Starting with polynomial:
P : 2*t
Extension levels are: 1 4 14 34
-------------------------------------------------
Trying to find an order 4 Kronrod extension for:
P1 : 2*t
Solvable: 1
-------------------------------------------------
Trying to find an order 14 Kronrod extension for:
P2 : 2*t^5 - 10*t^3 + 15/2*t
Solvable: 1
-------------------------------------------------
Trying to find an order 34 Kronrod extension for:
P3 : 2*t^19 - 10067/33*t^17 + 2327243/165*t^15 - 6549361/22*t^13 + 6515327/2*t^11 - 19095440*t^9 + 935949105/16*t^7 - 2754381357/32*t^5 + 6473363715/128*t^3 - 1927283085/256*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 2*t^53 - 418313987895796250264732305810739641229306913167703306430698070705020000777059650337582482009037701865687390802718891/365647758348046586595500362053237969559139497873017676422564541071752736738173161518266278197126512852408009787982*t^51 + 16462827807300024611693792015458431408196782819802555465548554989184822593357585388047232296287467361923027342877637513949/54847163752206987989325054307985695433870924680952651463384681160762910510725974227739941729568976927861201468197300*t^49 - 23710489848670123246244362811111077002587731742727486155419535769349673532697287270803940475807278854495788487699119647754247/493624473769862891903925488771871258904838322128573863170462130446866194596533768049659475566120792350750813213775700*t^47 + 54273887334014933163555752018813161981736077900906860808992473875832794843796756881526158763105992998400220411653169317035984853/10321238997006224103445714765230035413464801280870180775382390000252656796109342422856516307291616567333880639924401000*t^45 - 792165623399604973818709582586053773881244400594637393530755172050492269742458455356690862725646001363634880030192977328697052241/1892227149451141085631714373625506492468546901492866475486771500046320412620046110857027989670129704011211450652806850*t^43 + 3141036226349288422116928707818366107070283848370022169664592037871945220691781607559273691335097459914398580412840515848771463651897/124886991863775311651693148659283428502924095498529187382126919003057147232923043316563847318228560464739955743085252100*t^41 - 93336941376442000523112262838937597054902382383410385210592399869353138004978664663323931759466100129235184818887679756201971517158161/79927674792816199457083615141941394241871421119058679924561228161956574229070747722600862283666278697433571675574561344*t^39 + 945107384233772867978021198669837665615170397675727757852918779819896683395090870033928172464318655283522349971636173820424518357590349/22202131886893388738078781983872609511630950310849633312378118933876826174741874367389128412129521860398214354326267040*t^37 - 19675612583885186083146855202824090171091647337670888378128343488486281947418485898516603375736732432898573800221087929188251444272017010797/15985534958563239891416723028388278848374284223811735984912245632391314845814149544520172456733255739486714335114912268800*t^35 + 1501065663988698894945515035526991613253772712131281254939770275011319649024028970165661388262454584910409935217283710902255988448727586133/52844743664671867409642059597977781316939782558055325569957836801293602796079833205025363493333076824749468876412933120*t^33 - 50842181975364162569756560825615392102179494298368778588564284689384938365134053099845555614178146581126565962158203174421328480341344128611/96882030051898423584343775929625932414389601356434763544922700802371605126146360875879833071110640845374026273423710720*t^31 + 300865091693239466517814759591630576475650265599762404719827042201984664040630556326111596390224829753632215541097833412525264526263794363297/38752812020759369433737510371850372965755840542573905417969080320948642050458544350351933228444256338149610509369484288*t^29 - 3556336502562969241389964685162476808275324250122813154000732290357169407620863227654138669406861188701224861243954786294477150344227428479337/38752812020759369433737510371850372965755840542573905417969080320948642050458544350351933228444256338149610509369484288*t^27 + 7429420575595372640185907591154874165786516318876732511016952778828742152934074325362470500523397064309143814488983555612644704500052590201461/8611736004613193207497224527077860659056853453905312315104240071321920455657454300078207384098723630699913446526552064*t^25 - 9591616212851460206384901260359224489104185956086123111598198154454694966443898980114227347257495043120030602800675639322652624969486872915175/1497693218193598818695169482970062723314235383287880402626824360229899209679557269578818675495430196643463208091574272*t^23 + 20245279301030738131040344357715279603947975249740307275145339994889106990640528318965903289141957984874080192025417994395480201495617879226525/544615715706763206798243448352750081205176503013774691864299767356326985338020825301388609271065526052168439306027008*t^21 - 3990700336751610178349853028161271515584063384962194934400052274915505837893705066779359633459358062918955239717274094346609972030875138749395025/23963091491097581099122711727521003573027766132606086442029189763678387354872916313261098807926883146295411329465188352*t^19 + 27135560299877185261490284835057347844610551043411824292449073654870838868656336850490179640345778403073825981635738038691349092062199720944271925/47926182982195162198245423455042007146055532265212172884058379527356774709745832626522197615853766292590822658930376704*t^17 - 68506612845678183544803107619820902745731888836270474373747324414924817225584755890940899333019988767707143286465920010328647769368226650610258865/47926182982195162198245423455042007146055532265212172884058379527356774709745832626522197615853766292590822658930376704*t^15 + 249676922209743617518631686833453433035074261154824953873003060030490099093112806822655335027954728651072866623311211147729787249383297616516681075/95852365964390324396490846910084014292111064530424345768116759054713549419491665253044395231707532585181645317860753408*t^13 - 14376377758767161591715498244408053794002949593630378885118232778983628582369106673037073227913017966010960056397564975519954294096262756098154825/4356925725654105654385947586822000649641412024110197534914398138850615882704166602411108874168524208417347514448216064*t^11 + 24048898948409513915522011051840239720457300849031639554664535871909222978924532898702807180669779616140547095258426195187488284378862454089815125/8713851451308211308771895173644001299282824048220395069828796277701231765408333204822217748337048416834695028896432128*t^9 - 98724767160899566735103082734342816657805176155820245672356273754525872350836173889783921616874767688785562093876933531237230665303793540356319625/69710811610465690470175161389152010394262592385763160558630370221609854123266665638577741986696387334677560231171457024*t^7 + 