Starting with polynomial:
P : 3/2*t^2 - 1/2
Extension levels are: 2 4 13 20
-------------------------------------------------
Trying to find an order 4 Kronrod extension for:
P1 : 3/2*t^2 - 1/2
Solvable: 1
-------------------------------------------------
Trying to find an order 13 Kronrod extension for:
P2 : 3/2*t^6 - 25/14*t^4 + 45/98*t^2 - 1/98
Solvable: 1
-------------------------------------------------
Trying to find an order 20 Kronrod extension for:
P3 : 3/2*t^19 - 6523706162613/947242382590*t^17 + 1271968937263439/96145101832885*t^15 - 340906484373145/24723026185599*t^13 + 1742580135265346/206025218213325*t^11 - 382983832651706/123615130927995*t^9 + 100441415714497/152857419964725*t^7 - 117353462093153/1579526672968825*t^5 + 204124551917/54155200216074*t^3 - 3740307548549/66340120264690650*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 3/2*t^39 - 1344445754180518097109447979118758759085912648973728258690792576059201477408860617144130858207997080823015971828164889639496719049083009031601069392394094324602539/92594323749717591354902570863987050570255762965779187052986836507339682622136425014684879680892006064864412089275364873974496601830072069122724767653904655788670*t^37 + 49894278015132439477291531801584232577662580694954024181859365791818501558772471754726076065831822015139776534342449113995508036224376536121271014210644905942796509011/770662556568899512846854097300964221896238715164180173842009440250588178464041465397222253584064166477866501819038861846089735217031689831308438241183448450129100410*t^35 - 97061947005652528726092543928078926919954614528885382756659170264389029181693175243006619152541922177470707905382919206961144768041566714927206962161372693526703604823/550473254692071080604895783786403015640170510831557267030006743036134413188601046712301609702902976055618929870742044175778382297879778450934598743702463178663643150*t^33 + 348141047460653023896535100967675689720314842267645130145644883342048852561529462268714572823682572410185759262995700193091726318853897873003433020461358972034274375158/1061626991191851369738013297302348673020328842318003300700727290141116368292302018659438818712741453821550793322145370910429737288768144155373869005711893273137026075*t^31 - 36967927835826560061518931165445753891087451024358385954264392309889464734106061826312838807573168080675959653366950705327232005315190018085515766261076015833370323042/83805330277667784498070286516655376495966163529430630346425102106602682102277185317726484246665401940804298135317533869404498013091846679980995166724175157412600275*t^29 + 5202311076297272976747519215626072594859405972084156679244245434896428316028248168402544744637203269077543911445654216178278361996741539800300873246545720503914275439546482/11731633650868079412590814006803859181161092308845845807372501409948132665608137781849041425690571231031663474986451388249742800048891626198311989440033183850329422944625*t^27 - 20798560894566766342017181461219332183515136322814203411528817637570092938066545803519767880928853453928347750199523149846631131456137482196683512841019120885772289755782106/61265197954533303599085362035531264612730148723972750327389729585284692809286941749656105223050760873165353702707023916415323511366434047924518167075728848996164764266375*t^25 + 116617509886570178781629124927307174120015984690497434330489284871109304642022639181006969405744878395851780226724546254366892044176220719790510938974570243096000408883751/583478075757460034277003447957440615359334749752121431689425996050330407707494683330058144981435817839670035263876418251574509632061276646900173019768846180915854897775*t^23 - 338459689426466424484454465978449586120812226178139222651665963317039776505112041072452630549623098490805794703873480406318642680758407508171187678453314617191291770943789/3729185962449853262553022036945381324253139487546167411232418322582546518826161671718197709229176748801369355816949281868758822431000333351927192778522625591070898694475*t^21 + 315608311781597056983392395355626346542190225537001394322718652756456189969846520066167851809160282586248628864246351902600426650079908138940866255644214125591185975633065843/9955754489867195399991195031718271015911117159337895335375598161251158976359934869819333592933287035178604321090854969958141588832292575659163570458067874645830677231801415*t^19 - 2644335749347602719562931820689143256383849219779146946261475585947227252304933534868828222126110775359590494284184940310772577049610517788943923043926318426831702774896071/313074040561861490565760850054033679745632615073518721238226357272049024413834429868532502922430409911276865443108646854029609711707313699973697184215970900812285447540925*t^17 + 84237872617035290235376762390381501950189622076453877360383960882717250051850536856920403132788513559780973772656045129169014107989804784624179912787678140789359026808793094/49778772449335976999955975158591355079555585796689476676877990806255794881799674349096667964666435175893021605454274849790707944161462878295817852290339373229153386159007075*t^15 - 37263480627881570676023832592645243656724140310262614218155113871335197335836476421051997317818632217993813588560365885198574968099142210413934447825447212837245764028576982/149336317348007930999867925475774065238666757390068430030633972418767384645399023047290003893999305527679064816362824549372123832484388634887453556871018119687460158477021225*t^13 + 1306843674461392890983175717414575684685690469587847391084422127507965510959588460845704205491799565618824277730412454912906879940583106061435853841611462113639917513339814/49778772449335976999955975158591355079555585796689476676877990806255794881799674349096667964666435175893021605454274849790707944161462878295817852290339373229153386159007075*t^11 - 989800080960411478812950980900660604375477770455307700666616741325695438138999795968120235776882244638324120681881426106559322675134485673288335713119417257693772684646/525175931683295049460681303431536701349820700974715976284702568914553479751261453711399900251160348424055701566335514580888921021782875516904260948723943472525384561859065*t^9 + 54117144161150323772618330886879627098316192508833354261627599835374206278520990198522637279431825274012331527595552939245075766821803085035823223221396988265241331675794813/626515630047342606521445903346030795031286602837133753455186392287535434382330701357730663003291753123789569926247503259465850185216171786231163488926211351462124518197263045950*t^7 - 22604081382762299157453879121087123404884170539420159103280064816446785818515875752574330585741777811290508613752159515300699534652548951325305482570097353158319373315141/9944692540434009627324538148349695159226771473605297673891847496627546577497312719963978777830027827361739205178531797769299209289145583908431166490892243674001976479321635650*t^5 + 12691210334149593120992806642609292822752654609992102200210176739333419836407756986030275000806799132551828315453548368178335310989842148525415268760130220707316730596371/447511164319530433229604216675736282165204716312238395325133137348239595987379072398379045002351252231278264233033930899618464418011551275879402492090150965330088941569473604250*t^3 - 1105466255691747495110759655465045240359584436116033648646940438214251483381637760163518235359523916452071609514846422068882058827390071808014532759805906612100675262043/10292756779349199964280896983541934489799708475181483092478062159009510707709718665162718035054078801319400077359780410691224681614265679345226257318073472202592045656097892897750*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:
