Starting with polynomial:
P : 4*t^2 - 1
Extension levels are: 2 6 54
-------------------------------------------------
Trying to find an order 6 Kronrod extension for:
P1 : 4*t^2 - 1
Solvable: 1
-------------------------------------------------
Trying to find an order 54 Kronrod extension for:
P2 : 4*t^8 - 7*t^6 + 15/4*t^4 - 5/8*t^2 + 1/64
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 4*t^62 - 61*t^60 + 885/2*t^58 - 32509/16*t^56 + 212135/32*t^54 - 2093553/128*t^52 + 8117109/256*t^50 - 202927725/4096*t^48 + 520232895/8192*t^46 - 2215806775/32768*t^44 + 3955006055/65536*t^42 - 23813008485/524288*t^40 + 30349912775/1048576*t^38 - 65649195941/4194304*t^36 + 60290077905/8388608*t^34 - 751616304549/268435456*t^32 + 495746924277/536870912*t^30 - 551534301945/2147483648*t^28 + 257382674241/4294967296*t^26 - 400236215925/34359738368*t^24 + 128447901855/68719476736*t^22 - 67282234305/274877906944*t^20 + 14172532725/549755813888*t^18 - 18855630495/8796093022208*t^16 + 2417388525/17592186044416*t^14 - 463120749/70368744177664*t^12 + 31773357/140737488355328*t^10 - 5883955/1125899906842624*t^8 + 168113/2251799813685248*t^6 - 5115/9007199254740992*t^4 + 31/18014398509481984*t^2 - 1/1152921504606846976
-------------------------------------------------
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
Positive weights:   62 out of 62
Indefinite weights: 0 out of 62
Negative weights:   0 out of 62
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (0.62348980185873353053 + 2.7403951810344254912e-857j)  +/-  (3.1e-240, 3.1e-240j)
| (-0.98883082622512854507 - 6.196449171950993211e-848j)  +/-  (6.03e-234, 6.03e-234j)
| (-0.93969262078590838405 + 1.9409019461050623242e-851j)  +/-  (2.93e-234, 2.93e-234j)
| (0.98017248784854384262 + 8.8882962094842412833e-849j)  +/-  (8.19e-234, 8.19e-234j)
| (0.92147621187040765365 + 5.2930417468283132868e-858j)  +/-  (2.05e-234, 2.05e-234j)
| (0.90096886790241912624 - 1.0704233377755610167e-864j)  +/-  (9.3e-235, 9.3e-235j)
| (0.96907728622907794773 + 2.2568586201419319315e-870j)  +/-  (6.57e-234, 6.57e-234j)
| (-0.87822157337022853557 - 4.6349213868073733179e-883j)  +/-  (4.11e-235, 4.11e-235j)
| (0.99503077536540140991 + 1.8212935693528472742e-879j)  +/-  (3.6e-234, 3.6e-234j)
| (-0.95557280578614073281 - 3.6209907756730191486e-890j)  +/-  (4.84e-234, 4.84e-234j)
| (0.85329088163215566029 - 7.387831171992355269e-891j)  +/-  (1.51e-235, 1.51e-235j)
| (0.17364817766693034885 - 1.3711829884452159928e-908j)  +/-  (2.49e-251, 2.49e-251j)
| (-0.92147621187040765365 - 9.4069053317726421013e-892j)  +/-  (1.98e-234, 1.98e-234j)
| (-0.85329088163215566029 + 9.9310291920521033875e-893j)  +/-  (1.38e-235, 1.38e-235j)
| (-0.99875692121892236975 - 2.3351572929836249561e-891j)  +/-  (1.15e-234, 1.15e-234j)
| (0.87822157337022853557 + 1.3929861788123521607e-890j)  +/-  (3.7e-235, 3.7e-235j)
| (0.93969262078590838405 + 2.3409377650205016768e-888j)  +/-  (3.56e-234, 3.56e-234j)
| (-0.98017248784854384262 + 4.885233869385818907e-900j)  +/-  (7.12e-234, 7.12e-234j)
| (-0.7660444431189780352 - 1.0671616614064309036e-906j)  +/-  (2.86e-237, 2.86e-237j)
