Starting with polynomial:
P : 4*t^2 - 2
Extension levels are: 2 54
-------------------------------------------------
Trying to find an order 54 Kronrod extension for:
P1 : 4*t^2 - 2
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 4*t^56 - 8534356927971986410813862099312321/2845264038326038380917507559814*t^54 + 5942442592107288732311488554251426991/5690528076652076761835015119628*t^52 - 196470795276521120381312398399126202421/875465857946473347974617710712*t^50 + 58462678616552042308360469448321815439075/1750931715892946695949235421424*t^48 - 6402096673066718641193685104843586900421875/1750931715892946695949235421424*t^46 + 1071156551687148291975743346645591595832025525/3501863431785893391898470842848*t^44 - 140271721456813155279273558288508367281264088775/7003726863571786783796941685696*t^42 + 14613783788427381554149440380477957693814241854075/14007453727143573567593883371392*t^40 - 2449342749544642860370291102026901742223622266648375/56029814908574294270375533485568*t^38 + 166303763862726332803567281428731644471616815618239625/112059629817148588540751066971136*t^36 - 9187618312041135608141359271139310979354107373762913375/224119259634297177081502133942272*t^34 + 413763984433396423279665695826096598496855015628995804625/448238519268594354163004267884544*t^32 - 3796372675736911527150894836159797744608021802329796208625/224119259634297177081502133942272*t^30 + 113288712320038825826216774528064076750529489238032755044375/448238519268594354163004267884544*t^28 - 2737191295827955095882174779501307834198605186372620422883125/896477038537188708326008535769088*t^26 + 13302184193547700450104659738921957869410263348167422047821875/448238519268594354163004267884544*t^24 - 3300198587557141020598034434343641395336924975682862267247571875/14343632616595019333216136572305408*t^22 + 40360309867884152083094769497711196026870185485624201587148778125/28687265233190038666432273144610816*t^20 - 383680711954516610685147637546789941469165004499850040779537171875/57374530466380077332864546289221632*t^18 + 2782751188010966509126008987890979608422655379197454202510037203125/114749060932760154665729092578443264*t^16 - 7515271227342516990030395852997189041731995639917301694447471546875/114749060932760154665729092578443264*t^14 + 29284729749703945446034986745174259427515127630618673442583188578125/229498121865520309331458185156886528*t^12 - 78865881821583202634709573151946505914746175545401805732035702609375/458996243731040618662916370313773056*t^10 + 138182478286334259925950916288698762217037417239210648081235207109375/917992487462081237325832740627546112*t^8 - 287820799072128033402479897735195129890393691940976119329383776890625/3671969949848324949303330962510184448*t^6 + 153526642374731148790863313259829826393052059191992530936615782609375/7343939899696649898606661925020368896*t^4 - 31333960832513668684510203619514735248570954691187776228745846515625/14687879799393299797213323850040737792*t^2 + 1019674643792792614045464439014307863841956611338868691445212984375/29375759598786599594426647700081475584
-------------------------------------------------
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: 0
  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:
| (7.5936131643563784878 + 2.262059441993179528e-948j)  +/-  (2.01e-242, 2.01e-242j)
