Starting with polynomial:
P : t
Extension levels are: 1 6 8 30
-------------------------------------------------
Trying to find an order 6 Kronrod extension for:
P1 : t
Solvable: 1
-------------------------------------------------
Trying to find an order 8 Kronrod extension for:
P2 : t^7 - 21/13*t^5 + 105/143*t^3 - 35/429*t
Solvable: 1
-------------------------------------------------
Trying to find an order 30 Kronrod extension for:
P3 : t^15 - 825/221*t^13 + 336705/60401*t^11 - 8310395/1960287*t^9 + 8381629155/4854324041*t^7 - 250360401/693474863*t^5 + 300170185/9015173219*t^3 - 88221135/99166905409*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^45 - 3232440530576735386558545908660038456790189927305478232765833585032836202807513859959589576571342345563595154188691108580939747546010503689385150198523839178141/288680079658245938943979146781376854802048794428910998825108200510845605149058221800211268801688344445584249035472608263110782086440837052377370159112295870275*t^43 + 4381048259805730593678847996457551089477479786813074524220345930468244175185430301029072292942904519412877198134785310591076016719726138373853806421075529430273478418/74874663580879590937960927321538933453152593762232216854269488858297513761906081930098996577825104210506741088081494932594780438978073465438066120798797067577356475*t^41 - 723669349386760596191952196003650694169612975743313088976997492085197334861820689155257065188655200898886420987723926149504403971858460688955523119830692733466533668946/3818607842624859137836007293398485606110782281873843059567743931773173201857210178435048825469080314735843795492156241562333802387881746737341372160738650446445180225*t^39 + 7240880380867859036232251145694866700054012573399197617056437333870318754586677587716306560821502641851222948686857301554680927328671599761302604447873838247122290640198820273/16991239368378168576889338611504949450106927172341040566956475146192540715794726449586146811909960602493676392338912606076838237160269161667102866340941403453809559386208525*t^37 - 126952952366258342397143458993892272548546080747984575838860897441866072168264377918507290603923485218131872429480479715330300852469598024426314370266881199037788045494118645277/179749427002316414944987213732236570498499597981081534418855342336036878098670527177200816273363267426380471308427443885339183456274426394478298743922590636537669549296205975*t^35 + 52654328650659880025492494365339321568003174926899107798517512561704071221458279644475472782307268566521918454970048722128167353335564571812512975367007216659982097234770081568/58909476076389413301298330550901060919676338834135965061641666816012086099564290419418754913119054030494440176711515222926287015081534700711375218596479284243437919517243975*t^33 - 3950753533640388352972170130410603664119114545588945188410607616378561738238312511288523194359336427089795257136585741791375352122532204774632830769122636873731207868835928/4474024157088889899088503877185468285841599364634006612109187120529512121179030182989196849177417333522779689884674961868784614193174960181618836378558463146004246944425*t^31 + 252091731901596587513468973271943803295238084793359625887721227631467235190845791692975070513014338866253339610414512465045124489402390380989767735079264226127284315568404402774/365112742099119411851362380259327965806977950314243762066538459036139079087673864150301267081844832199695487512345701301452228077430474428473175820071227221594355875510619075*t^29 - 473107582812142238774611497746283168059581072441732444729462678564925739013625539832446854694808237357521397648020147331958229379737918008837282621228434179044767069917665331645802/1098624240976250310260749402200317849113196652495559480058214223239742488974810657228256512649271100088883721924648215216069754284988297555275786042594322709777416829411452796675*t^27 + 12783642866234239266446669694139725823555332232184994860192885017229377104859658817399095967553928611466711081241002381615671321019980041206290183664623319488587014861249194322428/59469688257973663518388144278649684140030588026825157040188234306424807095502571188993942280159974078885443636946769484630556499757201292165925740197413480016441366834238185575*t^25 - 7145873247318370602503749718296918308146506779870989315666273060704685225270828857446967833612634530888725008040145400086645628396255027772123539878619198794223593096093109719612/83257563561163128925743401990109557796042823237555219856263528028994729933703599664591519192223963710439621091725477278482779099660081809032296036276378872023017913567933459805*t^23 + 5024154727493287381722717272831500809902136612116255865035074886932110234785371129335120245097620110410934175810925944856916820908515445156418232996709048921932337973470679846/184062410231016497256617690471870798370028349088183979048482375893134996168836255706539836091873169588296877874116751536807912526883010631611560876071581883617578290864996595*t^21 - 663327662363403018504899810507532420372664585869806490384390735766863804504375426696676633317411196879531386632128051936002540443529589119337873238269669889846083776922670525666/96702884384705000677726808522673834210310608356663516230566954915664686320512876629059714838173175241318069218339529509790557090909536014217635768842750615331082918243500353935*t^19 + 4718421590406197612826648224305576373060920770701283425156905531358397542910077535554199598269698591010371278984521362711513085769788552760929050329601276340269336464634166415672/3506751965319039235102830056427487987942316271460061193834770101941735203938598526180112817026385144277271036391365043802404938717719490199786897091192377577006112140514302308485*t^17 - 675771568185686338042223429643845981204978847377688188460135150929892045382817145788487249258359571837748834119028618368906240301681950605365140692099508645489296931046411459912/3337670385506163669283021471257406599902667463771533653148426316891506891308965038900454532695315465189649482081270297235268731450712764539237866373198531020737736434607151763235*t^15 + 1548355470298173563358209581434482329569524551966206910448706779713624313213233270754928727171248525303975187757445766188072152754182215642815037913724408593781531218941216505657/67865964505291994608754769915567267531354238430021184280684668443460640123282289124309242164804747792189539468985829377117130872831159545631169949588370130755000640837012085852445*t^13 - 29159972907825534324989125012266176429452176577445062903299171310167099958821686021043986831993640276103546884102071724771511037637606554089422813216640165542629741297634479689/15661376424298152602020331518977061738004824253081811757081077333106301566911297490225209730339557182812970646689037548565491739884113741299500757597316184020384763270079712119795*t^11 + 3137942548214301293567913461236496406033145443586473948171082734723502006647771619276940767117727778147240826374911781811078421485804342132523888969269725750675973743657124798/29898991355478291331129723808956208772554664483156186081700238545021121173194295208611764030648245530824762143679071683625029685233308051571774173594876351311643638970152177683245*t^9 - 164526238192620288937331671117832359139554243293517373949699342604375775844224412923505645033972785704472133196825533740175723285937874167539802353513614896397756999594351762/43187431957913087478298489946270079338134515364558935451344789009474952805725093079105881377603021322302434207536436876347265100892556074492562695192599174116818589623553145542465*t^7 + 491548749907846346135079425616240490398919719978966379772807320795805838731039658987997799719516135253959338252756950570858313098354122777963650242498844368400483332611311/6169633136844726782614069992324297048304930766365562207334969858496421829389299011300840196800431617471776315362348125192466442984650867784651813598942739159545512803364735077495*t^5 - 1009747480253751009250903284786406223402971052950752934241781361928409800554831855991861974130488656096214969723446838629245776784230904523205045017786207917899847608727/1284290979506453330258439059626690405973679465651606826832993725646193931832058161536093265456416377514533028912162262795166484049866099008233642830800325294436004706006536689601*t^3 + 48474216029884369762093236348550967625212919717630721987048627564665694945507497624451874569625028319986189024237362286584935952129669693053385023533655079936987515528/20976752665272071060887837973902609964236764605642911504938897518887834219923616638422856669121467499404039472231983625654385906147812950467816166236405313142454743531440099263483*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:
