Starting with polynomial:
P : t
Extension levels are: 1 18 40
-------------------------------------------------
Trying to find an order 18 Kronrod extension for:
P1 : t
Solvable: 1
-------------------------------------------------
Trying to find an order 40 Kronrod extension for:
P2 : t^19 - 171/37*t^17 + 11628/1295*t^15 - 3876/407*t^13 + 75582/12617*t^11 - 75582/33263*t^9 + 16796/33263*t^7 - 50388/831575*t^5 + 12597/3825245*t^3 - 4199/80330145*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^59 - 171914093822198263725425749843114357063628104376920961079410214939961704128035901694754380302109829200852383/11564455998597563101639733358755404366028518282238671777600113609670182276139165429279527613851221617907061*t^57 + 1372739395822735312289645572931390020035665109780627364879627143117305473369743929589441475016477953787996405366/13087109371746242243355631584324865940888939856066763561650795234943422942497488877467998749674965797598157365*t^55 - 300524390912709656618263673642436843009410935957431526713049166926902967052654754867160984690359316048115612780982/643013307131798702223540031843161746562343244928080316329109072543553513908043286846261005234029986188656131867*t^53 + 29419606535743299102620746475435555206850603280614671553907202165324706247548303252744964446679266346962484061204459/19933412521085759768929740987138014143432640592770489806202381248850158931149341892234091162254929571848340087877*t^51 - 2403301449183584132632740947561987670942358876112733851901928356598151230838297364636320969944876571384094716755639432971/683855583360889160392672624045743851218743600816177193781385093504302402450940472296874965503479868821401003394796239*t^49 + 8141430471325774811825933918728972066775302512590794820577586615978777384987876767050544681060502883699807344586948061348/1242105039165696638264242113062677607315677152502852454011087210650671710574157184375956569996116496430707944941568679*t^47 - 70362353139236889192083446630531548356106582421029096076357167345332396235525019176723014911889795542548782773027530325604/7165990610571326759216781421515447734513522033670302619294733907600029099466291448322826365362210556331007374662896225*t^45 + 53227569002441745904157697426896163649305933959697703605111686179329107209642545777706692617187120984675541407795912242293179/4428104464625708515412023133068445670080389048672668998549525905969644648196870362300285172036155309775473823716692340635*t^43 - 3001771502146015604590384192901241710733255783143904852097229963630807100812625286876957060050045384094303723599220766041625822829/246614421948399584348841804349980944703787107287726954536218746281167419392028301087589782086209597667325463664253746526985055*t^41 + 1985232461090354053610262855754484516935933783558799184931815803459588566808523599978172646436570773400367196627351684318295103821618/193099092385596874545143132806035079703065305006290205401859278338154089383958159751582799373502114973515838049110683530629298065*t^39 - 974712031190880712197999746641735585471651748015524289459102678844504484218880843005455033878296467604261202959635783776857216538/133817804841023475083259274293856604090828347197706310049798529686870470813553818261665141630978596655243131011164714851440955*t^37 + 74585554167298787635663752426754120092228706551339237375872681469355447787304566036772797669182446528138413689173407863618839338767/17173284954598012635684940201044930858322971223705643123057477976481710421072740010247026509308919904089535146432805072601589225*t^35 - 3212687967582810392465988958273012555686123952084130791761196333363619732862528646144032525596671997335714366755959761352278409269/1471995853251258225915852017232422644999111819174769410547783826555575178949092000878316557940764563207674441122811863365850505*t^33 + 640177193201930777078129043355312013057819787188965571845012473075152018253223036115210151903130171557170459359180009714712/692778588022548418589980763683438189338574283616808310423939251126627377232225026074958928722560955137129808870137941155*t^31 - 81616609171883983614793418901622016673936331484103041642948704562323170211382978580231409911311480253198700549446326244767816/248086401262557425070929318305258813664865308115881182888021004239656045260574375716843050854613638589623898797116638582575*t^29 + 357784295639695560487788187345094393444843760789845945120905877222779074832184974902445742651303293704981768471054720071687334541/3646125839355806476267448191132388784432525433379105744905244699310224897194661599910442318410256646351702440621223237248104775*t^27 - 6195670786050985755921470238178641928888066990429979007279759362801313831648694816508902928969076567137554215112290201725659269103/254034209120929479706895856165648341092015411604803507098740054477582763136454271868404179192942525032851519046700895347300291375*t^25 + 374366367155930651996087070330751977948801522578484897359581301336940286830503172220839610606383465235608112191124441358860772882/74663967550325360122548521203468816773131486193411813390760120359498238208801342514365750058447455183568533424160784893380433465*t^23 - 40120598533766369651920434522566443953844097068440354737440201560068231035713629366315481185365837895738941453774411625615781798/47513433895661592805258149856752883401083673032171153975938258410589787951055399781869113673557471480452703088102317659423912205*t^21 + 3184190785134670683464258559694177997805653416482300666027827069425816619303123796482623638038714454063312314124917600985492520851/27677358432693685417735486436885863694593894766619348363851770770186308456016436121286811502435252809970520197771601723169254528295*t^19 - 4490372382623382687752975907237112138049554941770251628043900237594283241696350194437424677039877431267100847238061883680704838589/359805659625017910430561323679516228029720631966051528730073020012422009928213669576728549531658286529616762571030822401200308867835*t^17 + 5698897451384288865196872160177767279122146711311731801860279750566610502825682390092294633019008169087067517636340195579225843884/5397084894375268656458419855192743420445809479490772930951095300186330148923205043650928242974874297944251438565462336018004633017525*t^15 - 268484193968327408658532794781826677833994907957148522996285308208627129457106221578070571926585086533150928934376060413594030532/3957862255875197014736174560474678508326926951626566816030803220136642109210350365344014044848241151825784388281339046413203397546185*t^13 + 971924353672693915430925832797446941347184836008991231825482255354616642220069854309287299054743549059977655488125313564424023/304450942759630539595090350805744500640532842432812832002369478472049393016180797334154926526787780909675722175487618954861799811245*t^11 - 26088702174531252544875682138856748678333693864269260406028591585940272818857854762915555836318582761519465586563432065732119/249096225894243168759619377931972773251345052899574135274665936931676776104147925091581303521917275289734681779944415508523290754655*t^9 + 3023038259037529107475892917505711592350218996076432872397388912458108690242293365479751146041270824604713614208152192448482/1356190563201990585469038835407407321035100843564348069828736767739129114344805369943053763619327387688555489690808484435293471886455*t^7 - 