| (7.1777548903539816517 - 1.9545527852798663395e-948j)  +/-  (4.52e-242, 4.52e-242j)
| (9.6981317391639934429 - 2.4208319965560746397e-952j)  +/-  (1.14e-245, 1.14e-245j)
| (8.514694565872258919 + 1.5550727478765647054e-950j)  +/-  (1.85e-243, 1.85e-243j)
| (-3.6924653850112968219 - 5.9936615069446112732e-950j)  +/-  (1.17e-243, 1.17e-243j)
| (2.1629379422006617682 + 1.1085099873928219278e-954j)  +/-  (5.62e-247, 5.62e-247j)
| (-6.4017545803370678183 + 8.3712840448529774694e-948j)  +/-  (9.57e-242, 9.57e-242j)
| (-7.5936131643563784878 + 1.4495942122385421824e-952j)  +/-  (2.01e-242, 2.01e-242j)
| (-8.514694565872258919 + 1.2744561780006040569e-955j)  +/-  (1.53e-243, 1.53e-243j)
| (-9.0509297821272999595 - 1.2930529902913785572e-955j)  +/-  (2.11e-244, 2.11e-244j)
| (5.6780312413786005054 - 1.4811026165015793418e-953j)  +/-  (8.64e-242, 8.64e-242j)
| (6.0345303202777014212 + 2.4283177894538835008e-954j)  +/-  (1.04e-241, 1.04e-241j)
| (5.3306160183476654656 - 7.9134224915643966003e-954j)  +/-  (6.61e-242, 6.61e-242j)
| (-4.9909972945412723526 + 2.0977288620371687364e-952j)  +/-  (4.14e-242, 4.14e-242j)
| (-9.6981317391639934429 + 1.70441165125377766e-965j)  +/-  (1.23e-245, 1.23e-245j)
| (3.6924653850112968219 + 1.0550526745162692437e-964j)  +/-  (1.14e-243, 1.14e-243j)
| (0.99304379909595214441 - 7.243268468125684385e-972j)  +/-  (7.77e-251, 7.77e-251j)
| (-5.3306160183476654656 - 9.1214484480942976541e-962j)  +/-  (6.99e-242, 6.99e-242j)
| (-1.8663503464123781842 - 1.0463641683419351205e-975j)  +/-  (7.51e-248, 7.51e-248j)
| (9.0509297821272999595 + 6.8327741401059638874e-973j)  +/-  (2.25e-244, 2.25e-244j)
| (4.9909972945412723526 - 1.5436053032470076854e-970j)  +/-  (4.02e-242, 4.02e-242j)
| (2.4623916629971829548 + 1.0450407150508683017e-975j)  +/-  (3.39e-246, 3.39e-246j)
| (-6.7818553797444253459 - 1.3143962320233447079e-968j)  +/-  (7.09e-242, 7.09e-242j)
| (-4.6581432312152754103 + 7.3609988417962716939e-976j)  +/-  (2.06e-242, 2.06e-242j)
| (-2.1629379422006617682 + 2.7258365287869786875e-990j)  +/-  (5.98e-247, 5.98e-247j)
| (8.0357468890959015116 + 8.1256681740489797312e-986j)  +/-  (7.21e-243, 7.21e-243j)
| (-7.1777548903539816517 - 2.6153006620294220235e-984j)  +/-  (4.3e-242, 4.3e-242j)
| (4.6581432312152754103 + 5.2534583510211388011e-998j)  +/-  (2.24e-242, 2.24e-242j)
| (-8.0357468890959015116 - 3.3794331231567350644e-1001j)  +/-  (7.65e-243, 7.65e-243j)
| (-1.2814670369747010786 + 6.7088347150763232409e-1024j)  +/-  (9.29e-250, 9.29e-250j)
| (-2.7648455623246252208 + 9.98609803579971907e-1018j)  +/-  (2.04e-245, 2.04e-245j)
| (2.7648455623246252208 + 2.2581922854802753653e-1021j)  +/-  (1.82e-245, 1.82e-245j)
| (-6.0345303202777014212 - 9.5692558813845570177e-1022j)  +/-  (1.12e-241, 1.12e-241j)
| (0.7071067811865475244 - 3.697399932441439684e-1047j)  +/-  (5.81e-252, 5.81e-252j)
| (-0.99304379909595214441 + 1.179281145014113584e-1045j)  +/-  (8.68e-251, 8.68e-251j)
| (-3.0704931305826283516 - 1.2436826687205894166e-1038j)  +/-  (8.75e-245, 8.75e-245j)
| (-0.7071067811865475244 + 3.9517031992305250195e-1047j)  +/-  (5.68e-252, 5.68e-252j)
| (1.8663503464123781842 - 2.663669626441774433e-1042j)  +/-  (8.2e-248, 8.2e-248j)
| (4.3312128692511382684 + 1.2446473494425147252e-1037j)  +/-  (9.21e-243, 9.21e-243j)
