Starting with polynomial:
P : 16*t^4 - 48*t^2 + 12
Extension levels are: 4 54
-------------------------------------------------
Trying to find an order 54 Kronrod extension for:
P1 : 16*t^4 - 48*t^2 + 12
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 16*t^58 - 1927247844876430567926952406969296728032807680584/156076154376443784020471091257586920927888413*t^56 + 17279266019006778662638474953980504516346736311907584/3901903859411094600511777281439673023197210325*t^54 - 3828889861624268390184819835878807951217135362558191352/3901903859411094600511777281439673023197210325*t^52 + 34587858134481660284478592287171583651388751293211735489/229523756435946741206575134202333707246894725*t^50 - 313103327864853580056994855510085933893495397465880034137/18361900514875739296526010736186696579751578*t^48 + 13549036893792942307005253964464767077217346848673562347746/9180950257437869648263005368093348289875789*t^46 - 918984551499850730722192022466531110134736288657100004429986/9180950257437869648263005368093348289875789*t^44 + 794538845014129648470699268513392214962153278336572792544979633/146895204119005914372208085889493572638012624*t^42 - 69177487823800388923668858675473939865661041605149032198053267109/293790408238011828744416171778987145276025248*t^40 + 611018162814638624734923768212064396310093864334979262613006496555/73447602059502957186104042944746786319006312*t^38 - 70391911151115054771335792282248412102736027506400928801723763476995/293790408238011828744416171778987145276025248*t^36 + 779333637989924765643210269685418935211618979283419582967216903376845/138254309759064389997372316131288068365188352*t^34 - 29953719089485537915319425979961383177602128725119829198718300016537845/276508619518128779994744632262576136730376704*t^32 + 1892266351813845756512592142054480065040049169038662731934798533831435/1114954110960196693527196097832968293267648*t^30 - 3009432720079112753655048444871701110210837956184619529189167055982325/139369263870024586690899512229121036658456*t^28 + 15827838074432466441339204342458276552820853695777100397796891393111866025/71357063101452588385740550261309970769129472*t^26 - 260447175123455310528954174062809760942587897966400013532752871124826895125/142714126202905176771481100522619941538258944*t^24 + 3609087898174067165036330955440198293331153799181040284355460164140920284625/303267518181173500639397338610567375768800256*t^22 - 147237944811654950859198984232732669658481526220615165148338022124266693439875/2426140145449388005115178708884539006150402048*t^20 + 16670128167846588697048695682599561283528776789042767862362650047380160020625/70069029471462469461810215419048057939361792*t^18 - 1601719386333225827265394935155227513552067890041845876657879164516684547563125/2283426019246482828343697608361919064612143104*t^16 + 863240581079694267738270730915967127839910306325838177518432832035523339566875/570856504811620707085924402090479766153035776*t^14 - 1311159053249787030432329686074592697628660004794526232725541538969612634100625/570856504811620707085924402090479766153035776*t^12 + 42713170349850561155381000153393496356203614985665963913784416637898486396283125/18267408153971862626749580866895352516897144832*t^10 - 54370761792643034557102493761731183274925589864972879043430856425611512784715625/36534816307943725253499161733790705033794289664*t^8 + 4887206491208354686489118099189132270659035526237353219116101254423696673940625/9133704076985931313374790433447676258448572416*t^6 - 3393251311775997349379287530126235887554224439059568110763834623713159001044375/36534816307943725253499161733790705033794289664*t^4 + 1732666741636409132971923115171010390371477989116234686321365942463579342580625/292278530463549802027993293870325640270354317312*t^2 - 38861352563804617800545142221247228372176854072008492018589507033117973735625/584557060927099604055986587740651280540708634624
