Starting with polynomial:
P : 5/2*t^3 - 3/2*t
Extension levels are: 3 8 44
-------------------------------------------------
Trying to find an order 8 Kronrod extension for:
P1 : 5/2*t^3 - 3/2*t
Solvable: 1
-------------------------------------------------
Trying to find an order 44 Kronrod extension for:
P2 : 5/2*t^11 - 10483/1482*t^9 + 1617/221*t^7 - 69993/20995*t^5 + 68299/109174*t^3 - 3633/109174*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 5/2*t^55 - 48106547474891507491668710569229085124182174818121116041098367735045002141826423630832330137555103453161796171/1359841256226572063662913253219039721615613839684915681229206145046451559269328595259640600201088198811236174*t^53 + 23218537280159990477645402725921220597057911000296764564710959985817972836359294401014495368192138425679092025783471631/98034533903718712180558913549329792824777172382897782472970785037766310121778336035801618982915577315353088146033794*t^51 - 39099242110380644579816411419470897346330306800191356379574611109781369850636504457536859975561482221192719894569968900295/39188824366570850690687344520199735025857494379806609632871674403234152244170488956115443258915683818198106039866489378*t^49 + 9011484359616259099067369230094444319148164636789468891042725140366621917649527972793475323120919693923122338630804370616633/3037133888409240928528269200315479464503955814435012246547554766250646798923212894098946852565965495910353218089652926795*t^47 - 11770326206149984440087884554728636912509978492536941348839004085496714153295447677158873991897599509642976114436383614364905977/1776723324719405943189037482184555486734814151444482164230319538256628377370079543047883908751089815107556632582446962175075*t^45 + 455233409913674700701511905230665655074249760649149180092106892339926865089641848468253809437645361707667561821485781570562851/39482740549320132070867499604101233038551425587655159205118211961258408386001767623286309083357551446834591835165488048335*t^43 - 1633728649163505827515562436039043108246199378187773467277850618012475605095370948184110748304840449877900771418593558140388065927/101904953357795260874909016478185282472501229441737965908410105072007952044270562235701963744145840284280081526562124652752635*t^41 + 188224061322117237534601166684272961840751491877200935426311074649638664213235892824934610046533870831287122188824231583752299118311/10394305242495116609240719680774898812195125403057272522657830717344811108515597348041600301902875708996568315709336714580768770*t^39 - 528812859031953390899509210045780489190360837933787507199583466853567392710238879103938525825986323497187014454254601428189592933/31466875848090406629718048419021650852106189898739964962636318690579542692737884520095299451360057039308282095191849849006230*t^37 + 18282370789670376806177641508850257521531375701376353945932999562070454738807066339540472712810467943419217915163699963928283709683/1416009413164068298337312178855974288344778545443298423318634341076079421173204803404288475311202566768872694283633243205280350*t^35 - 32570210927174714055230339758400706434119509891036916895843734161808124072001277992933175120511871929074989819862942859916128551043/3948167422586872784775799839869010662796617826706608545017839280412127327271171040080192572338294215579092100532012689878252270*t^33 + 10360824181728099914896158332620412536306775637915986344703697680865293205840280566978994192758151173691532292771281518574160454/2358522952560855904883990346397258460451981975332502117692855006219908797653029295149457928517499531409254540341704115817355*t^31 - 7135119269801732882765532629926280438204804630857608959214030255274500262345806423933617464587419593780528301213335907223058678/3659776995353052266199295365099194162770316858274572251592361216548134341185735113162951958044395824600567390185402938337275*t^29 + 346068000608001699981774898039626840507705492504159414392940385536925019940496800533704850609828359798217257561161180900553199218/480894697189391067778587410974034112988019635177278793859236263854424852431805593869611887287033611352514555070361946097517935*t^27 - 95286694930662572348746490369820876830877067954223052439415159588087340866747361629442482091025060918672953924859047653342758474/433073611116777851500249951536737975927820828229157716438429410624862563706978655057615981701920172577733807838606014369910875*t^25 + 140047119960120091028162730849831964665328413748115261317020138698051149668391372294972743730921758887544486078442007998908619457/2529149888921982652761459716974549779418473636858281064000427758049197372048755345536477333139213807853965437777459123920279510*t^23 - 5780688133532986498226070485693904503539350822476109761285790729225032971499507182443414536865558683030063762051219968361516243489/508359127673318513205053403111884505663113201008514493864085979367888671781799824452831943960981975378647052993269283907976181510*t^21 + 4148966964485409178281925662231514609969783733287870267755886432621014637639146978652312386159736313157275092383635170920949772677/2202889553251046890555231413484832857873490537703562806744372577260850911054465905962271757164255226640803896304166896934563453210*t^19 - 162804407892139703561473239103953390955027222414750868774933157924043468979636236724418036891946721177446801729169524923438540437/657002147460838546305946211039336115506128756858957328327269014270780096279402112304537190733198927243748530476681355226097872010*t^17 + 448881002391420065508309486016115451698727557087875104982834280180617972687189435055135522634319668572868644740685104841717396189/17681087203725507937351199502970368990826700368410175159395622001698934943989792139960339103555206424353820746651865883290575084975*t^15 - 269691758519360562336286214655668081335148418380939894079833795392300982436484866918600742541100504215172805150249158820496262469/136693094864664099294970307881584714749770559399915905887465463888996593601465910268245104379899216563452641772391321759784377036255*t^13 + 72274655966839341006485015077918497372911936141577156651116752838048549313512550512874347612469833086915569741278090942270567449/643742694619059134286569569596181007069432292558578326017038210280659171576134329553872243703627934414208595013569387090950356811765*t^11 - 232276163193482256704029905493841064712277340009726069946029772045821407129251068966546460928021432733398109988649001889360838273/52143158264143789877212135137290661572624015697244844407380095032733392897666880693863651739993862687550896196099120354366978901752965*t^9 + 1329531183226440067260743266512565884452845715919381141023552501792945686219556854592271552797118080434483145247882924012033101/11587368503143064417158252252731258127249781266054409868306687785051865088370417931969700386665302819455754710244248967637106422611770*t^7 - 1689126886923769928511713872406929402786972751267496985707088644995265951037495678179745524408817876218668259514154267447996201/984926322767160475458451441482156940816231407614624838806068461729408532511485524217424532866550739653739150370761162249154045922000450*t^5 + 7196638623708693894664964252216353957025472484475841064075662110529714641925888231800346762838878005225557927629431355386269/590955793660296285275070864889294164489738844568774903283641077037645119506891314530454719719930443792243490222456697349492427553200270*t^3 - 76317189770530784003588676915963997969687603439154026431541653380119550986931296359986294036140248042318206323469407693/2940078575424359628234183407409423703929048977954103996436025258893756813467120967813207560795673849712654180211227349997474763946270*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:
| (-0.99925539339707464221 - 1.4650695128068277478e-887j)  +/-  (2.59e-235, 2.59e-235j)
| (-0.87255335150671091832 - 6.9678098870560902482e-890j)  +/-  (6.39e-237, 6.39e-237j)
| (-0.94263912812584987797 + 4.3653333912581713174e-888j)  +/-  (1.68e-235, 1.68e-235j)
| (0.99079325588510780584 + 6.4351748525019482724e-885j)  +/-  (1.02e-234, 1.02e-234j)
| (0.94263912812584987797 + 6.7526670271922155711e-899j)  +/-  (1.61e-235, 1.61e-235j)
| (0.95943209500616697645 - 1.5602537093374382815e-900j)  +/-  (3.79e-235, 3.79e-235j)
| (0.9961500922510981447 - 9.1951857151450157054e-916j)  +/-  (7.41e-235, 7.41e-235j)
| (-0.9225217132136291628 - 8.6439893820185269524e-941j)  +/-  (6.68e-236, 6.68e-236j)
| (-0.9728975066439420398 + 1.4000348575780230548e-938j)  +/-  (6.91e-235, 6.91e-235j)
| (-0.99079325588510780584 + 3.5105525033537497838e-938j)  +/-  (1.07e-234, 1.07e-234j)
| (0.87255335150671091832 + 2.6264033537128904358e-941j)  +/-  (6.58e-237, 6.58e-237j)
| (0.99925539339707464221 + 2.5614090468987338831e-938j)  +/-  (2.48e-235, 2.48e-235j)
| (-0.95943209500616697645 - 9.0347719712666135007e-949j)  +/-  (3.71e-235, 3.71e-235j)
| (-0.89913471668678478187 + 2.0099041931586521792e-952j)  +/-  (2.09e-236, 2.09e-236j)
| (0.69527583331321906591 - 2.4371324198085307578e-956j)  +/-  (1.88e-240, 1.88e-240j)
| (0.84286679618557505573 + 7.5983763855468828506e-953j)  +/-  (1.59e-237, 1.59e-237j)
| (0.9225217132136291628 + 1.3073723369191834119e-950j)  +/-  (6.58e-236, 6.58e-236j)
| (-0.9961500922510981447 - 1.9538740712988463534e-953j)  +/-  (7.31e-235, 7.31e-235j)
| (-0.73625128286813396221 + 7.3421361928661419275e-961j)  +/-  (1.34e-239, 1.34e-239j)
| (-0.84286679618557505573 + 6.3447837083633021968e-959j)  +/-  (1.68e-237, 1.68e-237j)
| (-0.9831964995514863944 - 2.332853908286636555e-955j)  +/-  (9.55e-235, 9.55e-235j)
| (0.73625128286813396221 - 5.308848097198859959e-961j)  +/-  (1.36e-239, 1.36e-239j)
| (-0.69527583331321906591 + 7.4786765024184905366e-963j)  +/-  (1.93e-240, 1.93e-240j)
| (-0.81017673653030383583 + 4.0144768765136689703e-961j)  +/-  (3.97e-238, 3.97e-238j)
| (-0.77459666924148337704 - 2.0791471795507325391e-962j)  +/-  (7.38e-239, 7.38e-239j)
| (0.89913471668678478187 - 2.5025665029613735009e-956j)  +/-  (2.21e-236, 2.21e-236j)
| (0.77459666924148337704 - 1.4238851290764095233e-963j)  +/-  (6.95e-239, 6.95e-239j)
| (0.9831964995514863944 - 2.0038636254990549325e-960j)  +/-  (1.01e-234, 1.01e-234j)
| (0.17688645164771626193 + 6.9499738445267215427e-1003j)  +/-  (1.11e-251, 1.11e-251j)
| (-0.65181551174545473569 - 6.7276016365053211426e-994j)  +/-  (2.48e-241, 2.48e-241j)
| (-0.34809060189060850632 - 5.008752941961456568e-1000j)  +/-  (7.45e-248, 7.45e-248j)
