Starting with polynomial:
P : 5014575/2048*t^14 - 16900975/2048*t^12 + 22309287/2048*t^10 - 14549535/2048*t^8 + 4849845/2048*t^6 - 765765/2048*t^4 + 45045/2048*t^2 - 429/2048
Extension levels are: 14 43
-------------------------------------------------
Trying to find an order 43 Kronrod extension for:
P1 : 5014575/2048*t^14 - 16900975/2048*t^12 + 22309287/2048*t^10 - 14549535/2048*t^8 + 4849845/2048*t^6 - 765765/2048*t^4 + 45045/2048*t^2 - 429/2048
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 5014575/2048*t^57 - 10617063794339461157794501728907298133132842299738545331741806539142367429952593122286587405896545/310108646915086542042038815027130505799200127666976893750128330098370698303742950213793062912*t^55 + 6818897272960484273077914428615716718822737760736308308721866427500407910812192624255547226585764761/30080538750763394578077765057631659062522412383696758693762448019541957735463066170737927102464*t^53 - 4408002863297574288770341301859909593926190429712182412399073283426276014547541986487061922528106544717/4662483506368326159602053583932907154690973919472997597533179443029003448996775256464378700881920*t^51 + 4914187761048695001661251969205248144364842634594963072647531621771243676888419872907682005601402014710535/1763351262108500953561496665443425485904126336344687691387048465353569104410580401994828024673542144*t^49 - 70787996456596313082234181616381546585859096790621561214254319517217796703237813023376438446548295776721655/11461783203705256198149728325382265658376821186240469994015815024798199178668772612966382160378023936*t^47 + 643142098425111627806023654460030075254910451111776342606213745482692796124630232293810493473453087261339383805/60185823602656300296484223436582276972136688048948707938577044695215343887189724990686472724145003687936*t^45 - 24162592453250296327843729205340290415775323531871614568928431592808859285265301041873501030640147877346115603585/1632783149994643501591717158392441772050546924166640754075590148021809813197630926360236243903417680695296*t^43 + 235336058189970432452895075295764167184432732748404168351110515298534389673606551153707886126635887717935330110861/14106175738478313530144835122505193670010462771079011104882557508319570025494286855604008205526247831580672*t^41 - 170214210715945709496784479756612809948533395031443815233610017542738500962516948834305354674313932115620780627638815/10987625809833184831249738496191353161732765078457389726772367486864920467550396053834322083781445041737375744*t^39 + 1181011007220625442928739727750449902309747012978197742678820488669017983743443868566387800044321000624042749716656895/98888632288498663481247646465722178455594885706116507540951307381784284207953564484508898754033005375636381696*t^37 - 20007065386667332639925055725133056696651245680292728480273740604290700595216023944377822187113339744804952939644016285/2604067316930464805006188023597350699330665323594401365245051094386986150809443864758734333856202474891758051328*t^35 + 1900531675336062426413561109941060565892165388529031241055819014126986059904318815264748701360545356534734035838707275/459541291223023200883444945340708946940705645340188476219714899009468144260490093780953117739329848510310244352*t^33 - 71386422532502986743012443526662700828054706969579302019339142851751550058072573412673554935403715227437498129554925/38295107601918600073620412111725745578392137111682373018309574917455678688374174481746093144944154042525853696*t^31 + 21123935918514135361570637209786824365669837475767260133305785296607531435586095403783844351459920561526075163447825/30059600590753309735207420259741714271211032356481862691791386763164134884422739109327578490117454248434272256*t^29 - 686937113596323816535097077653033511512832891997117400996486671085902851717672297012547119430837302200561733941125/3109613854215859627780077957904315269435624036877434071564626216879048436319593700964921912770771129148372992*t^27 + 7466297223604927565655768258466805185624804425981277822851328581431079941646801101863762209585469662144440157475/129567243925660817824169914912679802893151001536559752981859425703293684846649737540205079698782130381182208*t^25 - 51359471600845998637489599622566337007977466489496134019680056023119422201221391612673886603434318930936519749935/4146151805621146170373437277205753692580832049169912095419501622505397915092791601286562550361028172197830656*t^23 + 1411806911624605060849987996009361827821792146478135332672777511022826827715109837521508562615835538990088510217/649397270759938556805478127755118048235552007701311533017512302320122565014533624297895339213173087211708416*t^21 - 3334196822132195339310106132165735876395864944551259366262148956350993992873475724858465805277402311428695300021885/10833894668088054943185791605338634398713714144480980305331157739606604752137464454161787944093366613952931504128*t^19 + 7620501345410905643017890275973093996230027298991239671775499611801656597002722668727312028891759956813834969694015/220289191584457117178111095975218899440512187604446599541733540705334296626795110567956354863231787817042940583936*t^17 - 4187879563200529540184034811692494494621880963363363497722644784605419892504518038046884830491330502542671570136313315/1384187135320936295788661071560287954634458330812540208220482703021968052854467077253753755783116938748389317159161856*t^15 + 7115606520965481956995995115806937034579101461947788452764495984272447720525520621870216224689815292323138150992765/35491977828741956302273360809238152682934828995193338672320069308255591098832489160352660404695306121753572234850304*t^13 - 344743269046519573876094553282741123946210008213748259715054784629145742839432643584238078674976191537544915702679/35491977828741956302273360809238152682934828995193338672320069308255591098832489160352660404695306121753572234850304*t^11 + 11623743507104486215011709405481972594024620755904092659534189923272307587472717268460810871626957859997582011845/35491977828741956302273360809238152682934828995193338672320069308255591098832489160352660404695306121753572234850304*t^9 - 8630028091557431643087907788703995288452511813764908282004638669591012574294347940287393254826642800722016692135/1206727246177226514277294267514097191219784185836573514858882356480690097360304631451990453759640408139621455984910336*t^7 + 108998432706420210375371424453486946324458063416789364942346838911242379148164103099994699125401251826075664655/1206727246177226514277294267514097191219784185836573514858882356480690097360304631451990453759640408139621455984910336*t^5 - 650756451554876478230726060194995058000950412848179046314805025648786506792906922400306101149589136655790393/1206727246177226514277294267514097191219784185836573514858882356480690097360304631451990453759640408139621455984910336*t^3 + 5780370636796064397419265713787461759061929254405008102654792813825021604914015181857269089147709261807481/6033636230886132571386471337570485956098920929182867574294411782403450486801523157259952268798202040698107279924551680*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:
| (0.99893215460104979362 + 6.3151918841162527196e-852j)  +/-  (1.54e-236, 1.54e-236j)
| (-0.98628380869681233884 - 5.1382986218693907959e-869j)  +/-  (8.32e-236, 8.32e-236j)
| (-0.94416413527418410094 - 5.7957993904705441504e-869j)  +/-  (1.29e-235, 1.29e-235j)
| (-0.99438862086981446788 - 5.2758278104417974309e-870j)  +/-  (5.07e-236, 5.07e-236j)
| (0.91017959006984143439 + 2.8943775633288761925e-867j)  +/-  (4.97e-236, 4.97e-236j)
| (0.92843488366357351734 + 4.2736283236206329145e-886j)  +/-  (9.97e-236, 9.97e-236j)
| (-0.91017959006984143439 - 6.6973137481730817676e-901j)  +/-  (4.97e-236, 4.97e-236j)
| (-0.88641319650700038337 + 5.6232749413881426147e-901j)  +/-  (1.67e-236, 1.67e-236j)
| (0.9747805232373769043 - 1.7886774232298017592e-898j)  +/-  (1.11e-235, 1.11e-235j)
| (-0.16233196964705904636 + 3.1484762688026104189e-924j)  +/-  (9.74e-252, 9.74e-252j)
| (0.88641319650700038337 + 1.9821665498289281927e-908j)  +/-  (1.62e-236, 1.62e-236j)
| (-0.99893215460104979362 - 1.4627436208814467811e-909j)  +/-  (1.64e-236, 1.64e-236j)
| (-0.92843488366357351734 - 1.4143807557955475648e-909j)  +/-  (1.03e-235, 1.03e-235j)
| (-0.85841354551584302918 + 5.0037836762980536606e-911j)  +/-  (4.55e-237, 4.55e-237j)
| (0.98628380869681233884 + 1.0585883193176858439e-906j)  +/-  (7.61e-236, 7.61e-236j)
| (0.85841354551584302918 + 1.8790341028096666143e-920j)  +/-  (4.88e-237, 4.88e-237j)
| (0.82720131506976499319 - 7.7347687743542282036e-924j)  +/-  (1.48e-237, 1.48e-237j)
| (0.99438862086981446788 + 1.7043560225658398079e-920j)  +/-  (4.58e-236, 4.58e-236j)
| (-0.79349326720824406663 - 1.7082868014194903292e-941j)  +/-  (4.04e-238, 4.04e-238j)
| (-0.9747805232373769043 + 7.4238685589021620515e-938j)  +/-  (1.2e-235, 1.2e-235j)
| (0.94416413527418410094 - 1.4393769593382630082e-937j)  +/-  (1.37e-235, 1.37e-235j)
| (0.75821162956954500346 + 5.150816890014450577e-959j)  +/-  (1.02e-238, 1.02e-238j)
| (-0.2160873687309004158 + 1.131020400903317333e-973j)  +/-  (1.89e-250, 1.89e-250j)
| (-0.72266954424536410198 - 4.2356856812257188703e-961j)  +/-  (2.77e-239, 2.77e-239j)
| (-0.75821162956954500346 + 3.1576007832431155806e-960j)  +/-  (1.19e-238, 1.19e-238j)
| (-0.26851186740217750897 - 3.5258024801405217562e-972j)  +/-  (3.92e-249, 3.92e-249j)
| (0.72266954424536410198 + 1.0920763402863554506e-960j)  +/-  (2.7e-239, 2.7e-239j)
| (0.96030818961662669141 - 3.8312313819120480179e-958j)  +/-  (1.47e-235, 1.47e-235j)
| (-0.82720131506976499319 + 1.6579870689935973677e-966j)  +/-  (1.52e-237, 1.52e-237j)
| (-0.64968349270411743036 - 4.5444934119669571704e-971j)  +/-  (1.1e-240, 1.1e-240j)
| (0.10805494870734366207 + 6.9134280023324558576e-984j)  +/-  (3.72e-253, 3.72e-253j)
| (0.31911236892788976044 - 3.098316367003791933e-979j)  +/-  (6.13e-248, 6.13e-248j)
| (0.68729290481168547015 - 2.7750651579951166421e-971j)  +/-  (6.77e-240, 6.77e-240j)
| (0.16233196964705904636 + 9.6801649953214508887e-984j)  +/-  (9.96e-252, 9.96e-252j)
| (-0.60795362858421014596 + 1.5521573098335176274e-971j)  +/-  (1.28e-241, 1.28e-241j)
| (-0.68729290481168547015 + 3.3524619382519939385e-969j)  +/-  (5.89e-240, 5.89e-240j)
| (0.79349326720824406663 + 1.8396486421089297615e-969j)  +/-  (3.92e-238, 3.92e-238j)