| (0.91248695683407599658 - 4.1816586416096982296e-829j)  +/-  (9.87e-243, 9.87e-243j)
| (0.99696950640141468823 - 7.4987613106628083684e-825j)  +/-  (5.21e-241, 5.21e-241j)
| (-0.94562064776199820535 - 2.4473695639056537979e-826j)  +/-  (2.59e-242, 2.59e-242j)
| (0.98815206735195314452 - 9.3013081066727854872e-834j)  +/-  (1.45e-241, 1.45e-241j)
| (0.94562064776199820535 + 1.2394381486436296568e-835j)  +/-  (2.68e-242, 2.68e-242j)
| (0.64533686476208438476 + 5.9177592302821068366e-839j)  +/-  (5.83e-246, 5.83e-246j)
| (-0.97087318261011350743 + 2.6716210636504963978e-832j)  +/-  (6.14e-242, 6.14e-242j)
| (-0.91248695683407599658 + 2.8505676648065561972e-850j)  +/-  (8.77e-243, 8.77e-243j)
| (-0.99811631405225259237 + 5.8438269817156418575e-872j)  +/-  (4.16e-241, 4.16e-241j)
| (0.97087318261011350743 - 3.5371191771096991213e-916j)  +/-  (6.06e-242, 6.06e-242j)
| (0.82398556978138460773 - 1.3020556699515093651e-919j)  +/-  (7.57e-244, 7.57e-244j)
| (-0.99696950640141468823 - 5.2736976222504605348e-915j)  +/-  (5.59e-241, 5.59e-241j)
| (-0.36857946516169392398 - 1.1635830740103038662e-945j)  +/-  (1.2e-249, 1.2e-249j)
| (-0.76975497165152492021 - 2.9010216817852133819e-940j)  +/-  (1.76e-244, 1.76e-244j)
| (0.70988099191371433882 - 6.9036568053794999521e-940j)  +/-  (3.23e-245, 3.23e-245j)
| (0.87177824476366184668 + 1.1578997020660623883e-936j)  +/-  (2.93e-243, 2.93e-243j)
| (0.99811631405225259237 + 2.6605799734302605302e-936j)  +/-  (4.13e-241, 4.13e-241j)
| (-0.98815206735195314452 - 4.1354211271811236383e-939j)  +/-  (1.46e-241, 1.46e-241j)
| (-0.70988099191371433882 + 8.667591920700629252e-952j)  +/-  (3.16e-245, 3.16e-245j)
| (-0.87177824476366184668 - 6.8266171370170459843e-950j)  +/-  (3.04e-243, 3.04e-243j)
| (-0.079430655237557217284 + 1.2265005243623593043e-964j)  +/-  (1.74e-254, 1.74e-254j)
| (0.76975497165152492021 + 2.1263759196786515661e-954j)  +/-  (1.7e-244, 1.7e-244j)
| (-1.6029296871998806483e-983 + 6.224514816232671679e-984j)  +/-  (6.71e-982, 6.71e-982j)
| (-0.82398556978138460773 + 5.233252082900111499e-956j)  +/-  (7.34e-244, 7.34e-244j)
| (-0.57735026918962576451 + 1.8444962841124805337e-958j)  +/-  (7.51e-247, 7.51e-247j)
| (0.079430655237557217284 - 5.0180831197659711644e-969j)  +/-  (2.33e-254, 2.33e-254j)
| (0.57735026918962576451 - 3.2370410437382593211e-961j)  +/-  (7.71e-247, 7.71e-247j)
| (0.30008276830241539724 + 1.5550157809972471546e-965j)  +/-  (1.1e-250, 1.1e-250j)
| (-0.30008276830241539724 + 2.1159327494595330467e-964j)  +/-  (1.09e-250, 1.09e-250j)
| (-0.64533686476208438476 - 1.0733471158949326746e-961j)  +/-  (5.15e-246, 5.15e-246j)
| (-0.23000188558823461278 + 3.6621634781440559137e-968j)  +/-  (7.78e-252, 7.78e-252j)
| (0.36857946516169392398 + 6.3388900082696837454e-966j)  +/-  (1.32e-249, 1.32e-249j)
| (0.50748568302539522465 + 1.238097094579902339e-964j)  +/-  (1.1e-247, 1.1e-247j)
| (-0.15655801081562154215 - 5.3431959382619674417e-970j)  +/-  (4.88e-253, 4.88e-253j)
| (-0.50748568302539522465 - 2.865384888407760224e-964j)  +/-  (1.08e-247, 1.08e-247j)
| (-0.43750999202829047817 + 1.2079188180237240524e-965j)  +/-  (1.29e-248, 1.29e-248j)
| (0.23000188558823461278 + 1.1476685583831424085e-969j)  +/-  (9.01e-252, 9.01e-252j)