| (0.23486295963167437907 - 1.3073909386011448759e-1001j)  +/-  (2.04e-250, 2.04e-250j)
| (0.65181551174545473569 - 6.3748998010667295041e-992j)  +/-  (2.28e-241, 2.28e-241j)
| (-0.059244517225594210524 + 7.8018922715963344286e-1006j)  +/-  (2.44e-254, 2.44e-254j)
| (-0.55806685067819680295 - 3.7214255790559208362e-996j)  +/-  (2.66e-243, 2.66e-243j)
| (-0.60602480562886801376 + 7.5232878899295025162e-995j)  +/-  (2.64e-242, 2.64e-242j)
| (4.2098384512575354483e-1019 - 1.3182362230475214101e-1019j)  +/-  (2.43e-1017, 2.43e-1017j)
| (0.60602480562886801376 + 2.9380765806267991449e-992j)  +/-  (2.64e-242, 2.64e-242j)
| (0.81017673653030383583 + 4.5534900096575190405e-993j)  +/-  (3.6e-238, 3.6e-238j)
| (-0.17688645164771626193 + 6.3852929955023556808e-1013j)  +/-  (1.02e-251, 1.02e-251j)
| (-0.5081127709588822868 + 8.6228155838653973462e-1006j)  +/-  (2.36e-244, 2.36e-244j)
| (-0.11827707073203099456 - 6.0783174432633777391e-1013j)  +/-  (4.27e-253, 4.27e-253j)
| (0.5081127709588822868 - 2.6499189847991649759e-1002j)  +/-  (2.24e-244, 2.24e-244j)
| (0.55806685067819680295 + 6.2496249303200810065e-1005j)  +/-  (2.83e-243, 2.83e-243j)
| (0.059244517225594210524 + 1.6700279233858796989e-1016j)  +/-  (1.72e-254, 1.72e-254j)
| (-0.40293661887532529296 - 4.5621135680692649024e-1009j)  +/-  (1.22e-246, 1.22e-246j)
| (-0.23486295963167437907 - 8.4286278665202873273e-1013j)  +/-  (2.2e-250, 2.2e-250j)
| (0.11827707073203099456 - 1.6669192834872818967e-1016j)  +/-  (4.1e-253, 4.1e-253j)
| (0.45634100522928665108 - 2.1201429513293301163e-1009j)  +/-  (1.86e-245, 1.86e-245j)
| (0.2919991541426287378 - 2.59671603225033324e-1011j)  +/-  (4.63e-249, 4.63e-249j)
| (-0.2919991541426287378 - 1.0988759886663415487e-1011j)  +/-  (4.11e-249, 4.11e-249j)
| (-0.45634100522928665108 - 7.4672786985293938946e-1011j)  +/-  (1.69e-245, 1.69e-245j)
| (0.9728975066439420398 + 1.0066039022498596747e-1013j)  +/-  (7.01e-235, 7.01e-235j)
| (0.34809060189060850632 + 9.6083585548794913349e-1032j)  +/-  (7.67e-248, 7.67e-248j)
| (0.40293661887532529296 + 4.8745715205536037958e-1030j)  +/-  (1.18e-246, 1.18e-246j)
-------------------------------------------------
The weights are:
| (0.0019022057826325816507 - 2.2531420924298637129e-887j)  +/-  (4.98e-49, 2.82e-161j)
| (0.028149892264927714343 + 1.4911431179438031035e-887j)  +/-  (2.28e-49, 1.29e-161j)
| (0.0184618768697032951 - 2.5784351857344055938e-887j)  +/-  (2.31e-49, 1.3e-161j)
| (0.0064351434508495415018 - 1.3595906132547502107e-885j)  +/-  (1.51e-50, 8.57e-163j)
| (0.0184618768697032951 - 8.7119255610815402875e-886j)  +/-  (8.29e-51, 4.69e-163j)
| (0.015121827832568104168 + 1.5402877005520313002e-885j)  +/-  (6.09e-51, 3.45e-163j)
| (0.0042679287638907409519 - 4.3697584543200804995e-885j)  +/-  (5e-51, 2.83e-163j)
| (0.021763428681966138798 + 1.7422299384619509938e-887j)  +/-  (3.6e-51, 2.04e-163j)
| (0.011831975999487576753 - 3.880882366628017168e-887j)  +/-  (5.3e-52, 3e-164j)
| (0.0064351434508495415018 - 4.2431577389536175391e-887j)  +/-  (2.2e-52, 1.25e-164j)
| (0.028149892264927714343 + 2.3281908869132524068e-886j)  +/-  (1.05e-54, 5.94e-167j)
| (0.0019022057826325816507 + 8.1165135998323438933e-886j)  +/-  (4.73e-53, 2.68e-165j)
| (0.015121827832568104168 + 3.5255567046655570096e-887j)  +/-  (4.47e-52, 2.53e-164j)
| (0.02499795691595909575 - 1.6585739592731213141e-887j)  +/-  (7.05e-53, 3.99e-165j)
| (0.042242880209753900289 - 5.6305722852832361625e-887j)  +/-  (5.41e-57, 3.06e-169j)