| (0.40584515137739716691 + 7.9372751265572714528e-835j)  +/-  (3.97e-248, 3.97e-248j)
| (0.99835268195068022192 - 1.5816891509621783147e-825j)  +/-  (2.21e-240, 2.21e-240j)
| (-0.9270514837822925248 + 5.0508330840720395398e-825j)  +/-  (6.1e-240, 6.1e-240j)
| (0.97979918196163894495 - 1.9381644190916426382e-836j)  +/-  (1.18e-239, 1.18e-239j)
| (0.89853157089259661632 + 3.7246059146875651101e-837j)  +/-  (2.32e-240, 2.32e-240j)
| (0.78594489892280156558 - 5.2541786915206037746e-838j)  +/-  (6.77e-242, 6.77e-242j)
| (-0.99835268195068022192 + 5.4161145063695257284e-834j)  +/-  (2.15e-240, 2.15e-240j)
| (-0.89853157089259661632 - 7.075176806467663056e-849j)  +/-  (2.28e-240, 2.28e-240j)
| (-0.99145537112081263921 + 1.600322726819041369e-860j)  +/-  (6.89e-240, 6.89e-240j)
| (0.99145537112081263921 - 1.1966783373204601986e-873j)  +/-  (6.87e-240, 6.87e-240j)
| (0.86486442335976907279 - 6.1349275667814382744e-876j)  +/-  (7.92e-241, 7.92e-241j)
| (-0.13874140435443244801 + 1.7057250898948525162e-887j)  +/-  (4.3e-253, 4.3e-253j)
| (-0.82709899815463542678 - 3.6764964282503916602e-874j)  +/-  (2.42e-241, 2.42e-241j)
| (-0.86486442335976907279 - 2.5908472528938667242e-881j)  +/-  (7.88e-241, 7.88e-241j)
| (-0.94910791234275852453 - 1.2022289529288881665e-900j)  +/-  (1.23e-239, 1.23e-239j)
| (0.82709899815463542678 + 1.844188278754411743e-922j)  +/-  (2.6e-241, 2.6e-241j)
| (0.96540879923778891532 - 3.1472505397204931295e-919j)  +/-  (1.53e-239, 1.53e-239j)
| (-0.97979918196163894495 + 2.5214799610675073954e-918j)  +/-  (1.25e-239, 1.25e-239j)
| (-0.78594489892280156558 - 2.4248915448692618687e-935j)  +/-  (6.07e-242, 6.07e-242j)
| (-0.96540879923778891532 + 2.5477755336366940523e-934j)  +/-  (1.55e-239, 1.55e-239j)
| (0.46777619675071342071 + 3.253168465788817047e-949j)  +/-  (5.25e-247, 5.25e-247j)
| (0.74153118559939443986 - 1.3586700552103839593e-944j)  +/-  (1.46e-242, 1.46e-242j)
| (0.2077849550078984676 + 2.7942748724607231379e-954j)  +/-  (9.1e-252, 9.1e-252j)
| (-0.40584515137739716691 + 1.4864936389881792241e-950j)  +/-  (4.14e-248, 4.14e-248j)
| (-0.74153118559939443986 - 1.8746941354002214578e-943j)  +/-  (1.41e-242, 1.41e-242j)
| (-0.2077849550078984676 + 2.7359493246575576242e-954j)  +/-  (7.98e-252, 7.98e-252j)
| (0.69346481485539739439 + 2.2495388422964135237e-945j)  +/-  (2.54e-243, 2.54e-243j)
| (0.9270514837822925248 + 3.5277170648120669734e-941j)  +/-  (5.71e-240, 5.71e-240j)
| (-0.69346481485539739439 + 2.6610337916948259453e-949j)  +/-  (2.65e-243, 2.65e-243j)
| (-0.64152213004699282747 - 2.46388106355918329e-950j)  +/-  (4.29e-244, 4.29e-244j)
| (-0.069357229886135131524 + 2.6162447514176145958e-960j)  +/-  (2.59e-254, 2.59e-254j)
| (0.13874140435443244801 + 1.1702174446765594788e-959j)  +/-  (4.35e-253, 4.35e-253j)
| (0.64152213004699282747 - 1.0719389124511692865e-948j)  +/-  (4.26e-244, 4.26e-244j)
| (0.069357229886135131524 - 1.6383689834144019119e-960j)  +/-  (2.33e-254, 2.33e-254j)
| (-0.52793496731917939504 - 3.9085014224916193699e-952j)  +/-  (5.43e-246, 5.43e-246j)
| (-0.46777619675071342071 + 1.5207161186880071318e-953j)  +/-  (5.79e-247, 5.79e-247j)
| (0.94910791234275852453 + 5.1507885546684922814e-952j)  +/-  (1.17e-239, 1.17e-239j)
| (0.58608723546769113029 + 9.1594707127905622463e-958j)  +/-  (5.12e-245, 5.12e-245j)
| (0.27575337541918702946 + 1.4244708690066519472e-963j)  +/-  (1.79e-250, 1.79e-250j)
| (-0.27575337541918702946 - 5.1465131084970816075e-962j)  +/-  (1.58e-250, 1.58e-250j)
| (-0.58608723546769113029 - 1.7963267060790321892e-961j)  +/-  (5.14e-245, 5.14e-245j)
| (-0.34189357765262961812 - 2.1239965854193626156e-965j)  +/-  (2.89e-249, 2.89e-249j)
| (0.34189357765262961812 - 8.8800312438056337469e-965j)  +/-  (2.78e-249, 2.78e-249j)
