Starting with polynomial:
P : 231/16*t^6 - 315/16*t^4 + 105/16*t^2 - 5/16
Extension levels are: 6 8 27
-------------------------------------------------
Trying to find an order 8 Kronrod extension for:
P1 : 231/16*t^6 - 315/16*t^4 + 105/16*t^2 - 5/16
Solvable: 1
-------------------------------------------------
Trying to find an order 27 Kronrod extension for:
P2 : 231/16*t^14 - 3731/80*t^12 + 1182181/20400*t^10 - 200960617/5814000*t^8 + 14859361517/1482570000*t^6 - 123220867/98838000*t^4 + 4422019/98838000*t^2 - 22771/889542000
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 231/16*t^41 - 15066705271199837419359155216063026920047883178814983952403817420410238972115168762774382729835043942897474487578223427/107480474670152017732030602149232186203177001481046769518602893293331892139213664460310294441959547781661725048001600*t^39 + 17224292295940152514297628020636044598044215461261103299557583970016993101306132649898106387038419376226252235032413107449/27407521040888764521667803548054207481810135377666926227243737789799632495499484437379125082699684684323739887240408000*t^37 - 579565182072850484128266226904816807910901209381415939215241676766359522687702536436638336021775524080370540631948965473587501/335879170356091809213038932481404312689583209053308180914872006613994496232346181780081177888484635806387432318131200040000*t^35 + 16954838346976075556714698575581558294807728015626222285076693169226114797455015899864531247748803341236323972706590890668684792311/5224600494889008092308820594748244083886466816824208754130834062880684388894144857589162722055378509968356509708530816622200000*t^33 - 568955525718231732988680080199676560652239138002340191620015156860955226344252320682658695224455095370521728087012466722546931455037/128438095499354782269258506287561000395542309246928465205716337379150157893647727749066916917194721703388764197001382575295750000*t^31 + 191564834950763600356038931995420943790519461439116792253968210232775159184926310143248106352325623947654063819240167293184364778583/42220135198749841922420616253696522621372039371827696174889453463734480968500118118205387913956742428449593767180385275616250000*t^29 - 33190726319458237761246769922191113520202025829461559312342278654251695328870109306088264839226293361143829178719483161784754968235459453/9334238590415608801418361944448495703746037324520526208825434819029737724920848614163438186957126399793778438017075478659618631250000*t^27 + 1579226921436518479718709250246679714269965696342893920163031447608191178469760734373559609123136205010639078898727984440876076689415073/732910585617818172555812123045585588590429597332722798618885993197890517660451817112092183568485480280104084762822222768829314750000*t^25 - 25259215332653933323914200434921177160061927510857679590413006438055214699179817299063924865411674689060840546675201339792365881352840023/24918959911005817866897612183549910012074606309312575153042123768728277600455361781811134241328506329523538881935955574140196701500000*t^23 + 193431194272779501090401866857622353156858423254090415845323999173545345503376771910389708292938119559620527558910799895682738523624046023/523298158131122175204849855854548110253566732495564078213884599143293829609562597418033819067898632919994316520655067056944130731500000*t^21 - 