Starting with polynomial:
P : 16*t^4 - 48*t^2 + 12
Extension levels are: 4 36
-------------------------------------------------
Trying to find an order 36 Kronrod extension for:
P1 : 16*t^4 - 48*t^2 + 12
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 16*t^40 - 2731075565432413895055904/482488103220068946583*t^38 + 866827912104624957804625657/964976206440137893166*t^36 - 81777639157637308804245083715/964976206440137893166*t^34 + 1863522063074372953669375624785/350900438705504688424*t^32 - 10264152875608787984432631634005/43862554838188086053*t^30 + 2627397971294990805729610244743095/350900438705504688424*t^28 - 62180826700852334918609421822225855/350900438705504688424*t^26 + 4394939367298964202049283983610614125/1403601754822018753696*t^24 - 29072735180376002381847056896532487375/701800877411009376848*t^22 + 4595619962901554810261455292564586022125/11228814038576150029568*t^20 - 33644557457079201201492672073853471818875/11228814038576150029568*t^18 + 720768269075042383798316722614585318441375/44915256154304600118272*t^16 - 692973476168524550574833259689300204011875/11228814038576150029568*t^14 + 14920873379056689322130383356950643194641875/89830512308609200236544*t^12 - 27134221550208133978108046485752961093329375/89830512308609200236544*t^10 + 126916780419505443943935403625320930489674375/359322049234436800946176*t^8 - 44267242626592012305186761370471792815851875/179661024617218400473088*t^6 + 518264281322371435395988771873603714804021875/5749152787750988815138816*t^4 - 75931760376274454542746755157859973863115625/5749152787750988815138816*t^2 + 7549586918999902539895455536602404155765625/22996611151003955260555264
-------------------------------------------------
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:
| (6.0818525413845562136 + 1.2140276085510326865e-873j)  +/-  (3.33e-246, 3.33e-246j)
| (2.7412100537681325457 + 4.3818065785438090154e-885j)  +/-  (1.22e-247, 1.22e-247j)
| (-7.1757551183724865828 - 6.777601998257163245e-882j)  +/-  (2.96e-247, 2.96e-247j)
| (7.8691410264315522141 - 1.291956667962192245e-891j)  +/-  (3.02e-248, 3.02e-248j)
| (4.7182552184459086968 - 3.4500213525138411254e-896j)  +/-  (6.77e-246, 6.77e-246j)
| (7.1757551183724865828 + 4.18841531518661103e-909j)  +/-  (2.91e-247, 2.91e-247j)
| (-6.5989574110146619498 + 7.7169837189871323885e-915j)  +/-  (1.3e-246, 1.3e-246j)
| (-1.3288020992965759466 - 2.7223572632567760834e-925j)  +/-  (4.31e-250, 4.31e-250j)
| (6.5989574110146619498 + 1.2331914139098556921e-924j)  +/-  (1.35e-246, 1.35e-246j)
| (5.150446222895073286 + 1.2456501766543860295e-939j)  +/-  (6.79e-246, 6.79e-246j)
| (1.1182199966148406678 + 1.8182118163980696594e-955j)  +/-  (1.17e-250, 1.17e-250j)
| (-5.150446222895073286 - 1.5240484410647233851e-948j)  +/-  (7.17e-246, 7.17e-246j)
| (-3.5041106315543049126 - 4.2256015838944891313e-953j)  +/-  (1.25e-246, 1.25e-246j)
| (4.3017400149650737679 + 2.3236145962575473753e-958j)  +/-  (4.41e-246, 4.41e-246j)
