0957796571712921882e-806j)  +/-  (6.44e-230, 6.44e-230j)
| (0.89516329135506232207 - 1.1551101316018842636e-807j)  +/-  (3.48e-232, 3.48e-232j)
| (0.94816064759096585893 + 7.2870824731415978041e-807j)  +/-  (5.92e-231, 5.92e-231j)
| (-0.99573417629503452187 - 1.0444793000240324978e-802j)  +/-  (5.96e-230, 5.96e-230j)
| (-0.76933397098287890812 - 8.7705783821078323836e-818j)  +/-  (5.02e-235, 5.02e-235j)
| (-0.99893297480237244441 - 8.4739178584102986162e-811j)  +/-  (7.96e-230, 7.96e-230j)
| (0.85021713572961415213 + 3.5976326952914346717e-825j)  +/-  (3.63e-233, 3.63e-233j)
| (0.76933397098287890812 + 1.3366128229975111654e-827j)  +/-  (4.68e-235, 4.68e-235j)
| (-0.046183458645739591949 - 1.9450701974281936034e-846j)  +/-  (1.2e-254, 1.2e-254j)
| (-0.85021713572961415213 + 2.7008331472325015333e-821j)  +/-  (3.35e-233, 3.35e-233j)
| (-0.79801722728023950333 + 3.6671859152276926417e-828j)  +/-  (2.34e-234, 2.34e-234j)
| (0.96182564317281907041 + 1.0160303263484537747e-827j)  +/-  (1.19e-230, 1.19e-230j)
| (0.79801722728023950333 + 2.3665507652912472302e-833j)  +/-  (2.46e-234, 2.46e-234j)
| (-0.63884680565196131707 - 2.973813957195171511e-836j)  +/-  (3.26e-238, 3.26e-238j)
| (-0.82499747459830231554 + 1.0283815475717966382e-827j)  +/-  (8.85e-234, 8.85e-234j)
| (-0.67369564364655721171 - 1.2024988949154088896e-844j)  +/-  (2.64e-237, 2.64e-237j)
| (-0.73900891722065911592 + 4.113524061251230785e-838j)  +/-  (1.07e-235, 1.07e-235j)
| (0.67369564364655721171 - 3.7108140983203125132e-850j)  +/-  (2.49e-237, 2.49e-237j)
| (0.73900891722065911592 - 5.8395172783199474737e-848j)  +/-  (8.7e-236, 8.7e-236j)
| (-0.97343805436069282581 - 2.8615792534447226218e-841j)  +/-  (1.92e-230, 1.92e-230j)
| (-0.48660447856685628729 - 2.7380044066181681832e-872j)  +/-  (3.12e-242, 3.12e-242j)
| (-0.60263463637925638918 - 1.2765192529164167153e-868j)  +/-  (4.14e-239, 4.14e-239j)
| (1 + 2.9635753087577807179e-859j)  +/-  (4.13e-230, 4.13e-230j)
| (0.63884680565196131707 - 2.6607481388451971295e-869j)  +/-  (3.26e-238, 3.26e-238j)
| (0.91479386848802097 + 4.5408951013702797451e-862j)  +/-  (9.44e-232, 9.44e-232j)
| (-0.93247222940435580457 - 4.7244340028811940588e-859j)  +/-  (2.84e-231, 2.84e-231j)
| (-0.52643216287735580024 - 4.972113551645910379e-890j)  +/-  (4.1e-241, 4.1e-241j)
| (0.40392100487189496264 + 2.1491114002385488317e-894j)  +/-  (1.96e-244, 1.96e-244j)
| (0.56513641442259188898 + 4.2455732254107582158e-890j)  +/-  (3.69e-240, 3.69e-240j)
| (0.52643216287735580024 - 4.1308263399786171486e-891j)  +/-  (4.22e-241, 4.22e-241j)
| (-0.13815635495188219823 - 2.1587529667134266338e-901j)  +/-  (6.28e-252, 6.28e-252j)
