Starting with polynomial:
P : t^4 - 6*t^2 + 3
Extension levels are: 4 10 21
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Trying to find an order 10 Kronrod extension for:
P1 : t^4 - 6*t^2 + 3
Solvable: 1
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Trying to find an order 21 Kronrod extension for:
P2 : t^14 - 477/7*t^12 + 11241/7*t^10 - 112815/7*t^8 + 68715*t^6 - 108945*t^4 + 46845*t^2 - 2835
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^35 - 14602558521974242835294663578251/34192744932325195010790009931*t^33 + 35430736227998594174048418889694574/444505684120227535140270129103*t^31 - 26739889816070122155506965583817256710/3111539788841592745981890903721*t^29 + 1855295758756521871633264433905809458370/3111539788841592745981890903721*t^27 - 961248181396554029139704600388855863542290/34226937677257520205800799940931*t^25 + 31611817456056376264629221144820881717585790/34226937677257520205800799940931*t^23 - 105098839146474992485655693827634676320111910/4889562525322502886542971420133*t^21 + 1736779187201763322549255875828903007240479300/4889562525322502886542971420133*t^19 - 20281838454596826863278878948407539499290242600/4889562525322502886542971420133*t^17 + 165285300057057092984969360561723286175328907150/4889562525322502886542971420133*t^15 - 920442044629788177877472185881060033366563608650/4889562525322502886542971420133*t^13 + 261088255264203182077630300596751590178653951150/376120194255577145118690109241*t^11 - 55351148663453854916098251443928134075256834750/34192744932325195010790009931*t^9 + 10875289396171623593266363308793580272520589750/4884677847475027858684287133*t^7 - 7832002179841938121196963320382740906788095250/4884677847475027858684287133*t^5 + 2299898045864887188776939493575407290648603375/4884677847475027858684287133*t^3 - 128915419102045609903091065023757731672658875/4884677847475027858684287133*t
-------------------------------------------------
Computing nodes and weights
  current precision for roots: 53
  current precision for roots: 106
 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:
| (-3.7639349845003366709 + 1.3765216552130098837e-988j)  +/-  (4.16e-248, 4.16e-248j)
| (1.2002565703744637986 + 1.8519174668889535422e-992j)  +/-  (1.58e-251, 1.58e-251j)
| (-6.8992631581478644016 + 4.0823088846387395609e-989j)  +/-  (1.32e-247, 1.32e-247j)
| (8.5106683650681247269 + 5.4328631387869921922e-989j)  +/-  (2.29e-248, 2.29e-248j)
| (-9.5311710697915310512 + 5.2314511773397456542e-991j)  +/-  (2.64e-249, 2.64e-249j)
| (-8.5106683650681247269 + 1.3185613785375432541e-989j)  +/-  (2.43e-248, 2.43e-248j)
| (3.7639349845003366709 + 1.95043413938322073e-988j)  +/-  (4.07e-248, 4.07e-248j)
| (4.9040503098670620638 + 5.2582896088228170201e-1000j)  +/-  (1.32e-247, 1.32e-247j)
| (-7.6609958515756716808 + 7.197499424647478251e-1015j)  +/-  (6.78e-248, 6.78e-248j)
| (5.5317060638607199116 - 1.1252143655911362407e-1024j)  +/-  (1.83e-247, 1.83e-247j)
| (-2.8184875591789979264 + 1.1898512771683638816e-1044j)  +/-  (5.55e-249, 5.55e-249j)
| (6.1944744885532180613 - 4.5931193927028994271e-1066j)  +/-  (1.64e-247, 1.64e-247j)
| (7.6609958515756716808 + 4.5345153074248050406e-1090j)  +/-  (6.96e-248, 6.96e-248j)
| (-4.3114957943342286437 + 1.7875493060422604601e-1096j)  +/-  (7.54e-248, 7.54e-248j)
| (2.8184875591789979264 + 6.3015265609034757643e-1097j)  +/-  (5.99e-249, 5.99e-249j)
| (1.4656205133845524345 - 3.5677581089481918691e-1102j)  +/-  (6.75e-251, 6.75e-251j)
| (4.3114957943342286437 + 9.8228789845624650165e-1099j)  +/-  (7.98e-248, 7.98e-248j)
| (9.5311710697915310512 + 1.6877551258451765495e-1106j)  +/-  (2.83e-249, 2.83e-249j)
| (-0.74196378430272585765 + 1.5852481685206910527e-1111j)  +/-  (5.72e-253, 5.72e-253j)
| (-3.2762772292662860982 - 2.3182145355840008672e-1106j)  +/-  (1.66e-248, 1.66e-248j)
| (0.74196378430272585765 - 1.2168241702970799334e-1111j)  +/-  (5.69e-253, 5.69e-253j)
| (-6.1944744885532180613 - 2.4533672342080483171e-1106j)  +/-  (1.81e-247, 1.81e-247j)
| (-4.9040503098670620638 - 1.168453311888104874e-1108j)  +/-  (1.24e-247, 1.24e-247j)
| (6.8992631581478644016 - 3.9204901054578583886e-1109j)  +/-  (1.39e-247, 1.39e-247j)
