Starting with polynomial:
P : t^10 - 45*t^8 + 630*t^6 - 3150*t^4 + 4725*t^2 - 945
Extension levels are: 10 50
-------------------------------------------------
Trying to find an order 50 Kronrod extension for:
P1 : t^10 - 45*t^8 + 630*t^6 - 3150*t^4 + 4725*t^2 - 945
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^60 - 9492312571058968951805187175243884534893418794829241417956725055/6220146751176593171680212982440348523387779739533737982683084*t^58 + 289569461652281171936368882336014833847419423922444965975131802095485/267466310300593506382249158244934986505674528799950733255372612*t^56 - 444476881040471483842610519247339325614352858571271815305505070928268175/936132086052077272337872053857272452769860850799827566393804142*t^54 + 5542177081294463781808169967133566159293093638895968631678234400373949523825/38381415528135168165852754208148170563564294882792930222145969822*t^52 - 355109331476178551419205594774450558644348835627276455506956230103934755580315/10966118722324333761672215488042334446732655680797980063470277092*t^50 + 60966443099370377729126837729178350892445784833233454398642990970612320756040875/10966118722324333761672215488042334446732655680797980063470277092*t^48 - 2053059687514629304920361645665789629893168791122074029185885163909787252989209625/2741529680581083440418053872010583611683163920199495015867569273*t^46 + 220629333209978380816381282002344461923997129458666359405736409363415056634544986250/2741529680581083440418053872010583611683163920199495015867569273*t^44 - 161806840260447656030313538886419870869025034425079452090135602086207837078037763125/23184183345294574548989884752732208132627179029171205208182404*t^42 + 278347227111725076345589360732686897076634993163499849612007620598253322625627989125/565467886470599379243655725676395320307979976321248907516644*t^40 - 8022505071050841186752934233240525043231844333859878143026519027205289755014565624375/282733943235299689621827862838197660153989988160624453758322*t^38 + 378963633366278168606792729676396804029606790710339744988421399727883563088238058488125/282733943235299689621827862838197660153989988160624453758322*t^36 - 29360840282070420475070114379777809346899341524712047615322268367381755806428189366121875/565467886470599379243655725676395320307979976321248907516644*t^34 + 931820708516374283770996874732518598346194617807415403178109133981549769266677454869221875/565467886470599379243655725676395320307979976321248907516644*t^32 - 6041163634059030193955074599741601341922267353095875241959975115822938332517430125685148750/141366971617649844810913931419098830076994994080312226879161*t^30 + 127470764937521247835001761339776314630236345009719362595319040793633515967255190163557940625/141366971617649844810913931419098830076994994080312226879161*t^28 - 8702112542181446307115650910398999491918983261784683452722468016115544211262068281082491409375/565467886470599379243655725676395320307979976321248907516644*t^26 + 119195852961911610261236922206512921804877238225972308271295762575622301848499354087652228984375/565467886470599379243655725676395320307979976321248907516644*t^24 - 