| (-0.90096886790241912624 - 5.8875606289422997865e-904j)  +/-  (9.21e-235, 9.21e-235j)
| (0.82623877431599487195 - 6.6601794137260027275e-902j)  +/-  (4.5e-236, 4.5e-236j)
| (0.73305187182982632852 - 3.4267345495492860028e-906j)  +/-  (5.75e-238, 5.75e-238j)
| (-0.36534102436639501454 - 2.2087293759072714638e-917j)  +/-  (2.19e-246, 2.19e-246j)
| (-0.69823681808607283034 - 5.3470043914897584603e-908j)  +/-  (1.08e-238, 1.08e-238j)
| (-0.79713250722292247934 - 1.9285668812760917934e-905j)  +/-  (1.52e-236, 1.52e-236j)
| (0.95557280578614073281 + 1.0053103188187710262e-900j)  +/-  (4.77e-234, 4.77e-234j)
| (0.7660444431189780352 + 1.6448380204613029831e-917j)  +/-  (2.87e-237, 2.87e-237j)
| (-0.99503077536540140991 - 7.1586645627529403234e-912j)  +/-  (3.48e-234, 3.48e-234j)
| (-0.17364817766693034885 - 3.7782660101143778328e-936j)  +/-  (2.72e-251, 2.72e-251j)
| (-0.66168583759685941524 - 1.2821864365144432974e-922j)  +/-  (2.31e-239, 2.31e-239j)
| (-0.96907728622907794773 + 3.580470569041115182e-918j)  +/-  (6.86e-234, 6.86e-234j)
| (0.69823681808607283034 + 1.7864390326413770763e-922j)  +/-  (1.21e-238, 1.21e-238j)
| (0.66168583759685941524 + 9.2766600909455161725e-926j)  +/-  (2.14e-239, 2.14e-239j)
| (0.98883082622512854507 + 2.0798760711815190698e-922j)  +/-  (5.5e-234, 5.5e-234j)
| (-0.62348980185873353053 - 2.6612214718177361566e-952j)  +/-  (3.08e-240, 3.08e-240j)
| (-0.73305187182982632852 + 9.2450007722022647554e-950j)  +/-  (5.37e-238, 5.37e-238j)
| (0.22252093395631440429 - 6.4909199865079453742e-962j)  +/-  (4.78e-250, 4.78e-250j)
| (0.58374367223478987045 - 5.0419888460914328278e-952j)  +/-  (3.32e-241, 3.32e-241j)
| (0.79713250722292247934 + 8.1659560507024735037e-947j)  +/-  (1.38e-236, 1.38e-236j)
| (0.99875692121892236975 - 2.7432562965994058401e-958j)  +/-  (1.01e-234, 1.01e-234j)
| (-0.58374367223478987045 + 7.4882769859459590032e-971j)  +/-  (3.78e-241, 3.78e-241j)
| (-0.22252093395631440429 + 8.7843757008189295763e-981j)  +/-  (4.62e-250, 4.62e-250j)
| (0.45621065735316296398 - 3.2707508771330811334e-975j)  +/-  (4.15e-244, 4.15e-244j)
| (0.54254626386575940578 + 6.1687320455214115208e-974j)  +/-  (4.58e-242, 4.58e-242j)
| (-0.024930691738072875282 - 1.1928186587189608657e-988j)  +/-  (2.44e-255, 2.44e-255j)
| (-0.54254626386575940578 + 1.7511900503995644285e-971j)  +/-  (4.37e-242, 4.37e-242j)
| (-0.5 - 4.5106873483609675304e-973j)  +/-  (4.43e-243, 4.43e-243j)
| (0.024930691738072875282 - 2.8442044244964147669e-986j)  +/-  (2.44e-255, 2.44e-255j)
| (0.5 - 2.5261668437154123797e-974j)  +/-  (5.52e-243, 5.52e-243j)
| (0.27084046814300511738 - 5.4235954852156906341e-980j)  +/-  (1.13e-248, 1.13e-248j)
| (-0.12434370464748517431 + 5.7170898955545274447e-984j)  +/-  (1.26e-252, 1.26e-252j)
| (-0.41128710313061153946 + 6.0156195586308948556e-975j)  +/-  (3.56e-245, 3.56e-245j)
| (-0.074730093586424254291 - 1.533007435538822351e-985j)  +/-  (5.07e-254, 5.07e-254j)
| (0.31848665025168442738 + 1.0345217191505193695e-978j)  +/-  (1.41e-247, 1.41e-247j)
