Starting with polynomial:
P : 63/8*t^5 - 35/4*t^3 + 15/8*t
Extension levels are: 5 6 34
-------------------------------------------------
Trying to find an order 6 Kronrod extension for:
P1 : 63/8*t^5 - 35/4*t^3 + 15/8*t
Solvable: 1
-------------------------------------------------
Trying to find an order 34 Kronrod extension for:
P2 : 63/8*t^11 - 2233/104*t^9 + 71973/3380*t^7 - 6901587/746980*t^5 + 488523/298792*t^3 - 24129/298792*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 63/8*t^45 - 24291809171238710617666194820015160534234162785830695572148639771552593842650387229961876256494081536478850158425985/270344771370402966270015436902531855915486405513066522470786674197211775430987784866355963553204733161907875892536*t^43 + 18296670883567077606022779451341304563525299155223106003255019082108842459879961859860367594383245204564889786698927469/38219992052490719356423432392095441130051890579409779614307466064630814751555898085481074347334319150764725954307277*t^41 - 259830311192500977173833262030431551772597944669707702998823075643464920057893189526375002116441342448051790625623453340869/164272161703125973222829045071736005662558201702756985180887579315856664616997702102300104515487547456135120753402628772*t^39 + 539548369165586631853739459798819905522752225058799634225659046183725967999247306758485064133214533550367608796270722949402839/148617165096375079193473969408916719652835774788348947704247438210114768800933391175456974897131255540443611382458703038600*t^37 - 4085115835816238756237352908909408995241040548621519782881757566487499664945455515520427233579602698032252216960763019006917642563/664764579476085729232409065166084487007134420628284843081098791113843360846575058727819048714868106032404273713737778691657800*t^35 + 306349802400022054792325674150411046332187941759457564366937204680991097600511891097424579229266792112857444462950148973664548401/38545173095672197745408592854167924036548130271724079136635139988953942771776200884218079295231848164904113349788156915734780*t^33 - 1728072358678631179074539603385440861722500492246894441172397453653372499909953325830321151356807839787698316261657335298719588697/215210549784169770745197976769104242537393727350459441846212864938326180475750454936884276065044485587381299536317209446185855*t^31 + 2479274086046187675875737923374420062060749886534365780487302973731294416757745661937805367720190827373359812242918214220641444769/385894778923338899267251544551497262480843924904272102620795481958377978784104264024758012254562525880821640547879134179367740*t^29 - 3098078379056544205950239324149393867152078824563608323313666459354514946588332132484005820371722730881251622139347695788867592603/755011523980445672479405195861625078766868548725749765997208551657696045447160516570178719628491898462477122811067871220502100*t^27 + 1583573162609953176485401854159755318715288205378248217866094324734865646002754565027944157615123630721067323118538742758880772819/754473766484733104336613596719273493952932032665403790380401423059649253391998721330456370113086989702888463891686768748122825*t^25 - 3060317639324308572547706430501858764799567850875355079070835801352993444529948884718294185919003769828538403718011311291397645389/3561116177807940252468816176514970891457839194180705890595494716841544476010233964679754066933770591397633549568761548491139734*t^23 + 1823793805089286772458424844583464090306661204288716915534264404942420105192893665517350861302570453508758393897484340520093694371/6502907802953630026247403452766468584401271571982158582826555569884559477931731587676072643966015862552200394864695001592516036*t^21 - 22411630525610022891662276480816727420661004821374276219908661654937255601697949905180273464245570950450143938464180718106829091/309662276331125239345114450131736599257203408189626599182216931899264737044368170841717744950762660121533352136414047694881716*t^19 + 11293781177884300976115362453845367493948602623416839426642441586254302621954974720749323605366615203370411590198135381230517621/774155690827813098362786125329341498143008520474066497955542329748161842610920427104294362376906650303833380341035119237204290*t^17 - 36918364386804249209034057517281878052061402341627795537907800513354439820231351454588190691154927923520567105526661444147491/16355401918897459824565904056253693622739616629733799252581880205947081181920854093752697796695210921911972824106375758532485*t^15 + 2107038580649566002716244470515305628194756182630381932842643130434899743523309841393109241107172360141314639463403103859456923/8051219184609256222972975703425151580687288612930291578737640229380883163153572441884661368719829163159867155546765240066924616*t^13 - 237434695288732146589992802653071547608679149030262642555899528222612183190447518491381014365144374895455713965607829956943589843/10799162224771661596921521333894182162495711657205038019880633283054958439685295589934064637412897009078354122405303499311304963784*t^11 + 2215393544972406257205610239637826377419471839760531063782924024739969109181245572604528772665743801929560234314175256959362506/1735579643266874185219530214375850704686810802050809681766530349062404034949422505525117531012787019316164055386566633817888297751*t^9 - 9023298882593099303745992802655192186200826703598073014122382693113262162241855173009734402528696894641448220120407042836631807/188985338933504077946126623343148187843674954001088165347911082453461772694492672823846131154725697658871197142092811237947836866220*t^7 + 945195226468862653225549956508047140123182520431830278661502706556396456531899650644291720098441597345849658284716734677304311/917928789105591235738329313381005483812135490862428231689853829059671467373250125144395494180096245771660100404450797441460921921640*t^5 - 75127444783759921124496344856586008856289681442543532617106893871046137518732202648250717816590130346603384674733932061249673/7159844555023611638758968644371842773734656828726940207180859866665437445511350976126284854604750717018948783154716220043395190988792*t^3 + 38124188662713418875289843629681358018198989840867025211725001730187271435499993521530134373976375834719205862577030696939/1193307425837268606459828107395307128955776138121156701196809977777572907585225162687714142434125119503158130525786036673899198498132*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:
| (0.27963041316178319341 + 1.4262031467859592668e-864j)  +/-  (1.77e-250, 1.77e-250j)
| (0.9934090168285012076 + 3.5923536110032188508e-857j)  +/-  (2.65e-239, 2.65e-239j)
| (-0.9061798459386639928 + 3.2891480215024136672e-882j)  +/-  (5.49e-240, 5.49e-240j)
| (0.99873523456944300581 - 2.5761309276257276015e-879j)  +/-  (8.08e-240, 8.08e-240j)
| (0.95392965771413734692 + 1.3744422434034531382e-897j)  +/-  (2.2e-239, 2.2e-239j)
| (0.9324486125917015422 - 3.0979326922599928951e-912j)  +/-  (1.33e-239, 1.33e-239j)
| (-0.9934090168285012076 - 6.8332604080468308999e-916j)  +/-  (2.58e-239, 2.58e-239j)
| (-0.87506136954646878575 + 2.8413873845996109553e-920j)  +/-  (1.89e-240, 1.89e-240j)
| (-0.9840853600948424645 + 8.7432924836313243816e-918j)  +/-  (3.71e-239, 3.71e-239j)
