Starting with polynomial:
P : 5/2*t^3 - 3/2*t
Extension levels are: 3 4 48
-------------------------------------------------
Trying to find an order 4 Kronrod extension for:
P1 : 5/2*t^3 - 3/2*t
Solvable: 1
-------------------------------------------------
Trying to find an order 48 Kronrod extension for:
P2 : 5/2*t^7 - 77/18*t^5 + 3745/1782*t^3 - 155/594*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 5/2*t^55 - 474839113644184188621825289487691535573429410480327645265728043132751947353964525513/14118678702751239518330168255290973769408419170091742195466621159455722436355722042*t^53 + 30183139239392438277411077357007827756978203148660806287821806690016729049692496653758621/141172668348809643943783352384654446720314783281747330212470744973397768641120864697958*t^51 - 785640628973824815213272155236095584714712005587063612427527772269844467929205320481090563/919761324090729498421618810990930486208111466835626545323673035432743038116393512426090*t^49 + 38960257562054801714035525041153140199066368691865937902934769991394285135446726691042789095597/16192857991279338184461809976900826674936906429374623143695925625311157557558165983017527495*t^47 - 23449689441884579249147711180818260220051248683085457974530126422438670250666357542402658559407473/4614964527514611382571615843416735602357018332371767595953338803213679903904077305159995336075*t^45 + 127060815382349961177474955803700438599686143661951175317457236715670891814415246371369528613701/15211472658474529809645942705573503846152851494261009619835566496504420735887974105258889465*t^43 - 73622617746965728251881986718481236289578123744013491804180772642269115629372154311232338871541/6721348383977117822866811893160385420393120427696725180857575893804278929810965302323695345*t^41 + 41812423358109263472591337855285985772159720051320597895493571531046778247772546797487649216040669/3589200037043780917410877550947645814489926308390051246577945527291484948519055471440853314230*t^39 - 18556954954629221293936783967473103929768174660977154176026329139814423247793830095860780648141129/1826084229373151694823078052236521554740488823566868178083516145464088833457063310031311335310*t^37 + 22293395585031116478830334587560846636639453726402469735700053569003046513268760622491957298572477/3043473715621919491371796753727535924567481372611446963472526909106814722428438850052185558850*t^35 - 1992560228187609819174418801553014695637095769419996758747521890284360473544816779039534368715607099/454694973113914772010946435006893867130381717068150176342795520220558119530808764197796522492190*t^33 + 135177326058396061515606966495276740247204074406928535776557196019321164222994293551929716489824382/62003859970079287092401786591849163699597506872929569501290298211894289026928467845154071248935*t^31 - 162135332493668316254359544755952233686830681689312968090956102841499374031650067974550313990450246/179804296932143160678410965122303414643882870320052711557134379798007131805564533562087501385955*t^29 + 166867635072838778800335562690871077121425864267479257596326524199687887207708999480197908227390174/539412890796429482035232895366910243931648610960158134671403139394021395416693600686262504157865*t^27 - 481458210209043814311044555909422716011643879124650809526938493449598766969986446500088029187666462/5494020184037707687395890600959271003007532148668277297579106049383551249614471858841562542348625*t^25 + 653296398193156247338795172166394661502435716070202813789063669378191595527243110972820340324581251/32085077874780212894392001109602142657563987748222739417861979328399939297748515655634725247315970*t^23 - 2388441899390520165580053514675002667707330065768360692335760458415409174326092467684429237753178421/621283780666198667864136021485932398732829944579222136000418326995380642765493984968199679788936510*t^21 + 120645978546809248588458663014778862811270058034722215798124780572004985839718561841692921939856717/207094593555399555954712007161977466244276648193074045333472775665126880921831328322733226596312170*t^19 - 35826517675922202968761448446332952430946062360086946442346902564610371290451134140648288045863901/513901398822658157369100165920462601420982793664294853234913924798648185991211073986041710442700570*t^17 + 671217331811038524121581087918250340592352006828788483261522597313378993443388825007996739302019523/104065033261588276867242783598893676787749015717019707780070069771726257663220242482173446364646865425*t^15 - 1037467924572229930194702487238150271165801556459625160923157599321446620148063643674992158501143/2312556294701961708160950746642081706394422571489326839557112661593916836960449832937187696992152565*t^13 + 470154243703458388357418892898288043481983360037922598884473002385543820405647967621919453050529/20813006652317655373448556719778735357549803143403941556014013954345251532644048496434689272929373085*t^11 - 261656174903283143973116973292554729733110368797990534009391119811466388182172519922659087009403/334900197950929545554581321763712378026028650580227059583134588174464501934363325806267272846227185095*t^9 + 16310562012328497610288323206446139576819423207065928987669965787140916835859780104411788045830483/948809471928089061394523838036793134989742059166069951694529525474721763369155120156466991448122307283590*t^7 - 53247726615340387266997725770438813149535908913467009630186914986355026618282873959224810480541/249686703138970805630137852114945561839405805043702618866981454072295200886619768462228155644242712443050*t^5 + 37679601440216012641908220469817910998283880247038840872741718742364017354487271405562729030641/31310712573626939026019286655214173454661487952480308405919474340665818191182118965163410717788036140358470*t^3 - 250529212125800956619989303817271189760375193968256532155817725397359473132090875909223501/132112711281126325004300787574743347909964084187680626185314237724328346798236788882546036783915764305310*t
-------------------------------------------------
Computing nodes and weights
  current precision for roots: 53
  current precision for roots: 106
  current precision for roots: 212
 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:
| (-0.98665391451426154956 - 1.289469563120206045e-913j)  +/-  (1.85e-236, 1.85e-236j)
| (0.98665391451426154956 - 1.0036840811604723705e-911j)  +/-  (1.73e-236, 1.73e-236j)
