Starting with polynomial:
P : 1024*t^10 - 23040*t^8 + 161280*t^6 - 403200*t^4 + 302400*t^2 - 30240
Extension levels are: 10 52
-------------------------------------------------
Trying to find an order 52 Kronrod extension for:
P1 : 1024*t^10 - 23040*t^8 + 161280*t^6 - 403200*t^4 + 302400*t^2 - 30240
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 1024*t^62 - 88437343954737973965627027496681971519955707737968788538868579206267392/101475461435436910237680420608352651643167018189549275622186873811*t^60 + 35068473476588589116561335373086070928450403135860602202527786155104288000/101475461435436910237680420608352651643167018189549275622186873811*t^58 - 94789806804995861830542076945048954662621926168472817833641447124741637722240/1116230075789806012614484626691879168074837200085042031844055611921*t^56 + 63308232108104430303808866984399424970323494317531215394229803168188491828072000/4363444841723787140220258086159164020656181782150618851754035573873*t^54 - 87990434369128144687137598325424154891413011973521742661059590974111864293141100320/47997893258961658542422838947750804227217999603656807369294391312603*t^52 + 8538284123657420628277617559278514828943232400295716168299803925358887076511073258960/47997893258961658542422838947750804227217999603656807369294391312603*t^50 - 652302804190751483830285758340654087945128176852810521084934535413329023280219288935000/47997893258961658542422838947750804227217999603656807369294391312603*t^48 + 39908232192356241694076459290543970134332216111634069635376100510518464197921141234113500/47997893258961658542422838947750804227217999603656807369294391312603*t^46 - 86024690427050822417447854822023180094926266105359715040026034712528838937883941710793750/2086864924302680806192297345554382792487739113202469885621495274461*t^44 + 7366641037242394839892891233352775229242284593343933102331161307408895306742373742222375/4411976584149430879899148722102289201876826877806490244442907557*t^42 - 490192880626596863663520488275717975785506381146488855523874211172182443210375650287743625/8823953168298861759798297444204578403753653755612980488885815114*t^40 + 26878676635470392985961653312668887873738371081389494712728198354373198990992302193204490625/17647906336597723519596594888409156807507307511225960977771630228*t^38 - 1216108737650271487985181857741003590141739148221253358101256426732439457190096633232082781875/35295812673195447039193189776818313615014615022451921955543260456*t^36 + 45387024344909422387230270908445836871936626046204325655933480986309260763023423560086058859375/70591625346390894078386379553636627230029230044903843911086520912*t^34 - 1394757586110965916803920354147297997651503047076310979372041088632959499358724871614611451325625/141183250692781788156772759107273254460058460089807687822173041824*t^32 + 35175895699066884606633642672883126917142834904682392506918352678482786769463569838560143636719375/282366501385563576313545518214546508920116920179615375644346083648*t^30 - 724583159011489046182767925017490237996210174527250636844582824260153057988485397049910412274203125/564733002771127152627091036429093017840233840359230751288692167296*t^28 + 12112867882463018807217621517843256755119166990641116929880064627182694445248327017637868125624290625/1129466005542254305254182072858186035680467680718461502577384334592*t^26 - 