Starting with polynomial:
P : 4*t^2 - 2
Extension levels are: 2 52
-------------------------------------------------
Trying to find an order 52 Kronrod extension for:
P1 : 4*t^2 - 2
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 4*t^54 - 748279332105816668684900835531538/269406514469750166223704016775*t^52 + 240508958363437571882851396930078119/269406514469750166223704016775*t^50 - 3805067529518682995578750059063706053/21552521157580013297896321342*t^48 + 519136912213271876707000749525995198889/21552521157580013297896321342*t^46 - 103864175672232756364741332329869623771135/43105042315160026595792642684*t^44 + 1437160484067228024266246969612634793002207/7837280420938186653780480488*t^42 - 170428937370391744498457785627148012370031917/15674560841876373307560960976*t^40 + 31996991364100316192372602828428679314154512735/62698243367505493230243843904*t^38 - 64938495430945622438152534636856269789655914605/3389094236081378012445613184*t^36 + 3926650572873806373621663188062875644714095046475/6778188472162756024891226368*t^34 - 191870972613499965215625551394194120926673241114585/13556376944325512049782452736*t^32 + 1895988582107836655557644895370876367720252226875765/6778188472162756024891226368*t^30 - 60542311118164272822378015804289220488555632197835075/13556376944325512049782452736*t^28 + 1556332039084213692444986753729237680314745492171104825/27112753888651024099564905472*t^26 - 32023803022856493738191620082757772161167259825014356875/54225507777302048199129810944*t^24 + 2092568418723296665665188374595362226170537345056179535375/433804062218416385593038487552*t^22 - 26843483121697259167310635091998895177290782297944183006625/867608124436832771186076975104*t^20 + 266555794341172560669220865795171289995665260033345432729375/1735216248873665542372153950208*t^18 - 2011255148781985789977626803144431527755208218895991939973125/3470432497747331084744307900416*t^16 + 5628104071502535511067214639920082739793862242044080396534375/3470432497747331084744307900416*t^14 - 22630585018856159159540045105096440550729099252067468216980625/6940864995494662169488615800832*t^12 + 62618157183603993313366480311617567687054386365831764146936875/13881729990989324338977231601664*t^10 - 112195876912120778768046832124241809455933320604163067997040625/27763459981978648677954463203328*t^8 + 237715258737212070573922299215164185846208659844978292590753125/111053839927914594711817852813312*t^6 - 128184082807685394413441194084258489777143742968145655913046875/222107679855829189423635705626624*t^4 + 26247463932240818419045155839865800318437451545224077601148125/444215359711658378847271411253248*t^2 - 848666136225655543176212164056226036888725103337290740429375/888430719423316757694542822506496
-------------------------------------------------
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:
| (7.3765036833482451818 - 1.4521852239691022392e-640j)  +/-  (7.81e-243, 7.81e-243j)
| (-2.8049532348228767071 - 1.1937862302033377883e-660j)  +/-  (1.14e-245, 1.14e-245j)
| (-8.8452629519148849677 + 4.5256737981674636284e-657j)  +/-  (9.99e-245, 9.99e-245j)