79904854150492367940685511675532799274975269016675078059734198784700628696793835374591415025253073235897377983467135738542/2906122635432836968862226075873015687932358950495031578204435930869562387881725792735115207755701545046904620766018180932771725470975*t^5 + 841353867178736206980515903565963654924809991869555896047858687347774727801676870896152311413693967058336607121150207319/5231020743779106543952006936571428238278246110891056840767984675565212298187106426923207373960262781084428317378832725678989105847755*t^3 - 491302848161064982013290685404833384205766498681711121271039607740418515502016120330773364390855137435470846964365231/1743673581259702181317335645523809412759415370297018946922661558521737432729035475641069124653420927028142772459610908559663035282585*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:
| (0.99745790430631039555 - 1.2180578575320233095e-836j)  +/-  (5.66e-234, 5.66e-234j)
| (-0.99240684384358440319 - 1.2966657964533075583e-850j)  +/-  (6.26e-234, 6.26e-234j)
| (-0.94389282302164542535 - 1.9687541585852430724e-873j)  +/-  (1.27e-234, 1.27e-234j)
| (-0.99970314533145977656 - 1.8890985272986145083e-885j)  +/-  (2.44e-234, 2.44e-234j)
| (0.94389282302164542535 + 3.8735303444786901689e-909j)  +/-  (1.35e-234, 1.35e-234j)
| (0.92485736805271324595 - 2.365429737478107053e-909j)  +/-  (6.6e-235, 6.6e-235j)
| (-0.99745790430631039555 - 5.6695953052967832534e-907j)  +/-  (5.51e-234, 5.51e-234j)
| (-0.92485736805271324595 + 3.6800046612931082929e-915j)  +/-  (6.28e-235, 6.28e-235j)
| (-0.90315590361481790164 - 6.7545091984401608949e-916j)  +/-  (2.6e-235, 2.6e-235j)
| (0.99240684384358440319 - 1.9353252734221543178e-912j)  +/-  (6.15e-234, 6.15e-234j)
| (0.8788504359496339982 - 8.3924641681349943151e-918j)  +/-  (9.49e-236, 9.49e-236j)
| (0.98450013590965789476 - 7.7641249885367239052e-916j)  +/-  (5.25e-234, 5.25e-234j)
| (-0.8788504359496339982 + 1.8164874834109134282e-916j)  +/-  (9.49e-236, 9.49e-236j)
| (-0.85201085639550798071 - 7.9192576270932650994e-918j)  +/-  (2.98e-236, 2.98e-236j)
| (0.90315590361481790164 - 3.9908869670348552943e-917j)  +/-  (2.62e-235, 2.62e-235j)
| (0.85201085639550798071 + 3.7193268318846505175e-918j)  +/-  (3.07e-236, 3.07e-236j)
| (0.82271465653714282498 - 2.5609209860419594424e-919j)  +/-  (8.29e-237, 8.29e-237j)
| (0.96020815213483003085 - 7.409965391250259165e-917j)  +/-  (2.76e-234, 2.76e-234j)
| (-0.75709772144533270622 - 4.3112640774053848449e-919j)  +/-  (4.41e-238, 4.41e-238j)
| (0.68275590001938973784 + 1.0141156579833032772e-921j)  +/-  (1.32e-239, 1.32e-239j)
| (-0.1071633603483009117 - 7.3320019640752755968e-939j)  +/-  (4.54e-253, 4.54e-253j)
| (0.79104648483383354697 + 2.4531056494362270546e-919j)  +/-  (2.04e-237, 2.04e-237j)
| (0.99970314533145977656 + 9.3235726568357015064e-916j)  +/-  (2.43e-234, 2.43e-234j)
| (-0.82271465653714282498 + 5.3779310772601001712e-918j)  +/-  (8.61e-237, 8.61e-237j)
| (-0.72096617733522937862 + 8.5029377268517744133e-920j)  +/-  (8.5e-239, 8.5e-239j)
| (-0.9737569073197177217 - 1.4492734238949015235e-913j)  +/-  (4.17e-234, 4.17e-234j)
| (0.75709772144533270622 + 3.3501239894535562825e-928j)  +/-  (4.65e-238, 4.65e-238j)
| (0.72096617733522937862 - 7.3359196335313976168e-929j)  +/-  (8.69e-239, 8.69e-239j)
| (-0.96020815213483003085 - 8.8596951578905030733e-924j)  +/-  (2.51e-234, 2.51e-234j)
| (-0.64257698565468195327 - 5.3243694738767351246e-942j)  +/-  (1.93e-240, 1.93e-240j)
| (0.9737569073197177217 - 1.0857802227409544702e-937j)  +/-  (3.83e-234, 3.83e-234j)
| (0.55678212249147887559 + 2.8129557706573913447e-950j)  +/-  (2.69e-242, 2.69e-242j)
| (0.64257698565468195327 + 3.0536474588015115407e-948j)  +/-  (1.9e-240, 1.9e-240j)
| (0.05365905594595733233 - 1.6389027443916575351e-961j)  +/-  (1.95e-254, 1.95e-254j)