648705870199984056527684484837810503148136610357443937072556122139140385945947711597096852109375/282733943235299689621827862838197660153989988160624453758322*t^22 + 5541682051001726042978710648722706228280734199605255402561774963005718083223226889670865477390625/282733943235299689621827862838197660153989988160624453758322*t^20 - 73158146107495777283165409886560894765897068012710116076579816701768799620776246176513184819765625/565467886470599379243655725676395320307979976321248907516644*t^18 + 365824213267915985670125997764403343233518020381655162585091005731340775577037968031316943106015625/565467886470599379243655725676395320307979976321248907516644*t^16 - 337759620152323044340686035432792911562880570895605146716783696288875996344319601976384709566015625/141366971617649844810913931419098830076994994080312226879161*t^14 + 890973494967435964903096033963096529063366890373146756398463553141083490164425143751264799935937500/141366971617649844810913931419098830076994994080312226879161*t^12 - 6417382648111294718092783436413837505144315807783471194103484156121964730167335512325953303617484375/565467886470599379243655725676395320307979976321248907516644*t^10 + 7401941780673681563614877313638509127866991507254489097356668557302084069848092434054322529857109375/565467886470599379243655725676395320307979976321248907516644*t^8 - 2491486312349906606203601953419755331068570423456215044507572632218895056199136103649176482531015625/282733943235299689621827862838197660153989988160624453758322*t^6 + 847335992218394425614318893353462619561250434339540355625401298438747375623858005051074110010546875/282733943235299689621827862838197660153989988160624453758322*t^4 - 225265444131559660069100055029893479128732840061620884403503547992388035225307910268641281422265625/565467886470599379243655725676395320307979976321248907516644*t^2 + 5484937826469426761090580883942370416771820459429497666030730388927646928323064709801822892265625/565467886470599379243655725676395320307979976321248907516644
-------------------------------------------------
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
Positive weights:   60 out of 60
Indefinite weights: 0 out of 60
Negative weights:   0 out of 60
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (-10.198434808379956712 - 3.1243385208608565914e-694j)  +/-  (8.86e-242, 8.86e-242j)
| (10.198434808379956712 + 4.5297627381173428006e-704j)  +/-  (9.58e-242, 9.58e-242j)
| (-10.784418883772789755 - 1.4063825120936576647e-716j)  +/-  (4.35e-242, 4.35e-242j)
| (13.752114354839086174 + 1.9874556786135424499e-719j)  +/-  (2.15e-245, 2.15e-245j)
| (-12.082878495711971847 + 9.5581196147359120969e-719j)  +/-  (2.8e-243, 2.8e-243j)
| (9.105490163805167746 - 5.2819427235770384892e-721j)  +/-  (2.12e-241, 2.12e-241j)
| (-2.7899314613659834685 - 2.0998288468932911714e-738j)  +/-  (1.49e-246, 1.49e-246j)
| (-12.839122847740378053 - 2.5307812094049033159e-736j)  +/-  (3.98e-244, 3.98e-244j)
| (8.5885485175640551097 - 1.696783376086292484e-732j)  +/-  (2.14e-241, 2.14e-241j)
| (4.4272163421090473033 + 1.1257719104304193412e-741j)  +/-  (4.4e-244, 4.4e-244j)
| (2.2086180791003702969 + 4.2309147810373979115e-746j)  +/-  (9.45e-248, 9.45e-248j)
| (7.1207394622132696541 + 6.3999633158060514834e-738j)  +/-  (1.11e-241, 1.11e-241j)
