Starting with polynomial:
P : 131072*t^17 - 524288*t^15 + 860160*t^13 - 745472*t^11 + 366080*t^9 - 101376*t^7 + 14784*t^5 - 960*t^3 + 18*t
Extension levels are: 17 36
-------------------------------------------------
Trying to find an order 36 Kronrod extension for:
P1 : 131072*t^17 - 524288*t^15 + 860160*t^13 - 745472*t^11 + 366080*t^9 - 101376*t^7 + 14784*t^5 - 960*t^3 + 18*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 131072*t^53 - 1703936*t^51 + 10444800*t^49 - 40140800*t^47 + 108480512*t^45 - 219174912*t^43 + 343602336*t^41 - 428197440*t^39 + 431106390*t^37 - 354465254*t^35 + 1917334783/8*t^33 - 133767543*t^31 + 987331865/16*t^29 - 376038215/16*t^27 + 3771126099/512*t^25 - 483477705/256*t^23 + 6437887335/16384*t^21 - 1074687075/16384*t^19 + 2268783825/262144*t^17 - 57998985/65536*t^15 + 71645805/1048576*t^13 - 4032015/1048576*t^11 + 20160075/134217728*t^9 - 254475/67108864*t^7 + 118755/2147483648*t^5 - 819/2147483648*t^3 + 27/34359738368*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: 1
  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
-------------------------------------------------
The nodes are:
| (0.99830815827126820805 + 1.7776970631734220235e-886j)  +/-  (4.84e-238, 4.84e-238j)
| (0.99323835774194298855 - 9.1447762160019368262e-887j)  +/-  (1.43e-237, 1.43e-237j)
| (-0.91821610688027401476 - 3.0099822779299183831e-892j)  +/-  (9.46e-238, 9.46e-238j)
| (-0.98480775301220805937 - 1.1390498217909344604e-899j)  +/-  (2.61e-237, 2.61e-237j)
| (0.93969262078590838405 + 2.3407437563454132748e-915j)  +/-  (1.64e-237, 1.64e-237j)
| (0.80212319275504378508 + 1.1099643869330127556e-918j)  +/-  (1.97e-239, 1.97e-239j)
| (0.91821610688027401476 - 4.9197651504755803393e-918j)  +/-  (1.04e-237, 1.04e-237j)
| (-0.89363264032341224819 + 5.4311478693707794711e-916j)  +/-  (5.13e-238, 5.13e-238j)
| (-0.99323835774194298855 - 7.3407815295180520333e-917j)  +/-  (1.37e-237, 1.37e-237j)
| (0.98480775301220805937 - 7.6232105107020945133e-932j)  +/-  (2.55e-237, 2.55e-237j)
| (0.86602540378443864676 + 1.9808441909405353631e-936j)  +/-  (1.98e-238, 1.98e-238j)
| (-0.99830815827126820805 + 9.1947012126994245642e-932j)  +/-  (4.92e-238, 4.92e-238j)
| (-0.93969262078590838405 + 7.7270401989458839605e-947j)  +/-  (2.09e-237, 2.09e-237j)
| (-0.80212319275504378508 + 1.085039593488508914e-962j)  +/-  (2.46e-239, 2.46e-239j)
| (0.97304487057982383883 - 7.8384011237416230444e-960j)  +/-  (3.08e-237, 3.08e-237j)
| (0.89363264032341224819 + 3.3424645885181535381e-963j)  +/-  (4.73e-238, 4.73e-238j)
| (0.68624163786873358573 + 6.0145702377304869992e-968j)  +/-  (2.37e-241, 2.37e-241j)
| (-0.97304487057982383883 + 5.7885059528397978594e-969j)  +/-  (3.24e-237, 3.24e-237j)
| (-0.7660444431189780352 + 1.0114292151096167006e-992j)  +/-  (6.05e-240, 6.05e-240j)
| (-0.95798951231548887444 + 2.2404358398949388435e-991j)  +/-  (2.83e-237, 2.83e-237j)
| (0.83548781141293641965 + 3.8586313826464582465e-1001j)  +/-  (6.89e-239, 6.89e-239j)
| (0.7660444431189780352 + 2.241484999962408668e-1003j)  +/-  (6.3e-240, 6.3e-240j)
| (0.95798951231548887444 - 3.9699771006698260151e-1002j)  +/-  (2.46e-237, 2.46e-237j)
| (-0.83548781141293641965 - 3.9639426775536454267e-1003j)  +/-  (6.48e-239, 6.48e-239j)
| (-0.72737364157304869599 - 1.0538440630201015306e-1007j)  +/-  (1.18e-240, 1.18e-240j)
| (0.2868032327110902531 + 6.0057955670394370857e-1019j)  +/-  (2.07e-249, 2.07e-249j)
| (0.72737364157304869599 + 2.3527793410078674477e-1009j)  +/-  (1.1e-240, 1.1e-240j)