2586523853012743900618806839846486755227324914723511332802627681711037714638361369999150662430766380925699079421689150606640468232772337/24918959911005817866897612183549910012074606309312575153042123768728277600455361781811134241328506329523538881935955574140196701500000*t^19 + 6835777468303974393376265301266654579209418908300888177797751207457373256307853930351456432376228506225529811331798237694474806683691617/308208188372966694669523098059696255412501709615181850577099951876376065058263685196085081405905209865159559855523661048576117097500000*t^17 - 828384352832749685947130584567353132181029988019958075501206197198990601012610428507572254213127683571149871207844933250550714043862833/233875625294780609484520468527651864401251297296226227790858198776779484661858914060558679419775129838856371890367954560390112385750000*t^15 + 32129535459839301540652470237925106384147510155020444857525606913217968154877681903688172455154994375472012938495770697837525449838927/77958541764926869828173489509217288133750432432075409263619399592259828220619638020186226473258376612952123963455984853463370795250000*t^13 - 2628819870329507148616099185218994963152829158225025971559262580171544582402251599733616026963825518890605872475607954707942212574177/77958541764926869828173489509217288133750432432075409263619399592259828220619638020186226473258376612952123963455984853463370795250000*t^11 + 323536306682699000072976522825864849899791196273269027808748617225043631941639721991470379957436212116775836064511525485179354190827/175406718971085457113390351395738898300938472972169670843143649082584613496394185545419009564831347379142278917775965920292584289312500*t^9 - 97416965615696230226897167490579813640400409227123491213347525644863542979831733424962422416869072260443922134960554503733698494947/1559170835298537396563469790184345762675008648641508185272387991845196564412392760403724529465167532259042479269119697069267415905000000*t^7 + 357716470428170922354169454262714685634666212812216470292390445677787083639101861535093581441795206116760408586298044999457435131/311834167059707479312693958036869152535001729728301637054477598369039312882478552080744905893033506451808495853823939413853483181000000*t^5 - 7871218458313793899519415374514451461398264276526622674205887814307306904536384596510031099353995806524952157609365215447711851/935502501179122437938081874110607457605005189184904911163432795107117938647435656242234717679100519355425487561471818241560449543000000*t^3 + 1408604468164116557613084483749454877809852974098074568744137784453149575307917130526916471378915193578816290218323060099737/311834167059707479312693958036869152535001729728301637054477598369039312882478552080744905893033506451808495853823939413853483181000000*t
-------------------------------------------------
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:
| (0.98851944675836295466 + 8.0707122552952380251e-858j)  +/-  (4.74e-242, 4.74e-242j)
| (0.02411517758027983534 + 1.410651591384262616e-877j)  +/-  (2.53e-255, 2.53e-255j)
| (-0.90424740034500105472 - 1.6972072584189203565e-865j)  +/-  (3.52e-242, 3.52e-242j)
| (0.30122745929868194786 - 2.8214176556186650243e-873j)  +/-  (2.48e-250, 2.48e-250j)
| (0.86662751950151689594 - 8.3785623395542607181e-864j)  +/-  (9.85e-243, 9.85e-243j)
| (0.95310746197929789659 + 1.0680969739899556693e-868j)  +/-  (1.05e-241, 1.05e-241j)