| (-0.99873523456944300581 - 2.814329671552140398e-919j)  +/-  (9.4e-240, 9.4e-240j)
| (0.87506136954646878575 - 3.3034284534957849375e-918j)  +/-  (1.8e-240, 1.8e-240j)
| (-0.21082683075469763596 + 8.6093822867181242236e-938j)  +/-  (1.07e-251, 1.07e-251j)
| (-0.9324486125917015422 + 1.6241234650697431612e-924j)  +/-  (1.16e-239, 1.16e-239j)
| (-0.83921207487737441643 + 2.2180609977612196731e-927j)  +/-  (5.4e-241, 5.4e-241j)
| (0.9840853600948424645 - 7.9422544701244358606e-925j)  +/-  (3.67e-239, 3.67e-239j)
| (0.9061798459386639928 - 6.0784026587790328459e-940j)  +/-  (5.23e-240, 5.23e-240j)
| (0.79883268131626945437 - 3.2946431406817409792e-947j)  +/-  (1.2e-241, 1.2e-241j)
| (-0.97097943968239305255 - 3.3692997248192020779e-944j)  +/-  (3.58e-239, 3.58e-239j)
| (-0.70548804714027908278 + 2.5483328662716460995e-951j)  +/-  (4.24e-243, 4.24e-243j)
| (-0.95392965771413734692 - 1.3968668931852065522e-946j)  +/-  (2.51e-239, 2.51e-239j)
| (0.83921207487737441643 + 2.5173451355156454246e-948j)  +/-  (5.42e-241, 5.42e-241j)
| (0.70548804714027908278 + 1.3122531243165254276e-954j)  +/-  (4.33e-243, 4.33e-243j)
| (0.21082683075469763596 - 5.9706910100690583979e-964j)  +/-  (8.96e-252, 8.96e-252j)
| (-0.79883268131626945437 + 3.142238313917138591e-954j)  +/-  (1.28e-241, 1.28e-241j)
| (-0.75416672657084922044 - 2.1253118472751650147e-955j)  +/-  (2.4e-242, 2.4e-242j)
| (0.14107220146080813369 + 2.8018043521789045145e-965j)  +/-  (5.51e-253, 5.51e-253j)
| (0.75416672657084922044 - 8.5053585296601858097e-955j)  +/-  (2.47e-242, 2.47e-242j)
| (0.97097943968239305255 - 9.8947350204565815126e-965j)  +/-  (3.63e-239, 3.63e-239j)
| (-0.47692330950443648685 - 8.9902021584273248559e-990j)  +/-  (7.52e-247, 7.52e-247j)
| (-0.65309570580320731722 - 1.1397969156530544022e-988j)  +/-  (6.51e-244, 6.51e-244j)
| (-0.27963041316178319341 - 9.6943403064839944924e-995j)  +/-  (1.79e-250, 1.79e-250j)
| (0.47692330950443648685 + 3.1353514341141884795e-990j)  +/-  (6.6e-247, 6.6e-247j)
| (0.65309570580320731722 - 7.119867821628851569e-990j)  +/-  (6.14e-244, 6.14e-244j)
| (0.070691365143326506046 + 6.5299665121896013452e-997j)  +/-  (2.35e-254, 2.35e-254j)
| (-0.59731019807931748754 + 4.1324530069264034652e-992j)  +/-  (7.35e-245, 7.35e-245j)
| (-0.41302956639847532004 + 2.8594614247983419279e-996j)  +/-  (4.8e-248, 4.8e-248j)
| (-2.3295675398940533206e-998 - 1.5143947222838808224e-997j)  +/-  (6.89e-996, 6.89e-996j)
| (0.59731019807931748754 - 2.0420901751140757779e-991j)  +/-  (8.25e-245, 8.25e-245j)
| (0.41302956639847532004 + 7.0816861490245418982e-995j)  +/-  (4.7e-248, 4.7e-248j)
| (-0.34714693243573225245 + 2.8911982131889490047e-997j)  +/-  (3.02e-249, 3.02e-249j)
| (-0.53846931010568309104 - 6.8315260175179298465e-995j)  +/-  (7.97e-246, 7.97e-246j)
| (-0.14107220146080813369 + 1.4665288033973976239e-1000j)  +/-  (4.67e-253, 4.67e-253j)
| (0.34714693243573225245 - 1.6122624093581503844e-996j)  +/-  (3.33e-249, 3.33e-249j)
| (0.53846931010568309104 - 8.6952891622896062224e-995j)  +/-  (7.89e-246, 7.89e-246j)
| (-0.070691365143326506046 + 2.5828059397646244797e-1004j)  +/-  (2.53e-254, 2.53e-254j)
-------------------------------------------------
The weights are:
| (0.068217006621484546451 + 1.0734118158284420171e-858j)  +/-  (8.17e-74, 1.18e-188j)
| (0.0073741865251355972441 - 2.0573936344116378634e-857j)  +/-  (4.01e-74, 5.8e-189j)
| (0.028702944778344868856 + 4.7872225939064088254e-859j)  +/-  (1.4e-75, 2.03e-190j)
| (0.0032372332517993424487 - 1.4205084340738313791e-857j)  +/-  (2.97e-74, 4.3e-189j)