-------------------------------------------------
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:
| (-8.6011361033326890298 + 2.64380380822003672e-853j)  +/-  (1.89e-243, 1.89e-243j)
| (-9.7823697840363897941 + 2.2432510348001044998e-861j)  +/-  (1.42e-245, 1.42e-245j)
| (-7.2665291733582762961 - 8.5331345159854543806e-857j)  +/-  (6.05e-242, 6.05e-242j)
| (6.1249430375059790354 + 1.2915879941645988882e-864j)  +/-  (1.44e-241, 1.44e-241j)
| (8.1230539684537827762 + 2.0853203456374392766e-866j)  +/-  (9.34e-243, 9.34e-243j)
| (5.0822749096512038094 - 4.039365235598699331e-864j)  +/-  (6.06e-242, 6.06e-242j)
| (7.6816931804992916173 + 1.5139768460546130454e-864j)  +/-  (2.83e-242, 2.83e-242j)
| (9.1363800798052637972 - 2.2699546836825167669e-866j)  +/-  (2.72e-244, 2.72e-244j)
| (-4.1005163076501143942 + 1.5551993978479613483e-864j)  +/-  (5.96e-243, 5.96e-243j)
| (1.6506801238857845559 - 5.6903068200451537446e-870j)  +/-  (1.76e-248, 1.76e-248j)
| (1.3567085852167016573 + 3.4539661289881942417e-871j)  +/-  (1.83e-249, 1.83e-249j)
| (3.4694422855833650846 + 5.1140660911812183029e-866j)  +/-  (6e-244, 6e-244j)
| (-4.4224700589333822596 - 4.9960562357049459561e-864j)  +/-  (1.66e-242, 1.66e-242j)
| (-1.9474287434049067708 - 7.0886515084558479966e-873j)  +/-  (1.38e-247, 1.38e-247j)
| (-6.1249430375059790354 + 5.5789814380186115244e-866j)  +/-  (1.5e-241, 1.5e-241j)
| (9.7823697840363897941 - 4.4094622102486145362e-879j)  +/-  (1.3e-245, 1.3e-245j)
| (-3.7830132660143153446 + 5.8991934675213492445e-877j)  +/-  (2.21e-243, 2.21e-243j)
| (6.8712504495598105084 - 1.4779682202108940847e-875j)  +/-  (1.05e-241, 1.05e-241j)
| (-1.3567085852167016573 + 8.957795702288492479e-884j)  +/-  (1.87e-249, 1.87e-249j)
| (2.5482214265602677304 + 2.5080891771552530368e-879j)  +/-  (5.85e-246, 5.85e-246j)
| (5.4217078256025412214 + 2.1512258255663902628e-874j)  +/-  (9.57e-242, 9.57e-242j)
| (3.1593600576569770763 - 4.9010407092181443321e-881j)  +/-  (1.48e-244, 1.48e-244j)
| (6.4916970100253619349 - 5.0871732408705769243e-876j)  +/-  (1.38e-241, 1.38e-241j)
| (-2.5482214265602677304 - 4.1863809381562574188e-880j)  +/-  (6.02e-246, 6.02e-246j)
| (-8.1230539684537827762 + 7.5609333626461298195e-875j)  +/-  (9.4e-243, 9.4e-243j)
| (8.6011361033326890298 - 3.1687361744800035949e-890j)  +/-  (2.08e-243, 2.08e-243j)
| (-4.7494829909199538312 - 2.7943678072763988542e-887j)  +/-  (3.46e-242, 3.46e-242j)
| (2.2466149142557949592 - 1.0206594634207029047e-913j)  +/-  (9.77e-247, 9.77e-247j)
| (-6.4916970100253619349 + 1.1506438904802717203e-913j)  +/-  (1.41e-241, 1.41e-241j)
| (-2.2466149142557949592 + 1.6506437261119648348e-941j)  +/-  (9.6e-247, 9.6e-247j)
| (-7.6816931804992916173 - 1.2745558271895459425e-938j)  +/-  (2.7e-242, 2.7e-242j)
| (-1.6506801238857845559 - 1.2598436145587356354e-956j)  +/-  (1.72e-248, 1.72e-248j)
| (-9.1363800798052637972 + 8.8727186969007372956e-950j)  +/-  (2.46e-244, 2.46e-244j)
| (7.2665291733582762961 + 3.1886236415413138327e-953j)  +/-  (6.32e-242, 6.32e-242j)
| (1.9474287434049067708 - 1.9254601611579132462e-958j)  +/-  (1.34e-247, 1.34e-247j)
| (-1.0666659919288952338 - 3.3097047227241103294e-960j)  +/-  (1.71e-250, 1.71e-250j)