| (0.36534102436639501454 + 5.9440148418570774646e-978j)  +/-  (2.2e-246, 2.2e-246j)
| (-0.82623877431599487195 + 3.1490095274131800319e-981j)  +/-  (5.1e-236, 5.1e-236j)
| (-0.45621065735316296398 - 2.9232766791469649623e-990j)  +/-  (4.18e-244, 4.18e-244j)
| (-0.31848665025168442738 + 8.7297764832312710076e-994j)  +/-  (1.56e-247, 1.56e-247j)
| (0.12434370464748517431 - 2.1060151336173923122e-999j)  +/-  (1.26e-252, 1.26e-252j)
| (0.41128710313061153946 + 4.5072344236040097644e-991j)  +/-  (2.86e-245, 2.86e-245j)
| (0.074730093586424254291 + 2.2046031969212132262e-1002j)  +/-  (5.05e-254, 5.05e-254j)
| (-0.27084046814300511738 + 6.0409752488380823263e-996j)  +/-  (9.21e-249, 9.21e-249j)
-------------------------------------------------
The weights are:
| (0.009702547094891384161 - 6.1454757358713919313e-850j)  +/-  (2.81e-51, 1.85e-162j)
| (0.00035259677947507354912 - 1.4605975878413337318e-849j)  +/-  (9.19e-52, 6.06e-163j)
| (0.0018567901339763648 - 2.3496202885801223417e-849j)  +/-  (7.05e-52, 4.65e-163j)
| (0.00062320466769517735201 - 2.2703601813113527849e-850j)  +/-  (2.52e-52, 1.66e-163j)
| (0.0023949458882057711877 - 4.4032306810292872879e-850j)  +/-  (4.23e-52, 2.79e-163j)
| (0.0029881761757243370593 + 4.3328318180134217896e-850j)  +/-  (3.46e-52, 2.28e-163j)
| (0.0009664954494426306701 + 8.048315477489812316e-850j)  +/-  (1.36e-52, 8.96e-164j)
| (0.0036305852074146078907 + 2.050110809144942752e-849j)  +/-  (3.52e-54, 2.33e-165j)
| (0.00015736120755123934427 + 8.9220715471912717336e-851j)  +/-  (1.33e-53, 8.76e-165j)
| (0.0013790573466984533973 + 2.5774005332470699978e-849j)  +/-  (3.05e-54, 2.01e-165j)
| (0.0043157884337050558414 + 4.4745503535200507404e-850j)  +/-  (4.19e-54, 2.76e-165j)
| (0.015394385879253241143 - 9.8996388012102129588e-850j)  +/-  (7.74e-56, 5.11e-167j)
| (0.0023949458882057711877 + 2.2119300920627734117e-849j)  +/-  (2.57e-54, 1.7e-165j)
| (0.0043157884337050558414 - 1.992991964919899524e-849j)  +/-  (3.13e-55, 2.06e-166j)
| (3.9438290750782461032e-05 + 2.4600678674368307775e-850j)  +/-  (3.16e-56, 2.08e-167j)
| (0.0036305852074146078907 - 4.3697666331816801298e-850j)  +/-  (5.67e-55, 3.74e-166j)
| (0.0018567901339763648 + 4.6734194080840818677e-850j)  +/-  (6.02e-55, 3.97e-166j)
| (0.00062320466769517735201 + 4.463167334144357812e-849j)  +/-  (1.69e-55, 1.12e-166j)
| (0.0065583477962942035805 + 1.8567493534101660209e-849j)  +/-  (4.71e-58, 3.11e-169j)
| (0.0029881761757243370593 - 2.1200272501657954475e-849j)  +/-  (2.67e-55, 1.76e-166j)
| (0.0050369759970921030592 - 4.6274183970542565129e-850j)  +/-  (6.41e-57, 4.23e-168j)
| (0.0073434119556632995691 + 5.2830205304641075846e-850j)  +/-  (2.04e-58, 1.35e-169j)
| (0.013754379935157351814 + 1.4573509938850908883e-849j)  +/-  (2.45e-61, 1.62e-172j)
| (0.0081343705693497847245 + 1.7769465534130748228e-849j)  +/-  (1.18e-59, 7.78e-171j)
| (0.0057869804115634514493 - 1.8987341410241410687e-849j)  +/-  (3.23e-58, 2.13e-169j)
| (0.0013790573466984533973 - 5.4221143019933431847e-850j)  +/-  (2.68e-57, 1.77e-168j)
| (0.0065583477962942035805 - 5.0373220806406089977e-850j)  +/-  (6e-59, 3.96e-170j)