| (-7.8691410264315522141 + 1.3718072863757192982e-970j)  +/-  (3.13e-248, 3.13e-248j)
| (3.5041106315543049126 - 3.2711007359996063215e-970j)  +/-  (1.2e-246, 1.2e-246j)
| (5.6027416271776414347 + 2.0563968940258511056e-974j)  +/-  (5.63e-246, 5.63e-246j)
| (-2.3699726573381913448 + 1.7833871539543396124e-979j)  +/-  (3.36e-248, 3.36e-248j)
| (-1.1182199966148406678 + 3.4879864851899985446e-982j)  +/-  (1.26e-250, 1.26e-250j)
| (-5.6027416271776414347 - 1.6767480466803633951e-977j)  +/-  (5.3e-246, 5.3e-246j)
| (2.0054120826782321487 - 1.624903600328389685e-980j)  +/-  (7.08e-249, 7.08e-249j)
| (1.6506801238857845559 - 3.6311118193107656103e-982j)  +/-  (1.61e-249, 1.61e-249j)
| (-3.8977865806597510803 + 6.9484392746062106678e-978j)  +/-  (2.55e-246, 2.55e-246j)
| (-4.3017400149650737679 - 7.2165605932694158169e-978j)  +/-  (4.91e-246, 4.91e-246j)
| (-0.52464762327529031788 + 9.6133293980075882687e-987j)  +/-  (5.27e-253, 5.27e-253j)
| (1.3288020992965759466 - 1.2823037074777877499e-983j)  +/-  (4.38e-250, 4.38e-250j)
| (0.86077491772386684102 + 5.0243053184492441582e-986j)  +/-  (1.19e-251, 1.19e-251j)
| (3.1190022609547154489 - 9.6252942877011155333e-980j)  +/-  (4.33e-247, 4.33e-247j)
| (-2.7412100537681325457 + 6.6164838560827169969e-982j)  +/-  (1.29e-247, 1.29e-247j)
| (-0.86077491772386684102 + 2.0544892165276112332e-986j)  +/-  (1.21e-251, 1.21e-251j)
| (-3.1190022609547154489 - 7.2974495173161815081e-982j)  +/-  (4.48e-247, 4.48e-247j)
| (0.52464762327529031788 + 6.8554677031350538055e-988j)  +/-  (4.99e-253, 4.99e-253j)
| (2.3699726573381913448 + 3.8580940967294284533e-983j)  +/-  (3.47e-248, 3.47e-248j)
| (-6.0818525413845562136 - 8.2112059863087885688e-981j)  +/-  (3.15e-246, 3.15e-246j)
| (-2.0054120826782321487 - 6.6755559237606640129e-985j)  +/-  (6.43e-249, 6.43e-249j)
| (-1.6506801238857845559 + 3.1761845349323893067e-985j)  +/-  (1.53e-249, 1.53e-249j)
| (-4.7182552184459086968 + 2.7142256371766522822e-988j)  +/-  (6.73e-246, 6.73e-246j)
| (0.17554314051442082052 + 1.8245532418848655452e-999j)  +/-  (2.8e-254, 2.8e-254j)
| (3.8977865806597510803 - 7.2926251148203038873e-998j)  +/-  (2.63e-246, 2.63e-246j)
| (-0.17554314051442082052 - 5.9157373409534353817e-1012j)  +/-  (2.8e-254, 2.8e-254j)
-------------------------------------------------
The weights are:
| (2.412917873854331739e-17 - 1.8814372321455560883e-889j)  +/-  (6.15e-93, 2.49e-214j)
| (0.00011519005097641559667 - 1.0995770872360320613e-883j)  +/-  (3.12e-80, 1.26e-201j)
| (1.5174909356089076178e-23 + 1.2459100378641594019e-894j)  +/-  (3.16e-97, 1.28e-218j)
| (5.7683739523869159341e-28 - 4.7173944133988861329e-896j)  +/-  (7.8e-98, 3.15e-219j)
| (5.1321150560284312381e-11 + 5.3343941466187120445e-887j)  +/-  (6.12e-90, 2.47e-211j)
| (1.5174909356089076178e-23 + 1.5099847166450527422e-893j)  +/-  (2.27e-96, 9.17e-218j)
| (3.7447806340914450117e-20 - 7.6878423376291353881e-893j)  +/-  (4.11e-98, 1.66e-219j)