| (-0.56513641442259188898 - 2.9421807952484841871e-888j)  +/-  (3.86e-240, 3.86e-240j)
| (-0.94816064759096585893 - 1.0733643125069607467e-885j)  +/-  (7.09e-231, 7.09e-231j)
| (0.31779141958190162617 - 2.3111154843367017546e-915j)  +/-  (9.6e-247, 9.6e-247j)
| (0.48660447856685628729 - 5.024305856011058421e-912j)  +/-  (3.32e-242, 3.32e-242j)
| (0.27366299007208286354 + 1.8484505441410681961e-916j)  +/-  (4.86e-248, 4.86e-248j)
| (5.49627914158234792e-937 - 8.3683221643489779231e-937j)  +/-  (6.91e-935, 6.91e-935j)
| (-0.4457383557765382674 - 6.3741869555643603016e-911j)  +/-  (2.72e-243, 2.72e-243j)
| (-0.91479386848802097 - 1.1922343424966663303e-911j)  +/-  (1.03e-231, 1.03e-231j)
| (0.13815635495188219823 + 2.076804900458512744e-933j)  +/-  (5.26e-252, 5.26e-252j)
| (0.60263463637925638918 - 1.9436355786020779707e-918j)  +/-  (3.91e-239, 3.91e-239j)
| (-0.27366299007208286354 - 2.3448061321255161725e-929j)  +/-  (4.9e-248, 4.9e-248j)
| (-0.40392100487189496264 + 3.3575775342871971103e-925j)  +/-  (2.05e-244, 2.05e-244j)
| (-0.22895054995013407691 + 2.0313861193236072339e-930j)  +/-  (2.29e-249, 2.29e-249j)
| (0.7071067811865475244 - 1.2055563328252058203e-925j)  +/-  (1.41e-236, 1.41e-236j)
| (0.4457383557765382674 - 8.1803348641692948649e-933j)  +/-  (2.7e-243, 2.7e-243j)
| (0.09226835946330199524 + 2.3161195661731320482e-945j)  +/-  (2.25e-253, 2.25e-253j)
| (-0.18374951781657033157 - 1.6931055815400635048e-941j)  +/-  (1.05e-250, 1.05e-250j)
| (-0.36124166618715294874 + 3.5144282661593162754e-936j)  +/-  (1.46e-245, 1.46e-245j)
| (0.046183458645739591949 + 3.4151517476480623372e-946j)  +/-  (1.2e-254, 1.2e-254j)
| (0.22895054995013407691 - 8.3442595519214239246e-940j)  +/-  (2.51e-249, 2.51e-249j)
| (0.18374951781657033157 + 5.8940023965030973908e-941j)  +/-  (1.13e-250, 1.13e-250j)
| (0.36124166618715294874 + 1.6767820220688453291e-935j)  +/-  (1.24e-245, 1.24e-245j)
| (-0.31779141958190162617 + 1.8425507357834915566e-936j)  +/-  (8.59e-247, 8.59e-247j)
| (-0.09226835946330199524 + 2.3885136091036041379e-945j)  +/-  (2.25e-253, 2.25e-253j)
-------------------------------------------------
The weights are:
| (0.014705882352941176471 - 4.9519089953358218287e-786j)  +/-  (1.27e-30, 9.22e-139j)
| (0.014705882352941176471 + 1.0513684865651001146e-787j)  +/-  (9.57e-32, 6.93e-140j)
| (0.014705882352941176471 - 6.6771972608658479793e-786j)  +/-  (3.46e-31, 2.51e-139j)
| (0.014705882352941176471 - 2.5663273724241136085e-785j)  +/-  (7.5e-31, 5.43e-139j)
| (0.014705882352941176471 - 9.9260485390018427163e-788j)  +/-  (5.96e-32, 4.32e-140j)
| (0.014705882352941176471 + 9.6357156717903363116e-788j)  +/-  (1.13e-32, 8.21e-141j)
| (0.014705882352941176471 + 9.5944353130168097185e-788j)  +/-  (3.31e-33, 2.39e-141j)