| (-0.68275590001938973784 - 3.7702187681392015761e-945j)  +/-  (1.39e-239, 1.39e-239j)
| (-0.51141367077233682686 - 6.5355505843551740701e-951j)  +/-  (2.63e-243, 2.63e-243j)
| (-0.98450013590965789476 + 2.3062840514070897229e-948j)  +/-  (5.19e-234, 5.19e-234j)
| (0.60054530466168102347 - 3.5242251371936602463e-966j)  +/-  (2.33e-241, 2.33e-241j)
| (0.16035864564022537587 - 1.9493626112321675402e-977j)  +/-  (9.6e-252, 9.6e-252j)
| (-0.46457074137596094572 + 8.5334609650796911505e-968j)  +/-  (2.03e-244, 2.03e-244j)
| (-0.55678212249147887559 + 1.0089229903417514862e-965j)  +/-  (2.57e-242, 2.57e-242j)
| (-0.79104648483383354697 + 4.0949202788427733228e-968j)  +/-  (2.18e-237, 2.18e-237j)
| (0.26521014873858215426 + 3.6968102946538249361e-983j)  +/-  (3.81e-249, 3.81e-249j)
| (0.51141367077233682686 - 8.0647927474485095548e-977j)  +/-  (2.4e-243, 2.4e-243j)
| (-0.16035864564022537587 + 2.0099855588444361808e-984j)  +/-  (9.21e-252, 9.21e-252j)
| (-0.60054530466168102347 + 5.3415357548641439571e-978j)  +/-  (2.5e-241, 2.5e-241j)
| (-0.31656409996362983199 - 1.2829638550426249566e-984j)  +/-  (7.09e-248, 7.09e-248j)
| (0.1071633603483009117 - 2.2329306470388395331e-990j)  +/-  (4.68e-253, 4.68e-253j)
| (0.46457074137596094572 - 2.2796370977068348483e-981j)  +/-  (2.07e-244, 2.07e-244j)
| (0.21309157512383738278 - 1.4452316914345162148e-988j)  +/-  (2.03e-250, 2.03e-250j)
| (-0.26521014873858215426 - 2.5807875375256843965e-986j)  +/-  (4.17e-249, 4.17e-249j)
| (-0.41638833322671202616 + 4.9202876659906434098e-983j)  +/-  (1.56e-245, 1.56e-245j)
| (1.7369936186619900695e-1007 - 2.9524121721986719212e-1006j)  +/-  (1.74e-1004, 1.74e-1004j)
| (0.36700532233383386631 - 9.6221176446362243337e-984j)  +/-  (1.1e-246, 1.1e-246j)
| (0.41638833322671202616 + 1.1124695978723064277e-982j)  +/-  (1.71e-245, 1.71e-245j)
| (-0.05365905594595733233 - 1.0771701388279288158e-991j)  +/-  (2e-254, 2e-254j)
| (-0.36700532233383386631 + 1.2550159786369044351e-984j)  +/-  (1.1e-246, 1.1e-246j)
| (-0.21309157512383738278 - 1.3148507276678709195e-987j)  +/-  (1.96e-250, 1.96e-250j)
| (0.31656409996362983199 - 2.3995650799160023958e-985j)  +/-  (7.11e-248, 7.11e-248j)
-------------------------------------------------
The weights are:
| (0.0036237386194622620156 + 8.9599926967209807387e-838j)  +/-  (3.84e-44, 3.75e-155j)
| (0.0064805333990708356163 - 3.0755634017838737732e-839j)  +/-  (1.9e-44, 1.86e-155j)
| (0.017683763091761857832 - 5.3157079545090768351e-839j)  +/-  (5.16e-45, 5.03e-156j)
| (0.0009673520738117121872 - 8.5720561959980599484e-840j)  +/-  (7.72e-45, 7.53e-156j)
| (0.017683763091761857832 - 1.9265635851275971844e-837j)  +/-  (1.42e-46, 1.38e-157j)
| (0.020378131804375597213 + 1.5277215916986934988e-837j)  +/-  (1.27e-46, 1.24e-157j)
| (0.0036237386194622620156 + 2.212586255519231474e-839j)  +/-  (6.04e-45, 5.89e-156j)
| (0.020378131804375597213 + 5.7697823243872422454e-839j)  +/-  (1.5e-46, 1.46e-157j)
| (0.023014462730663130946 - 6.2064196480601318451e-839j)  +/-  (4.59e-47, 4.48e-158j)
| (0.0064805333990708356163 - 1.2116178848127285315e-836j)  +/-  (1.08e-48, 1.05e-159j)
| (0.025584818951938154905 + 1.0491356607888098101e-837j)  +/-  (6.34e-50, 6.18e-161j)
| (0.0093293986980405226875 + 5.7276644405635645856e-837j)  +/-  (6.09e-49, 5.94e-160j)
| (0.025584818951938154905 + 6.631923017083835469e-839j)  +/-  (3.61e-49, 3.52e-160j)
| (0.028081417025431725745 - 7.0513210499809018034e-839j)  +/-  (7.22e-50, 7.04e-161j)
| (0.023014462730663130946 - 1.2508755693787542534e-837j)  +/-  (4.66e-50, 4.55e-161j)
| (0.028081417025431725745 - 8.9662858001863254421e-838j)  +/-  (2.33e-51, 2.27e-162j)
| (0.030496867253207798605 + 7.7795980455262661193e-838j)  +/-  (2.85e-52, 2.78e-163j)