| (0.026779028849132494004 + 7.9737953216565799473e-882j)  +/-  (2.19e-75, 8.87e-197j)
| (3.7447806340914450117e-20 - 1.8852636950825286864e-891j)  +/-  (5.2e-95, 2.1e-216j)
| (7.5101015071770136145e-13 - 7.8499164019553792331e-888j)  +/-  (5.7e-92, 2.31e-213j)
| (0.030351399582949004467 + 1.9904858053947068408e-881j)  +/-  (2.79e-75, 1.13e-196j)
| (7.5101015071770136145e-13 + 6.509335331308192021e-889j)  +/-  (5.51e-96, 2.23e-217j)
| (1.0207694844813045849e-06 + 2.0431237338418836098e-885j)  +/-  (3e-91, 1.21e-212j)
| (2.1251393963924038642e-09 - 3.2036750568429680254e-886j)  +/-  (8.91e-91, 3.6e-212j)
| (5.7683739523869159341e-28 - 6.0435522887707585819e-897j)  +/-  (1.86e-102, 7.53e-224j)
| (1.0207694844813045849e-06 - 7.5978035487223436869e-885j)  +/-  (1.74e-89, 7.02e-211j)
| (6.1013635033311544967e-15 + 1.153150749704489693e-888j)  +/-  (1.8e-93, 7.28e-215j)
| (0.00075506991934194870675 - 1.5996405878953513563e-883j)  +/-  (1.06e-88, 4.3e-210j)
| (0.030351399582949004467 - 1.3722117212671379613e-881j)  +/-  (2.48e-81, 1e-202j)
| (6.1013635033311544967e-15 - 4.7283482177244600853e-890j)  +/-  (8.94e-98, 3.61e-219j)
| (0.0036473348921918639526 - 1.1509381754849764701e-882j)  +/-  (1.22e-86, 4.92e-208j)
| (0.012809162393619258918 + 3.7105934052276866209e-882j)  +/-  (2.97e-85, 1.2e-206j)
| (5.6717460833825013284e-08 - 3.6559969152076940056e-886j)  +/-  (2.25e-94, 9.1e-216j)
| (2.1251393963924038642e-09 + 5.4922441925911108043e-887j)  +/-  (1.44e-95, 5.81e-217j)
| (0.14828134474689613003 - 1.1306191907113325778e-881j)  +/-  (2.62e-85, 1.06e-206j)
| (0.026779028849132494004 - 1.2432262065507001169e-881j)  +/-  (3.41e-86, 1.37e-207j)
| (0.085324481655865656754 - 1.7577315299583510705e-881j)  +/-  (6.32e-86, 2.55e-207j)
| (1.2816645623966863797e-05 + 3.050556427593140577e-884j)  +/-  (2.69e-91, 1.09e-212j)
| (0.00011519005097641559667 + 4.1632267218306059823e-884j)  +/-  (2.6e-92, 1.05e-213j)
| (0.085324481655865656754 + 1.3218687170229146527e-881j)  +/-  (3.64e-87, 1.47e-208j)
| (1.2816645623966863797e-05 - 9.8234990804357366887e-885j)  +/-  (3.64e-93, 1.47e-214j)
| (0.14828134474689613003 + 1.3441003075626303628e-881j)  +/-  (8.77e-88, 3.53e-209j)
| (0.00075506991934194870675 + 3.6423693881037452583e-883j)  +/-  (4.99e-91, 2.02e-212j)
| (2.412917873854331739e-17 + 2.4082748185511218314e-891j)  +/-  (1.9e-100, 7.64e-222j)
| (0.0036473348921918639526 + 5.8013511730753938191e-883j)  +/-  (6.01e-92, 2.38e-213j)
| (0.012809162393619258918 - 2.1263702122366261575e-882j)  +/-  (2.52e-91, 9.92e-213j)
| (5.1321150560284312381e-11 - 6.735105894003534217e-888j)  +/-  (2.35e-97, 9.59e-219j)
| (0.19192309159924026294 - 1.1870614949014478787e-881j)  +/-  (1.01e-90, 3.53e-212j)
| (5.6717460833825013284e-08 + 1.6705246300202727744e-885j)  +/-  (9.82e-96, 4.26e-217j)
| (0.19192309159924026294 + 1.1204583045807402683e-881j)  +/-  (7.87e-91, 2.53e-212j)