| (0.031206260050471151073 - 1.6491282300854327132e-886j)  +/-  (7.7e-56, 4.35e-168j)
| (0.021763428681966138798 + 5.3007477199840295174e-886j)  +/-  (7.09e-55, 4.01e-167j)
| (0.0042679287638907409519 + 4.3221217045618967785e-887j)  +/-  (4.71e-53, 2.66e-165j)
| (0.039683809728861196358 + 1.055413102503039491e-887j)  +/-  (6.22e-58, 3.52e-170j)
| (0.031206260050471151073 - 1.3406459608877554313e-887j)  +/-  (3.83e-56, 2.17e-168j)
| (0.0088482276536203588304 + 4.234799487458166219e-887j)  +/-  (2.08e-53, 1.18e-165j)
| (0.039683809728861196358 + 7.0944109589654070415e-887j)  +/-  (7.34e-61, 4.15e-173j)
| (0.042242880209753900289 - 9.9514313702354209789e-888j)  +/-  (3.11e-59, 1.76e-171j)
| (0.034154932903472714203 + 1.2257326020343204393e-887j)  +/-  (2.23e-57, 1.26e-169j)
| (0.036984409831104488575 - 1.1312977663197313214e-887j)  +/-  (4.99e-58, 2.82e-170j)
| (0.02499795691595909575 - 3.4263537724234236499e-886j)  +/-  (2.66e-60, 1.51e-172j)
| (0.036984409831104488575 - 9.1447892235289178873e-887j)  +/-  (5.1e-62, 2.88e-174j)
| (0.0088482276536203588304 + 6.9054255070642256091e-885j)  +/-  (4.77e-60, 2.7e-172j)
| (0.058327731179369061339 - 1.3174156142621049973e-887j)  +/-  (1.34e-66, 7.58e-179j)
| (0.044652004221524791089 + 9.4798260740917550337e-888j)  +/-  (3.83e-62, 2.17e-174j)
| (0.055501830378936087354 + 8.6050945203078676216e-888j)  +/-  (4.04e-66, 2.28e-178j)
| (0.057590698903673320801 + 1.4437201089653807301e-887j)  +/-  (8.4e-67, 4.75e-179j)
| (0.044652004221524791089 + 4.560009240093433826e-887j)  +/-  (1.8e-65, 1.02e-177j)
| (0.059173824899248551709 - 1.0015365382488636329e-887j)  +/-  (2.46e-67, 1.39e-179j)
| (0.048985170265446043909 + 8.856516749251887028e-888j)  +/-  (4.24e-65, 2.4e-177j)
| (0.046902207732156751403 - 9.1197555164594572316e-888j)  +/-  (2.98e-64, 1.69e-176j)
| (0.059279869681883143604 + 1.0585113327137501844e-887j)  +/-  (8.35e-68, 4.73e-180j)
| (0.046902207732156751403 - 3.7604879673560017842e-887j)  +/-  (3.55e-67, 2.01e-179j)
| (0.034154932903472714203 + 1.2097841935529039e-886j)  +/-  (8.01e-65, 4.53e-177j)
| (0.058327731179369061339 - 9.1952080191456424161e-888j)  +/-  (1.63e-68, 9.21e-181j)
| (0.050893237911152420008 - 8.6794274607743866127e-888j)  +/-  (3.23e-67, 1.82e-179j)
| (0.058856068070695330068 + 9.5566970362105366135e-888j)  +/-  (2.41e-68, 1.36e-180j)
| (0.050893237911152420008 - 2.6823501226284947477e-887j)  +/-  (1.15e-69, 6.53e-182j)
| (0.048985170265446043909 + 3.1523613856054028026e-887j)  +/-  (6.15e-69, 3.48e-181j)
| (0.059173824899248551709 - 1.128428090347442269e-887j)  +/-  (5.88e-70, 3.33e-182j)
| (0.054157491512282913023 - 8.5570442993319997513e-888j)  +/-  (9.43e-70, 5.33e-182j)
| (0.057590698903673320801 + 8.9205775043324317706e-888j)  +/-  (5.23e-70, 2.96e-182j)
| (0.058856068070695330068 + 1.2136855088582858442e-887j)  +/-  (1.37e-70, 7.77e-183j)
| (0.052619437613637271613 + 2.3139731808359774523e-887j)  +/-  (6.34e-72, 3.58e-184j)
| (0.056647605531667287534 - 1.5980043040934652696e-887j)  +/-  (3.34e-72, 1.89e-184j)
| (0.056647605531667287534 - 8.7254621931100990262e-888j)  +/-  (2.42e-71, 1.37e-183j)
| (0.052619437613637271613 + 8.581123527543564766e-888j)  +/-  (2.77e-71, 1.57e-183j)
| (0.011831975999487576753 - 2.9814152835015723742e-885j)  +/-  (2.68e-71, 1.51e-183j)
| (0.055501830378936087354 + 1.787454278364683292e-887j)  +/-  (5.09e-73, 2.89e-185j)
| (0.054157491512282913023 - 2.0217281122308332301e-887j)  +/-  (5.01e-73, 2.81e-185j)