| (6.4017545803370678183 - 3.9891497557363214839e-1036j)  +/-  (1.03e-241, 1.03e-241j)
| (-0.42328527052643751803 + 5.2805875342021594359e-1051j)  +/-  (3.65e-253, 3.65e-253j)
| (1.2814670369747010786 + 5.5591102802502233202e-1047j)  +/-  (9.36e-250, 9.36e-250j)
| (3.3795915350636249759 + 4.3056897380151128591e-1041j)  +/-  (3.71e-244, 3.71e-244j)
| (4.0095124501934250296 + 5.8305827644148584021e-1040j)  +/-  (3.3e-243, 3.3e-243j)
| (6.7818553797444253459 + 7.6283794425439318463e-1040j)  +/-  (7.09e-242, 7.09e-242j)
| (-2.4623916629971829548 - 1.1194662184330265209e-1043j)  +/-  (3.52e-246, 3.52e-246j)
| (-3.3795915350636249759 - 1.9420903010739279499e-1039j)  +/-  (3.39e-244, 3.39e-244j)
| (-5.6780312413786005054 - 1.2933644053566307163e-1043j)  +/-  (9.37e-242, 9.37e-242j)
| (-0.14092043411825147389 + 1.3723924719780407652e-1067j)  +/-  (2.04e-254, 2.04e-254j)
| (3.0704931305826283516 - 1.3623825866589121434e-1059j)  +/-  (8.46e-245, 8.46e-245j)
| (-4.0095124501934250296 - 4.1787713430700699271e-1061j)  +/-  (3.6e-243, 3.6e-243j)
| (-4.3312128692511382684 + 2.3163723445431851875e-1076j)  +/-  (9.38e-243, 9.38e-243j)
| (-1.5725451197585416372 + 9.4616131831174641701e-1084j)  +/-  (8.77e-249, 8.77e-249j)
| (0.42328527052643751803 - 2.1167836366827076821e-1088j)  +/-  (3.65e-253, 3.65e-253j)
| (0.14092043411825147389 + 7.2207720951880083307e-1089j)  +/-  (2.12e-254, 2.12e-254j)
| (1.5725451197585416372 - 6.7867544670794773128e-1084j)  +/-  (9.04e-249, 9.04e-249j)
-------------------------------------------------
The weights are:
| (2.1870046696082441411e-26 - 1.8883367423109579064e-967j)  +/-  (6.67e-60, 3.99e-181j)
| (9.6384664334530491249e-24 + 4.3418012962321717596e-966j)  +/-  (1.03e-58, 6.17e-180j)
| (5.9974082151052294676e-42 - 2.0836292339628083667e-975j)  +/-  (6.91e-67, 4.13e-188j)
| (9.2566639748152735365e-33 - 1.0181011203663802031e-970j)  +/-  (2.81e-63, 1.68e-184j)
| (2.1295076470131796096e-07 - 4.9982772376062046538e-956j)  +/-  (7.53e-48, 4.5e-169j)
| (0.0015627356574277506822 - 2.8015346162590527845e-955j)  +/-  (1.21e-35, 7.24e-157j)
| (3.3494144496598032844e-19 + 3.6426510513795220798e-963j)  +/-  (9.96e-61, 5.96e-182j)
| (2.1870046696082441411e-26 - 5.4689744418105405027e-967j)  +/-  (6.47e-65, 3.87e-186j)
| (9.2566639748152735365e-33 - 2.5802381037195756831e-970j)  +/-  (5.33e-68, 3.19e-189j)
| (8.6221302606313086284e-37 + 2.1130080189548951008e-972j)  +/-  (1.12e-69, 6.71e-191j)
| (1.9767312268636436592e-15 + 8.9719566983107093746e-962j)  +/-  (5.18e-60, 3.1e-181j)
| (3.122632297082646589e-17 - 1.0271549144539653286e-962j)  +/-  (2.9e-61, 1.74e-182j)
| (8.8399857985441396167e-14 - 6.5991940097416968143e-961j)  +/-  (2.86e-59, 1.71e-180j)
| (2.8811867454052577318e-12 + 2.7877547453526796191e-959j)  +/-  (1.48e-60, 8.84e-182j)
| (5.9974082151052294676e-42 - 4.6507929860011658815e-975j)  +/-  (3.35e-74, 2.01e-195j)
| (2.1295076470131796096e-07 + 1.7189928180913697308e-957j)  +/-  (1.63e-55, 9.76e-177j)
| (0.060428756312179493667 - 3.0099252766213187721e-954j)  +/-  (6.43e-46, 3.85e-167j)
| (8.8399857985441396167e-14 - 3.6473397292808617502e-960j)  +/-  (6.88e-62, 4.12e-183j)
| (0.0051139732356104537937 - 1.7451295740247144047e-954j)  +/-  (6.02e-46, 3.6e-167j)