| (0.43750999202829047817 - 2.183052343772990895e-966j)  +/-  (1.18e-248, 1.18e-248j)
| (0.15655801081562154215 + 1.3849598375167015103e-971j)  +/-  (4.59e-253, 4.59e-253j)
-------------------------------------------------
The weights are:
| (0.036988897636096325959 + 4.3140121669533887635e-827j)  +/-  (2.74e-79, 3.63e-195j)
| (0.0023125410246750197295 - 1.1057557160664450265e-824j)  +/-  (8.39e-80, 1.11e-195j)
| (0.029226796498778145972 + 6.1629029642417881309e-827j)  +/-  (3.78e-81, 5e-197j)
| (0.01330540641815222634 - 7.2924445915413125092e-826j)  +/-  (1.03e-79, 1.36e-195j)
| (0.029226796498778145972 - 7.3704186034830068827e-827j)  +/-  (7.63e-80, 1.01e-195j)
| (0.066496236956708527454 - 2.9621395720620080986e-827j)  +/-  (1.85e-81, 2.45e-197j)
| (0.021263490861379560331 - 3.3790703959709396127e-826j)  +/-  (8.77e-82, 1.16e-197j)
| (0.036988897636096325959 + 2.0163941373052868679e-826j)  +/-  (5.15e-82, 6.81e-198j)
| (0.0035431418226279533674 + 4.9782675630613338806e-826j)  +/-  (8.33e-83, 1.1e-198j)
| (0.021263490861379560331 + 1.7053599005863505076e-826j)  +/-  (1.74e-81, 2.3e-197j)
| (0.051131390013911103682 + 2.55381242263371275e-827j)  +/-  (2e-83, 2.64e-199j)
| (0.0023125410246750197295 - 6.5924196030217059321e-826j)  +/-  (8.32e-83, 1.1e-198j)
| (0.06844378884048377399 - 1.2901250277007866759e-826j)  +/-  (5.32e-86, 7.04e-202j)
| (0.057197851637378113595 - 5.0795198190727919281e-827j)  +/-  (1.29e-85, 1.71e-201j)
| (0.062389206241345713178 + 2.5335243841750375905e-827j)  +/-  (3.57e-84, 4.72e-200j)
| (0.044346148859850729857 - 3.1016587409422850172e-827j)  +/-  (4.44e-83, 5.88e-199j)
| (0.0035431418226279533674 + 1.1664320628352467581e-824j)  +/-  (1.88e-81, 2.49e-197j)
| (0.01330540641815222634 + 2.9329273799901979828e-826j)  +/-  (4.88e-84, 6.45e-200j)
| (0.062389206241345713178 + 4.8393318337562901255e-827j)  +/-  (2.99e-87, 3.95e-203j)
| (0.044346148859850729857 - 9.2222920165087860679e-827j)  +/-  (2.83e-86, 3.75e-202j)
| (0.078619789176418544995 - 1.2015288339842045705e-826j)  +/-  (4.36e-89, 5.77e-205j)
| (0.057197851637378113595 - 2.4016389624828980681e-827j)  +/-  (1.99e-86, 2.63e-202j)
| (0.079842677449243834913 + 1.1280490954886174501e-826j)  +/-  (2.68e-89, 3.55e-205j)
| (0.051131390013911103682 + 6.1773602185757871594e-827j)  +/-  (5.31e-87, 7.03e-203j)
| (0.069215372809710239872 + 6.1615183363906110542e-827j)  +/-  (3.32e-89, 4.4e-205j)
| (0.078619789176418544995 - 1.1297633325644369026e-826j)  +/-  (5.83e-90, 7.71e-206j)
| (0.069215372809710239872 + 3.7893070556794085953e-827j)  +/-  (1.21e-89, 1.61e-205j)
| (0.068919679956020597435 + 1.1482560865697581869e-826j)  +/-  (6.47e-91, 8.56e-207j)
| (0.068919679956020597435 + 1.4546187095709066259e-826j)  +/-  (9.32e-91, 1.23e-206j)
| (0.066496236956708527454 - 5.1953481350244406389e-827j)  +/-  (3.09e-90, 4.08e-206j)
| (0.071558550766694178842 - 1.4530822891572320657e-826j)  +/-  (4.75e-91, 6.29e-207j)
| (0.06844378884048377399 - 9.6207159234077067737e-827j)  +/-  (3.3e-92, 4.37e-208j)
| (0.070206161623595427579 - 5.1824175393987723749e-827j)  +/-  (4.89e-92, 6.47e-208j)
| (0.075388114281295362414 + 1.3336008459194911947e-826j)  +/-  (1.26e-91, 1.66e-207j)
| (0.070206161623595427579 - 7.8632686965445616404e-827j)  +/-  (2.48e-92, 3.28e-208j)
| (0.069526095850256537951 + 1.0297484037897293719e-826j)  +/-  (2.18e-92, 2.89e-208j)
| (0.071558550766694178842 - 1.2138284628769138278e-826j)  +/-  (2.93e-93, 3.88e-209j)
| (0.069526095850256537951 + 7.2349442341740376572e-827j)  +/-  (1.78e-93, 2.39e-209j)
| (0.075388114281295362414 + 1.1806761768904064397e-826j)  +/-  (2.69e-93, 3.53e-209j)