| (-0.98851944675836295466 - 7.0191119506388036351e-882j)  +/-  (5.28e-242, 5.28e-242j)
| (-0.93246951420315202781 + 1.5554327116707991929e-880j)  +/-  (7.67e-242, 7.67e-242j)
| (-0.21947779751454411103 - 6.841810334375038948e-892j)  +/-  (3.37e-251, 3.37e-251j)
| (0.93246951420315202781 - 4.7473732030135650846e-883j)  +/-  (7.32e-242, 7.32e-242j)
| (0.90424740034500105472 - 6.2543231777485019567e-899j)  +/-  (3.09e-242, 3.09e-242j)
| (-0.99779344994558984008 - 2.5934768603191693618e-903j)  +/-  (1.54e-242, 1.54e-242j)
| (-0.97268012553880794579 + 1.1531029221128372023e-908j)  +/-  (8.84e-242, 8.84e-242j)
| (-0.82190330787833020415 - 1.06871078227224821e-917j)  +/-  (2.78e-243, 2.78e-243j)
| (0.97268012553880794579 + 9.868269487137680874e-929j)  +/-  (8.78e-242, 8.78e-242j)
| (0.77178951338710911891 - 8.9832702025970450076e-940j)  +/-  (7.08e-244, 7.08e-244j)
| (0.82190330787833020415 + 6.944711193858758099e-941j)  +/-  (2.59e-243, 2.59e-243j)
| (-0.66120938646626451366 + 1.2352967934782231821e-943j)  +/-  (2.86e-245, 2.86e-245j)
| (-0.77178951338710911891 - 8.5993917642694374016e-942j)  +/-  (6.78e-244, 6.78e-244j)
| (-0.38394829373348502256 - 9.4791505150635294815e-951j)  +/-  (2.51e-249, 2.51e-249j)
| (0.21947779751454411103 + 1.3935220723147427449e-948j)  +/-  (3.01e-251, 3.01e-251j)
| (0.71789193809322230261 - 8.1470701644858625205e-944j)  +/-  (1.51e-244, 1.51e-244j)
| (0.12832794326223409598 - 1.0391085303213869951e-950j)  +/-  (1.88e-253, 1.88e-253j)
| (-0.86662751950151689594 + 4.5998495127389163721e-941j)  +/-  (9.94e-243, 9.94e-243j)
| (-0.71789193809322230261 - 1.9761234754817633948e-948j)  +/-  (1.38e-244, 1.38e-244j)
| (-0.95310746197929789659 + 3.3113566588132654077e-951j)  +/-  (9.87e-242, 9.87e-242j)
| (0.66120938646626451366 + 9.3167675788951801719e-956j)  +/-  (2.71e-245, 2.71e-245j)
| (0.38394829373348502256 - 1.115696353787019404e-960j)  +/-  (2.55e-249, 2.55e-249j)
| (-0.12832794326223409598 + 9.6318526398383303836e-963j)  +/-  (1.88e-253, 1.88e-253j)
| (-0.60074015792161858991 - 2.2895900845479076422e-966j)  +/-  (4.02e-246, 4.02e-246j)
| (0.99779344994558984008 + 2.3627522241547777304e-969j)  +/-  (1.43e-242, 1.43e-242j)
| (0.46194088448213480754 + 1.6801855981085593167e-989j)  +/-  (3.16e-248, 3.16e-248j)
| (0.53447674291514872645 + 1.8957407514288683403e-989j)  +/-  (3.68e-247, 3.68e-247j)
| (9.7280200713349823059e-992 - 1.9283016393390887295e-992j)  +/-  (4.07e-990, 4.07e-990j)
| (-0.46194088448213480754 - 3.3660130130466486294e-994j)  +/-  (3.03e-248, 3.03e-248j)
| (-0.30122745929868194786 - 1.7228311988235459484e-995j)  +/-  (2.49e-250, 2.49e-250j)
| (-0.02411517758027983534 + 2.2164367398688412575e-993j)  +/-  (2.44e-255, 2.44e-255j)
| (0.60074015792161858991 - 1.8657932612577156726e-992j)  +/-  (3.9e-246, 3.9e-246j)
| (0.23861918608319690863 + 1.9094212725858277371e-995j)  +/-  (8.04e-251, 8.04e-251j)
| (-0.23861918608319690863 + 9.8429665234537383961e-997j)  +/-  (7.74e-251, 7.74e-251j)
| (-0.53447674291514872645 - 3.9403144533888238226e-994j)  +/-  (3.66e-247, 3.66e-247j)
-------------------------------------------------
The weights are:
| (0.012789513763556092355 - 6.9566750241521077106e-858j)  +/-  (1.29e-79, 3.33e-197j)
| (0.21183750883948712875 - 3.0612554627585570442e-856j)  +/-  (4.36e-80, 1.12e-197j)
| (0.0333335277877712704 - 4.8275398227605911637e-859j)  +/-  (8.85e-81, 2.28e-198j)