| (0.014939157845547229435 + 2.5415408333940609322e-837j)  +/-  (5.61e-51, 5.47e-162j)
| (0.035056980818955040341 + 8.3105400837218083076e-839j)  +/-  (2.01e-55, 1.96e-166j)
| (0.039213437473595434585 + 4.9015535361615897905e-838j)  +/-  (1.73e-55, 1.69e-166j)
| (0.053375442619707221489 + 1.6299335974995081666e-838j)  +/-  (1.39e-58, 1.35e-169j)
| (0.032824241173995523909 - 6.8342865594933248042e-838j)  +/-  (1.51e-53, 1.47e-164j)
| (0.0009673520738117121872 + 7.6249171283865888438e-837j)  +/-  (1.06e-51, 1.04e-162j)
| (0.030496867253207798605 + 7.4686997159443862307e-839j)  +/-  (3.85e-55, 3.76e-166j)
| (0.037188763267942325469 - 8.7406854277204203324e-839j)  +/-  (8.69e-57, 8.47e-168j)
| (0.012151855837637440013 - 4.3187203874324137008e-839j)  +/-  (7.64e-55, 7.45e-166j)
| (0.035056980818955040341 + 6.0664394091266225773e-838j)  +/-  (3.17e-55, 3.09e-166j)
| (0.037188763267942325469 - 5.432424504555892972e-838j)  +/-  (5.03e-56, 4.9e-167j)
| (0.014939157845547229435 + 4.8359507417628797058e-839j)  +/-  (9.95e-56, 9.7e-167j)
| (0.041125073040165041391 - 9.6327932944140720848e-839j)  +/-  (4.92e-60, 4.8e-171j)
| (0.012151855837637440013 - 3.5918850163904398323e-837j)  +/-  (3.41e-53, 3.33e-164j)
| (0.044587248202755999874 - 3.7333316158514649914e-838j)  +/-  (6.13e-60, 5.98e-171j)
| (0.041125073040165041391 - 4.4516670974154966748e-838j)  +/-  (3.69e-58, 3.6e-169j)
| (0.053607447464419574197 - 1.9118187735675474616e-838j)  +/-  (9.38e-64, 9.15e-175j)
| (0.039213437473595434585 + 9.1805502250878784139e-839j)  +/-  (9.28e-60, 9.05e-171j)
| (0.046127850790381172738 + 1.1090811939675525567e-838j)  +/-  (1.06e-62, 1.03e-173j)
| (0.0093293986980405226875 + 3.7446680388214992557e-839j)  +/-  (3.52e-57, 3.43e-168j)
| (0.042918070689264171092 + 4.0663817085276407314e-838j)  +/-  (3.75e-60, 3.65e-171j)
| (0.052989565176036478981 - 2.1430282415985883592e-838j)  +/-  (1.49e-64, 1.46e-175j)
| (0.047535502837062019492 - 1.1619996747889313576e-838j)  +/-  (1.49e-63, 1.45e-174j)
| (0.044587248202755999874 - 1.058516574160710486e-838j)  +/-  (1.11e-62, 1.08e-173j)
| (0.032824241173995523909 - 7.8874550064988359695e-839j)  +/-  (4.76e-60, 4.64e-171j)
| (0.051761141782127752262 - 2.4212555316942542541e-838j)  +/-  (6.75e-66, 6.58e-177j)
| (0.046127850790381172738 + 3.4430222036877457879e-838j)  +/-  (7.39e-64, 7.21e-175j)
| (0.052989565176036478981 - 1.5494055188842448466e-838j)  +/-  (1.85e-66, 1.8e-177j)
| (0.042918070689264171092 + 1.0100093203952316029e-838j)  +/-  (4.43e-63, 4.32e-174j)
| (0.050922068434661495292 + 1.3382532286092215965e-838j)  +/-  (1.28e-66, 1.25e-177j)
| (0.053375442619707221489 + 2.022318707883549928e-838j)  +/-  (9.95e-67, 9.7e-178j)
| (0.047535502837062019492 - 3.1880610549383700899e-838j)  +/-  (1.82e-66, 1.78e-177j)
| (0.052450953941967454695 + 2.2754225203676645359e-838j)  +/-  (5.84e-67, 5.69e-178j)
| (0.051761141782127752262 - 1.4041369974187958439e-838j)  +/-  (9.49e-68, 9.25e-179j)
| (0.048806161512217219695 + 1.2175933538458084755e-838j)  +/-  (4.62e-67, 4.5e-178j)
| (0.053684864333279033459 + 1.8102774378525076217e-838j)  +/-  (4.72e-68, 4.59e-179j)
| (0.049936121277158290567 - 2.7620609026220129237e-838j)  +/-  (1.28e-68, 1.24e-179j)
| (0.048806161512217219695 + 2.9626224945519340598e-838j)  +/-  (2.51e-68, 2.46e-179j)
| (0.053607447464419574197 - 1.7166237678571093611e-838j)  +/-  (6.9e-69, 6.78e-180j)
| (0.049936121277158290567 - 1.276214993284367553e-838j)  +/-  (3.65e-69, 3.58e-180j)
| (0.052450953941967454695 + 1.4743427178871660492e-838j)  +/-  (2.64e-69, 2.6e-180j)
| (0.050922068434661495292 + 2.5826262163971133503e-838j)  +/-  (2e-69, 1.85e-180j)