| (-7.8222747489710367792 + 8.7441037135944740136e-661j)  +/-  (2.69e-243, 2.69e-243j)
| (-9.4970835245009833739 - 7.9936068257223903654e-667j)  +/-  (5.95e-246, 5.95e-246j)
| (6.557644658215203785 + 3.8729934813726463124e-672j)  +/-  (2.5e-242, 2.5e-242j)
| (8.3049952807380589999 - 6.6956600240385424033e-687j)  +/-  (6.65e-244, 6.65e-244j)
| (8.8452629519148849677 + 9.1773937527163682146e-697j)  +/-  (9.44e-245, 9.44e-245j)
| (3.4349541804640816027 - 6.8828399781647474298e-707j)  +/-  (1.84e-244, 1.84e-244j)
| (6.9570790805126789851 - 1.0332161757185581965e-722j)  +/-  (1.71e-242, 1.71e-242j)
| (9.4970835245009833739 - 6.3320829121103171834e-734j)  +/-  (5.69e-246, 5.69e-246j)
| (-4.4122465150669981052 + 6.8246668545324349488e-731j)  +/-  (4.49e-243, 4.49e-243j)
| (-8.3049952807380589999 - 6.2038146757879607685e-734j)  +/-  (6.36e-244, 6.36e-244j)
| (-0.99604630187189663776 + 2.9722399332000362856e-741j)  +/-  (5.88e-251, 5.88e-251j)
| (-6.1740132917345514481 + 5.3801891272152234116e-731j)  +/-  (3.36e-242, 3.36e-242j)
| (2.8049532348228767071 + 4.0789200321150673207e-744j)  +/-  (1.19e-245, 1.19e-245j)
| (2.1888581949538741655 - 4.0227015570554972687e-745j)  +/-  (3.68e-247, 3.68e-247j)
| (-7.3765036833482451818 + 2.9805200512498662003e-739j)  +/-  (8.57e-243, 8.57e-243j)
| (-1.8856194376348622753 - 2.3347399275860897256e-757j)  +/-  (4.9e-248, 4.9e-248j)
| (2.4952748779465442051 + 1.2158617880498622296e-753j)  +/-  (2.16e-246, 2.16e-246j)
| (5.0921302179711997603 + 2.7487829834443434953e-751j)  +/-  (1.85e-242, 1.85e-242j)
| (0.14030424177347960115 - 1.8222008818724252203e-770j)  +/-  (2.49e-254, 2.49e-254j)
| (-5.0921302179711997603 - 1.8707488661371316653e-758j)  +/-  (1.79e-242, 1.79e-242j)
| (-5.4431664149412417357 + 1.1499720954787718093e-762j)  +/-  (2.55e-242, 2.55e-242j)
| (-3.1180842239819330924 - 1.9857425599374064376e-768j)  +/-  (4.89e-245, 4.89e-245j)
| (-3.7559402270592970053 + 4.0062306302413011035e-767j)  +/-  (6.07e-244, 6.07e-244j)
| (3.7559402270592970053 + 1.3238148431790481478e-764j)  +/-  (6.24e-244, 6.24e-244j)
| (3.1180842239819330924 + 3.8045683173884966848e-768j)  +/-  (5.13e-245, 5.13e-245j)
| (-6.9570790805126789851 + 1.0162158538183979243e-765j)  +/-  (1.63e-242, 1.63e-242j)
| (-1.2889758960285045456 + 2.4613938547630602847e-786j)  +/-  (7.25e-250, 7.25e-250j)
| (-6.557644658215203785 + 1.1934234162664313784e-777j)  +/-  (2.57e-242, 2.57e-242j)
| (1.2889758960285045456 - 1.2754790564051669023e-802j)  +/-  (6.85e-250, 6.85e-250j)
| (0.99604630187189663776 + 1.2887461924609253847e-803j)  +/-  (6.21e-251, 6.21e-251j)
| (6.1740132917345514481 - 8.0990984523333120786e-794j)  +/-  (3.07e-242, 3.07e-242j)
| (-1.5855992256102699172 - 4.7112388449333161772e-809j)  +/-  (6.42e-249, 6.42e-249j)
| (7.8222747489710367792 + 3.4334603649465760128e-801j)  +/-  (3.18e-243, 3.18e-243j)
| (4.4122465150669981052 + 1.8755380523335214441e-807j)  +/-  (4.52e-243, 4.52e-243j)
| (-4.0815129628992363816 + 3.597525573586541255e-817j)  +/-  (1.83e-243, 1.83e-243j)
| (5.8032428405535376017 - 6.5059303709790248682e-813j)  +/-  (3.04e-242, 3.04e-242j)