| (-11.407609633746237376 - 3.4173524641792135067e-752j)  +/-  (1.37e-242, 1.37e-242j)
| (9.6407468739027313832 + 1.0541988719177517129e-748j)  +/-  (1.52e-241, 1.52e-241j)
| (7.5982263984939797468 - 1.5519416040581417977e-757j)  +/-  (1.77e-241, 1.77e-241j)
| (-13.752114354839086174 - 1.1662938675015964395e-768j)  +/-  (2.19e-245, 2.19e-245j)
| (4.0010376876102191191 + 1.2462352120549183273e-768j)  +/-  (1.15e-244, 1.15e-244j)
| (-8.0868954325726278213 - 1.2754802210577654105e-763j)  +/-  (2.18e-241, 2.18e-241j)
| (-7.1207394622132696541 - 4.2612667813747198751e-764j)  +/-  (1.09e-241, 1.09e-241j)
| (-6.652997885167562342 - 2.0177374608431350276e-765j)  +/-  (6.1e-242, 6.1e-242j)
| (12.839122847740378053 - 5.7608645387730239821e-768j)  +/-  (4.31e-244, 4.31e-244j)
| (11.407609633746237376 - 6.8187515220638746319e-765j)  +/-  (1.46e-242, 1.46e-242j)
| (5.742333725335459198 - 4.9657131546201699831e-766j)  +/-  (1.23e-242, 1.23e-242j)
| (12.082878495711971847 - 1.1800094819318810131e-766j)  +/-  (3.09e-243, 3.09e-243j)
| (10.784418883772789755 + 9.8518185452641288637e-769j)  +/-  (3.92e-242, 3.92e-242j)
| (-3.1731049597568504118 - 1.5057573890548744198e-779j)  +/-  (5.76e-246, 5.76e-246j)
| (2.4843258416389545809 - 6.8083502504977337804e-781j)  +/-  (5.14e-247, 5.14e-247j)
| (-2.4843258416389545809 + 1.3962679115589966168e-780j)  +/-  (4.61e-247, 4.61e-247j)
| (-9.6407468739027313832 - 9.690270911055069936e-774j)  +/-  (1.68e-241, 1.68e-241j)
| (-3.5818234835519269228 - 8.5459877981425608316e-780j)  +/-  (2.7e-245, 2.7e-245j)
| (-5.742333725335459198 - 1.8801214428109860257e-776j)  +/-  (1.32e-242, 1.32e-242j)
| (-1.8512438791190664634 - 1.0905360013304390817e-783j)  +/-  (8.08e-249, 8.08e-249j)
| (-8.5885485175640551097 + 1.9699438417175022952e-775j)  +/-  (2.3e-241, 2.3e-241j)
| (-2.2086180791003702969 - 1.7067908568140997527e-781j)  +/-  (9.3e-248, 9.3e-248j)
| (-1.0857566371832125352 + 1.308180303568304934e-786j)  +/-  (5.07e-251, 5.07e-251j)
| (-4.0010376876102191191 - 4.4346072354175125276e-779j)  +/-  (1.14e-244, 1.14e-244j)
| (-9.105490163805167746 + 1.0048865168463523661e-776j)  +/-  (2.01e-241, 2.01e-241j)
| (1.4659890943911581833 - 1.8696288113161670639e-784j)  +/-  (5.29e-250, 5.29e-250j)
| (6.1938420132132985002 - 1.1908130168246476658e-774j)  +/-  (3.2e-242, 3.2e-242j)
| (8.0868954325726278213 + 5.9363617149980976378e-791j)  +/-  (2.11e-241, 2.11e-241j)
| (-0.74779309566459435673 + 1.3331227262856101683e-807j)  +/-  (5.32e-252, 5.32e-252j)
| (4.8594628283323121502 + 3.0039783627747772053e-795j)  +/-  (1.48e-243, 1.48e-243j)
| (1.0857566371832125352 - 1.7306911314387449239e-804j)  +/-  (4.72e-251, 4.72e-251j)
| (0.17582387532560275953 + 2.4956774158166543221e-807j)  +/-  (3.71e-254, 3.71e-254j)
| (-5.2977264848189744724 - 1.2469204284983740538e-796j)  +/-  (4.73e-243, 4.73e-243j)
| (-4.4272163421090473033 + 1.2373008657489891859e-798j)  +/-  (4.2e-244, 4.2e-244j)
| (-4.8594628283323121502 - 4.7864384969260437475e-799j)  +/-  (1.5e-243, 1.5e-243j)
| (2.7899314613659834685 - 1.5693925431494810521e-800j)  +/-  (1.51e-246, 1.51e-246j)
