Starting with polynomial:
P : 3/2*t^2 - 1/2
Extension levels are: 2 16 36
-------------------------------------------------
Trying to find an order 16 Kronrod extension for:
P1 : 3/2*t^2 - 1/2
Solvable: 1
-------------------------------------------------
Trying to find an order 36 Kronrod extension for:
P2 : 3/2*t^18 - 318937/47234*t^16 + 9281490/732127*t^14 - 272844390/21231683*t^12 + 132075125/17371377*t^10 - 25545611/9650765*t^8 + 115155586/221967595*t^6 - 6801938/133180557*t^4 + 3276767/1686953722*t^2 - 20605/1686953722
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 3/2*t^54 - 82740788358096810438077362969570516632375881407855667669131232804654981127305795521629432250687987291844048672677674232673956066314243143750686237157/4085991826319221288695615990031968088438325227377131578711875688535798404418174336743303173544285294844330141116857794003824470904952186922009437926*t^52 + 376152084351613833899736582309241191619720796572977727351313736063276336890706068545338375171564243397193893869165352662708816135871398757673433163128148017/2912932174925757091260125508605720274024301122873748742384747161486990433098547411884658035541935796691586867913195739349884492079436748722008982363510882*t^50 - 188347428600536635287738200919953467622372423655400146470166570739697270804045077370150087553125624072496334118553947156293254245347768275054087912514853530089/364116521865719636407515688575715034253037640359218592798093395185873804137318426485582254442741974586448358489149467418735561509929593590251122795438860250*t^48 + 11715786720875037046466613472342149381576128461374012253482927704871330420973887826799738471252854085799637663525944898241028256629372168275240798168447074697199457/8023853734093930767694219471298744352317063961775920520195185103013508084872017505249533350027483522974269251846142238772966201213563489151568867481688443899125*t^46 - 47907028602130367696929419671659615765506157524885332150374795337522707867326180869770369547927735026918290795806568744441063944925888000409404181288260201566189719/15512783885914932817542157644510905747812990326100113005710691199159448964085900510149097810053134811083587220235874994961067989012889412359699810464597658204975*t^44 + 1575280348471274788459203040071652787801939301835479285413318697710058198510382384028169269924397392594787374721435893711102254380937002115068689929509182631928613291047/310054011527781762224215104840839473181538237647762958645139584997599906445184893496350017929532005469127657770854433524286865896400620684833320111755913394542835325*t^42 - 1048704546422734420923451296299848894044728705576801729305856195837277596563495800186357655290204453868522744519128369069576773454582373618176242877462778139042185544987/157412036621796894667678437842272347922934797575018117465993943152627644810632330544300778333454710468941733945203020096945639608941853578453839441353002184921747165*t^40 + 1764188906179468304635964964052111504273586630514335541147119360076680646304473290315461353117880386965684187260961704816572341184903660496446215859022955314569983227270953/249235724651178416557157526583597884211313429493778685987823743324993770950167856695142899027969958242491078746571448486830596047491268165885245782142253459459433011250*t^38 - 17701296258977536743093250103000199349920785335784999588464672800186621845374199210378783595298703321746834704249931737490023431581987324996978427721027267148354545505782061/2872769668347793327685131490621470349593560055744080643754389462535454517794040032433489204585548466058186644499955116769257922863188827806782569804692289874821885761250*t^36 + 7629949068406619421342069825394464347787170128919630034921604461710998127445924378233909586320394371666005231412242885706647728565935510059253943479497807860259665794318101/1723661801008675996611078894372882209756136033446448386252633677521272710676424019460093522751329079634911986699973070061554753717913296684069541882815373924893131456750*t^34 - 137660076355195435810314240555333681757613205197588891285076857092199472356758025793331990401850564604244592545862460178349444956306208691467699818736107419320366715950993/52232175788141696867002390738572188174428364649892375340988899318826445778073455135154349174282699382876120809090093032168325870239796869214228541903496179542216104750*t^32 + 5048460236667730244528612432877380013252454672714215801519834223892055110974709952624194257742410809788186094841521496832389447726443838098265032217214886656991163692698/3875290461700835574003403183829549445199523828862982686589498981719381460953836993898548487124200276794034769706684321741520951662952670941700827302517458482164420675*t^30 - 16065317722166972815023475713023326688696711707906989253800569368049405378219315616220515447752745156166276089490701273047020243481684773995893319276909036225419175301306/30066908754575448418991921253849952592065271086005900154573698996098649266021149090592186538032588354436476661517378358339386693936701757306299522174704419258172229375*t^28 + 201966664159577143448717464671211826837994748353125979273129999476208889394659118462454416240147019525818155680358336591727836721977186651407782595702538576378552180586/1113589213132424015518219305698146392298713743926144450169396259114764787630412929281192094001206976090239876352495494753310618293951916937270352673137200713265638125*t^26 - 1790915660057767088449230171440971061409536837077213444953067781921233901935996035008091175533265316872283714520516534955941517465600527861798527791102542829405911388898/35323049840560489772237916376745203563715199957337301959373249339120339063636698116799413221718285281582408877901157093575012812284154805250215586791912006624786041325*t^24 + 422152661899718626874274354338024904575105109352115342919565719137041450256041969508720488754420452942215219732573323898442885849602975581410278068064673314240806352919477/36425743309496247670345169592332292961921613590788092516191944688054617474405878518880368817074534361242242337654767128061397994858938420474983186414372564048985883832450*t^22 - 5208390781998866888053337481739072893128971080277903550370406360592919321745232512661269395727192594067116050714851468631548419776285285737620936977312705383090994595423/2428382887299749844689677972822152864128107572719206167746129645870307831627058567925357921138302290749482822510317808537426532990595894698332212427624837603265725588830*t^20 + 1002524062472174794341092609733140000352715139474017411259552626255741329890697081010229211445569660925016766664740586687089112381103891474347961204884122675317759386641491/3160945058301841047837730827956835644806753357156166695016212089041184027501221235916174227348356815125576807300930347446216870442758989598995763176624996946917552808127050*t^18 - 1047840592153994998724799493171574047939690168139092931536480800725449079265595657208830954547998987901368666384487561326300527138846212924849603031064756956400709461010063/28448505524716569430539577451611520803260780214405500255145908801370656247510991123245568046135211336130191265708373127015951833984830906390961868589624972522257975273143450*t^16 + 239549941438836746155813789337361369700859256659365833358176365424020977427862862561868819195587408180839498950939316643873355886604322860513132248988986136033882312283/72944885960811716488563019106696207187848154395911539115758740516335016019258951598065559092654388041359464783867623402605004702525207452284517611768269160313481987879855*t^14 - 15908764574280236390998371357346939377171080774122947978066788148234806357077496619372432639070426732857701367884787252952005551694743012330616761455035205809829958687/72944885960811716488563019106696207187848154395911539115758740516335016019258951598065559092654388041359464783867623402605004702525207452284517611768269160313481987879855*t^12 + 1388380029399866106290189640367034466213964671145212587032278574260306062609691958348979038776812972873216554003366815256435918420680076575013512844927894878570803/134117257129173738181219034108328062245277505528744402868606468773649671945522076482653734797525943283398403075548235060969365132324181219726385803046868731934900488441*t^10 - 1893326464295464279733261733841149250146477395473472562534572559204001293563883202461175761746915683455202699636968432914278619570011558152872360191028404991742311/5716683852728190947379546951935439434784338118801844758288302548302117242888632570381313408515234172520334230710628793307602249414201210994084452332936454570022099363625*t^8 + 2167632736425294824775601987295939251954820487769455491879048493047820258783696216441789598349337221568882602395670317740414411540014409741221914880670685813659731/331567663458235074948013723212255487217491610890506995980721547801522800087540689082116177693883582006179385381216470011840930466023670237656898235310314365061281763090250*t^6 - 13677485324276128669736133703030519558675731633959346359808237247701178090415367211471693837362627388599285328736984568744602566209487240718251536746807673406273/198940598074941044968808233927353292330494966534304197588432928680913680052524413449269706616330149203707631228729882007104558279614202142594138941186188619036769057854150*t^4 + 19125422676584440545983974969118066241174970154191604348115803879833432487231308504404185140558225371170422220251907507536165892117156910844988417193610899989/66313532691647014989602744642451097443498322178101399196144309560304560017508137816423235538776716401235877076243294002368186093204734047531379647062062873012256352618050*t^2 - 76142446328277678870143918429869254399082476146911793033405120790089363283924192492172788499342655802307692716765181871481442013755835303540044540802949/377798237223776097392039624649646432211834519155600175330357385800835574312640065520852016562745910531778610029571989818589366048242862639609059458524496128105808305770
-------------------------------------------------
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:
| (-0.96271923788205868743 - 1.470836311134743304e-902j)  +/-  (2.39e-235, 2.39e-235j)
| (-0.98312996144425388873 + 2.8082362260215795139e-916j)  +/-  (2.66e-236, 2.66e-236j)
| (-0.95378711948073128028 - 4.9116493687508536536e-923j)  +/-  (8.54e-236, 8.54e-236j)
| (0.99315423719328915677 - 3.2402215915388444079e-936j)  +/-  (1.09e-236, 1.09e-236j)
| (0.95378711948073128028 - 3.640627079848024737e-935j)  +/-  (8.42e-236, 8.42e-236j)
| (0.93059140224660180505 - 3.5434767163634927791e-936j)  +/-  (1.34e-236, 1.34e-236j)
| (-0.99870082735222896567 - 7.7386559240265820335e-934j)  +/-  (3.02e-237, 3.02e-237j)
| (-0.90534757705968229871 + 2.5889809789271476994e-947j)  +/-  (4.9e-237, 4.9e-237j)
| (-0.99315423719328915677 - 4.0117799812064436664e-957j)  +/-  (1.19e-236, 1.19e-236j)
| (0.98312996144425388873 + 9.7533062369858755443e-967j)  +/-  (2.5e-236, 2.5e-236j)
| (0.90534757705968229871 - 1.8968879881078276032e-969j)  +/-  (5.12e-237, 5.12e-237j)
| (0.99870082735222896567 - 3.9859712401923742852e-970j)  +/-  (3.04e-237, 3.04e-237j)
| (-0.84977900022586230979 - 3.1222370639473943553e-968j)  +/-  (8.62e-238, 8.62e-238j)
| (-0.87797644345555917584 + 1.7523268366462811598e-969j)  +/-  (2.22e-237, 2.22e-237j)
| (0.96703520933045389304 + 2.8006481742512434534e-968j)  +/-  (1.82e-235, 1.82e-235j)
| (0.82060265915549183574 - 5.1333373802652127935e-982j)  +/-  (2.84e-238, 2.84e-238j)
| (0.84977900022586230979 + 8.2327834835088904804e-980j)  +/-  (8.76e-238, 8.76e-238j)
| (0.37220065339355154369 - 1.2540251317736793684e-991j)  +/-  (2.65e-247, 2.65e-247j)
| (-0.78783435001750848408 + 2.1686363592397852887e-979j)  +/-  (7.06e-239, 7.06e-239j)
| (-0.37220065339355154369 + 8.6087491412447687882e-992j)  +/-  (2.69e-247, 2.69e-247j)
