Starting with polynomial:
P : 35/8*t^4 - 15/4*t^2 + 3/8
Extension levels are: 4 10 31
-------------------------------------------------
Trying to find an order 10 Kronrod extension for:
P1 : 35/8*t^4 - 15/4*t^2 + 3/8
Solvable: 1
-------------------------------------------------
Trying to find an order 31 Kronrod extension for:
P2 : 35/8*t^14 - 436215/27784*t^12 + 12954799/583464*t^10 - 3039465/194488*t^8 + 2679105/472328*t^6 - 8846695/8974232*t^4 + 1485/22952*t^2 - 273/390184
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 35/8*t^45 - 186351634472447025351916417876504129169878255040499886260043989704660653575856503536325977181587885059405/3620193068153829975520193990552136469942822189325233180144569676434276373904370618200702083638611341412*t^43 + 136444996270588478906122151310074808712048575910864272177248229071426057215946882459469670848022718903867159/482587475954767074128039772827515235514986644890050649144489157736847450538730448495797938627651407511704*t^41 - 379367797001425424348909849059424290769309719889611130740462169032266871888329599030620683008269295492573849971/394032674117067316025544474513666189797986595552726355026475397292135943364873411196819016889477374233306316*t^39 + 10989712606718589921473224877340430690096523962197458904047724382980349166052006214576300144318417054467478444662759/4827425634832897377734287205425095713278399777648301484214358917358388154144185785042628715585283804190313446088*t^37 - 39181892611941279860390800324576244880834611708493483592092963236096823488217736803338809597324403468239501636698752281/9876395624692947367268165805813450283398326116520819661543555377888402336076774382005963784725106525822932348541110*t^35 + 17398276396639214718151272821226162864593499771665150472075014370842023986422206066174976917635607183758100840212347/3296252190135318270260547619795894963170071294625221413948620902090413795937179601837618284430573725764850178904*t^33 - 106118215066602606530773267757852512874325210735913942833409946139438222360249506694971304270875130232929652423848073/19365481617044994837780717266300882908624168855923175806948147799781181051130930160796007421029620638868494801061*t^31 + 191339250078332958074544401372121894402983708596335631462816500817747131158337562337733268452104429759474151223543434299/42526597631030808663766455116796738867338674807607294072058132568319473588283522633108032296581046922955214583129956*t^29 - 957396776896688158271766366268933310696234965251880513934349416334809690787672216353107719454445431653756252434660432529/325249718918809703298806406726612095411312457324848378736296458346591529480761015693955876638666155170009326348753182*t^27 + 95092640288607999035065264275394738108580956632197152765527746114387691993613898361187165025793564653452567685416719994141/61797446594573843626773217278056298128149366891721191959896327085852390601344592981851616561346569482301772006263104580*t^25 - 11901539939261473533143909553454530301567885982901277200653642689810673615489336638025362773300122722101918361797346655185/18539233978372153088031965183416889438444810067516357587968898125755717180403377894555484968403970844690531601878931374*t^23 + 16324240524198499917464416969149727419858209037879881172912823606538822563101150212787644386115053462224134016841428415/76767014403197321275494679848517140531862567567355517962604133025903590809123717989877784548256608052548785100947956*t^21 - 18079171374082280760510598814391886583685965005244596687652651422955979418889360343937569381272558217653359198176216640/326259811213588615420852389356197847260415912161260951341067565360090260938775801456980584330090584223332336679028813*t^19 + 122347148254896757123948650655219646006332126701421126546914342737205873539138179699914740113237975339140044279205927605/10921117891149597863561164191081148992506553691292735002785209029948284524055863669823139559680926924528387690940122372*t^17 - 30340026290847008846893778275240369164890499449164132406899436643070287594962846764508263911833675139790393358827343867/17612979344059890672115799112086754992816941982526028509393792994377380433403819349861828015367769402793331129016177747*t^15 + 3275841376650134032949004355785971937816405027299568410823993969045248138177916660798265019256852554366929007877000585/16717404123175489451499741530116242027080487305448433839424617079409039055434133620207836760349069263668246495337389048*t^13 - 70393977123001540154244011798180155591037278647121009849660075691072980532850372229863437423993671356373719255660042145/4438470794703092449373181376245862258189869379596559184367235834583099869217762476165180659872677889503919444512076792244*t^11 + 851339520845161997240450063877202782743238482726752030676402789921032047750105959854958451912469539594453845222806045/986326843267353877638484750276858279597748751021457596526052407685133304270613883592262368860595086556426543224905953832*t^9 - 2041079163630228208244533771524759670816154699497625561415564671933941777097119999443431773761682584047541110381915/70451917376239562688463196448347019971267767930104114037575171977509521733615277399447312061471077611173324516064710988*t^7 + 219345760923144445679815429341496325512142908209795550951974081424678086530456908351679494533237774022918588639507/422711504257437376130779178690082119827606607580624684225451031865057130401691664396683872368826465667039947096388265928*t^5 - 96886402052695157856681918082731097632255985985193879894154275508915664720638658013449699908283627574893624685/26036578160784186210953789991780420424164175104603694318234302687340475423292602517187050109674093899781446016806523626*t^3 + 66558796376138769398053018856028103433276726867201902262609878220923709936866678295032036462553033747153615/14878044663305249263402165709588811670950957202630682467562458678480271670452915724106885776956625085589397723889442072*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:
| (0.26656865496010310601 - 2.2368394159604991435e-921j)  +/-  (5.56e-251, 5.56e-251j)
| (0.99850165393616251647 + 1.0809994352923734396e-905j)  +/-  (1.97e-237, 1.97e-237j)
| (-0.92773572234309641574 - 2.4509393214836332396e-915j)  +/-  (1.4e-239, 1.4e-239j)
| (0.99981191608233013828 + 1.3914013313114275033e-910j)  +/-  (1.21e-237, 1.21e-237j)
| (0.95280406968027788258 + 5.3654020371120942394e-922j)  +/-  (4.93e-239, 4.93e-239j)
| (0.97222404322963102332 + 3.8204907071017295827e-921j)  +/-  (1.57e-238, 1.57e-238j)
| (-0.99850165393616251647 - 4.3050005754147671689e-923j)  +/-  (2.08e-237, 2.08e-237j)
| (-0.89712440708660493986 + 1.3358535299416000035e-950j)  +/-  (3.41e-240, 3.41e-240j)
| (-0.99444997880691468328 - 1.1977332401147386862e-960j)  +/-  (1.14e-237, 1.14e-237j)
| (-0.99981191608233013828 + 2.4023314659680015411e-992j)  +/-  (1.27e-237, 1.27e-237j)
| (0.86113631159405257522 - 4.685492396696714738e-1013j)  +/-  (7.78e-241, 7.78e-241j)
| (-0.19155680515427105618 + 6.50816816490220479e-1025j)  +/-  (2.37e-252, 2.37e-252j)
| (-0.95280406968027788258 - 5.2746524804170254381e-1009j)  +/-  (4.91e-239, 4.91e-239j)
| (-0.86113631159405257522 + 3.9594146745919305176e-1016j)  +/-  (7.52e-241, 7.52e-241j)
| (0.99444997880691468328 + 9.7798900134578988126e-1012j)  +/-  (1.13e-237, 1.13e-237j)
| (0.72317255923281838433 - 4.2382717234648963196e-1021j)  +/-  (3.8e-243, 3.8e-243j)
| (0.92773572234309641574 - 1.0914030731505570785e-1017j)  +/-  (1.32e-239, 1.32e-239j)
| (-0.98600625619481567695 - 2.1965385900711962404e-1016j)  +/-  (4.57e-238, 4.57e-238j)
| (-0.72317255923281838433 - 2.3816769748854413007e-1032j)  +/-  (3.41e-243, 3.41e-243j)
| (-0.97222404322963102332 - 7.073409230397116461e-1029j)  +/-  (1.45e-238, 1.45e-238j)
| (0.89712440708660493986 + 8.8328709867383734894e-1028j)  +/-  (3.27e-240, 3.27e-240j)