| (5.7688303734004363856 + 1.2910412573049747203e-952j)  +/-  (1.25e-241, 1.25e-241j)
| (0.78435365442643530878 + 1.2296834125099891044e-962j)  +/-  (1.97e-251, 1.97e-251j)
| (4.1005163076501143942 + 1.1944835365026020649e-953j)  +/-  (6.12e-243, 6.12e-243j)
| (-0.78435365442643530878 - 1.1640286957621636244e-961j)  +/-  (1.97e-251, 1.97e-251j)
| (-3.1593600576569770763 - 1.1187825339812177829e-954j)  +/-  (1.5e-244, 1.5e-244j)
| (-6.8712504495598105084 + 5.713522642672072004e-951j)  +/-  (1.02e-241, 1.02e-241j)
| (0.1186452755556124823 - 9.2043418009104622103e-967j)  +/-  (2.06e-254, 2.06e-254j)
| (2.8523902057741847709 - 1.8893707315631992095e-958j)  +/-  (3.18e-245, 3.18e-245j)
| (4.7494829909199538312 + 5.4096155845245143696e-956j)  +/-  (3.48e-242, 3.48e-242j)
| (-0.1186452755556124823 + 9.7171770121288158304e-967j)  +/-  (2.06e-254, 2.06e-254j)
| (-3.4694422855833650846 - 1.1536029324008738269e-957j)  +/-  (5.83e-244, 5.83e-244j)
| (4.4224700589333822596 + 7.8518321886513310907e-957j)  +/-  (1.62e-242, 1.62e-242j)
| (0.32146911575613605212 - 3.1534556855567878107e-966j)  +/-  (2.57e-253, 2.57e-253j)
| (-5.0822749096512038094 + 1.2366695823805393976e-953j)  +/-  (6.38e-242, 6.38e-242j)
| (0.52464762327529031788 + 1.2081093835273346056e-972j)  +/-  (2.07e-252, 2.07e-252j)
| (-0.52464762327529031788 - 1.1154508512494696041e-970j)  +/-  (1.99e-252, 1.99e-252j)
| (-5.4217078256025412214 - 2.3855390307308786782e-962j)  +/-  (9.17e-242, 9.17e-242j)
| (3.7830132660143153446 + 9.7629109162858758053e-975j)  +/-  (2.1e-243, 2.1e-243j)
| (1.0666659919288952338 - 2.0213079467396932172e-982j)  +/-  (1.81e-250, 1.81e-250j)
| (-5.7688303734004363856 + 7.0078461323336116182e-980j)  +/-  (1.28e-241, 1.28e-241j)
| (-0.32146911575613605212 + 1.611386196980277875e-991j)  +/-  (2.95e-253, 2.95e-253j)
| (-2.8523902057741847709 - 5.4881422753013644707e-988j)  +/-  (3.47e-245, 3.47e-245j)
-------------------------------------------------
The weights are:
| (2.1043214177409166335e-33 + 8.4177923819721917841e-886j)  +/-  (4.78e-72, 1.12e-191j)
| (1.1600314393262236166e-42 - 5.0699949926664229698e-890j)  +/-  (1.97e-75, 4.64e-195j)
| (2.6694095571968344075e-24 - 1.6909977187540460191e-879j)  +/-  (2.59e-68, 6.1e-188j)
| (1.0388517396585548693e-17 - 6.3192170891699033243e-878j)  +/-  (2.11e-66, 4.96e-186j)
| (5.6920559324973648515e-30 + 2.7169171493531513388e-884j)  +/-  (1.63e-73, 3.83e-193j)
| (1.1483885907798848089e-12 + 5.8319078815568199067e-875j)  +/-  (3.88e-63, 9.14e-183j)
| (5.6857060927813665791e-27 - 9.7269844120367542551e-883j)  +/-  (2.85e-72, 6.71e-192j)
| (1.8191259745339734668e-37 + 3.6906557213232737246e-888j)  +/-  (4.06e-77, 9.56e-197j)
| (8.9898083325942298404e-09 + 1.2046161072200383474e-871j)  +/-  (4.11e-61, 9.69e-181j)
| (0.010928980462165859227 - 8.2551953633530579814e-869j)  +/-  (6.43e-42, 1.51e-161j)
| (0.026175131725653390045 + 1.9311605590112065478e-868j)  +/-  (3.95e-38, 9.31e-158j)
| (1.0414243468576165756e-06 - 3.3962696246889518475e-871j)  +/-  (3.07e-57, 7.23e-177j)
| (5.8672434521941723369e-10 - 8.3532393671169759983e-873j)  +/-  (4.67e-63, 1.1e-182j)
| (0.0037894185733042754764 - 6.1881882566312414996e-869j)  +/-  (6.19e-48, 1.46e-167j)
| (1.0388517396585548693e-17 + 3.6767285503215294365e-877j)  +/-  (2.73e-70, 6.43e-190j)
| (1.1600314393262236166e-42 - 7.9001109004995933955e-891j)  +/-  (2.68e-80, 6.32e-200j)
| (1.08416397442637372e-07 - 3.2041262384705596053e-871j)  +/-  (1.2e-60, 2.83e-180j)
| (6.8257075442501844749e-22 - 4.2449530505551300579e-880j)  +/-  (9.15e-72, 2.16e-191j)