27811808018867978513676067850237877759781646985539311844315241022996848507886318210082790811109802717512123514456992864783154169412472047049130725/69710811610465690470175161389152010394262592385763160558630370221609854123266665638577741986696387334677560231171457024*t^5 - 28599230390192992312300186415823301038870396008838771089465037831926841345196879265270546102731887793373731462880112003127270458629143582999630875/557686492883725523761401291113216083154100739086105284469042961772878832986133325108621935893571098677420481849371656192*t^3 + 2261401261503784852686748288065936459450081809965977621022129425940392794138749914464118549708448634974341368003205127494969342536214366421290375/1115372985767451047522802582226432166308201478172210568938085923545757665972266650217243871787142197354840963698743312384*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:
| (9.5373016113985254056 + 6.4510107630046086137e-776j)  +/-  (9.64e-248, 9.64e-248j)
| (7.1367100154060233997 - 1.7885686990725394232e-772j)  +/-  (2.19e-244, 2.19e-244j)
| (8.3164917928578351245 - 5.1894831146955325576e-774j)  +/-  (4.93e-246, 4.93e-246j)
| (-6.6487597653347047321 - 4.788742782633926986e-769j)  +/-  (7.44e-244, 7.44e-244j)
| (6.6487597653347047321 + 2.580030886331125144e-776j)  +/-  (7.04e-244, 7.04e-244j)
| (4.7503167383358089531 + 6.2106103288804597596e-773j)  +/-  (9.53e-242, 9.53e-242j)
| (-5.7648721335022539447 - 8.8400777471829042735e-780j)  +/-  (3.3e-243, 3.3e-243j)
| (-7.677249233842524962 + 5.9063314627869720196e-790j)  +/-  (4.6e-245, 4.6e-245j)
| (1.2224662777326842461 + 3.8816789856488019951e-802j)  +/-  (1.23e-249, 1.23e-249j)
| (7.677249233842524962 - 2.4111864647193094955e-797j)  +/-  (4.6e-245, 4.6e-245j)
| (-9.5373016113985254056 - 5.0641936307567752057e-799j)  +/-  (1.09e-247, 1.09e-247j)
| (-4.6929196191131403725 - 3.185289790104706054e-792j)  +/-  (6.86e-242, 6.86e-242j)
| (-1.2224662777326842461 + 2.5824844153587487373e-812j)  +/-  (1.14e-249, 1.14e-249j)
| (4.2506849648097262168 + 4.2823432855714155677e-805j)  +/-  (2.51e-243, 2.51e-243j)
| (-7.1367100154060233997 + 1.0566039249585398075e-806j)  +/-  (2.33e-244, 2.33e-244j)
| (5.7648721335022539447 - 5.8829202068510638018e-806j)  +/-  (3.16e-243, 3.16e-243j)
| (4.6929196191131403725 + 5.2575106341576850545e-804j)  +/-  (7.37e-242, 7.37e-242j)
| (1.7401216243880737282 + 8.6543754256861665958e-811j)  +/-  (5.07e-248, 5.07e-248j)
| (-1.7401216243880737282 + 1.7282341459511386841e-809j)  +/-  (5.03e-248, 5.03e-248j)
| (-3.5413763571493274326 - 7.445107279186150223e-806j)  +/-  (2.25e-244, 2.25e-244j)
| (6.1949082287014924018 - 1.0598826177051330198e-806j)  +/-  (1.66e-243, 1.66e-243j)
| (0.95857246461381850711 - 6.7983401181768430311e-813j)  +/-  (1.16e-250, 1.16e-250j)
| (-4.2506849648097262168 + 3.4949850544705796546e-804j)  +/-  (2.34e-243, 2.34e-243j)
| (-3.8879058412990795166 + 1.1292493040429650497e-811j)  +/-  (6.33e-244, 6.33e-244j)
| (-2.8938768036069171042 + 1.6028785122559722094e-815j)  +/-  (2.21e-245, 2.21e-245j)
| (-6.1949082287014924018 + 2.9953198791139339769e-812j)  +/-  (1.69e-243, 1.69e-243j)
| (2.8938768036069171042 - 1.8489314751171231179e-825j)  +/-  (2.3e-245, 2.3e-245j)
| (3.2095060327776332981 + 5.6415006744089276824e-825j)  +/-  (7.47e-245, 7.47e-245j)
| (5.3500686641720315041 - 3.0142339959091464517e-822j)  +/-  (5.99e-243, 5.99e-243j)