| (-0.89649714092533581661 + 1.2253135059311957141e-927j)  +/-  (3.38e-237, 3.38e-237j)
| (0.99896672095990331616 - 6.3931458815090244836e-924j)  +/-  (3.86e-237, 3.86e-237j)
| (0.92098382515801065045 + 1.8606613913758706784e-933j)  +/-  (6.7e-237, 6.7e-237j)
| (0.94235998510772295663 + 4.4981089094431937498e-943j)  +/-  (1.18e-236, 1.18e-236j)
| (0.97528003238311993722 - 1.2363184224420794085e-964j)  +/-  (1.89e-236, 1.89e-236j)
| (-0.92098382515801065045 - 7.5918096232350897395e-984j)  +/-  (6.7e-237, 6.7e-237j)
| (-1.1958721654576937355e-1004 - 3.0180305743887730122e-1004j)  +/-  (1.79e-1002, 1.79e-1002j)
| (0.9945606278002295985 + 1.7773915786804216976e-989j)  +/-  (1.14e-236, 1.14e-236j)
| (0.83911234808857255807 + 7.0440015999795006486e-1005j)  +/-  (6.84e-238, 6.84e-238j)
| (-0.99896672095990331616 - 6.481010838003329559e-1003j)  +/-  (3.92e-237, 3.92e-237j)
| (-0.74289300837461692886 - 1.0614054269213645244e-1008j)  +/-  (3.26e-239, 3.26e-239j)
| (-0.8071760988284091133 - 1.3910928148596563152e-1006j)  +/-  (2.84e-238, 2.84e-238j)
| (0.96049126870802028342 - 1.8829988269777583766e-1003j)  +/-  (1.52e-236, 1.52e-236j)
| (0.8071760988284091133 - 4.3618547883903320366e-1014j)  +/-  (2.64e-238, 2.64e-238j)
| (0.89649714092533581661 - 5.7614061218563005503e-1012j)  +/-  (3.46e-237, 3.46e-237j)
| (-0.83911234808857255807 - 5.5325117300203911029e-1017j)  +/-  (7.11e-238, 7.11e-238j)
| (-0.77459666924148337704 + 1.1227324240524693607e-1018j)  +/-  (1.04e-238, 1.04e-238j)
| (-0.9945606278002295985 + 1.5632193771130131972e-1014j)  +/-  (1.19e-236, 1.19e-236j)
| (-0.96049126870802028342 + 3.5739684173294125205e-1016j)  +/-  (1.56e-236, 1.56e-236j)
| (0.77459666924148337704 + 5.2175862091581014728e-1021j)  +/-  (1.01e-238, 1.01e-238j)
| (-0.94235998510772295663 - 3.4182727584665392156e-1019j)  +/-  (1.11e-236, 1.11e-236j)
| (-0.67242224729723229726 + 1.2005981956287864847e-1025j)  +/-  (1.16e-240, 1.16e-240j)
| (-0.71005241704422017889 - 7.1533481911218798485e-1024j)  +/-  (8.33e-240, 8.33e-240j)
| (0.86909747750776410279 + 3.7233730969700652456e-1022j)  +/-  (1.64e-237, 1.64e-237j)
| (0.74289300837461692886 - 8.9013811010814986999e-1032j)  +/-  (3.28e-239, 3.28e-239j)
| (0.71005241704422017889 + 1.9632808350758651037e-1031j)  +/-  (8.52e-240, 8.52e-240j)
| (-0.049533121846925956131 - 4.2760128309240952567e-1046j)  +/-  (1.91e-254, 1.91e-254j)
| (-0.63022206698533544489 + 1.3899207358017923084e-1032j)  +/-  (1.47e-241, 1.47e-241j)
| (-0.86909747750776410279 - 2.6290542593762455674e-1027j)  +/-  (1.62e-237, 1.62e-237j)
| (0.67242224729723229726 + 7.0649119660016932104e-1033j)  +/-  (1.25e-240, 1.25e-240j)
| (0.63022206698533544489 - 3.629560003856628845e-1033j)  +/-  (1.43e-241, 1.43e-241j)
| (-0.97528003238311993722 + 2.2367993071195901747e-1038j)  +/-  (1.95e-236, 1.95e-236j)
| (-0.53657499352412296393 + 1.6540473380438615803e-1044j)  +/-  (1.4e-243, 1.4e-243j)
| (-0.58469104119450947156 - 1.9744888912661770586e-1045j)  +/-  (1.37e-242, 1.37e-242j)
| (0.21372528681388302214 + 1.2832647126924362914e-1052j)  +/-  (8.56e-251, 8.56e-251j)
| (0.58469104119450947156 + 2.5351986571931857717e-1045j)  +/-  (1.46e-242, 1.46e-242j)