| (0.52793496731917939504 - 2.1485849976480415152e-963j)  +/-  (5.42e-246, 5.42e-246j)
| (9.6759874954815444306e-1096 + 6.3378810828369124022e-1096j)  +/-  (5.21e-1094, 5.21e-1094j)
-------------------------------------------------
The weights are:
| (0.062882807167183198001 + 4.6734190531296641003e-826j)  +/-  (1.77e-75, 1.17e-190j)
| (0.0042136618925809827678 + 2.2036133303072182037e-825j)  +/-  (6.98e-76, 4.62e-191j)
| (0.025506105286681120862 - 9.084258371650347142e-826j)  +/-  (1.11e-76, 7.34e-192j)
| (0.013488100772283700015 + 3.8624428321885671254e-825j)  +/-  (4.7e-76, 3.11e-191j)
| (0.031294787496357463723 + 1.8095167758774118957e-825j)  +/-  (2.85e-76, 1.89e-191j)
| (0.0427464292323689842 - 1.1072691055050396443e-825j)  +/-  (1.32e-76, 8.74e-192j)
| (0.0042136618925809827678 + 6.7154966720663362324e-827j)  +/-  (6.72e-78, 4.45e-193j)
| (0.031294787496357463723 - 4.3928085341190203462e-825j)  +/-  (1.51e-77, 9.98e-193j)
| (0.0094787643221966490242 - 3.074848207289398506e-826j)  +/-  (7.29e-78, 4.82e-193j)
| (0.0094787643221966490242 - 4.0051593322288416984e-825j)  +/-  (3.44e-77, 2.27e-192j)
| (0.035867073280631924684 - 1.4300819078604016438e-825j)  +/-  (5.57e-78, 3.69e-193j)
| (0.069314020708758152207 + 5.4966724138143118948e-828j)  +/-  (1.78e-79, 1.18e-194j)
| (0.039539494092080440839 - 1.4241063997682206634e-825j)  +/-  (1.15e-78, 7.63e-194j)
| (0.035867073280631924684 + 2.100194691622543718e-825j)  +/-  (2.45e-78, 1.62e-193j)
| (0.018598883145710692459 + 5.8699990591710693463e-825j)  +/-  (1.58e-78, 1.04e-193j)
| (0.039539494092080440839 + 1.2353552860159914759e-825j)  +/-  (1.8e-79, 1.19e-194j)
| (0.014961066991750523661 - 4.2362807649600148416e-825j)  +/-  (3.13e-79, 2.07e-194j)
| (0.013488100772283700015 + 9.7022226649850575591e-826j)  +/-  (3.12e-79, 2.06e-194j)
| (0.0427464292323689842 + 1.0992108387539221675e-825j)  +/-  (1.76e-81, 1.16e-196j)
| (0.014961066991750523661 - 2.5858742653256325812e-825j)  +/-  (3.44e-79, 2.28e-194j)
| (0.061032466387741206251 - 5.3108886235513959767e-826j)  +/-  (9.91e-84, 6.56e-199j)
| (0.046161599301510327286 + 9.8616373788588943769e-826j)  +/-  (5.92e-83, 3.92e-198j)
| (0.068644269437206330015 - 2.6924939287430906632e-826j)  +/-  (1.18e-84, 7.82e-200j)
| (0.062882807167183198001 - 2.376483865721671119e-826j)  +/-  (3.47e-85, 2.3e-200j)
| (0.046161599301510327286 - 8.7884245466462832422e-826j)  +/-  (4.83e-83, 3.19e-198j)
| (0.068644269437206330015 + 4.8759544904774766793e-827j)  +/-  (2.25e-85, 1.49e-200j)
| (0.050016607671858993477 - 8.6079040625113575032e-826j)  +/-  (3.95e-84, 2.61e-199j)
| (0.025506105286681120862 - 2.5769282892980829307e-825j)  +/-  (2.16e-83, 1.43e-198j)
| (0.050016607671858993477 + 7.0215006339143448492e-826j)  +/-  (3.59e-84, 2.37e-199j)
| (0.053799455658085390697 - 5.6252702033075240902e-826j)  +/-  (6.27e-85, 4.15e-200j)
| (0.069392015363109410825 - 5.8844242708946664964e-827j)  +/-  (9.67e-87, 6.39e-202j)
| (0.069314020708758152207 + 2.1508644913588578264e-826j)  +/-  (2.37e-87, 1.57e-202j)
| (0.053799455658085390697 + 7.4753938363214106737e-826j)  +/-  (5.19e-87, 3.43e-202j)
| (0.069392015363109410825 - 1.6377509806826442728e-826j)  +/-  (1.59e-87, 1.05e-202j)
| (0.059244906367265269041 - 3.7655386043010301444e-826j)  +/-  (6.54e-88, 4.32e-203j)
| (0.061032466387741206251 + 3.0621582743895259177e-826j)  +/-  (4.45e-88, 2.94e-203j)
| (0.018598883145710692459 + 3.7201585544302121777e-825j)  +/-  (8.8e-87, 5.8e-202j)
| (0.056933318526005502725 - 6.5878953196856743986e-826j)  +/-  (2.2e-88, 1.45e-203j)
| (0.067159505886484837413 + 3.3020076830172666782e-826j)  +/-  (5.4e-89, 3.59e-204j)
| (0.067159505886484837413 - 1.0655386014644852286e-826j)  +/-  (2.75e-89, 1.84e-204j)
| (0.056933318526005502725 + 4.5752930783725119391e-826j)  +/-  (6.47e-89, 4.26e-204j)
| (0.065057233686168050268 + 1.6996772884426205392e-826j)  +/-  (1.85e-89, 1.24e-204j)
| (0.065057233686168050268 - 3.9813991788649849784e-826j)  +/-  (8.63e-90, 5.54e-205j)
| (0.059244906367265269041 + 5.9101051488751760169e-826j)  +/-  (8.18e-90, 5.12e-205j)
| (0.069334854651961699118 + 1.1189178564346814211e-826j)  +/-  (5.76e-90, 4e-205j)