| (-0.23061587074244017845 - 7.1666009312184069428e-1019j)  +/-  (1.05e-250, 1.05e-250j)
| (-0.44879918020046217279 + 4.8275401645533388099e-1013j)  +/-  (4.39e-246, 4.39e-246j)
| (-0.64278760968653932632 + 3.9499849335485590359e-1009j)  +/-  (3.52e-242, 3.52e-242j)
| (-0.86602540378443864676 + 2.7825217378545972045e-1010j)  +/-  (2.16e-238, 2.16e-238j)
| (0.64278760968653932632 + 1.5124035699114148231e-1016j)  +/-  (3.67e-242, 3.67e-242j)
| (0.59715859170278616485 - 3.722517572308746453e-1018j)  +/-  (4.03e-243, 4.03e-243j)
| (-0.11609291412523022968 - 4.5930629536185260025e-1028j)  +/-  (2.88e-253, 2.88e-253j)
| (-0.68624163786873358573 + 2.6310983217943019444e-1016j)  +/-  (2.34e-241, 2.34e-241j)
| (-0.59715859170278616485 - 2.4217259860365566429e-1021j)  +/-  (4.51e-243, 4.51e-243j)
| (0.058144828910475828539 + 4.676671138378557992e-1035j)  +/-  (9.65e-255, 9.65e-255j)
| (0.54950897807080603526 + 2.243143080747632279e-1023j)  +/-  (5.65e-244, 5.65e-244j)
| (0.34202014332566873304 + 1.1603865984159020251e-1028j)  +/-  (3.03e-248, 3.03e-248j)
| (1.2083256141880908085e-1043 + 1.6904325545393518572e-1043j)  +/-  (1.1e-1041, 1.1e-1041j)
| (-0.5 - 2.6240211059154854916e-1023j)  +/-  (5.15e-245, 5.15e-245j)
| (-0.17364817766693034885 + 4.1272896565029035511e-1033j)  +/-  (4.5e-252, 4.5e-252j)
| (0.3960797660391568237 - 6.8832465682209194303e-1028j)  +/-  (4.37e-247, 4.37e-247j)
| (0.5 - 2.2335453385856913937e-1027j)  +/-  (4.75e-245, 4.75e-245j)
| (0.11609291412523022968 + 1.4214437785153886087e-1035j)  +/-  (2.87e-253, 2.87e-253j)
| (-0.54950897807080603526 + 3.9337755975880047599e-1026j)  +/-  (5.76e-244, 5.76e-244j)
| (-0.2868032327110902531 - 4.408512254055693281e-1031j)  +/-  (1.8e-249, 1.8e-249j)
| (0.17364817766693034885 - 9.9899105182512934622e-1036j)  +/-  (4.64e-252, 4.64e-252j)
| (0.44879918020046217279 + 8.3101172859001125908e-1029j)  +/-  (5.42e-246, 5.42e-246j)
| (0.23061587074244017845 + 2.0087626726622084668e-1033j)  +/-  (9.81e-251, 9.81e-251j)
| (-0.34202014332566873304 - 7.7782222227305957915e-1030j)  +/-  (3.05e-248, 3.05e-248j)
| (-0.3960797660391568237 + 1.620365969853337048e-1028j)  +/-  (4.25e-247, 4.25e-247j)
| (-0.058144828910475828539 - 1.5763952472715212664e-1036j)  +/-  (9.65e-255, 9.65e-255j)
-------------------------------------------------
The weights are:
| (6.2607798685713069001e-05 - 3.8003895914926615799e-888j)  +/-  (5.11e-61, 1.35e-174j)
| (0.00024958453166829778858 + 1.1274580961284231434e-887j)  +/-  (4e-61, 1.06e-174j)
| (0.0029051700197339482803 - 4.0846958893917299051e-889j)  +/-  (9.01e-63, 2.38e-176j)
| (0.00055840165938973718468 - 7.586916889990478722e-890j)  +/-  (2.81e-63, 7.41e-177j)
| (0.0021662551563057589333 + 1.0269463356462322352e-887j)  +/-  (4.11e-62, 1.09e-175j)
| (0.0066036737711936087676 - 9.1436377840434150753e-888j)  +/-  (3.95e-63, 1.04e-176j)
| (0.0029051700197339482803 - 9.9894544986762550734e-888j)  +/-  (1.8e-62, 4.76e-176j)
| (0.0037300130397890169921 + 5.3129969652587721277e-889j)  +/-  (2.87e-63, 7.58e-177j)
| (0.00024958453166829778858 + 3.3767110776103979914e-890j)  +/-  (7.7e-64, 2.03e-177j)
| (0.00055840165938973718468 - 1.3409931538204808066e-887j)  +/-  (2.57e-62, 6.8e-176j)
| (0.0046296296296296296296 - 9.5496178237430042082e-888j)  +/-  (1.61e-63, 4.26e-177j)
| (6.2607798685713069001e-05 - 8.448903238675133579e-891j)  +/-  (2.63e-64, 6.95e-178j)
| (0.0021662551563057589333 + 3.0116317935034337246e-889j)  +/-  (1.81e-64, 4.79e-178j)