| (0.27002159285246639447 - 8.5756049962907869531e-1055j)  +/-  (1.62e-249, 1.62e-249j)
| (-0.27002159285246639447 - 2.2285209015526718904e-1055j)  +/-  (1.52e-249, 1.52e-249j)
| (-0.48631750354619633507 - 1.5957974514216831937e-1050j)  +/-  (1.11e-244, 1.11e-244j)
| (-0.21372528681388302214 + 3.4388537593836865762e-1056j)  +/-  (9.63e-251, 9.63e-251j)
| (0.434243749346802558 - 2.6053513981432832593e-1049j)  +/-  (7.95e-246, 7.95e-246j)
| (0.53657499352412296393 - 1.4534738958685721002e-1048j)  +/-  (1.34e-243, 1.34e-243j)
| (0.049533121846925956131 + 1.8061224320043308334e-1061j)  +/-  (1.41e-254, 1.41e-254j)
| (-0.38064000825613705824 + 1.0649265476963267013e-1056j)  +/-  (4.82e-247, 4.82e-247j)
| (-0.32579293603171046543 - 1.8043479083295791506e-1058j)  +/-  (3.22e-248, 3.22e-248j)
| (0.10225086942592806394 - 3.5976864623187574932e-1060j)  +/-  (2.66e-253, 2.66e-253j)
| (0.48631750354619633507 + 8.0560111027191856009e-1053j)  +/-  (1.12e-244, 1.12e-244j)
| (0.15748196067160482019 - 6.0090102467278992973e-1061j)  +/-  (4.93e-252, 4.93e-252j)
| (-0.15748196067160482019 + 2.7739526093923672078e-1061j)  +/-  (4.66e-252, 4.66e-252j)
| (-0.434243749346802558 - 7.7502466449377391147e-1054j)  +/-  (7.59e-246, 7.59e-246j)
| (-0.10225086942592806394 + 2.788596871508772173e-1061j)  +/-  (2.82e-253, 2.82e-253j)
| (0.32579293603171046543 + 3.2764300357162591527e-1058j)  +/-  (3.15e-248, 3.15e-248j)
| (0.38064000825613705824 - 8.4423965836244494896e-1056j)  +/-  (5.15e-247, 5.15e-247j)
-------------------------------------------------
The weights are:
| (0.0096474814543814148977 - 4.026398431187417493e-915j)  +/-  (4.72e-46, 8.92e-159j)
| (0.0096474814543814148977 + 4.1322333387710090279e-912j)  +/-  (1.96e-46, 3.71e-159j)
| (0.025983610379168538016 - 2.9790997690222561356e-913j)  +/-  (8.19e-47, 1.55e-159j)
| (0.0026511683097546702811 - 1.0770415914178779774e-912j)  +/-  (9.09e-47, 1.72e-159j)
| (0.022957801452241373332 + 8.1055820306275462022e-912j)  +/-  (2.12e-47, 4.02e-160j)
| (0.019772518264465307785 - 8.3325213323669483691e-912j)  +/-  (2.09e-47, 3.95e-160j)
| (0.013091600034806328255 - 1.4335976398774905268e-911j)  +/-  (2.21e-47, 4.18e-160j)
| (0.022957801452241373332 + 1.7497523339941028478e-913j)  +/-  (2.45e-50, 4.63e-163j)
| (0.048709591285374252492 - 1.1028541908588525024e-911j)  +/-  (2.78e-51, 5.27e-164j)
| (0.0061602551893151194599 + 5.9981794600111628363e-912j)  +/-  (3.35e-47, 6.34e-160j)
| (0.031107509551345270332 - 1.1350257267569073966e-911j)  +/-  (3.3e-50, 6.24e-163j)
| (0.0026511683097546702811 + 2.0514232240523722988e-914j)  +/-  (8.33e-53, 1.58e-165j)
| (0.031486540008112702226 + 2.722771264975018714e-912j)  +/-  (1.7e-52, 3.22e-165j)
| (0.032551948253083088531 + 1.2585334328592923656e-912j)  +/-  (1.55e-52, 2.92e-165j)
| (0.016473947718604246065 + 9.5908316208334725358e-912j)  +/-  (4.49e-48, 8.49e-161j)
| (0.032551948253083088531 + 1.4413263214740896223e-911j)  +/-  (3.09e-51, 5.85e-164j)
| (0.025983610379168538016 - 8.4996489583229118085e-912j)  +/-  (1.27e-49, 2.4e-162j)
| (0.031107509551345270332 - 7.7220376983390870997e-913j)  +/-  (8.17e-53, 1.55e-165j)
| (0.032268905542861532611 - 2.0053712584268706022e-912j)  +/-  (7.38e-53, 1.4e-165j)
