Starting with polynomial:
P : t^4 - 6*t^2 + 3
Extension levels are: 4 36
-------------------------------------------------
Trying to find an order 36 Kronrod extension for:
P1 : t^4 - 6*t^2 + 3
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^40 - 341384445679051736881988/482488103220068946583*t^38 + 866827912104624957804625657/3859904825760551572664*t^36 - 81777639157637308804245083715/1929952412880275786332*t^34 + 1863522063074372953669375624785/350900438705504688424*t^32 - 20528305751217575968865263268010/43862554838188086053*t^30 + 2627397971294990805729610244743095/87725109676376172106*t^28 - 62180826700852334918609421822225855/43862554838188086053*t^26 + 4394939367298964202049283983610614125/87725109676376172106*t^24 - 58145470360752004763694113793064974750/43862554838188086053*t^22 + 4595619962901554810261455292564586022125/175450219352752344212*t^20 - 33644557457079201201492672073853471818875/87725109676376172106*t^18 + 720768269075042383798316722614585318441375/175450219352752344212*t^16 - 1385946952337049101149666519378600408023750/43862554838188086053*t^14 + 14920873379056689322130383356950643194641875/87725109676376172106*t^12 - 27134221550208133978108046485752961093329375/43862554838188086053*t^10 + 126916780419505443943935403625320930489674375/87725109676376172106*t^8 - 88534485253184024610373522740943585631703750/43862554838188086053*t^6 + 518264281322371435395988771873603714804021875/350900438705504688424*t^4 - 75931760376274454542746755157859973863115625/175450219352752344212*t^2 + 7549586918999902539895455536602404155765625/350900438705504688424
-------------------------------------------------
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:
| (5.5123026456048717599 - 6.9009908531403708225e-535j)  +/-  (3.76e-246, 3.76e-246j)
| (9.3323350681793814475 - 1.1984544361322161411e-545j)  +/-  (1.73e-246, 1.73e-246j)
| (11.128645963806039161 + 1.3966198142750824452e-551j)  +/-  (4.05e-248, 4.05e-248j)
| (-9.3323350681793814475 - 3.4208499686413913655e-555j)  +/-  (1.78e-246, 1.78e-246j)
| (2.8360809654704305057 - 3.2502792494206547871e-553j)  +/-  (1.02e-248, 1.02e-248j)
| (-7.283830900691493529 + 1.8124674969009861058e-554j)  +/-  (8.67e-246, 8.67e-246j)
| (-4.9555607791998494739 + 1.2321426857887107852e-555j)  +/-  (1.68e-246, 1.68e-246j)
| (-8.6010383483793147253 - 8.7008552527413834562e-555j)  +/-  (4.41e-246, 4.41e-246j)
| (7.9234731956269234609 - 5.6963394377870255633e-563j)  +/-  (6.73e-246, 6.73e-246j)
| (-10.148050208670524599 - 7.6364070563863418381e-580j)  +/-  (4.04e-247, 4.04e-247j)
| (4.9555607791998494739 + 3.0513470541843707657e-599j)  +/-  (1.81e-246, 1.81e-246j)
| (6.0835790709666481797 + 9.0705195573789759448e-632j)  +/-  (6.49e-246, 6.49e-246j)
| (-11.128645963806039161 - 1.2681945300772861787e-649j)  +/-  (4.35e-248, 4.35e-248j)
| (10.148050208670524599 + 3.7901216038029073478e-648j)  +/-  (4.02e-247, 4.02e-247j)