| (-2.0201828704560856329 - 2.2159633870424088712e-826j)  +/-  (3.35e-247, 3.35e-247j)
| (-5.3500686641720315041 + 3.6375526966456322459e-821j)  +/-  (6.04e-243, 6.04e-243j)
| (3.5413763571493274326 - 2.573027922079071672e-844j)  +/-  (2.19e-244, 2.19e-244j)
| (-4.9065719267593294531 - 9.9935918331574579238e-846j)  +/-  (3.05e-242, 3.05e-242j)
| (-3.2095060327776332981 - 5.1656079051187842101e-866j)  +/-  (7.77e-245, 7.77e-245j)
| (-0.69245329978726446238 + 2.2979482164028225165e-887j)  +/-  (1.07e-251, 1.07e-251j)
| (2.594640160845429473 + 1.2323030474838835379e-879j)  +/-  (5.89e-246, 5.89e-246j)
| (-4.7503167383358089531 + 8.2115192501720123922e-878j)  +/-  (1e-241, 1e-241j)
| (2.0201828704560856329 + 8.7904505322889088764e-895j)  +/-  (2.99e-247, 2.99e-247j)
| (0.69245329978726446238 + 1.1105840435448887418e-899j)  +/-  (1.2e-251, 1.2e-251j)
| (-8.3164917928578351245 - 9.1501635939306665734e-895j)  +/-  (5.1e-246, 5.1e-246j)
| (-1.4759224472426343846 + 4.4700258580168518851e-898j)  +/-  (9.03e-249, 9.03e-249j)
| (4.9065719267593294531 - 4.9082621621723734273e-892j)  +/-  (3.02e-242, 3.02e-242j)
| (2.3058709799993757952 - 1.1029553058374849323e-898j)  +/-  (1.38e-246, 1.38e-246j)
| (1.4759224472426343846 + 4.5838665680009043828e-901j)  +/-  (8.52e-249, 8.52e-249j)
| (-2.594640160845429473 + 2.2905054308090912349e-898j)  +/-  (5.81e-246, 5.81e-246j)
| (-0.46844531406652970763 - 1.2257111155325455302e-907j)  +/-  (1.19e-252, 1.19e-252j)
| (-0.95857246461381850711 - 1.6784094579814190281e-904j)  +/-  (1.21e-250, 1.21e-250j)
| (-2.3058709799993757952 - 5.9077749003949493035e-900j)  +/-  (1.34e-246, 1.34e-246j)
| (0.25995837394388799914 - 1.4611732873737203105e-906j)  +/-  (1.17e-253, 1.17e-253j)
| (3.8879058412990795166 + 3.7284404471662355207e-902j)  +/-  (6.8e-244, 6.8e-244j)
| (-8.1811956468270767676e-937 - 2.3698109612093467021e-936j)  +/-  (1.33e-934, 1.33e-934j)
| (-0.25995837394388799914 - 5.4299647239177604108e-913j)  +/-  (1.12e-253, 1.12e-253j)
| (0.46844531406652970763 - 1.6119033752186258803e-911j)  +/-  (1.24e-252, 1.24e-252j)
-------------------------------------------------
The weights are:
| (1.5440111084716206997e-39 - 1.6852596819687659426e-800j)  +/-  (8.46e-83, 6.6e-204j)
| (2.1838622048811742759e-23 + 9.0450450636230052147e-792j)  +/-  (1.19e-76, 9.28e-198j)
| (3.7546383737659892368e-31 + 3.5230543482176514261e-796j)  +/-  (4.48e-80, 3.5e-201j)
| (1.6748016754317815248e-20 - 6.4928052097601458828e-788j)  +/-  (4.48e-78, 3.5e-199j)
| (1.6748016754317815248e-20 - 4.7283203251107726662e-790j)  +/-  (1.6e-75, 1.25e-196j)
| (-1.1444195078768980587e-10 + 1.4577409747598575758e-781j)  +/-  (8.59e-70, 6.7e-191j)
| (8.7551948258744416149e-16 - 9.6527517617067261573e-786j)  +/-  (1.26e-75, 9.84e-197j)
| (8.2352151912197738969e-27 + 1.5522633031372396653e-792j)  +/-  (5.66e-82, 4.42e-203j)
| (0.032461097542052436777 + 8.3920774843847130386e-777j)  +/-  (3.01e-47, 2.35e-168j)
| (8.2352151912197738969e-27 - 9.4727328807480676619e-794j)  +/-  (2.58e-79, 2.01e-200j)
| (1.5440111084716206997e-39 + 1.0482994101866014479e-799j)  +/-  (1.47e-87, 1.14e-208j)
| (2.0241316990158214336e-10 - 1.2945368235229939666e-781j)  +/-  (3.37e-73, 2.63e-194j)
| (0.032461097542052436777 + 1.1707050202334529884e-776j)  +/-  (4.62e-50, 3.61e-171j)
| (3.0018569961484434466e-09 + 3.6038308124806585283e-782j)  +/-  (1.62e-70, 1.26e-191j)