| (8.6221302606313086284e-37 + 8.8749729973130910891e-973j)  +/-  (9.95e-72, 5.95e-193j)
| (2.8811867454052577318e-12 + 4.1533884523178097069e-960j)  +/-  (7.36e-60, 4.4e-181j)
| (0.00039499943532179117596 + 1.186497842877147762e-955j)  +/-  (2.39e-50, 1.43e-171j)
| (2.3166931490999194433e-21 - 2.4983100529569419052e-964j)  +/-  (9.11e-67, 5.45e-188j)
| (7.0174454940992388789e-11 - 1.96692616963350883e-958j)  +/-  (3.61e-61, 2.16e-182j)
| (0.0015627356574277506822 + 1.0567575468955977061e-954j)  +/-  (1.36e-51, 8.13e-173j)
| (2.3374161055904308565e-29 + 5.6286519976287668647e-969j)  +/-  (7.31e-70, 4.37e-191j)
| (9.6384664334530491249e-24 + 1.3552793472220984955e-965j)  +/-  (4.77e-68, 2.86e-189j)
| (7.0174454940992388789e-11 - 2.2657779129164311467e-959j)  +/-  (6.79e-62, 4.06e-183j)
| (2.3374161055904308565e-29 + 1.5216699803994033344e-968j)  +/-  (1.3e-70, 7.78e-192j)
| (0.031640563304104243491 - 3.9003817707026771666e-954j)  +/-  (5.13e-49, 3.07e-170j)
| (8.2112542034731397073e-05 + 3.3846603840151725318e-955j)  +/-  (2.32e-57, 1.39e-178j)
| (8.2112542034731397073e-05 - 4.8046573024495801996e-956j)  +/-  (9.29e-58, 5.55e-179j)
| (3.122632297082646589e-17 - 4.2847913058879553402e-962j)  +/-  (6.8e-66, 4.07e-187j)
| (0.097456454765972437836 + 4.3488282620063522012e-954j)  +/-  (2.06e-49, 1.23e-170j)
| (0.060428756312179493667 + 5.2071041179620276034e-954j)  +/-  (3.99e-50, 2.39e-171j)
| (1.3948429939901309086e-05 - 1.9238403384280312454e-955j)  +/-  (8.73e-59, 5.22e-180j)
| (0.097456454765972437836 - 6.3955448218228595557e-954j)  +/-  (2.2e-50, 1.32e-171j)
| (0.0051139732356104537937 + 5.8447906953102225006e-955j)  +/-  (5.4e-55, 3.23e-176j)
| (1.3036046452169927472e-09 + 1.0827506544471238938e-958j)  +/-  (8.95e-63, 5.35e-184j)
| (3.3494144496598032844e-19 + 9.7040958473070058978e-964j)  +/-  (3e-68, 1.79e-189j)
| (0.13345466282003530186 + 7.1849159857793980452e-954j)  +/-  (1.77e-54, 1.06e-175j)
| (0.031640563304104243491 + 1.9005321959979094754e-954j)  +/-  (3.05e-55, 1.82e-176j)
| (1.9218857684121982142e-06 - 5.7885024298343722596e-957j)  +/-  (1.8e-61, 1.08e-182j)
| (1.8784715838239271645e-08 - 4.5724638326127188244e-958j)  +/-  (1.28e-62, 7.68e-184j)
| (2.3166931490999194433e-21 - 7.3691667332224684055e-965j)  +/-  (1.25e-69, 7.49e-191j)
| (0.00039499943532179117596 - 6.0730335649830571977e-955j)  +/-  (1.05e-61, 6.27e-183j)
| (1.9218857684121982142e-06 + 1.3169389725547443535e-955j)  +/-  (2.15e-64, 1.29e-185j)
| (1.9767312268636436592e-15 + 4.2492185386932965665e-961j)  +/-  (1.31e-69, 7.86e-191j)
| (0.15593456464366216921 - 7.3446037492644065866e-954j)  +/-  (2.51e-60, 1.5e-181j)
| (1.3948429939901309086e-05 + 1.7546679522662737251e-956j)  +/-  (1.84e-63, 1.1e-184j)
| (1.8784715838239271645e-08 - 1.1160099517199776989e-956j)  +/-  (1.02e-66, 6.12e-188j)
| (1.3036046452169927472e-09 + 1.3658331227568807923e-957j)  +/-  (2.29e-67, 1.37e-188j)
| (0.013915073855712078771 + 2.7037239169631292657e-954j)  +/-  (4.42e-63, 2.64e-184j)
| (0.13345466282003530186 - 5.7136849045412127964e-954j)  +/-  (1.39e-63, 8.31e-185j)
| (0.15593456464366216921 + 6.8071513790110808286e-954j)  +/-  (1.42e-63, 8.42e-185j)
| (0.013915073855712078771 - 1.0983046710544819051e-954j)  +/-  (1.83e-64, 1.12e-185j)
