Starting with polynomial:
P : t^4 - 6*t^2 + 3
Extension levels are: 4 10 23
-------------------------------------------------
Trying to find an order 10 Kronrod extension for:
P1 : t^4 - 6*t^2 + 3
Solvable: 1
-------------------------------------------------
Trying to find an order 23 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^37 - 6226182996938848703671947830267937459/9317405211111424789646489158029125*t^35 + 1701569291963629280644285373462088586314/9317405211111424789646489158029125*t^33 - 258921363264247493928437277716237672558172/9317405211111424789646489158029125*t^31 + 64550863379083319227901606179277777991378984/24225253548889704453080871810875725*t^29 - 2237403230307982824204075877211952093325520472/13044367295555994705505084821240775*t^27 + 1301824950326976875322138441601756371669444509892/169576774842227931171566102676130075*t^25 - 41293931112551612462680410155624348980525323604692/169576774842227931171566102676130075*t^23 + 605169555288450519382885973313343549650650322258/109616531895428526937017519506225*t^21 - 433601256383989459287846970930926638450697535220478/4845050709777940890616174362175145*t^19 + 4991981906330563494448299725330181345523890509862096/4845050709777940890616174362175145*t^17 - 338290227103599079848570712355177937242680365698556/40714711846873452862320792959455*t^15 + 214529596760313530496117411501691319100625361400192/4672180048001871639938451651085*t^13 - 3691770165235902081097018470979844213185024069244112/21923306379085705387403503901245*t^11 + 1715501667182893427870462777457673216139529754905876/4384661275817141077480700780249*t^9 - 336302133329431666289465328000456015231649574072556/626380182259591582497242968607*t^7 + 241928371312403394361155293027901613139704049285979/626380182259591582497242968607*t^5 - 71011801504343804759464408169161466973021180635709/626380182259591582497242968607*t^3 + 3980015100000250097438378837886072145509678545682/626380182259591582497242968607*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
Sufficient bits for target precision reached
-------------------------------------------------
The nodes are:
| (-7.6567333049057025629 + 1.5613247538458893415e-283j)  +/-  (5.67e-120, 5.67e-120j)
| (9.5177820789020370168 - 4.2090998763114523843e-284j)  +/-  (2.86e-121, 2.86e-121j)
| (15.545121643955324332 + 3.2951671842111652179e-296j)  +/-  (1.32e-123, 1.32e-123j)
| (6.8971841195318471302 - 6.5438234961197092172e-294j)  +/-  (9.29e-120, 9.29e-120j)
| (-9.5177820789020370168 - 1.9863323560572805255e-308j)  +/-  (2.93e-121, 2.93e-121j)
| (-15.545121643955324332 + 5.3016181467246634308e-312j)  +/-  (1.49e-123, 1.49e-123j)
| (7.6567333049057025629 - 2.2752751861315414094e-306j)  +/-  (5.86e-120, 5.86e-120j)
| (-3.763589069880561535 + 6.9249313261282390635e-319j)  +/-  (2.14e-120, 2.14e-120j)
| (-2.3344142183389772393 + 5.1887139609379279202e-321j)  +/-  (5.8e-122, 5.8e-122j)