162990866372126975738617598841460071856308822543503899388408739729661411295451105310280479146849609375/2258932011084508610508364145716372071360935361436923005154768669184*t^24 + 1747339300379341849555913465298996237804046959118564614909904733224304302211328611138969879881954734375/4517864022169017221016728291432744142721870722873846010309537338368*t^22 - 14734604769531831025120213321775826244688557867243615612837505121174692026730588509766538893592095203125/9035728044338034442033456582865488285443741445747692020619074676736*t^20 + 96187995731369364582769761159115962481988466861235162773966162292452864576064026263323424451421503515625/18071456088676068884066913165730976570887482891495384041238149353472*t^18 - 476416953982346333374280400802081513522573020368376073781847667386163319964768949370979520784331782109375/36142912177352137768133826331461953141774965782990768082476298706944*t^16 + 1744670961858846666358167366217680648982873901547990063454214950153397625556962084992047344662318138671875/72285824354704275536267652662923906283549931565981536164952597413888*t^14 - 4565854350926319628486257332059919198158310547808245694081831274094936965714874181368416693205039638390625/144571648709408551072535305325847812567099863131963072329905194827776*t^12 + 8153929335856065225860478158689508724892463147476812202546316596095284146100010210713785817471267945578125/289143297418817102145070610651695625134199726263926144659810389655552*t^10 - 9313804694797647552241053246381048885017921796295129608379870075855675448459420976372221918498633701171875/578286594837634204290141221303391250268399452527852289319620779311104*t^8 + 6192593075976735294765326912462689173696793482082832330122283031918102074603500872016849641779727381796875/1156573189675268408580282442606782500536798905055704578639241558622208*t^6 - 2075939214028246177646325399533159116635895508239832332901722226051742460172745655591161156428541369140625/2313146379350536817160564885213565001073597810111409157278483117244416*t^4 + 274591347976453695623915472153995092028901194403164022194310349231035450499083665497307910319311949453125/4626292758701073634321129770427130002147195620222818314556966234488832*t^2 - 6977984422267839807015969524030087277670123576645954116060601956714911016648503989842375111068104921875/9252585517402147268642259540854260004294391240445636629113932468977664
-------------------------------------------------
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:   62 out of 62
Indefinite weights: 0 out of 62
Negative weights:   0 out of 62
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (6.7704110475790315154 + 1.9387686905404912258e-869j)  +/-  (4.14e-241, 4.14e-241j)
| (10.173248034157624754 - 4.2472778883436100026e-883j)  +/-  (2.12e-245, 2.12e-245j)
| (-7.1531713950687693606 + 4.4461402480336306899e-878j)  +/-  (2.98e-241, 2.98e-241j)
| (5.6953299116997824551 + 1.963285390595332492e-878j)  +/-  (4.08e-241, 4.08e-241j)
| (9.4731375003859377157 - 2.2112768210308190208e-885j)  +/-  (4.67e-244, 4.67e-244j)
| (7.5528329047880997085 - 2.0481289248692740388e-882j)  +/-  (1.56e-241, 1.56e-241j)
| (-7.5528329047880997085 - 2.4341259153244696704e-885j)  +/-  (1.58e-241, 1.58e-241j)
| (8.4240682095336656567 - 1.0535036947294784786e-885j)  +/-  (1.97e-242, 1.97e-242j)
| (-3.4361591188377376033 - 1.184813281395689738e-889j)  +/-  (1.53e-243, 1.53e-243j)