| (0.085392915667189647793 - 4.2390959463756275201e-857j)  +/-  (3.84e-80, 9.88e-198j)
| (0.041492147477729670199 + 7.6245350157612210469e-858j)  +/-  (1.76e-80, 4.52e-198j)
| (0.019828081847916027513 - 1.7820248799741248705e-857j)  +/-  (7.09e-81, 1.82e-198j)
| (0.012789513763556092355 - 5.2209651496827450075e-860j)  +/-  (5e-82, 1.29e-199j)
| (0.02315670778511534307 + 4.6423822915223186123e-859j)  +/-  (2.01e-81, 5.16e-199j)
| (0.10043817138465912966 - 1.1288016619652107422e-856j)  +/-  (1.25e-81, 3.22e-199j)
| (0.02315670778511534307 + 1.5910746162202476946e-857j)  +/-  (5.65e-81, 1.45e-198j)
| (0.0333335277877712704 - 1.08427372702327743e-857j)  +/-  (4.11e-81, 1.06e-198j)
| (0.0056478092405815067844 + 1.2244175603419295417e-860j)  +/-  (9.41e-83, 2.42e-200j)
| (0.01845570310158893408 + 1.4582255198805670415e-859j)  +/-  (1.78e-82, 4.57e-200j)
| (0.047685986505037837279 - 5.9503411902436006474e-859j)  +/-  (8.31e-84, 2.14e-201j)
| (0.01845570310158893408 + 1.8055511555075736901e-857j)  +/-  (1.14e-82, 2.94e-200j)
| (0.052266911843278546704 + 6.4026226148156660973e-858j)  +/-  (1.77e-84, 4.56e-202j)
| (0.047685986505037837279 - 6.4655455303997959994e-858j)  +/-  (8.63e-84, 2.22e-201j)
| (0.058221866351470081131 + 1.5134824425838129481e-858j)  +/-  (1.27e-86, 3.26e-204j)
| (0.052266911843278546704 + 7.8829312846274151395e-859j)  +/-  (4.35e-86, 1.12e-203j)
| (0.080397680544613586606 + 6.9846292607348172937e-858j)  +/-  (4.14e-87, 1.07e-204j)
| (0.10043817138465912966 - 1.7731020524547799722e-856j)  +/-  (5.66e-87, 1.46e-204j)
| (0.055326690477084901352 - 6.9439494966205117027e-858j)  +/-  (1.06e-86, 2.73e-204j)
| (0.091418299878320037609 + 5.2795322905508672875e-857j)  +/-  (4.26e-87, 1.09e-204j)
| (0.041492147477729670199 + 5.0096835600304922062e-859j)  +/-  (9.88e-87, 2.54e-204j)
| (0.055326690477084901352 - 1.1012721503384230023e-858j)  +/-  (2.24e-87, 5.76e-205j)
| (0.019828081847916027513 - 3.2501124165678089278e-859j)  +/-  (9.98e-87, 2.57e-204j)
| (0.058221866351470081131 + 7.6283509277843695953e-858j)  +/-  (2.68e-88, 6.9e-206j)
| (0.080397680544613586606 + 1.5856163032289752482e-857j)  +/-  (6.05e-89, 1.56e-206j)
| (0.091418299878320037609 + 4.0662751276896012381e-857j)  +/-  (2.57e-89, 6.61e-207j)
| (0.063113493922892466103 - 1.9832283095258003502e-858j)  +/-  (1.97e-89, 5.08e-207j)
| (0.0056478092405815067844 - 2.622466001689239167e-858j)  +/-  (2.94e-89, 7.55e-207j)
| (0.075435621000394506616 - 1.0445715645766021172e-857j)  +/-  (1.2e-89, 3.1e-207j)
| (0.069477074425770834196 + 8.7317297744695928829e-858j)  +/-  (7.13e-90, 1.83e-207j)
| (-0.25925882982598693776 + 5.4918258133996071558e-856j)  +/-  (9.97e-90, 2.57e-207j)
| (0.075435621000394506616 - 3.7922371786498562544e-858j)  +/-  (1.19e-91, 3.08e-209j)
| (0.085392915667189647793 - 2.2589676869368855531e-857j)  +/-  (2.01e-91, 5.18e-209j)
| (0.21183750883948712875 - 2.9154521875531571529e-856j)  +/-  (2.83e-90, 7.25e-208j)
| (0.063113493922892466103 - 8.1279869124610954402e-858j)  +/-  (7.57e-92, 1.94e-209j)
| (-0.016086296931464079321 + 1.8343760904641336229e-856j)  +/-  (1.21e-90, 3.1e-208j)
| (-0.016086296931464079321 + 1.1209809866539845567e-856j)  +/-  (2.89e-91, 7.53e-209j)
| (0.069477074425770834196 + 2.6031436592223596384e-858j)  +/-  (6.63e-93, 1.64e-210j)