| (0.0061602551893151194599 - 1.0099340584830327628e-913j)  +/-  (8.34e-54, 1.58e-166j)
| (0.016473947718604246065 + 5.6504314169909217712e-915j)  +/-  (2.5e-54, 4.72e-167j)
| (0.032268905542861532611 - 1.8616382471136503192e-911j)  +/-  (7.25e-56, 1.37e-168j)
| (0.019772518264465307785 - 8.4304903698148285496e-914j)  +/-  (3.61e-54, 6.83e-167j)
| (0.040152078378836624841 + 2.5941700522913974295e-912j)  +/-  (5.97e-57, 1.13e-169j)
| (0.034966474339073395544 - 2.8878779693065916336e-912j)  +/-  (4.86e-56, 9.19e-169j)
| (0.028763717647483354159 + 9.509370445576176956e-912j)  +/-  (1.94e-55, 3.68e-168j)
| (0.031486540008112702226 + 2.1217916083048156431e-911j)  +/-  (7.09e-58, 1.34e-170j)
| (0.034966474339073395544 - 1.9189777457915173624e-911j)  +/-  (6.68e-59, 1.26e-171j)
| (0.050978523586183076162 + 9.5335148810268447469e-912j)  +/-  (1.22e-62, 2.3e-175j)
| (0.044029532436293616557 - 2.2959111397882247158e-912j)  +/-  (4.03e-60, 7.62e-173j)
| (0.028763717647483354159 + 4.8061166701651573787e-913j)  +/-  (1.47e-57, 2.79e-170j)
| (0.040152078378836624841 + 1.4657579504727281183e-911j)  +/-  (2.05e-60, 3.87e-173j)
| (0.044029532436293616557 - 1.1028118839080978791e-911j)  +/-  (1.64e-61, 3.1e-174j)
| (0.013091600034806328255 + 1.0107736648362811108e-913j)  +/-  (8.68e-59, 1.64e-171j)
| (0.049247036534649652257 - 2.0809410404293642988e-912j)  +/-  (3.53e-63, 6.68e-176j)
| (0.046913984487643166094 + 2.1305886817180646156e-912j)  +/-  (3.62e-62, 6.85e-175j)
| (0.056388939605747759791 - 6.5500493572788328119e-912j)  +/-  (8.95e-67, 1.69e-179j)
| (0.046913984487643166094 + 8.7404493414444177577e-912j)  +/-  (1.22e-64, 2.3e-177j)
| (0.056110658653857366708 + 5.9972613058144306508e-912j)  +/-  (7.51e-67, 1.42e-179j)
| (0.056110658653857366708 + 3.36762421061328742e-912j)  +/-  (2.13e-67, 4.03e-180j)
| (0.051214916398111582984 + 2.1249402706207739465e-912j)  +/-  (8.61e-66, 1.63e-178j)
| (0.056388939605747759791 - 4.1679292967993955763e-912j)  +/-  (1.13e-67, 2.15e-180j)
| (0.052885466692156046358 - 5.9723196922066552017e-912j)  +/-  (4.83e-68, 9.13e-181j)
| (0.049247036534649652257 - 7.3348376285060843596e-912j)  +/-  (6.55e-67, 1.24e-179j)
| (0.050978523586183076162 + 1.0568992661881053982e-911j)  +/-  (2.19e-68, 4.13e-181j)
| (0.054274726063310766821 + 2.4850057377832610616e-912j)  +/-  (3e-68, 5.67e-181j)
| (0.055366964902350441904 - 2.8378902017698165149e-912j)  +/-  (2.69e-68, 5.08e-181j)
| (0.054255738040637461724 - 8.9590165945260772515e-912j)  +/-  (1.59e-69, 3e-182j)
| (0.051214916398111582984 + 6.4732769677367953769e-912j)  +/-  (1.3e-69, 2.46e-182j)
| (0.055943160432838970059 + 7.5081394957276544433e-912j)  +/-  (7.41e-70, 1.4e-182j)
| (0.055943160432838970059 + 5.3950297330473081363e-912j)  +/-  (2.63e-70, 4.98e-183j)
| (0.052885466692156046358 - 2.2564331567640185956e-912j)  +/-  (4.05e-70, 7.66e-183j)
| (0.054255738040637461724 - 7.2368826543015388634e-912j)  +/-  (2.27e-70, 4.3e-183j)
| (0.055366964902350441904 - 5.7460999346882195084e-912j)  +/-  (6.35e-72, 1.2e-184j)
| (0.054274726063310766821 + 5.7411819382459904374e-912j)  +/-  (5.59e-72, 1.05e-184j)