| (-9.4731375003859377157 + 1.0435857049086232517e-890j)  +/-  (4.83e-244, 4.83e-244j)
| (1.7566836492998817735 - 4.4973111684326498191e-893j)  +/-  (4.45e-247, 4.45e-247j)
| (-6.4013235235100146411 + 2.1281865904720389271e-885j)  +/-  (4.89e-241, 4.89e-241j)
| (-10.173248034157624754 - 5.4315178570572721461e-892j)  +/-  (1.92e-245, 1.92e-245j)
| (-7.9740575737278658946 + 3.3881774424294849468e-887j)  +/-  (6.62e-242, 6.62e-242j)
| (-6.0435567402123180657 + 1.1887815201183606399e-887j)  +/-  (4.84e-241, 4.84e-241j)
| (1.3148812167302054686 + 1.2091599210289714926e-895j)  +/-  (6.38e-249, 6.38e-249j)
| (3.1312663501029920078 - 1.5704317510831103842e-888j)  +/-  (4.3e-244, 4.3e-244j)
| (-4.3738282684413406881 + 1.7940210486492581789e-889j)  +/-  (3.65e-242, 3.65e-242j)
| (-1.0366108297895136542 - 4.628256150187311677e-897j)  +/-  (3.73e-250, 3.73e-250j)
| (-5.022219471514041099 - 7.2784168088692158252e-889j)  +/-  (1.67e-241, 1.67e-241j)
| (-8.9152863669286970739 - 5.3275341545666238508e-891j)  +/-  (3.87e-243, 3.87e-243j)
| (0.51406427121786557621 - 2.3785195777492577173e-902j)  +/-  (3.52e-252, 3.52e-252j)
| (4.6953248707547538339 - 1.9788412846227778819e-887j)  +/-  (8.49e-242, 8.49e-242j)
| (6.0435567402123180657 + 7.9462826881332388626e-898j)  +/-  (4.66e-241, 4.66e-241j)
| (-8.4240682095336656567 + 2.7286984649729218e-909j)  +/-  (1.92e-242, 1.92e-242j)
| (2.8299730478216811798 - 1.27119024670897795e-908j)  +/-  (9.77e-245, 9.77e-245j)
| (2.2415993110132416628 + 8.5443852878768133691e-912j)  +/-  (5.99e-246, 5.99e-246j)
| (8.9152863669286970739 + 2.9840281103246364749e-907j)  +/-  (3.97e-243, 3.97e-243j)
| (1.9667790639659690155 - 4.8731710014171998621e-917j)  +/-  (1.61e-246, 1.61e-246j)
| (-1.9667790639659690155 - 3.4322931517065263304e-917j)  +/-  (1.44e-246, 1.44e-246j)
| (1.5731226439116375556 - 3.7052461306531689464e-918j)  +/-  (9.53e-248, 9.53e-248j)
| (-5.3552539105010696872 - 1.3812313905621756903e-910j)  +/-  (2.78e-241, 2.78e-241j)
| (-4.0571169939798256623 + 4.5800725969378866999e-913j)  +/-  (1.42e-242, 1.42e-242j)
| (-5.6953299116997824551 + 5.6288208679378389301e-911j)  +/-  (3.96e-241, 3.96e-241j)
| (7.1531713950687693606 + 5.1752726662790841872e-924j)  +/-  (2.95e-241, 2.95e-241j)
| (-2.8299730478216811798 - 4.185129652366189651e-944j)  +/-  (9.54e-245, 9.54e-245j)
| (6.4013235235100146411 - 2.4303473210015828178e-939j)  +/-  (5.18e-241, 5.18e-241j)
| (-1.3148812167302054686 + 8.8432931022824999689e-966j)  +/-  (6.48e-249, 6.48e-249j)
| (-1.7566836492998817735 - 2.2221279278650884771e-964j)  +/-  (4.42e-247, 4.42e-247j)
| (5.022219471514041099 + 8.2554197836687881148e-958j)  +/-  (1.64e-241, 1.64e-241j)
| (-0.76075525574901505848 - 9.0752297678938600616e-982j)  +/-  (2.84e-251, 2.84e-251j)
| (2.5327316742327897964 + 1.862966658527720684e-975j)  +/-  (2.3e-245, 2.3e-245j)
| (-2.5327316742327897964 - 6.026036780903966441e-976j)  +/-  (2.3e-245, 2.3e-245j)
| (5.3552539105010696872 + 1.8882240861881962149e-971j)  +/-  (2.76e-241, 2.76e-241j)
| (-1.5731226439116375556 + 5.4853861971585545814e-982j)  +/-  (1e-247, 1e-247j)
| (3.4361591188377376033 + 1.5244510270532031308e-977j)  +/-  (1.55e-243, 1.55e-243j)
| (4.3738282684413406881 - 5.7793355580872086796e-977j)  +/-  (3.92e-242, 3.92e-242j)
| (0.1280217523482756657 - 1.9118534453857289387e-993j)  +/-  (3.6e-254, 3.6e-254j)