| (8.5029902406661750889 + 5.7040471691146923021e-317j)  +/-  (1.95e-120, 1.95e-120j)
| (-5.5317060638607199116 + 3.7040128457777886468e-324j)  +/-  (9.32e-120, 9.32e-120j)
| (1.8380774758626777716 + 9.9420154783286267713e-327j)  +/-  (1.17e-122, 1.17e-122j)
| (-3.2762772292662860982 + 2.1009306730250915055e-326j)  +/-  (8.83e-121, 8.83e-121j)
| (-8.5029902406661750889 + 3.9140968544821997688e-325j)  +/-  (1.84e-120, 1.84e-120j)
| (-4.3114957943342286437 - 6.856747974260210421e-325j)  +/-  (4.68e-120, 4.68e-120j)
| (2.8191722894727907771 - 2.8430863447247330165e-325j)  +/-  (2.5e-121, 2.5e-121j)
| (2.3344142183389772393 - 6.9286706300024430908e-327j)  +/-  (5.8e-122, 5.8e-122j)
| (3.2762772292662860982 + 3.6318378430789264321e-326j)  +/-  (8.1e-121, 8.1e-121j)
| (-1.8380774758626777716 - 1.0482768510752488777e-332j)  +/-  (1.26e-122, 1.26e-122j)
| (-4.9042594254541000712 - 2.811565521736016287e-329j)  +/-  (6.92e-120, 6.92e-120j)
| (1.4656205133845524345 - 2.4248490157472719434e-336j)  +/-  (3.84e-123, 3.84e-123j)
| (1.2028603468802868357 + 1.9739116399342374676e-337j)  +/-  (7.99e-124, 7.99e-124j)
| (-6.1937496639017461275 - 1.4064264548679517013e-331j)  +/-  (1.01e-119, 1.01e-119j)
| (-2.8191722894727907771 - 1.0304397851687213339e-341j)  +/-  (2.54e-121, 2.54e-121j)
| (-0.74196378430272585765 + 1.1968501825712939598e-346j)  +/-  (3.21e-125, 3.21e-125j)
| (5.5317060638607199116 - 1.3689234627338940868e-344j)  +/-  (8.87e-120, 8.87e-120j)
| (-8.061836871210089571e-375 + 1.8614964696572679703e-374j)  +/-  (7.51e-373, 7.51e-373j)
| (4.9042594254541000712 + 2.2769248643183835632e-354j)  +/-  (7.4e-120, 7.4e-120j)
| (-1.4656205133845524345 - 7.2971554844132951287e-366j)  +/-  (3.32e-123, 3.32e-123j)
| (-1.2028603468802868357 - 1.5046572373637181419e-366j)  +/-  (8.23e-124, 8.23e-124j)
| (-6.8971841195318471302 + 2.7105978857370508083e-364j)  +/-  (8.99e-120, 8.99e-120j)
| (3.763589069880561535 - 1.6445079061637532617e-362j)  +/-  (2.22e-120, 2.22e-120j)
| (0.74196378430272585765 - 9.9838525286771038649e-376j)  +/-  (3.21e-125, 3.21e-125j)
| (6.1937496639017461275 + 2.2035009079629670789e-373j)  +/-  (1.09e-119, 1.09e-119j)
| (-0.26842728825432580984 + 2.9438747163636731453e-386j)  +/-  (1.51e-126, 1.51e-126j)
| (0.26842728825432580984 - 2.3399698990506630646e-385j)  +/-  (1.96e-126, 1.96e-126j)
| (4.3114957943342286437 - 2.1879758881571275183e-382j)  +/-  (4.08e-120, 4.08e-120j)
-------------------------------------------------
The weights are:
| (5.9054254528635485708e-14 + 4.2615012347365812987e-296j)  +/-  (2.18e-33, 7.95e-94j)
| (9.9363310638063447158e-21 + 6.354224656864338423e-302j)  +/-  (4.06e-37, 1.48e-97j)
| (1.0357815592198300837e-37 - 5.3172604241824987309e-311j)  +/-  (4.89e-45, 1.78e-105j)
| (1.3589136147015022226e-11 - 1.8337585123759317509e-296j)  +/-  (9.75e-33, 3.56e-93j)