| (0.87797644345555917584 - 1.9506750168545862915e-979j)  +/-  (2.12e-237, 2.12e-237j)
| (0.78783435001750848408 - 7.3788861319947585359e-982j)  +/-  (7.07e-239, 7.07e-239j)
| (0.96271923788205868743 + 4.0232076562733348968e-978j)  +/-  (2.39e-235, 2.39e-235j)
| (-0.71021983147737219669 + 2.5321490771654052122e-984j)  +/-  (2.17e-240, 2.17e-240j)
| (-0.82060265915549183574 + 2.8767907284787961854e-983j)  +/-  (3.15e-238, 3.15e-238j)
| (-0.96703520933045389304 + 3.5642571797378848571e-996j)  +/-  (1.76e-235, 1.76e-235j)
| (0.75066968757514256976 - 6.5583970074026664173e-1021j)  +/-  (1.24e-239, 1.24e-239j)
| (0.71021983147737219669 - 1.1257567442233136706e-1020j)  +/-  (2.29e-240, 2.29e-240j)
| (-0.93059140224660180505 - 2.02750738354355155e-1024j)  +/-  (1.33e-236, 1.33e-236j)
| (-0.66759199652362935353 - 1.6766256436874163149e-1029j)  +/-  (3.54e-241, 3.54e-241j)
| (-0.75066968757514256976 - 1.9734044312996345262e-1032j)  +/-  (1.44e-239, 1.44e-239j)
| (0.66759199652362935353 - 1.8869137925007714102e-1033j)  +/-  (3.49e-241, 3.49e-241j)
| (0.62335068183607652185 + 1.0739947595303042834e-1036j)  +/-  (4.97e-242, 4.97e-242j)
| (0.088015843352330596119 - 2.2035350856558790164e-1049j)  +/-  (1.03e-253, 1.03e-253j)
| (-0.57735026918962576451 - 8.0235948382951230212e-1037j)  +/-  (5.94e-243, 5.94e-243j)
| (-0.62335068183607652185 - 2.9539455833198361766e-1039j)  +/-  (4.9e-242, 4.9e-242j)
| (0.029360782014582056673 + 3.4700727923424459901e-1053j)  +/-  (5.91e-255, 5.91e-255j)
| (0.57735026918962576451 + 1.4657512871082126324e-1040j)  +/-  (5.45e-243, 5.45e-243j)
| (0.31721987716584234272 - 5.1447742797842174366e-1047j)  +/-  (1.53e-248, 1.53e-248j)
| (-0.31721987716584234272 - 6.7531826631705991817e-1047j)  +/-  (1.49e-248, 1.49e-248j)
| (-0.52912210363569147552 + 3.6678603562340847639e-1043j)  +/-  (5.91e-244, 5.91e-244j)
| (-0.1464099011094258128 - 1.7716337018900598303e-1051j)  +/-  (2.14e-252, 2.14e-252j)
| (0.52912210363569147552 + 9.1948764836293765265e-1043j)  +/-  (6.03e-244, 6.03e-244j)
| (0.47857287185031041153 - 6.1279523522553993907e-1044j)  +/-  (4.77e-245, 4.77e-245j)
| (-0.029360782014582056673 + 1.2097506844618959713e-1054j)  +/-  (4.72e-255, 4.72e-255j)
| (-0.42609429851921162076 + 7.2917716840354151982e-1046j)  +/-  (3.71e-246, 3.71e-246j)
| (-0.26123161566203463135 - 2.1778868146103645452e-1051j)  +/-  (8e-250, 8e-250j)
| (0.1464099011094258128 - 2.1361829171432498172e-1052j)  +/-  (2e-252, 2e-252j)
| (0.42609429851921162076 + 7.2660865413164245062e-1046j)  +/-  (3.83e-246, 3.83e-246j)
| (0.2042461252283935838 - 2.0548801170326605429e-1051j)  +/-  (4.49e-251, 4.49e-251j)
| (-0.2042461252283935838 - 1.1064906057830447075e-1050j)  +/-  (4.16e-251, 4.16e-251j)
| (-0.47857287185031041153 + 5.280330140247290892e-1045j)  +/-  (4.93e-245, 4.93e-245j)
| (-0.088015843352330596119 + 7.5042460494051072821e-1054j)  +/-  (1.07e-253, 1.07e-253j)
| (0.26123161566203463135 - 9.0796333397910706849e-1049j)  +/-  (7.97e-250, 7.97e-250j)
-------------------------------------------------
The weights are:
| (-0.021228883329892287003 - 3.0144699949576734167e-902j)  +/-  (5.26e-50, 4.63e-162j)
| (0.012345833590973072464 - 7.632483868632267617e-904j)  +/-  (1.18e-50, 1.04e-162j)
| (0.025651349537367921086 - 1.7378784351486537815e-902j)  +/-  (3.93e-50, 3.46e-162j)
| (0.0077656606877039017422 + 2.3983895694098813522e-906j)  +/-  (1.78e-52, 1.56e-164j)
| (0.025651349537367921086 + 8.0996005519251623553e-905j)  +/-  (2.25e-52, 1.98e-164j)
| (0.023904749590336716185 - 3.2998160131798479353e-905j)  +/-  (1.42e-52, 1.25e-164j)
| (0.0033339308170478968525 - 2.9483023189287294069e-905j)  +/-  (2.78e-52, 2.45e-164j)
| (0.026492616548990534386 - 1.104189654361535931e-903j)  +/-  (3.63e-53, 3.2e-165j)
| (0.0077656606877039017422 + 1.5413000321565165925e-904j)  +/-  (4.99e-52, 4.39e-164j)