| (-0.26842728825432580984 + 9.8141521297915410109e-1119j)  +/-  (4.95e-254, 4.95e-254j)
| (3.2762772292662860982 - 1.2686947246886566013e-1113j)  +/-  (1.74e-248, 1.74e-248j)
| (1.8397904266075822243 - 6.4115095615240589324e-1116j)  +/-  (2.77e-250, 2.77e-250j)
| (-5.5317060638607199116 - 1.7963073380253209806e-1115j)  +/-  (1.69e-247, 1.69e-247j)
| (-1.4656205133845524345 - 4.917833961610246697e-1118j)  +/-  (7.05e-251, 7.05e-251j)
| (-1.8397904266075822243 - 8.8402249885990651205e-1117j)  +/-  (2.69e-250, 2.69e-250j)
| (-1.2002565703744637986 - 2.1539252120115722437e-1118j)  +/-  (1.65e-251, 1.65e-251j)
| (-2.3344142183389772393 - 9.5753556064003086258e-1119j)  +/-  (1.16e-249, 1.16e-249j)
| (2.3344142183389772393 + 4.2269179395096236005e-1119j)  +/-  (1.17e-249, 1.17e-249j)
| (0.26842728825432580984 + 1.199367169555816014e-1123j)  +/-  (3.11e-254, 3.11e-254j)
| (-4.1732989253412995606e-1252 - 9.5297796884323463023e-1251j)  +/-  (3.34e-1249, 3.34e-1249j)
-------------------------------------------------
The weights are:
| (0.00017362535084538573795 + 8.6567828961994154618e-992j)  +/-  (3.16e-83, 5.11e-206j)
| (0.076478665538196355079 - 1.5583683873221609507e-989j)  +/-  (2.71e-67, 4.38e-190j)
| (1.342736260725539166e-11 + 4.2578666359193229722e-998j)  +/-  (1.78e-92, 2.88e-215j)
| (6.8056640408691447333e-17 - 1.8658178448080982266e-1001j)  +/-  (6.89e-97, 1.11e-219j)
| (8.8046544495310886826e-21 - 7.3053293173115086906e-1004j)  +/-  (8.74e-98, 1.41e-220j)
| (6.8056640408691447333e-17 + 1.583028657879902138e-1001j)  +/-  (5.6e-96, 9.05e-219j)
| (0.00017362535084538573795 - 1.2593972818119395547e-991j)  +/-  (4.24e-87, 6.84e-210j)
| (1.4603646030259957498e-06 + 4.2436484941611588372e-994j)  +/-  (9.46e-91, 1.53e-213j)
| (5.735176371030755269e-14 - 1.0709710269887353135e-999j)  +/-  (1.93e-95, 3.12e-218j)
| (5.8283096513337657795e-08 - 2.4170692184617404963e-995j)  +/-  (1.2e-92, 1.94e-215j)
| (0.00350804789303054478 + 4.4349071371608746962e-991j)  +/-  (3.65e-86, 5.9e-209j)
| (1.2661155888499371608e-09 + 1.225077363906292071e-996j)  +/-  (1.49e-94, 2.4e-217j)
| (5.735176371030755269e-14 + 1.2958864559562520674e-999j)  +/-  (7.69e-98, 1.24e-220j)
| (2.1005343270391736037e-05 + 6.0902412305730334073e-993j)  +/-  (6.95e-92, 1.12e-214j)
| (0.00350804789303054478 - 7.1058242081122870623e-991j)  +/-  (4.45e-88, 7.19e-211j)
| (0.031495023636390003241 + 1.3430042957403039481e-989j)  +/-  (3.4e-83, 5.48e-206j)
| (2.1005343270391736037e-05 - 8.2383688039196567526e-993j)  +/-  (4.87e-91, 7.86e-214j)
| (8.8046544495310886826e-21 + 8.4329395443986010198e-1004j)  +/-  (8.42e-102, 1.36e-224j)
| (0.14602632808656426995 - 7.810848707132554505e-991j)  +/-  (5.04e-83, 8.15e-206j)
| (0.00085875586622269928947 - 2.4558011578261012863e-991j)  +/-  (1.74e-90, 2.81e-213j)
| (0.14602632808656426995 + 1.2539487341177729453e-989j)  +/-  (5.54e-84, 8.94e-207j)
| (1.2661155888499371608e-09 - 1.0089645205087947057e-996j)  +/-  (7.3e-97, 1.18e-219j)
| (1.4603646030259957498e-06 - 3.2621817905772268449e-994j)  +/-  (7.61e-95, 1.23e-217j)
| (1.342736260725539166e-11 - 4.8457952935233936076e-998j)  +/-  (6.88e-98, 1.11e-220j)
| (0.17235610557276633886 - 7.7968695139915691442e-990j)  +/-  (3.54e-87, 5.72e-210j)
| (0.00085875586622269928947 + 3.6739253255787767092e-991j)  +/-  (1.07e-91, 1.73e-214j)
| (0.035000623278839521639 - 5.1185264815214669029e-990j)  +/-  (1.64e-89, 2.66e-212j)
| (5.8283096513337657795e-08 + 1.9222491324062482081e-995j)  +/-  (3.51e-96, 5.67e-219j)
| (0.031495023636390003241 - 5.1403908787854722634e-990j)  +/-  (1.83e-90, 2.95e-213j)
| (0.035000623278839521639 + 2.4340677913499257754e-990j)  +/-  (2.07e-91, 3.34e-214j)
| (0.076478665538196355079 + 4.584396766501796846e-990j)  +/-  (1.69e-90, 2.73e-213j)
| (0.013013961824612033931 - 9.1795740345655244856e-991j)  +/-  (3e-92, 4.84e-215j)
| (0.013013961824612033931 + 1.6313252782028901656e-990j)  +/-  (2.66e-92, 4.3e-215j)
| (0.17235610557276633886 - 1.8623379523534909357e-989j)  +/-  (4.59e-91, 7.36e-214j)
| (0.042132675363925090273 + 1.9529278318776719997e-989j)  +/-  (5.69e-91, 9.21e-214j)