| (9.9363310638063447158e-21 - 5.6571125092287738094e-301j)  +/-  (2.57e-38, 9.39e-99j)
| (1.0357815592198300837e-37 + 1.5661474684452711419e-310j)  +/-  (3.22e-46, 1.17e-106j)
| (5.9054254528635485708e-14 + 6.0407121767166536281e-298j)  +/-  (1.5e-34, 5.47e-95j)
| (0.00017390901214626988832 + 1.5453874042436079162e-290j)  +/-  (7.99e-27, 2.91e-87j)
| (0.013048284595671165157 - 8.9262166061821737423e-289j)  +/-  (2.21e-21, 8.08e-82j)
| (7.230985853717059309e-17 - 1.0728871671861773202e-299j)  +/-  (2.1e-36, 7.68e-97j)
| (5.8242216760878342386e-08 - 3.4061835887701088195e-293j)  +/-  (4.43e-32, 1.62e-92j)
| (0.035256567595909779768 + 2.3352388558305159523e-288j)  +/-  (4.41e-21, 1.61e-81j)
| (0.00085715504425765891454 - 7.5221031796499375866e-290j)  +/-  (6.43e-26, 2.35e-86j)
| (7.230985853717059309e-17 + 2.0358187306556272518e-298j)  +/-  (1.34e-37, 4.88e-98j)
| (2.1018612183796994376e-05 - 2.3284202032411810745e-291j)  +/-  (4.18e-29, 1.53e-89j)
| (0.0035006165684144058781 + 1.2284974179907836196e-289j)  +/-  (1.72e-27, 6.28e-88j)
| (0.013048284595671165157 - 4.756805310024915398e-289j)  +/-  (9.11e-26, 3.33e-86j)
| (0.00085715504425765891454 - 3.0155176310225666942e-290j)  +/-  (2.55e-29, 9.32e-90j)
| (0.035256567595909779768 + 3.8095186293023810133e-288j)  +/-  (1.84e-24, 6.73e-85j)
| (1.4589155149651045309e-06 + 2.986682495512970427e-292j)  +/-  (4.36e-32, 1.59e-92j)
| (0.030489897905075539007 - 8.3532647625142237861e-288j)  +/-  (5.01e-24, 1.83e-84j)
| (0.077007403194591314308 + 1.1927830782454246542e-287j)  +/-  (2.47e-23, 9.02e-84j)
| (1.2699190635734279014e-09 + 3.4826074443455172737e-294j)  +/-  (3.09e-35, 1.13e-95j)
| (0.0035006165684144058781 + 2.659116085610339768e-289j)  +/-  (5.2e-28, 1.9e-88j)
| (0.14633025836694990441 - 1.7235853073321781107e-287j)  +/-  (1.58e-24, 5.75e-85j)
| (5.8242216760878342386e-08 - 5.495221514556736058e-294j)  +/-  (8.74e-37, 3.19e-97j)
| (0.042584834614766567629 - 5.3794168866441862663e-287j)  +/-  (4.67e-26, 1.7e-86j)
| (1.4589155149651045309e-06 + 6.5512597809496213786e-293j)  +/-  (8.4e-36, 3.06e-96j)
| (0.030489897905075539007 - 1.2305415299348399474e-287j)  +/-  (1.12e-27, 4.11e-88j)
| (0.077007403194591314308 + 1.6370989327880460731e-287j)  +/-  (1.89e-27, 6.92e-88j)
| (1.3589136147015022226e-11 - 3.5060418573989562335e-295j)  +/-  (8.86e-38, 3.24e-98j)
| (0.00017390901214626988832 + 5.2717060895605860574e-291j)  +/-  (4.24e-34, 1.55e-94j)
| (0.14633025836694990441 - 1.4192123775648194178e-287j)  +/-  (1.31e-29, 5.16e-90j)
| (1.2699190635734279014e-09 + 3.6845228284322865849e-295j)  +/-  (1.24e-38, 4.69e-99j)
| (0.17202095335611782958 + 3.7522225863980713764e-287j)  +/-  (5.31e-30, 2.79e-90j)
| (0.17202095335611782958 + 3.49818654059596567e-287j)  +/-  (3.08e-30, 1.8e-90j)
| (2.1018612183796994376e-05 - 6.513480142966186561e-292j)  +/-  (2.37e-35, 8.45e-96j)