| (0.0066036737711936087676 - 9.8840783248388704533e-889j)  +/-  (1.39e-66, 3.66e-180j)
| (0.00098488295996840510933 + 1.139042610306738813e-887j)  +/-  (3.51e-63, 9.26e-177j)
| (0.0037300130397890169921 + 9.7591716236108516216e-888j)  +/-  (1.03e-63, 2.72e-177j)
| (0.009797637304726628042 + 8.4997645040169554012e-888j)  +/-  (5.63e-67, 1.49e-180j)
| (0.00098488295996840510933 + 1.34612753871041716e-889j)  +/-  (3.58e-65, 9.45e-179j)
| (0.0076514057623432375106 + 1.1686638813430385983e-888j)  +/-  (4.47e-68, 1.18e-181j)
| (0.0015232610054357738921 - 2.0979826377235005494e-889j)  +/-  (1.76e-65, 4.65e-179j)
| (0.0055918540181559553361 + 9.3468610118841315925e-888j)  +/-  (1.54e-65, 4.07e-179j)
| (0.0076514057623432375106 + 8.9359898579498967827e-888j)  +/-  (6.1e-67, 1.61e-180j)
| (0.0015232610054357738921 - 1.0668107957674418601e-887j)  +/-  (1.33e-64, 3.52e-178j)
| (0.0055918540181559553361 + 8.2172704805945582256e-889j)  +/-  (4.1e-68, 1.08e-181j)
| (0.0087208812137918904765 - 1.361889055279483529e-888j)  +/-  (1.1e-69, 2.91e-183j)
| (0.016995257513082744626 + 6.4463038431868129719e-888j)  +/-  (5.77e-73, 1.52e-186j)
| (0.0087208812137918904765 - 8.7217447492846897514e-888j)  +/-  (2.95e-68, 7.78e-182j)
| (0.017533635558550113409 - 3.8464643963274755857e-888j)  +/-  (9.36e-74, 2.47e-187j)
| (0.014788505478729501526 - 2.7545242835036009136e-888j)  +/-  (1.91e-73, 5.04e-187j)
| (0.010867112756175281008 - 1.7846098243989565825e-888j)  +/-  (4.16e-72, 1.1e-185j)
| (0.0046296296296296296296 - 6.6918356611525624482e-889j)  +/-  (6.41e-69, 1.69e-182j)
| (0.010867112756175281008 - 8.2695466556859532107e-888j)  +/-  (6.5e-72, 1.72e-185j)
| (0.011914844747324909751 + 8.0309994104132085328e-888j)  +/-  (6.18e-73, 1.63e-186j)
| (0.01826893398685022073 - 4.4202747485870874986e-888j)  +/-  (6.7e-76, 1.77e-189j)
| (0.009797637304726628042 + 1.567434325848891427e-888j)  +/-  (3.71e-72, 9.8e-186j)
| (0.011914844747324909751 + 2.0126871953595917255e-888j)  +/-  (1.39e-73, 3.67e-187j)
| (0.01845591071983280545 + 5.2946219522939885457e-888j)  +/-  (4.31e-77, 1.14e-190j)
| (0.012926664500362563182 - 7.7843084560450059131e-888j)  +/-  (5.16e-75, 1.36e-188j)
| (0.016352263362212759585 - 6.7256434355835166633e-888j)  +/-  (7.55e-77, 1.99e-190j)
| (0.018518518518518518519 - 5.0026224199912351803e-888j)  +/-  (1.84e-77, 4.85e-191j)
| (0.013888888888888888889 + 2.4984571412895484967e-888j)  +/-  (8.93e-77, 2.36e-190j)
| (0.017960116859128781334 + 4.1318275986357565474e-888j)  +/-  (1.82e-77, 4.79e-191j)
| (0.015613348498784570238 + 6.9998529704844394456e-888j)  +/-  (1.42e-77, 3.75e-191j)
| (0.013888888888888888889 + 7.5298544590602965678e-888j)  +/-  (3.21e-77, 8.48e-191j)
| (0.01826893398685022073 - 5.5859123576687160131e-888j)  +/-  (1.52e-78, 4.02e-192j)
| (0.012926664500362563182 - 2.250902143453414726e-888j)  +/-  (7.85e-78, 2.07e-191j)
| (0.016995257513082744626 + 3.5651276678047144219e-888j)  +/-  (3.21e-79, 8.46e-193j)
| (0.017960116859128781334 + 5.8755620324132115909e-888j)  +/-  (3.89e-79, 1.03e-192j)
| (0.014788505478729501526 - 7.268159823800103969e-888j)  +/-  (1.21e-78, 3.18e-192j)
| (0.017533635558550113409 - 6.1626563453071064322e-888j)  +/-  (2.93e-79, 7.75e-193j)
| (0.016352263362212759585 - 3.2887495870576856341e-888j)  +/-  (3.52e-80, 9.21e-194j)
| (0.015613348498784570238 + 3.0182482803541297686e-888j)  +/-  (3.49e-80, 9.07e-194j)
| (0.01845591071983280545 + 4.7108568339116124047e-888j)  +/-  (2.75e-80, 7.59e-194j)