| (2.1838622048811742759e-23 - 3.0964458718511817571e-790j)  +/-  (1.87e-80, 1.46e-201j)
| (8.7551948258744416149e-16 - 4.2612392490301731342e-787j)  +/-  (1.02e-75, 7.99e-197j)
| (2.0241316990158214336e-10 - 1.5781898939687020631e-781j)  +/-  (2.19e-71, 1.71e-192j)
| (0.00747346416696310876 + 1.6386239066267221523e-777j)  +/-  (6.18e-59, 4.82e-180j)
| (0.00747346416696310876 + 2.6383602934560595018e-777j)  +/-  (6.44e-60, 5.02e-181j)
| (6.8459409303688327738e-07 + 1.8231471756542142735e-780j)  +/-  (2.81e-71, 2.2e-192j)
| (5.352544459061152108e-18 + 1.653424197891863833e-788j)  +/-  (2.84e-77, 2.21e-198j)
| (0.060749995158456637497 - 1.5905522285552515691e-776j)  +/-  (3.79e-57, 2.96e-178j)
| (3.0018569961484434466e-09 + 9.8586611845506589316e-782j)  +/-  (4.67e-74, 3.65e-195j)
| (5.4390458483482717595e-08 - 4.0731742407439368876e-781j)  +/-  (7.53e-73, 5.87e-194j)
| (3.9960104294883245134e-05 + 3.2417735404116282991e-779j)  +/-  (5.73e-70, 4.47e-191j)
| (5.352544459061152108e-18 + 6.4601589516246349485e-787j)  +/-  (2.21e-80, 1.73e-201j)
| (3.9960104294883245134e-05 + 1.4564135216115274129e-779j)  +/-  (1.82e-71, 1.42e-192j)
| (6.1436542154789987687e-06 - 3.2980826685339371956e-780j)  +/-  (1.18e-72, 9.2e-194j)
| (8.6083015792596419291e-14 + 7.5565435836075927552e-786j)  +/-  (5.67e-78, 4.42e-199j)
| (0.0027094503498386385668 - 1.00005916548020982e-777j)  +/-  (2.03e-68, 1.58e-189j)
| (8.6083015792596419291e-14 + 1.839356773011735803e-784j)  +/-  (1.67e-79, 1.3e-200j)
| (6.8459409303688327738e-07 + 6.9296153450693920585e-781j)  +/-  (5.03e-75, 3.92e-196j)
| (1.3196266713027581056e-11 - 1.4765651877208534235e-782j)  +/-  (3.55e-78, 2.77e-199j)
| (6.1436542154789987687e-06 - 7.9963813730997080934e-780j)  +/-  (1.06e-74, 8.31e-196j)
| (0.088695626110698927293 + 3.8948447414184214524e-776j)  +/-  (2.36e-68, 1.84e-189j)
| (0.00019669023039080363819 - 5.6309164301903920527e-779j)  +/-  (3.87e-74, 3.02e-195j)
| (-1.1444195078768980587e-10 + 1.217338808356491639e-781j)  +/-  (2.75e-77, 2.15e-198j)
| (0.0027094503498386385668 - 5.7429072105628346728e-778j)  +/-  (4.5e-73, 3.51e-194j)
| (0.088695626110698927293 + 3.2277259209734123216e-776j)  +/-  (3.7e-70, 2.89e-191j)
| (3.7546383737659892368e-31 - 3.6201879378644059842e-795j)  +/-  (2.09e-91, 1.63e-212j)
| (0.016310724138184862519 - 6.115779088619528941e-777j)  +/-  (7.16e-72, 5.59e-193j)
| (1.3196266713027581056e-11 + 2.8520756144940784979e-783j)  +/-  (1.89e-79, 1.47e-200j)
| (0.00079337230202003917395 + 1.8862111270576607842e-778j)  +/-  (4.46e-74, 3.48e-195j)
| (0.016310724138184862519 - 4.0877700150172594944e-777j)  +/-  (1.94e-72, 1.52e-193j)
| (0.00019669023039080363819 - 1.1527707394919532705e-778j)  +/-  (8.2e-76, 6.4e-197j)
| (0.088888303936965807354 - 6.150503099467752847e-776j)  +/-  (4.86e-73, 3.8e-194j)
| (0.060749995158456637497 - 2.0638688674242814367e-776j)  +/-  (3.88e-73, 3.02e-194j)
| (0.00079337230202003917395 + 3.5596231159144498465e-778j)  +/-  (1.7e-75, 1.33e-196j)
| (0.12527950938315767265 + 6.0198514855867381048e-776j)  +/-  (6.54e-74, 5.07e-195j)
| (5.4390458483482717595e-08 - 1.4564503352305248739e-781j)  +/-  (7.08e-80, 5.51e-201j)
| (0.15278984167019547457 - 5.6803678712568488227e-776j)  +/-  (4.17e-74, 3.26e-195j)
| (0.12527950938315767265 + 6.4590678553250799413e-776j)  +/-  (4.59e-74, 3.66e-195j)
| (0.088888303936965807354 - 5.4170943130161653104e-776j)  +/-  (3.27e-74, 2.43e-195j)