| (7.9740575737278658946 + 7.3756749851799610885e-981j)  +/-  (6.28e-242, 6.28e-242j)
| (-0.34290132722370460879 - 6.7652255897025658037e-995j)  +/-  (4.67e-253, 4.67e-253j)
| (-6.7704110475790315154 - 6.5384879046528671931e-983j)  +/-  (4.18e-241, 4.18e-241j)
| (-2.2415993110132416628 + 6.1253181158826720866e-989j)  +/-  (5.46e-246, 5.46e-246j)
| (0.76075525574901505848 + 2.0461460850372132663e-995j)  +/-  (2.83e-251, 2.83e-251j)
| (3.7446906040787134765 + 8.4572399292448908391e-987j)  +/-  (5.16e-243, 5.16e-243j)
| (-3.7446906040787134765 - 1.2432402612556538931e-984j)  +/-  (4.59e-243, 4.59e-243j)
| (1.0366108297895136542 - 7.9972740082961939492e-994j)  +/-  (3.89e-250, 3.89e-250j)
| (-0.51406427121786557621 + 1.3533702123655344741e-995j)  +/-  (3.72e-252, 3.72e-252j)
| (-4.6953248707547538339 - 3.4841482042352869932e-988j)  +/-  (8.41e-242, 8.41e-242j)
| (4.0571169939798256623 + 1.3919759446382906358e-996j)  +/-  (1.49e-242, 1.49e-242j)
| (0.34290132722370460879 - 2.6721363352295038807e-1007j)  +/-  (4.41e-253, 4.41e-253j)
| (-3.1312663501029920078 - 1.0605127451297164371e-1002j)  +/-  (4.28e-244, 4.28e-244j)
| (-0.1280217523482756657 + 1.140696026423524106e-1012j)  +/-  (3.6e-254, 3.6e-254j)
-------------------------------------------------
The weights are:
| (2.6218622177868732513e-21 - 3.706220520679170376e-889j)  +/-  (1.16e-62, 2.4e-180j)
| (5.3830748281803492834e-46 - 2.709478834139351673e-903j)  +/-  (7.89e-74, 1.63e-191j)
| (1.3219446732873764129e-23 - 2.1434349820262977404e-892j)  +/-  (2.27e-66, 4.69e-184j)
| (1.5878143666294308237e-15 + 6.9691464945748343818e-887j)  +/-  (3.42e-59, 7.08e-177j)
| (3.6397609750437095648e-40 + 2.7662053796256794891e-900j)  +/-  (4.3e-72, 8.9e-190j)
| (3.8835749284658800716e-26 + 1.7279157742423614791e-892j)  +/-  (1.74e-66, 3.59e-184j)
| (3.8835749284658800716e-26 + 9.4389142012597565544e-894j)  +/-  (2.01e-69, 4.16e-187j)
| (3.998371056986348962e-32 + 6.0071344847300954263e-896j)  +/-  (1.69e-69, 3.49e-187j)
| (1.2891922615350942402e-06 + 1.733494842640283647e-882j)  +/-  (4.27e-52, 8.84e-170j)
| (3.6397609750437095648e-40 + 4.6026244423877578347e-901j)  +/-  (2.45e-76, 5.06e-194j)
| (0.0042336089571149561209 - 1.2595873849039085521e-878j)  +/-  (2.94e-38, 6.09e-156j)
| (3.2762685876255842065e-19 - 5.2745754702840824094e-890j)  +/-  (1.16e-66, 2.39e-184j)
| (5.3830748281803492834e-46 - 5.4415127072839850316e-904j)  +/-  (1.06e-78, 2.18e-196j)
| (5.9450072685636616399e-29 - 3.0325760010204344048e-895j)  +/-  (1.01e-71, 2.08e-189j)
| (2.7318299154981410925e-17 + 6.1235171417056959775e-889j)  +/-  (3.44e-66, 7.12e-184j)
| (0.027483150205033302914 - 2.1622091922574284598e-878j)  +/-  (4.29e-38, 8.88e-156j)
| (9.4372603472388132801e-06 + 2.0318426471871491616e-881j)  +/-  (1.33e-55, 2.75e-173j)
| (8.8514757981774903377e-10 - 1.4495595447309428633e-884j)  +/-  (2.67e-61, 5.52e-179j)
| (0.053816282800061594468 - 2.4375232046610577883e-878j)  +/-  (6.6e-36, 1.37e-153j)
| (2.068422590305354141e-12 - 3.7574277856722849922e-886j)  +/-  (9.44e-64, 1.95e-181j)
| (8.8586772853407435146e-36 - 8.2275594529205003985e-899j)  +/-  (1.01e-75, 2.08e-193j)
| (0.09055105434808180938 + 1.5126931093069749128e-877j)  +/-  (9.62e-39, 1.99e-156j)
| (4.8707181657731585023e-11 - 1.3612077033314506565e-884j)  +/-  (9.18e-66, 1.9e-183j)
| (2.7318299154981410925e-17 - 1.0795375987425524003e-887j)  +/-  (8.37e-70, 1.73e-187j)