| (-7.9234731956269234609 + 4.5028595646137748967e-653j)  +/-  (7.6e-246, 7.6e-246j)
| (1.581401884929504107 + 4.2174720237278437834e-657j)  +/-  (1.76e-250, 1.76e-250j)
| (-4.4109352985145059565 + 2.4992516998205288474e-653j)  +/-  (6.04e-247, 6.04e-247j)
| (-6.0835790709666481797 + 1.0247248053782115323e-652j)  +/-  (7.24e-246, 7.24e-246j)
| (-1.2173195627956775176 - 2.7964602703260167044e-661j)  +/-  (1.66e-251, 1.66e-251j)
| (-3.8766564353523741483 + 4.7472221049723693927e-655j)  +/-  (1.76e-247, 1.76e-247j)
| (7.283830900691493529 - 5.4715939873869736659e-662j)  +/-  (9.97e-246, 9.97e-246j)
| (1.2173195627956775176 + 4.4294835580586370347e-685j)  +/-  (1.62e-251, 1.62e-251j)
| (8.6010383483793147253 + 1.2940665088661997146e-684j)  +/-  (4.39e-246, 4.39e-246j)
| (6.6726205206638343035 - 1.4374386793279902894e-705j)  +/-  (9.87e-246, 9.87e-246j)
| (-1.581401884929504107 + 2.4918328182555740868e-723j)  +/-  (1.97e-250, 1.97e-250j)
| (-5.5123026456048717599 - 2.7718026094660202667e-718j)  +/-  (3.58e-246, 3.58e-246j)
| (1.8792099505350578479 + 5.0099896811295637466e-718j)  +/-  (6.39e-250, 6.39e-250j)
| (-2.3344142183389772393 + 1.4567070101237262538e-721j)  +/-  (2.47e-249, 2.47e-249j)
| (3.3516474744610740846 - 5.1910024147153209632e-718j)  +/-  (5.05e-248, 5.05e-248j)
| (-0.24825549009705985753 + 8.3576120513854566164e-735j)  +/-  (4.17e-254, 4.17e-254j)
| (-6.6726205206638343035 + 5.522681183786850684e-726j)  +/-  (9.32e-246, 9.32e-246j)
| (2.3344142183389772393 + 2.3530361114755730939e-730j)  +/-  (2.41e-249, 2.41e-249j)
| (0.24825549009705985753 + 1.9645976674456194452e-741j)  +/-  (4.17e-254, 4.17e-254j)
| (-3.3516474744610740846 + 2.4974019384104658751e-736j)  +/-  (4.61e-248, 4.61e-248j)
| (-0.74196378430272585765 - 1.2996374126389275139e-745j)  +/-  (6.28e-253, 6.28e-253j)
| (-2.8360809654704305057 - 4.7179602631971538572e-739j)  +/-  (1.03e-248, 1.03e-248j)
| (4.4109352985145059565 - 1.65261742905314861e-741j)  +/-  (6.04e-247, 6.04e-247j)
| (0.74196378430272585765 - 5.3183334449292044302e-765j)  +/-  (7.79e-253, 7.79e-253j)
| (3.8766564353523741483 + 2.8782501610342906439e-764j)  +/-  (1.81e-247, 1.81e-247j)
| (-1.8792099505350578479 + 2.2718727935144604934e-779j)  +/-  (6.66e-250, 6.66e-250j)
-------------------------------------------------
The weights are:
| (5.6717460833825013284e-08 + 1.2340522255588673427e-541j)  +/-  (1.7e-79, 3.57e-202j)
| (3.7447806340914450117e-20 - 2.737739197708239154e-549j)  +/-  (1.16e-88, 2.43e-211j)
| (5.7683739523869159341e-28 - 1.6104656319622521995e-553j)  +/-  (9.1e-92, 1.91e-214j)
| (3.7447806340914450117e-20 - 7.0451382522373119155e-550j)  +/-  (1.16e-90, 2.43e-213j)
| (0.0036473348921918639526 - 1.8806855126822417046e-539j)  +/-  (6.98e-72, 1.46e-194j)
| (7.5101015071770136145e-13 + 6.129628436756628666e-546j)  +/-  (3.5e-87, 7.34e-210j)
| (1.0207694844813045849e-06 + 2.0071504745547184292e-542j)  +/-  (4.72e-82, 9.91e-205j)