| (0.014705882352941176471 - 2.0039054945829247481e-786j)  +/-  (2.26e-34, 1.63e-142j)
| (0.014705882352941176471 - 9.6720309686890246982e-788j)  +/-  (3.82e-33, 2.77e-141j)
| (0.0073529411764705882353 + 9.9517644466532416724e-786j)  +/-  (1.76e-34, 1.27e-142j)
| (0.014705882352941176471 + 1.0239426259229771451e-787j)  +/-  (1.46e-34, 1.06e-142j)
| (0.014705882352941176471 + 9.718991441644386494e-788j)  +/-  (1.07e-33, 7.75e-142j)
| (0.014705882352941176471 + 6.7371622787812344062e-787j)  +/-  (1.94e-37, 1.4e-145j)
| (0.014705882352941176471 + 1.6342963358974547644e-786j)  +/-  (2.46e-36, 1.78e-144j)
| (0.014705882352941176471 - 9.6098876946489359724e-788j)  +/-  (2.16e-33, 1.56e-141j)
| (0.014705882352941176471 - 1.0122450475272082593e-787j)  +/-  (2.07e-35, 1.5e-143j)
| (0.014705882352941176471 + 9.8457192685622984194e-788j)  +/-  (1.29e-34, 9.35e-143j)
| (0.014705882352941176471 + 3.585187703603043111e-785j)  +/-  (6.73e-36, 4.87e-144j)
| (0.014705882352941176471 + 8.6334956832159734203e-787j)  +/-  (1.02e-39, 7.41e-148j)
| (0.014705882352941176471 - 2.2395457012446959862e-785j)  +/-  (9.99e-36, 7.24e-144j)
| (0.014705882352941176471 - 1.03696298844226349e-787j)  +/-  (2.62e-37, 1.9e-145j)
| (0.014705882352941176471 + 1.084624937610913346e-787j)  +/-  (1.29e-39, 9.31e-148j)
| (0.014705882352941176471 + 2.021402393936636848e-787j)  +/-  (2.62e-43, 1.9e-151j)
| (0.014705882352941176471 - 1.3614507457087335794e-786j)  +/-  (1.81e-39, 1.31e-147j)
| (0.014705882352941176471 - 9.9206345467996818102e-787j)  +/-  (2.79e-40, 2.02e-148j)
| (0.014705882352941176471 - 9.7768025468054483061e-788j)  +/-  (1.03e-36, 7.43e-145j)
| (0.014705882352941176471 - 1.0672294478183112289e-787j)  +/-  (2.49e-39, 1.8e-147j)
| (0.014705882352941176471 + 5.429067529099390478e-787j)  +/-  (6.31e-43, 4.57e-151j)
| (0.014705882352941176471 + 1.1538773655524652007e-786j)  +/-  (2.07e-40, 1.5e-148j)
| (0.014705882352941176471 - 6.0264399992768129139e-787j)  +/-  (1.52e-42, 1.1e-150j)
| (0.014705882352941176471 - 7.5920889830201435567e-787j)  +/-  (1.47e-41, 1.07e-149j)
| (0.014705882352941176471 - 1.1469597348989250512e-787j)  +/-  (1.66e-45, 1.2e-153j)
| (0.014705882352941176471 - 1.1036436386456523045e-787j)  +/-  (9.08e-44, 6.58e-152j)
| (0.014705882352941176471 + 1.1245700678573950957e-785j)  +/-  (1.38e-41, 9.99e-150j)
| (0.014705882352941176471 + 3.788487717052738573e-787j)  +/-  (3.03e-47, 2.19e-155j)
| (0.014705882352941176471 - 4.9220778841769516845e-787j)  +/-  (5.4e-45, 3.91e-153j)
| (0.0073529411764705882353 - 4.7946459499632317412e-788j)  +/-  (2.4e-41, 1.74e-149j)
| (0.014705882352941176471 + 1.1714925177474156947e-787j)  +/-  (9.69e-48, 7.01e-156j)