| (3.998371056986348962e-32 + 6.537729181445785685e-897j)  +/-  (2.8e-74, 5.8e-192j)
| (5.6174477223094288803e-05 - 7.54667992346979975e-881j)  +/-  (5.77e-57, 1.19e-174j)
| (0.0010615075678386853961 - 1.0836364181832426299e-879j)  +/-  (2.05e-53, 4.24e-171j)
| (8.8586772853407435146e-36 - 6.0169012403699236187e-898j)  +/-  (6.24e-79, 1.29e-196j)
| (0.0030144610649661857844 + 4.5720478359710018274e-879j)  +/-  (2.53e-51, 5.23e-169j)
| (0.0030144610649661857844 - 2.513672734907413493e-879j)  +/-  (1.72e-54, 3.56e-172j)
| (0.010861618240953454025 + 1.8193218599776130655e-878j)  +/-  (1.05e-48, 2.16e-166j)
| (6.6565180746683894441e-14 + 5.0810532424764812743e-887j)  +/-  (9.6e-68, 1.99e-185j)
| (1.2602731074649181448e-08 + 7.7433043415146545676e-884j)  +/-  (8.91e-65, 1.84e-182j)
| (1.5878143666294308237e-15 - 6.0104055394128905896e-888j)  +/-  (1.24e-68, 2.58e-186j)
| (1.3219446732873764129e-23 - 7.7971254594896254257e-891j)  +/-  (1.12e-75, 2.31e-193j)
| (5.6174477223094288803e-05 + 3.0975039246487732398e-881j)  +/-  (1.56e-62, 3.22e-180j)
| (3.2762685876255842065e-19 + 1.8823544651513257759e-888j)  +/-  (1.45e-73, 3e-191j)
| (0.027483150205033302914 + 1.4589450589316843995e-878j)  +/-  (4.78e-55, 9.9e-173j)
| (0.0042336089571149561209 + 7.4060724591243204611e-879j)  +/-  (4.99e-58, 1.03e-175j)
| (2.068422590305354141e-12 + 2.5346152353203087417e-885j)  +/-  (7.14e-71, 1.48e-188j)
| (0.085113225945721233492 + 5.2407503743612699363e-878j)  +/-  (3.65e-55, 7.55e-173j)
| (0.00027230718161959350206 + 2.7966380126092532931e-880j)  +/-  (4.88e-62, 1.01e-179j)
| (0.00027230718161959350206 - 1.2738981442463210581e-880j)  +/-  (2.87e-63, 5.93e-181j)
| (6.6565180746683894441e-14 - 4.3536558008328956887e-886j)  +/-  (1.12e-71, 2.31e-189j)
| (0.010861618240953454025 - 1.1332777211045232473e-878j)  +/-  (1.63e-59, 3.38e-177j)
| (1.2891922615350942402e-06 - 5.3064478913579146801e-882j)  +/-  (2.88e-67, 5.97e-185j)
| (8.8514757981774903377e-10 + 6.7405281685734515523e-884j)  +/-  (3.59e-70, 7.39e-188j)
| (0.13895243716278695992 + 1.7479121832993617349e-877j)  +/-  (5.93e-60, 1.21e-177j)
| (5.9450072685636616399e-29 - 3.7148557155418642382e-894j)  +/-  (3.35e-80, 6.86e-198j)
| (0.08457328969484546358 + 1.8423918843235150321e-877j)  +/-  (8.27e-61, 1.69e-178j)
| (2.6218622177868732513e-21 + 3.7539685628302150838e-891j)  +/-  (4.27e-77, 8.73e-195j)
| (0.0010615075678386853961 + 5.4456059095264178309e-880j)  +/-  (4.2e-65, 8.62e-183j)
| (0.085113225945721233492 - 6.5675910818873270808e-878j)  +/-  (4.01e-62, 8.24e-180j)
| (1.4236242245385972869e-07 + 1.3202367328801914027e-882j)  +/-  (2.44e-69, 5.05e-187j)
| (1.4236242245385972869e-07 - 3.7989818166372098631e-883j)  +/-  (3.77e-70, 7.68e-188j)
| (0.053816282800061594468 + 3.3188802717272808298e-878j)  +/-  (4.81e-64, 1.08e-181j)
| (0.09055105434808180938 - 1.2991921008190701755e-877j)  +/-  (6.88e-64, 1.74e-181j)
| (4.8707181657731585023e-11 + 2.4635352222101586903e-885j)  +/-  (2.1e-72, 4.36e-190j)
| (1.2602731074649181448e-08 - 3.0900014610552472363e-883j)  +/-  (8.19e-71, 1.84e-188j)
| (0.08457328969484546358 - 2.0389714580409625016e-877j)  +/-  (3.79e-64, 1.05e-181j)
| (9.4372603472388132801e-06 - 7.4675936316220459102e-882j)  +/-  (6.51e-69, 1.25e-186j)
| (0.13895243716278695992 - 1.683036358102781591e-877j)  +/-  (1.93e-64, 6.18e-182j)