| (1.8856194376348622753 + 1.6717105733573243385e-831j)  +/-  (5.26e-248, 5.26e-248j)
| (-0.7071067811865475244 + 1.4677014131635301284e-835j)  +/-  (4.89e-252, 4.89e-252j)
| (-4.7488368171512616675 - 4.1770177668742317462e-826j)  +/-  (9.52e-243, 9.52e-243j)
| (4.7488368171512616675 - 2.2277023911814804507e-825j)  +/-  (9.35e-243, 9.35e-243j)
| (1.5855992256102699172 - 7.0758621901629980885e-847j)  +/-  (6.67e-249, 6.67e-249j)
| (-0.14030424177347960115 - 7.8213428142537647169e-852j)  +/-  (2.49e-254, 2.49e-254j)
| (-2.1888581949538741655 - 3.0976915735881518079e-845j)  +/-  (3.57e-247, 3.57e-247j)
| (-2.4952748779465442051 + 3.9265597148693012897e-845j)  +/-  (2.35e-246, 2.35e-246j)
| (5.4431664149412417357 + 3.9623065770873588763e-839j)  +/-  (2.45e-242, 2.45e-242j)
| (0.42213707163209713661 + 7.1371188233265901428e-863j)  +/-  (3.09e-253, 3.09e-253j)
| (4.0815129628992363816 - 1.8436036914075295728e-851j)  +/-  (1.81e-243, 1.81e-243j)
| (-3.4349541804640816027 + 5.7909138901969098782e-865j)  +/-  (2e-244, 2e-244j)
| (-0.42213707163209713661 + 2.314489943328869964e-875j)  +/-  (3.09e-253, 3.09e-253j)
| (-5.8032428405535376017 + 6.8706639285019103299e-863j)  +/-  (3.05e-242, 3.05e-242j)
| (0.7071067811865475244 + 1.2389133189773593467e-886j)  +/-  (5.23e-252, 5.23e-252j)
-------------------------------------------------
The weights are:
| (5.6886313196864588691e-25 + 6.2026828074353613229e-664j)  +/-  (4.01e-70, 9.86e-191j)
| (6.7261790850119303657e-05 + 2.155798837408496957e-655j)  +/-  (2.42e-48, 5.95e-169j)
| (3.445706583629362038e-35 + 3.3188208500683914233e-671j)  +/-  (8.77e-75, 2.16e-195j)
| (6.9568685471518239335e-28 + 1.7950894447893911232e-667j)  +/-  (2.15e-72, 5.3e-193j)
| (2.8640459800951226715e-40 - 8.5780136705415599927e-674j)  +/-  (1.29e-76, 3.17e-197j)
| (4.6528594992176480206e-20 + 3.2340208434860136938e-662j)  +/-  (3.31e-70, 8.13e-191j)
| (3.17378574487511583e-31 - 5.919407509370890076e-668j)  +/-  (1.09e-75, 2.68e-196j)
| (3.445706583629362038e-35 + 3.6654840913142728202e-670j)  +/-  (1.68e-77, 4.12e-198j)
| (1.3515128857388858629e-06 - 6.6246355851881229989e-656j)  +/-  (1.65e-60, 4.07e-181j)
| (2.2001433213546471951e-22 - 4.100156552337847719e-663j)  +/-  (3.46e-72, 8.51e-193j)
| (2.8640459800951226715e-40 - 6.8255794438226173514e-673j)  +/-  (9e-80, 2.21e-200j)
| (6.6032231318984450355e-10 - 3.8988604942898819686e-658j)  +/-  (1.82e-67, 4.48e-188j)
| (3.17378574487511583e-31 - 3.5048436039951832378e-669j)  +/-  (1.99e-78, 4.89e-199j)
| (0.060870856473252671374 + 1.5298493371474636152e-653j)  +/-  (2.78e-56, 6.85e-177j)
| (5.9277788532023397421e-18 + 2.3379155564313651652e-662j)  +/-  (4.44e-74, 1.09e-194j)
| (6.7261790850119303657e-05 - 4.8012535920114368516e-655j)  +/-  (1.5e-60, 3.7e-181j)
| (0.0014279899287823010619 - 2.3791520568944292017e-654j)  +/-  (5.31e-57, 1.31e-177j)
| (5.6886313196864588691e-25 - 5.5994999139498141725e-666j)  +/-  (5.49e-77, 1.35e-197j)
| (0.0048614345417642836821 - 2.7429063911920968807e-654j)  +/-  (1.98e-56, 4.87e-177j)