| (0.01918133222811505049 + 2.2248648002907248682e-857j)  +/-  (7.19e-75, 1.04e-189j)
| (0.023842189218222908621 - 1.5180893971905377393e-857j)  +/-  (2.58e-75, 3.73e-190j)
| (0.0073741865251355972441 - 1.3333219194256889285e-859j)  +/-  (1.9e-76, 2.76e-191j)
| (0.033512568024971637492 - 4.6528260029482403506e-859j)  +/-  (3e-76, 4.34e-191j)
| (0.011229298755450869691 + 2.5573405599958515871e-859j)  +/-  (1.13e-76, 1.63e-191j)
| (0.0032372332517993424487 + 3.7978854831186050573e-860j)  +/-  (8.48e-77, 1.23e-191j)
| (0.033512568024971637492 - 7.3458744680573347922e-858j)  +/-  (3.69e-78, 5.35e-193j)
| (0.069334148942641515964 - 6.4579448427579677591e-859j)  +/-  (1.03e-79, 1.49e-194j)
| (0.023842189218222908621 - 4.8053045114867522517e-859j)  +/-  (2.28e-77, 3.3e-192j)
| (0.038152018316431882339 + 4.5123061719845405695e-859j)  +/-  (1.47e-78, 2.13e-193j)
| (0.011229298755450869691 + 5.4239744502733105444e-857j)  +/-  (2.33e-77, 3.38e-192j)
| (0.028702944778344868856 + 1.0425132602776573654e-857j)  +/-  (6.74e-78, 9.76e-193j)
| (0.042566010217433294068 - 4.0626648578031950868e-858j)  +/-  (7.71e-80, 1.12e-194j)
| (0.015010001853183767955 - 3.7313662281707656704e-859j)  +/-  (6.93e-78, 1e-192j)
| (0.050587267937995836128 - 4.373075054735129706e-859j)  +/-  (1.73e-81, 2.51e-196j)
| (0.01918133222811505049 + 4.5105774008019696389e-859j)  +/-  (3.04e-78, 4.41e-193j)
| (0.038152018316431882339 + 5.3628492029049013573e-858j)  +/-  (4.91e-80, 7.11e-195j)
| (0.050587267937995836128 - 2.5803631614059560956e-858j)  +/-  (3.72e-82, 5.39e-197j)
| (0.069334148942641515964 - 9.937460898241337021e-859j)  +/-  (1.99e-83, 2.88e-198j)
| (0.042566010217433294068 - 4.4106675836757144915e-859j)  +/-  (7.54e-81, 1.09e-195j)
| (0.046720186759934449317 + 4.3629794453116211349e-859j)  +/-  (1.52e-81, 2.2e-196j)
| (0.070121004190021381076 + 9.2346709399814402163e-859j)  +/-  (1.45e-84, 2.11e-199j)
| (0.046720186759934449317 + 3.1869947257955000095e-858j)  +/-  (1.48e-82, 2.15e-197j)
| (0.015010001853183767955 - 3.2679413392749106772e-857j)  +/-  (1.01e-80, 1.46e-195j)
| (0.062779744011821579905 - 4.9867683923817197082e-859j)  +/-  (1.42e-85, 2.06e-200j)
| (0.054143930282476030032 + 4.4411839542070758925e-859j)  +/-  (4.9e-84, 7.1e-199j)
| (0.068217006621484546451 + 6.0184952173394253845e-859j)  +/-  (3.08e-86, 4.46e-201j)
| (0.062779744011821579905 - 1.4196348348381045292e-858j)  +/-  (2.04e-86, 2.95e-201j)
| (0.054143930282476030032 + 2.1487354749386554411e-858j)  +/-  (3.28e-85, 4.75e-200j)
| (0.070588124415944907596 - 8.5971269668837954737e-859j)  +/-  (1.49e-86, 2.16e-201j)
| (0.057370707049116947669 - 4.5666718085637248725e-859j)  +/-  (1.17e-85, 1.69e-200j)
| (0.064947843084942799064 + 5.2792687524719236428e-859j)  +/-  (1.06e-86, 1.54e-201j)
| (0.070742939712152473948 + 8.0069564369069879569e-859j)  +/-  (1.74e-87, 2.52e-202j)
| (0.057370707049116947669 - 1.8339603840254268236e-858j)  +/-  (2.13e-87, 3.09e-202j)
| (0.064947843084942799064 + 1.2793308370324631031e-858j)  +/-  (6.36e-88, 9.21e-203j)
| (0.066758183146113024707 - 5.6242265510946334314e-859j)  +/-  (9.53e-88, 1.38e-202j)
| (0.060252600532341525912 + 4.7488122315734932592e-859j)  +/-  (1.96e-87, 2.84e-202j)
| (0.070121004190021381076 + 6.9380200801255184318e-859j)  +/-  (9.29e-89, 1.34e-203j)
| (0.066758183146113024707 - 1.1666476739029155392e-858j)  +/-  (6.47e-89, 9.5e-204j)
| (0.060252600532341525912 + 1.5990263725118378236e-858j)  +/-  (5.93e-89, 8.76e-204j)
| (0.070588124415944907596 - 7.4548626514188281266e-859j)  +/-  (5.89e-89, 8.46e-204j)