| (0.00015736120755123934427 - 1.5719604388097540593e-849j)  +/-  (3.95e-57, 2.61e-168j)
| (0.015394385879253241143 + 1.2883721581258003351e-849j)  +/-  (1.22e-63, 8.06e-175j)
| (0.0089233627352975013834 - 1.7378571921458995256e-849j)  +/-  (3.65e-61, 2.41e-172j)
| (0.0009664954494426306701 - 3.0368260606324112424e-849j)  +/-  (7.59e-57, 5.01e-168j)
| (0.0081343705693497847245 - 5.551157359274682478e-850j)  +/-  (6.98e-61, 4.6e-172j)
| (0.0089233627352975013834 + 5.8392941183524631222e-850j)  +/-  (1.87e-61, 1.24e-172j)
| (0.00035259677947507354912 - 3.5091735464963558205e-850j)  +/-  (2.26e-60, 1.49e-171j)
| (0.009702547094891384161 + 1.6988032684142066531e-849j)  +/-  (4.11e-63, 2.71e-174j)
| (0.0073434119556632995691 - 1.8164083745542157082e-849j)  +/-  (2.67e-61, 1.76e-172j)
| (0.015087054507162056557 + 9.4849075339651338471e-850j)  +/-  (2.09e-66, 1.38e-177j)
| (0.01046417976390225736 + 6.4680549009419108887e-850j)  +/-  (4.21e-64, 2.78e-175j)
| (0.0057869804115634514493 + 4.8172802436100720843e-850j)  +/-  (2.38e-61, 1.57e-172j)
| (3.9438290750782461032e-05 - 1.763285750802303914e-851j)  +/-  (4.1e-62, 2.71e-173j)
| (0.01046417976390225736 - 1.6595630160717302729e-849j)  +/-  (4.01e-65, 2.65e-176j)
| (0.015087054507162056557 - 1.3310424371097729365e-849j)  +/-  (9.74e-68, 6.42e-179j)
| (0.012569394224085633892 - 7.5203312952406687217e-850j)  +/-  (3.42e-67, 2.26e-178j)
| (0.01120069129468739317 - 6.8055848688090522465e-850j)  +/-  (1.12e-65, 7.42e-177j)
| (0.015863150168404145792 - 1.1597093564972850716e-849j)  +/-  (1.61e-69, 1.06e-180j)
| (0.01120069129468739317 + 1.6199952037945463597e-849j)  +/-  (2.3e-67, 1.52e-178j)
| (0.011904761904761904762 - 1.5800163022922168845e-849j)  +/-  (3.93e-68, 2.59e-179j)
| (0.015863150168404145792 + 1.1168923845196141974e-849j)  +/-  (4.37e-70, 2.88e-181j)
| (0.011904761904761904762 + 7.1567519168869458187e-850j)  +/-  (6.24e-68, 4.12e-179j)
| (0.014708657790731394129 - 9.0760484025631036141e-850j)  +/-  (4.89e-70, 3.23e-181j)
| (0.015627597509754586887 - 1.2455378956969571036e-849j)  +/-  (1.68e-70, 1.11e-181j)
| (0.013187982838070312819 - 1.4986918259486714955e-849j)  +/-  (1.14e-70, 7.49e-182j)
| (0.015784371636707369405 + 1.2026214094324234198e-849j)  +/-  (1.22e-70, 8.04e-182j)
| (0.014262956406531130788 + 8.6740989815285797525e-850j)  +/-  (4.39e-71, 2.9e-182j)
| (0.013754379935157351814 - 8.2801122744193111641e-850j)  +/-  (2.94e-71, 1.94e-182j)
| (0.0050369759970921030592 + 1.9435343463770624146e-849j)  +/-  (3.42e-70, 2.25e-181j)
| (0.012569394224085633892 + 1.5395850598805014754e-849j)  +/-  (3.66e-71, 2.41e-182j)
| (0.014262956406531130788 - 1.4155955396986259267e-849j)  +/-  (4.65e-72, 3.07e-183j)
| (0.015627597509754586887 + 1.0319219717351903137e-849j)  +/-  (1.04e-72, 6.9e-184j)
| (0.013187982838070312819 + 7.8951588461012616691e-850j)  +/-  (1.69e-72, 1.12e-183j)
| (0.015784371636707369405 - 1.0742643985802979545e-849j)  +/-  (8.31e-73, 5.55e-184j)
| (0.014708657790731394129 + 1.3734729972884833001e-849j)  +/-  (6.37e-73, 4.06e-184j)