| (0.56274799436430992765 - 4.8249669565268131904e-974j)  +/-  (1.26e-242, 1.26e-242j)
| (0.60795362858421014596 - 7.3858498236430438899e-973j)  +/-  (1.39e-241, 1.39e-241j)
| (-0.96030818961662669141 + 2.1993592372031113407e-974j)  +/-  (1.35e-235, 1.35e-235j)
| (-0.56274799436430992765 - 7.6330086643177934091e-983j)  +/-  (1.27e-242, 1.27e-242j)
| (-0.10805494870734366207 - 6.8429915435659397358e-993j)  +/-  (3.78e-253, 3.78e-253j)
| (0.64968349270411743036 + 2.194914494280225057e-986j)  +/-  (1.01e-240, 1.01e-240j)
| (0.51524863635815409197 - 2.5683325858245363086e-991j)  +/-  (1.29e-243, 1.29e-243j)
| (-0.053886919281470330235 + 1.9722272915520326517e-1001j)  +/-  (2.12e-254, 2.12e-254j)
| (-0.51524863635815409197 - 8.2187728411222503324e-992j)  +/-  (1.35e-243, 1.35e-243j)
| (-0.36834977762414851236 + 2.3839090602852816633e-994j)  +/-  (1.02e-246, 1.02e-246j)
| (-2.3571780292754887763e-1025 + 1.1548023403568195677e-1026j)  +/-  (1.35e-1023, 1.35e-1023j)
| (0.46647476321043984962 - 1.2057759865204087471e-992j)  +/-  (1.22e-244, 1.22e-244j)
| (0.26851186740217750897 + 2.7409923947912453444e-998j)  +/-  (4.15e-249, 4.15e-249j)
| (-0.31911236892788976044 - 6.3505661930874259846e-996j)  +/-  (7.24e-248, 7.24e-248j)
| (-0.46647476321043984962 + 4.1640643434298944409e-993j)  +/-  (1.22e-244, 1.22e-244j)
| (0.2160873687309004158 + 9.9534977938670153124e-1000j)  +/-  (1.85e-250, 1.85e-250j)
| (0.41732951659399820412 + 1.1062055210660378076e-993j)  +/-  (1.08e-245, 1.08e-245j)
| (0.36834977762414851236 - 3.1214410006639343383e-995j)  +/-  (9.35e-247, 9.35e-247j)
| (0.053886919281470330235 - 3.1725508586769279877e-1002j)  +/-  (2.69e-254, 2.69e-254j)
| (-0.41732951659399820412 - 4.7969493641066223649e-994j)  +/-  (1.05e-245, 1.05e-245j)
-------------------------------------------------
The weights are:
| (0.0027387834317650137633 - 8.4582324685470844183e-852j)  +/-  (6.45e-52, 1.35e-164j)
| (0.0098441611754055913232 - 7.8249183953326520539e-854j)  +/-  (3.16e-52, 6.61e-165j)
| (0.016135469411231162368 + 6.9779440399086816871e-853j)  +/-  (1.12e-52, 2.35e-165j)
| (0.0063403149411846893764 + 3.3327718089120231038e-854j)  +/-  (1.96e-52, 4.11e-165j)
| (0.02111078074392412469 + 2.3670450581764609023e-851j)  +/-  (5.68e-54, 1.19e-166j)
| (0.015952211610427105045 - 2.8534646148331818542e-851j)  +/-  (5.79e-54, 1.21e-166j)
| (0.02111078074392412469 + 1.1004139483218137866e-852j)  +/-  (4.15e-54, 8.68e-167j)
| (0.026113517469186724837 - 1.0256848701713968688e-852j)  +/-  (1.51e-54, 3.16e-167j)
| (0.013099302938077268697 + 1.339996143170764496e-851j)  +/-  (3.28e-56, 6.86e-169j)
| (0.054147918626606877833 + 7.4135496550285523072e-852j)  +/-  (2.28e-57, 4.78e-170j)
| (0.026113517469186724837 - 1.718617230763155002e-851j)  +/-  (5.84e-56, 1.22e-168j)
| (0.0027387834317650137633 - 8.6572160186104254561e-855j)  +/-  (6.91e-55, 1.45e-167j)
| (0.015952211610427105045 - 1.0437112603291140643e-852j)  +/-  (2.52e-54, 5.26e-167j)
| (0.029729304320585701658 + 1.0562919353922271287e-852j)  +/-  (8.92e-56, 1.86e-168j)
| (0.0098441611754055913232 - 1.2281568694854565278e-851j)  +/-  (1.12e-56, 2.34e-169j)
| (0.029729304320585701658 + 1.3961846740734957645e-851j)  +/-  (2.68e-57, 5.6e-170j)
| (0.032583478522746653177 - 1.3029444617575492481e-851j)  +/-  (4.25e-58, 8.9e-171j)
| (0.0063403149411846893764 + 1.4621401929818479879e-851j)  +/-  (6.6e-57, 1.38e-169j)