| (2.412917873854331739e-17 + 2.2266386342840082229e-548j)  +/-  (1.22e-89, 2.55e-212j)
| (6.1013635033311544967e-15 - 2.4581183591347715695e-546j)  +/-  (2.91e-89, 6.1e-212j)
| (1.5174909356089076178e-23 + 1.1315089089826986377e-551j)  +/-  (6.58e-93, 1.38e-215j)
| (1.0207694844813045849e-06 - 3.7738453506900201167e-541j)  +/-  (4.82e-83, 1.01e-205j)
| (2.1251393963924038642e-09 + 1.0709242812293986183e-542j)  +/-  (1.16e-85, 2.43e-208j)
| (5.7683739523869159341e-28 - 5.4353439239327142674e-554j)  +/-  (2.11e-95, 4.42e-218j)
| (1.5174909356089076178e-23 + 3.8224317720844573807e-551j)  +/-  (1.27e-93, 2.66e-216j)
| (6.1013635033311544967e-15 - 4.4113139918765624153e-547j)  +/-  (1.35e-89, 2.83e-212j)
| (0.030351399582949004467 + 2.6963314326625082305e-538j)  +/-  (9.83e-75, 2.06e-197j)
| (1.2816645623966863797e-05 - 9.7712137779820960705e-542j)  +/-  (1.09e-84, 2.3e-207j)
| (2.1251393963924038642e-09 + 5.2759575353338957666e-544j)  +/-  (7.25e-88, 1.52e-210j)
| (0.085324481655865656754 + 1.4629477764410451631e-538j)  +/-  (1.02e-74, 2.13e-197j)
| (0.00011519005097641559667 + 4.1970050058229084583e-541j)  +/-  (4.99e-84, 1.05e-206j)
| (7.5101015071770136145e-13 + 4.4275638190189863274e-545j)  +/-  (8.15e-91, 1.71e-213j)
| (0.085324481655865656754 - 2.292229248928389707e-538j)  +/-  (5.59e-77, 1.17e-199j)
| (2.412917873854331739e-17 + 1.0174166176731083236e-547j)  +/-  (3.9e-93, 8.19e-216j)
| (5.1321150560284312381e-11 - 6.7251680575402641237e-544j)  +/-  (6.59e-90, 1.38e-212j)
| (0.030351399582949004467 - 1.4941433258268967919e-538j)  +/-  (1.58e-81, 3.32e-204j)
| (5.6717460833825013284e-08 - 3.5503010592102940454e-543j)  +/-  (6.94e-89, 1.46e-211j)
| (0.026779028849132494004 - 1.7448277665414989625e-538j)  +/-  (1.46e-82, 3.06e-205j)
| (0.012809162393619258918 - 2.2479160150541454829e-539j)  +/-  (8.66e-85, 1.82e-207j)
| (0.00075506991934194870675 + 6.7126645421793327443e-540j)  +/-  (7.23e-87, 1.52e-209j)
| (0.19192309159924026294 + 1.3056655487645629059e-538j)  +/-  (5.34e-82, 1.12e-204j)
| (5.1321150560284312381e-11 - 6.4040885637599665826e-545j)  +/-  (6.44e-91, 1.35e-213j)
| (0.012809162393619258918 + 5.5504656339462411006e-539j)  +/-  (6.63e-85, 1.39e-207j)
| (0.19192309159924026294 - 1.4288174245498109423e-538j)  +/-  (4.41e-83, 9.24e-206j)
| (0.00075506991934194870675 - 1.6362629706568657909e-540j)  +/-  (4.38e-87, 9.18e-210j)
| (0.14828134474689613003 - 1.2812051884031971116e-538j)  +/-  (1.34e-83, 2.82e-206j)
| (0.0036473348921918639526 + 6.0288692722239280298e-540j)  +/-  (1.15e-86, 2.42e-209j)
| (1.2816645623966863797e-05 + 8.8037909947059996542e-541j)  +/-  (1.67e-89, 3.53e-212j)
| (0.14828134474689613003 + 1.6797545903198727708e-538j)  +/-  (9.1e-86, 1.9e-208j)
| (0.00011519005097641559667 - 2.4091706394233578695e-540j)  +/-  (7.73e-89, 1.64e-211j)
| (0.026779028849132494004 + 8.5762162078806153331e-539j)  +/-  (1.41e-86, 2.46e-209j)