| (0.026175131725653390045 - 2.8953920942414277928e-868j)  +/-  (1.4e-45, 3.29e-165j)
| (0.00025858153215758021879 + 5.6621203207716659214e-870j)  +/-  (2.47e-55, 5.82e-175j)
| (3.3172375135687517428e-14 - 3.0705685244111963435e-876j)  +/-  (8.82e-68, 2.08e-187j)
| (8.0482497718407936037e-06 + 1.0032752310004303983e-870j)  +/-  (2.69e-59, 6.34e-179j)
| (1.0489090935776302325e-19 + 5.8279427978887048451e-879j)  +/-  (9.95e-71, 2.34e-190j)
| (0.00025858153215758021879 - 1.1692034488815696755e-869j)  +/-  (2.06e-58, 4.85e-178j)
| (5.6920559324973648515e-30 + 2.858606984664242126e-883j)  +/-  (1.27e-79, 2.99e-199j)
| (2.1043214177409166335e-33 - 4.578758427175548579e-886j)  +/-  (4.47e-78, 1.05e-197j)
| (2.9716819107824230735e-11 - 1.88517215623472947e-873j)  +/-  (3.95e-69, 9.31e-189j)
| (0.0010891684032654553499 - 1.4250058163954504593e-869j)  +/-  (1.24e-57, 2.93e-177j)
| (1.0489090935776302325e-19 - 6.0140517206177458293e-878j)  +/-  (2.42e-75, 5.7e-195j)
| (0.0010891684032654553499 + 2.7462386850830278969e-869j)  +/-  (1.06e-59, 2.5e-179j)
| (5.6857060927813665791e-27 - 2.3133608867245216395e-881j)  +/-  (1.16e-78, 2.74e-198j)
| (0.010928980462165859227 + 1.3494509633678463519e-868j)  +/-  (3.06e-57, 7.2e-177j)
| (1.8191259745339734668e-37 + 3.3444916848399676093e-887j)  +/-  (2e-83, 4.7e-203j)
| (2.6694095571968344075e-24 + 2.3732502987920099246e-881j)  +/-  (1.34e-76, 3.16e-196j)
| (0.0037894185733042754764 + 3.4891988155876893274e-869j)  +/-  (9.73e-61, 2.29e-180j)
| (0.051943757078499865379 + 6.2875341005920333837e-868j)  +/-  (3.17e-57, 7.45e-177j)
| (6.984499218113769747e-16 + 5.3694784180445750362e-877j)  +/-  (5.14e-73, 1.21e-192j)
| (0.083978805659205157232 + 1.1428058922607664904e-867j)  +/-  (3.75e-58, 8.82e-178j)
| (8.9898083325942298404e-09 - 2.3756253245035852694e-873j)  +/-  (2.72e-70, 6.4e-190j)
| (0.083978805659205157232 - 1.4424971760708500399e-867j)  +/-  (3.63e-59, 8.55e-179j)
| (8.0482497718407936037e-06 - 1.8750600465787145036e-870j)  +/-  (1.48e-68, 3.49e-188j)
| (6.8257075442501844749e-22 + 9.6050245744262227308e-879j)  +/-  (1.4e-78, 3.29e-198j)
| (0.12796196866842482283 - 6.1303039455057955982e-867j)  +/-  (1.22e-60, 2.87e-180j)
| (5.0465280883787814142e-05 - 2.2430035759380380153e-870j)  +/-  (2.24e-66, 5.28e-186j)
| (2.9716819107824230735e-11 - 2.5762705994686961293e-874j)  +/-  (5.44e-72, 1.28e-191j)
| (0.12796196866842482283 + 6.349587988801093574e-867j)  +/-  (3.43e-62, 8.09e-182j)
| (1.0414243468576165756e-06 + 7.3331065911371221161e-871j)  +/-  (3.58e-70, 8.43e-190j)
| (5.8672434521941723369e-10 + 9.5491398068467011752e-874j)  +/-  (1.75e-71, 4.12e-191j)
| (0.092638821999250012982 + 5.2649305786943391791e-867j)  +/-  (2.1e-63, 4.94e-183j)
| (1.1483885907798848089e-12 + 9.924627465559610461e-875j)  +/-  (2.01e-75, 4.73e-195j)
| (0.10117569291924188556 - 2.9563926471839156506e-867j)  +/-  (6.39e-65, 1.5e-184j)
| (0.10117569291924188556 + 3.454034023376594617e-867j)  +/-  (2.17e-65, 5.12e-185j)
| (3.3172375135687517428e-14 + 7.3334885675360815262e-877j)  +/-  (9.21e-77, 2.17e-196j)
| (1.08416397442637372e-07 - 1.3110827682477412987e-872j)  +/-  (2.83e-72, 6.63e-192j)
| (0.051943757078499865379 - 4.5776465803511952805e-868j)  +/-  (7.49e-68, 1.76e-187j)
| (6.984499218113769747e-16 - 1.6478797243153034556e-876j)  +/-  (1.08e-77, 2.54e-197j)
| (0.092638821999250012982 - 5.7911365287319043746e-867j)  +/-  (1.2e-67, 3.66e-187j)
| (5.0465280883787814142e-05 + 4.7664819577064897792e-870j)  +/-  (1.92e-71, 4.37e-191j)