| (0.034684483416130381526 + 1.5714865662890203221e-852j)  +/-  (2.3e-59, 4.8e-172j)
| (0.013099302938077268697 + 1.6397063889789275323e-853j)  +/-  (4.03e-57, 8.42e-170j)
| (0.016135469411231162368 + 2.4756814910508313009e-851j)  +/-  (2.63e-57, 5.49e-170j)
| (0.035644554932182305464 - 1.5778570202317136238e-851j)  +/-  (1.93e-60, 4.04e-173j)
| (0.053220423785700302648 - 7.1533444794277224995e-852j)  +/-  (1.94e-62, 4.05e-175j)
| (0.035302565980277920814 + 2.9519652576048370933e-852j)  +/-  (2.8e-61, 5.85e-174j)
| (0.035644554932182305464 - 2.1615907232890861583e-852j)  +/-  (1.2e-60, 2.5e-173j)
| (0.051532372345033352558 + 7.0110822076564914766e-852j)  +/-  (3.12e-63, 6.52e-176j)
| (0.035302565980277920814 + 1.8395932753567010666e-851j)  +/-  (6.77e-63, 1.42e-175j)
| (0.015652922223729747131 - 1.7422179453658396304e-851j)  +/-  (3.67e-59, 7.68e-172j)
| (0.032583478522746653177 - 1.2252978766146646492e-852j)  +/-  (1.36e-60, 2.84e-173j)
| (0.039626682238080955821 + 3.6852372609743714662e-852j)  +/-  (1.54e-63, 3.22e-176j)
| (0.054296182106140736191 - 9.7892243414583067377e-852j)  +/-  (1.4e-66, 2.92e-179j)
| (0.049748393656651868378 - 1.3064897507294033759e-851j)  +/-  (2.79e-67, 5.84e-180j)
| (0.035941697417795366338 - 1.9279097635697436266e-851j)  +/-  (4.47e-65, 9.34e-178j)
| (0.054147918626606877833 + 1.0290565795404482748e-851j)  +/-  (5.11e-67, 1.07e-179j)
| (0.043673471925926407513 - 3.5672427446338611036e-852j)  +/-  (2.86e-65, 5.98e-178j)
| (0.035941697417795366338 - 3.5630614610229532258e-852j)  +/-  (7.83e-64, 1.64e-176j)
| (0.034684483416130381526 + 1.3710999447064162082e-851j)  +/-  (3.11e-64, 6.49e-177j)
| (0.04653512918201916377 + 1.2811088348507841623e-851j)  +/-  (4.95e-68, 1.04e-180j)
| (0.043673471925926407513 - 1.4661039597034112552e-851j)  +/-  (1.61e-67, 3.37e-180j)
| (0.015652922223729747131 - 3.4345640704899413568e-853j)  +/-  (6.09e-65, 1.27e-177j)
| (0.04653512918201916377 + 3.5781935351580915699e-852j)  +/-  (4.3e-68, 8.98e-181j)
| (0.054296182106140736191 - 7.8781376974682474259e-852j)  +/-  (6.84e-70, 1.43e-182j)
| (0.039626682238080955821 + 1.7396028890920568136e-851j)  +/-  (1.71e-67, 3.57e-180j)
| (0.04829644008607836668 - 1.2064259045644878535e-851j)  +/-  (1.96e-69, 4.1e-182j)
| (0.054010306473327133416 + 8.4702142265979493326e-852j)  +/-  (1.68e-70, 3.5e-183j)
| (0.04829644008607836668 - 3.8537559682649629022e-852j)  +/-  (3.17e-70, 6.62e-183j)
| (0.048942046095399998131 + 6.1198792491888345587e-852j)  +/-  (3.1e-71, 6.48e-184j)
| (0.053819440751960542222 - 9.0238603241109223777e-852j)  +/-  (2.37e-71, 4.95e-184j)
| (0.049097283871297202779 + 1.2176483789241881238e-851j)  +/-  (6.17e-72, 1.29e-184j)
| (0.051532372345033352558 + 1.2165809722982088015e-851j)  +/-  (1.16e-72, 2.43e-185j)
| (0.049748393656651868378 - 6.7386007564223385256e-852j)  +/-  (6.56e-72, 1.37e-184j)
| (0.049097283871297202779 + 4.424340240192462103e-852j)  +/-  (3.79e-72, 7.93e-185j)
| (0.053220423785700302648 - 1.1102396485866308069e-851j)  +/-  (5.42e-73, 1.13e-185j)
| (0.049090080697107606964 - 1.2777388015895743143e-851j)  +/-  (1.54e-73, 3.21e-186j)
| (0.048942046095399998131 + 1.3269638718625841312e-851j)  +/-  (1.35e-73, 2.81e-186j)
| (0.054010306473327133416 + 9.4361653435751091899e-852j)  +/-  (6.9e-74, 1.47e-186j)
| (0.049090080697107606964 - 5.2471677572224585967e-852j)  +/-  (4.64e-74, 9.16e-187j)