| (0.012345833590973072464 - 8.0059913373349265261e-906j)  +/-  (4.18e-53, 3.68e-165j)
| (0.026492616548990534386 + 3.3911631975318967555e-905j)  +/-  (5.02e-54, 4.41e-166j)
| (0.0033339308170478968525 - 5.4085611518887873548e-907j)  +/-  (1.59e-53, 1.4e-165j)
| (0.028366518367443847289 - 8.7165431703419524294e-904j)  +/-  (1.05e-54, 9.21e-167j)
| (0.027998039504153776599 + 9.2679221781812204967e-904j)  +/-  (4.02e-54, 3.54e-166j)
| (0.029818866005156485377 + 1.0477014551963884894e-904j)  +/-  (1.66e-53, 1.46e-165j)
| (0.030555359637271501009 - 6.0388069424545477847e-905j)  +/-  (8.62e-57, 7.59e-169j)
| (0.028366518367443847289 + 5.4314450436466020446e-905j)  +/-  (2.28e-56, 2.01e-168j)
| (0.054468507067320010722 - 7.3344742492863629931e-905j)  +/-  (1.94e-60, 1.71e-172j)
| (0.035086417915338467405 - 5.8816420075036755035e-904j)  +/-  (8.07e-59, 7.1e-171j)
| (0.054468507067320010722 + 1.6580232738825223045e-904j)  +/-  (3.44e-61, 3.03e-173j)
| (0.027998039504153776599 - 4.2668086412616712953e-905j)  +/-  (2.97e-56, 2.61e-168j)
| (0.035086417915338467405 + 5.8759143967476361128e-905j)  +/-  (2.98e-58, 2.63e-170j)
| (-0.021228883329892287003 - 1.6216676273732428304e-904j)  +/-  (1.87e-54, 1.65e-166j)
| (0.041687370550809277802 - 3.7486317900203561763e-904j)  +/-  (2.19e-61, 1.93e-173j)
| (0.030555359637271501009 + 7.5776779521136544401e-904j)  +/-  (1.2e-59, 1.06e-171j)
| (0.029818866005156485377 + 4.6844761757343132758e-902j)  +/-  (5.33e-58, 4.69e-170j)
| (0.039023068850582716114 - 5.6115297844823857693e-905j)  +/-  (4.64e-61, 4.08e-173j)
| (0.041687370550809277802 + 5.6578707446429369838e-905j)  +/-  (3.14e-62, 2.77e-174j)
| (0.023904749590336716185 + 1.9445993309692091359e-903j)  +/-  (4.4e-59, 3.87e-171j)
| (0.04346958998320312666 + 3.3001143542287207947e-904j)  +/-  (1.68e-63, 1.48e-175j)
| (0.039023068850582716114 + 4.5341916423255920431e-904j)  +/-  (8.01e-62, 7.05e-174j)
| (0.04346958998320312666 - 5.9740350491170615588e-905j)  +/-  (7.73e-64, 6.8e-176j)
| (0.045044133097049075559 + 6.355242268545541595e-905j)  +/-  (7.66e-65, 6.74e-177j)
| (0.058566810220927836064 + 9.2525289217257968448e-905j)  +/-  (2.65e-69, 2.33e-181j)
| (0.047050008757008797706 + 2.6428924910261321731e-904j)  +/-  (9.05e-67, 7.96e-179j)
| (0.045044133097049075559 - 2.9701804763831669115e-904j)  +/-  (7e-66, 6.16e-178j)
| (0.05871175666529238623 - 9.8024183103663617178e-905j)  +/-  (4.8e-70, 4.22e-182j)
| (0.047050008757008797706 - 6.6132648491190287494e-905j)  +/-  (1.21e-67, 1.07e-179j)
| (0.055483367328881259788 + 7.6887897277088867857e-905j)  +/-  (9.21e-70, 8.1e-182j)
| (0.055483367328881259788 - 1.5245844254522187105e-904j)  +/-  (2.1e-70, 1.84e-182j)
| (0.049422630654599711043 - 2.3156451875714258718e-904j)  +/-  (7.84e-69, 6.9e-181j)
| (0.058169757682603474165 + 1.1932417370688118449e-904j)  +/-  (1.9e-71, 1.67e-183j)
| (0.049422630654599711043 + 6.7303210423225982658e-905j)  +/-  (1.32e-69, 1.16e-181j)
| (0.051602997793639884461 - 6.8328164570309880153e-905j)  +/-  (2.75e-70, 2.42e-182j)
| (0.05871175666529238623 + 1.0419130282957688489e-904j)  +/-  (3.24e-72, 2.85e-184j)
| (0.053263012308283733009 - 1.819481596235739274e-904j)  +/-  (1.37e-71, 1.21e-183j)
| (0.056495576808156316283 + 1.4028422331455054073e-904j)  +/-  (2.82e-72, 2.48e-184j)
| (0.058169757682603474165 - 8.7821547262004266159e-905j)  +/-  (4.33e-73, 3.81e-185j)
| (0.053263012308283733009 + 7.0303116700737503421e-905j)  +/-  (2.12e-72, 1.86e-184j)
| (0.057450953359750561006 + 8.3900082604100550707e-905j)  +/-  (1.66e-73, 1.46e-185j)
| (0.057450953359750561006 - 1.2908630342681380481e-904j)  +/-  (8.61e-74, 7.62e-186j)
| (0.051602997793639884461 + 2.0341130570672073051e-904j)  +/-  (1.37e-73, 1.21e-185j)
| (0.058566810220927836064 - 1.1114575282310360596e-904j)  +/-  (5.41e-74, 4.81e-186j)
| (0.056495576808156316283 - 8.0401632110436700491e-905j)  +/-  (4.69e-74, 4.03e-186j)