| (0.000343494707263600685 + 1.1189539090327650783e-654j)  +/-  (3.1e-59, 7.61e-180j)
| (1.0728907653654470705e-12 + 7.0908068438668506832e-659j)  +/-  (1.49e-71, 3.65e-192j)
| (0.15534917118543772211 + 3.6228957715888735676e-653j)  +/-  (2.69e-57, 6.62e-178j)
| (1.0728907653654470705e-12 - 1.2991039061569624855e-659j)  +/-  (5.72e-72, 1.41e-192j)
| (2.7210382191299875151e-14 + 1.8888925915438858448e-660j)  +/-  (5.25e-73, 1.29e-193j)
| (1.0647654341065482485e-05 - 7.6024869097834986031e-656j)  +/-  (6.59e-66, 1.62e-186j)
| (1.3622496225591380523e-07 - 6.8737703010032306226e-657j)  +/-  (1.68e-68, 4.13e-189j)
| (1.3622496225591380523e-07 + 2.1135346257143921577e-656j)  +/-  (1.46e-69, 3.59e-190j)
| (1.0647654341065482485e-05 + 1.8735816856567229139e-655j)  +/-  (2.16e-66, 5.31e-187j)
| (2.2001433213546471951e-22 + 1.1997743774736492783e-664j)  +/-  (4.33e-78, 1.06e-198j)
| (0.031581877265039573614 - 9.4514935275245484754e-654j)  +/-  (3.99e-60, 9.81e-181j)
| (4.6528594992176480206e-20 - 1.9005159774464924386e-663j)  +/-  (4.01e-77, 9.85e-198j)
| (0.031581877265039573614 + 1.3454020586262830499e-653j)  +/-  (2.97e-61, 7.3e-182j)
| (0.060870856473252671374 - 2.007495588590787452e-653j)  +/-  (4.78e-61, 1.18e-181j)
| (5.9277788532023397421e-18 - 2.6345295272092438016e-661j)  +/-  (5.67e-79, 1.4e-199j)
| (0.013623838414846746299 + 5.3260960462870341666e-654j)  +/-  (5.52e-64, 1.36e-184j)
| (6.9568685471518239335e-28 + 6.120443617498987091e-666j)  +/-  (4.5e-83, 1.11e-203j)
| (6.6032231318984450355e-10 + 1.5505635915955410876e-657j)  +/-  (3.13e-75, 7.69e-196j)
| (1.077854615088083312e-08 + 1.7415609353286270839e-657j)  +/-  (3.49e-74, 8.6e-195j)
| (4.8735214913864057891e-16 + 1.9376589249289060319e-660j)  +/-  (9.18e-79, 2.26e-199j)
| (0.0048614345417642836821 + 4.6267842438422172051e-654j)  +/-  (5.89e-69, 1.45e-189j)
| (0.098177026925758146497 - 2.246714947716032668e-653j)  +/-  (3.92e-67, 9.68e-188j)
| (3.0807771345047889343e-11 + 7.6447952765207001585e-659j)  +/-  (2.72e-76, 6.71e-197j)
| (3.0807771345047889343e-11 - 3.5276825595571050871e-658j)  +/-  (1.89e-76, 4.66e-197j)
| (0.013623838414846746299 - 8.2427574532973819707e-654j)  +/-  (8e-69, 1.98e-189j)
| (0.15534917118543772211 - 3.4876501594899167427e-653j)  +/-  (1.35e-67, 3.34e-188j)
| (0.0014279899287823010619 + 1.2903011495684581151e-654j)  +/-  (1.03e-71, 2.56e-192j)
| (0.000343494707263600685 - 5.5328125652220238721e-655j)  +/-  (1.87e-72, 4.62e-193j)
| (2.7210382191299875151e-14 - 1.252496409492779428e-659j)  +/-  (1.5e-78, 3.67e-199j)
| (0.1336849019040389452 - 3.3273708660178285521e-653j)  +/-  (1.28e-70, 2.96e-191j)
| (1.077854615088083312e-08 - 6.0561124062373430702e-657j)  +/-  (1.58e-75, 3.88e-196j)
| (1.3515128857388858629e-06 + 2.4151533903657703588e-656j)  +/-  (3.6e-75, 8.77e-196j)
| (0.1336849019040389452 + 2.9671525566436304032e-653j)  +/-  (3.19e-71, 6.09e-192j)
| (4.8735214913864057891e-16 - 2.3129753734372000899e-661j)  +/-  (1.46e-80, 4.35e-201j)
| (0.098177026925758146497 + 2.7231200556673920407e-653j)  +/-  (1.56e-71, 2.41e-192j)