| (0.48493570751549765305 + 7.4586620439019174282e-807j)  +/-  (7.25e-253, 7.25e-253j)
| (5.2977264848189744724 - 2.9888822943685050304e-795j)  +/-  (4.61e-243, 4.61e-243j)
| (-6.1938420132132985002 + 1.4183319834791834277e-798j)  +/-  (3.16e-242, 3.16e-242j)
| (-1.4659890943911581833 + 5.5195479206088738346e-807j)  +/-  (5.92e-250, 5.92e-250j)
| (-7.5982263984939797468 - 1.4088917820647372849e-802j)  +/-  (1.6e-241, 1.6e-241j)
| (1.8512438791190664634 + 6.2487331407114796752e-810j)  +/-  (7.06e-249, 7.06e-249j)
| (0.74779309566459435673 + 1.6689759777331976297e-814j)  +/-  (5.35e-252, 5.35e-252j)
| (3.5818234835519269228 + 4.8755954204977867991e-808j)  +/-  (2.57e-245, 2.57e-245j)
| (-0.48493570751549765305 - 2.5596547281799334275e-820j)  +/-  (7.29e-253, 7.29e-253j)
| (-0.17582387532560275953 - 7.8540983239411247136e-821j)  +/-  (3.71e-254, 3.71e-254j)
| (6.652997885167562342 - 4.0177941046532835126e-818j)  +/-  (6.12e-242, 6.12e-242j)
| (3.1731049597568504118 + 4.4354110986269648262e-833j)  +/-  (6.14e-246, 6.14e-246j)
-------------------------------------------------
The weights are:
| (5.9186765099051558177e-24 - 1.0315566558740053694e-716j)  +/-  (6.66e-54, 6.13e-174j)
| (5.9186765099051558177e-24 + 9.0660719290788833114e-719j)  +/-  (4.26e-55, 3.92e-175j)
| (1.3366547759284405239e-26 - 1.1411685120342795783e-718j)  +/-  (1.73e-55, 1.59e-175j)
| (3.6052600440202927013e-42 - 1.3911338970614126533e-728j)  +/-  (2.64e-63, 2.43e-183j)
| (5.6095528750638312207e-33 - 1.3170868249183139172e-722j)  +/-  (4.59e-59, 4.23e-179j)
| (2.0788917410413362019e-19 + 3.1223208641306721223e-716j)  +/-  (3.84e-53, 3.53e-173j)
| (0.0029020956417171514321 - 5.9782093607677265765e-705j)  +/-  (3.6e-27, 3.32e-147j)
| (5.20424345248916579e-37 + 6.7199035038504819935e-725j)  +/-  (4.25e-61, 3.91e-181j)
| (1.9500349785160435621e-17 - 4.1317684697618534214e-715j)  +/-  (4.09e-52, 3.77e-172j)
| (9.4950644721908657554e-06 + 9.9091199330631791392e-708j)  +/-  (2.6e-39, 2.39e-159j)
| (0.011172212168569619533 + 1.6495183767358130694e-704j)  +/-  (6.53e-25, 6.01e-145j)
| (1.8398583417528953495e-12 + 3.4327854743975308539e-712j)  +/-  (3.47e-49, 3.2e-169j)
| (1.4223374980994953027e-29 + 1.3702100289239091625e-720j)  +/-  (1.53e-59, 1.41e-179j)
| (1.4299029017898560622e-21 - 1.9067294769190114629e-717j)  +/-  (2.63e-55, 2.42e-175j)
| (5.5990782862712460918e-14 - 4.2463348969569406969e-713j)  +/-  (1.68e-50, 1.55e-170j)
| (3.6052600440202927013e-42 - 9.3757527449396325739e-728j)  +/-  (1.17e-65, 1.07e-185j)
| (5.6370779062322567676e-05 - 4.2723755463656854283e-707j)  +/-  (7.31e-40, 6.73e-160j)
| (1.2427750714944909315e-15 - 3.9351064221469849951e-713j)  +/-  (2.91e-55, 2.68e-175j)
| (1.8398583417528953495e-12 - 1.9317379800335138516e-711j)  +/-  (2.02e-53, 1.86e-173j)
| (4.5216333461882884417e-11 + 1.1586403184633086928e-710j)  +/-  (1.82e-52, 1.67e-172j)
| (5.20424345248916579e-37 + 7.7027127160373233207e-726j)  +/-  (9.83e-67, 9.05e-187j)
| (1.4223374980994953027e-29 + 7.6683331886866448891e-722j)  +/-  (9.93e-64, 9.14e-184j)
| (1.2354894564439568017e-08 - 8.7845526428717777198e-710j)  +/-  (5.65e-52, 5.2e-172j)
| (5.6095528750638312207e-33 - 1.1139271385111640887e-723j)  +/-  (1.63e-65, 1.5e-185j)