| (0.014705882352941176471 + 1.0018152188258556392e-787j)  +/-  (2.68e-42, 1.94e-150j)
| (0.014705882352941176471 - 3.2943077522053217458e-786j)  +/-  (9.12e-45, 6.6e-153j)
| (0.014705882352941176471 - 4.1136897862417813739e-787j)  +/-  (6.31e-48, 4.57e-156j)
| (0.014705882352941176471 + 1.368873004757578819e-787j)  +/-  (5.97e-52, 4.32e-160j)
| (0.014705882352941176471 + 1.2270042961724545427e-787j)  +/-  (3.21e-50, 2.33e-158j)
| (0.014705882352941176471 - 1.2583129389558329253e-787j)  +/-  (7.53e-51, 5.45e-159j)
| (0.014705882352941176471 + 2.2395465343102753246e-787j)  +/-  (2.04e-54, 1.48e-162j)
| (0.014705882352941176471 + 4.4880773060742240643e-787j)  +/-  (1.44e-49, 1.04e-157j)
| (0.014705882352941176471 + 4.5175679369688336454e-786j)  +/-  (7.64e-47, 5.53e-155j)
| (0.014705882352941176471 + 1.4589970664029273741e-787j)  +/-  (1.64e-54, 1.19e-162j)
| (0.014705882352941176471 + 1.292243327996905378e-787j)  +/-  (8.34e-53, 6.04e-161j)
| (0.014705882352941176471 - 1.5099302227633758897e-787j)  +/-  (4.49e-55, 3.25e-163j)
| (0.014705882352941176471 - 1.9271431343840002446e-787j)  +/-  (2.85e-56, 2.07e-164j)
| (0.014705882352941176471 - 3.5042418169688164158e-787j)  +/-  (1.93e-54, 1.39e-162j)
| (0.014705882352941176471 + 2.5241330762845717706e-786j)  +/-  (6e-50, 4.34e-158j)
| (0.014705882352941176471 + 1.6912270377360298779e-787j)  +/-  (5.18e-57, 3.75e-165j)
| (0.014705882352941176471 - 1.1981222008785610828e-787j)  +/-  (4.07e-53, 2.95e-161j)
| (0.014705882352941176471 - 2.6629500901329106986e-787j)  +/-  (3.18e-57, 2.3e-165j)
| (0.014705882352941176471 + 3.2543854628389191007e-787j)  +/-  (5.62e-56, 4.07e-164j)
| (0.014705882352941176471 + 2.5065833537667254982e-787j)  +/-  (1.59e-57, 1.15e-165j)
| (0.014705882352941176471 + 1.1243848654463640594e-787j)  +/-  (3.11e-54, 2.25e-162j)
| (0.014705882352941176471 - 1.3290145699517951992e-787j)  +/-  (3.12e-56, 2.26e-164j)
| (0.014705882352941176471 - 1.7629075946758114942e-787j)  +/-  (1.17e-58, 8.48e-167j)
| (0.014705882352941176471 - 2.3661276146996559383e-787j)  +/-  (2.49e-58, 1.8e-166j)
| (0.014705882352941176471 - 3.0336259032796726904e-787j)  +/-  (5.62e-58, 4.07e-166j)
| (0.014705882352941176471 + 1.8412829569783207615e-787j)  +/-  (6.88e-59, 4.98e-167j)
| (0.014705882352941176471 + 1.5652974730983550457e-787j)  +/-  (1.3e-59, 9.42e-168j)
| (0.014705882352941176471 - 1.625555925500352808e-787j)  +/-  (1.11e-59, 8.02e-168j)
| (0.014705882352941176471 - 1.4120961053718338432e-787j)  +/-  (1.49e-59, 1.09e-167j)
| (0.014705882352941176471 + 2.8376579163598672474e-787j)  +/-  (3.29e-60, 2.49e-168j)
| (0.014705882352941176471 - 2.1251233216193995256e-787j)  +/-  (3.23e-60, 2.27e-168j)