| (1.3366547759284405239e-26 - 3.18691913250492069e-720j)  +/-  (3.09e-62, 2.84e-182j)
| (0.0010402834055984889795 + 1.480839773050397885e-705j)  +/-  (3.44e-47, 3.17e-167j)
| (0.004702101760960172488 - 9.9408035950363834108e-705j)  +/-  (9.92e-43, 9.13e-163j)
| (0.004702101760960172488 + 1.6343667587170797766e-704j)  +/-  (9.07e-44, 8.35e-164j)
| (1.4299029017898560622e-21 + 6.7829964336539158037e-716j)  +/-  (6.22e-64, 5.73e-184j)
| (0.00027104987811853176207 - 3.7641985328196681384e-706j)  +/-  (5.01e-50, 4.61e-170j)
| (1.2354894564439568017e-08 + 3.1424897642478088734e-709j)  +/-  (2.63e-57, 2.42e-177j)
| (0.027289043534765728291 + 3.367494029969813741e-704j)  +/-  (4.45e-43, 4.09e-163j)
| (1.9500349785160435621e-17 + 4.8216737990299402723e-714j)  +/-  (1.09e-62, 1e-182j)
| (0.011172212168569619533 - 2.561468233273739589e-704j)  +/-  (1.81e-45, 1.66e-165j)
| (0.081571626616788455788 + 1.0278135569731695058e-703j)  +/-  (8.2e-41, 7.55e-161j)
| (5.6370779062322567676e-05 + 9.7888642436938204966e-707j)  +/-  (4.1e-53, 3.77e-173j)
| (2.0788917410413362019e-19 - 5.5147393011440767492e-715j)  +/-  (1.28e-63, 1.18e-183j)
| (0.052663240435384405684 + 3.9832931065694663518e-704j)  +/-  (1.64e-45, 1.51e-165j)
| (8.4827747116981941085e-10 + 1.5412356563026147541e-710j)  +/-  (2.94e-60, 2.71e-180j)
| (1.2427750714944909315e-15 + 4.5441520817890803435e-714j)  +/-  (5.33e-63, 4.91e-183j)
| (0.08878508756801837802 - 2.0824275119678063169e-703j)  +/-  (1.27e-45, 1.17e-165j)
| (1.2936776964684078923e-06 - 2.1968619048102249285e-708j)  +/-  (7.52e-58, 6.92e-178j)
| (0.081571626616788455788 - 8.3002262140698128596e-704j)  +/-  (1.31e-46, 1.2e-166j)
| (0.13549037821437248194 + 2.4342554462712285049e-703j)  +/-  (3.15e-46, 2.9e-166j)
| (1.4166688762467908876e-07 - 1.4447788458085070584e-708j)  +/-  (5.14e-59, 4.73e-179j)
| (9.4950644721908657554e-06 - 2.5112085470564845871e-707j)  +/-  (2.76e-57, 2.54e-177j)
| (1.2936776964684078923e-06 + 6.1959721497088787907e-708j)  +/-  (2.16e-58, 1.99e-178j)
| (0.0029020956417171514321 + 3.4099426464410458534e-705j)  +/-  (2.63e-56, 2.42e-176j)
| (0.094045566337302498881 - 2.5013472967915282631e-703j)  +/-  (1.73e-50, 1.6e-170j)
| (1.4166688762467908876e-07 + 4.5691572115636048561e-709j)  +/-  (5.26e-61, 4.85e-181j)
| (8.4827747116981941085e-10 - 6.3088465748662429704e-710j)  +/-  (1.09e-61, 1.01e-181j)
| (0.052663240435384405684 - 5.3207109267838852684e-704j)  +/-  (4.94e-54, 4.55e-174j)
| (5.5990782862712460918e-14 + 2.9063279434886223319e-712j)  +/-  (1.99e-64, 1.83e-184j)
| (0.027289043534765728291 - 2.3327688934482733629e-704j)  +/-  (5.61e-56, 5.16e-176j)
| (0.08878508756801837802 + 1.7979048563565820741e-703j)  +/-  (2.19e-54, 2.01e-174j)
| (0.00027104987811853176207 + 1.8073854718638457243e-706j)  +/-  (7.92e-60, 7.3e-180j)
| (0.094045566337302498881 + 2.7511012956101234334e-703j)  +/-  (2.61e-55, 2.43e-175j)
| (0.13549037821437248194 - 2.5196623784730182103e-703j)  +/-  (2.57e-55, 2.4e-175j)
| (4.5216333461882884417e-11 - 2.4377073675580441545e-711j)  +/-  (5.86e-65, 5.5e-185j)
| (0.0010402834055984889795 - 7.7802467307102592193e-706j)  +/-  (2.81e-59, 2.56e-179j)