| (0.81998025049963826018 - 6.436296946702630509e-1030j)  +/-  (1.47e-241, 1.47e-241j)
| (0.11539569344883949077 + 2.6342435986676192764e-1043j)  +/-  (1.15e-253, 1.15e-253j)
| (-0.81998025049963826018 - 1.1939071880919663065e-1032j)  +/-  (1.49e-241, 1.49e-241j)
| (-0.77390041851546803851 - 5.6145487864248125851e-1033j)  +/-  (2.63e-242, 2.63e-242j)
| (0.19155680515427105618 - 1.0766884324692793206e-1042j)  +/-  (2.48e-252, 2.48e-252j)
| (0.77390041851546803851 + 1.9337656927602644495e-1030j)  +/-  (2.7e-242, 2.7e-242j)
| (0.98600625619481567695 + 9.3556523940535729507e-1035j)  +/-  (4.56e-238, 4.56e-238j)
| (-0.41135322485812128646 + 8.6022233494781910976e-1046j)  +/-  (1.8e-248, 1.8e-248j)
| (-0.66810126169681993167 - 5.5845796520388304764e-1042j)  +/-  (4.47e-244, 4.47e-244j)
| (-0.3399810435848562648 - 1.2507473391315955093e-1049j)  +/-  (1.04e-249, 1.04e-249j)
| (0.54627694908708365616 + 6.4286059855773347276e-1043j)  +/-  (3.97e-246, 3.97e-246j)
| (0.60901761612930277641 - 4.3332963969570431048e-1040j)  +/-  (4.29e-245, 4.29e-245j)
| (0.038542302523980961805 - 5.3552044088075789622e-1053j)  +/-  (5.96e-255, 5.96e-255j)
| (-0.60901761612930277641 + 1.3853593333139015705e-1043j)  +/-  (4.42e-245, 4.42e-245j)
| (-0.48025653205070437685 + 7.21105437004808778e-1046j)  +/-  (2.88e-247, 2.88e-247j)
| (-1.2638331165903340566e-1078 - 1.9459859319067913254e-1078j)  +/-  (1.04e-1076, 1.04e-1076j)
| (0.66810126169681993167 + 8.5747145656151885493e-1046j)  +/-  (4.36e-244, 4.36e-244j)
| (0.41135322485812128646 + 2.3312337576900732748e-1050j)  +/-  (1.79e-248, 1.79e-248j)
| (-0.26656865496010310601 + 3.9831071027515523404e-1053j)  +/-  (5.33e-251, 5.33e-251j)
| (-0.54627694908708365616 - 2.0630108971843155861e-1047j)  +/-  (3.73e-246, 3.73e-246j)
| (-0.038542302523980961805 + 7.1030910414780857917e-1056j)  +/-  (5.96e-255, 5.96e-255j)
| (0.3399810435848562648 + 1.8899256117606121959e-1052j)  +/-  (9.72e-250, 9.72e-250j)
| (0.48025653205070437685 - 6.9925592714601293628e-1049j)  +/-  (2.78e-247, 2.78e-247j)
| (-0.11539569344883949077 - 6.4506692420407172849e-1055j)  +/-  (1.01e-253, 1.01e-253j)
-------------------------------------------------
The weights are:
| (0.074286453023451687855 + 8.0180961420594656642e-910j)  +/-  (4.09e-65, 3.71e-178j)
| (0.0023745572945208021657 + 7.6732451189011681073e-906j)  +/-  (2.04e-65, 1.85e-178j)
| (0.027863384625369328434 + 8.5623326749245198798e-910j)  +/-  (1.37e-67, 1.24e-180j)
| (0.00053980275279394401551 - 1.1212930409944448878e-905j)  +/-  (1.88e-65, 1.71e-178j)
| (0.022254991438713482309 - 5.6229177546438945633e-908j)  +/-  (5.33e-67, 4.85e-180j)
| (0.016584254117604096934 + 1.680886777981917154e-907j)  +/-  (1.07e-66, 9.71e-180j)
| (0.0023745572945208021657 - 1.285368416576207501e-908j)  +/-  (1.6e-69, 1.45e-182j)
| (0.033331293323278613079 - 6.0647201856691801578e-910j)  +/-  (5.39e-70, 4.89e-183j)
| (0.0060182101857583409461 + 8.3035502448123593398e-909j)  +/-  (4.87e-70, 4.43e-183j)
| (0.00053980275279394401551 + 7.352052486307148853e-909j)  +/-  (1.05e-69, 9.52e-183j)
| (0.038609988268433962542 + 6.2442915170592883864e-909j)  +/-  (4.11e-73, 3.74e-186j)
| (0.075662168850049121326 - 6.5647553635541658106e-910j)  +/-  (4.05e-74, 3.68e-187j)
| (0.022254991438713482309 - 1.3168338894433300189e-909j)  +/-  (2.39e-71, 2.18e-184j)
| (0.038609988268433962542 + 4.6124473177029379392e-910j)  +/-  (2.06e-72, 1.87e-185j)
| (0.0060182101857583409461 + 4.0843783465192295856e-906j)  +/-  (2.84e-71, 2.58e-184j)
| (0.052952627376448386226 - 1.7708028227779478993e-909j)  +/-  (3.25e-75, 2.95e-188j)
| (0.027863384625369328434 + 2.3306501796135644611e-908j)  +/-  (5.22e-73, 4.74e-186j)
| (0.011023155871683362247 - 4.2340656913383279248e-909j)  +/-  (1e-71, 9.09e-185j)
| (0.052952627376448386226 - 2.8318560963192464318e-910j)  +/-  (2.3e-76, 2.09e-189j)
| (0.016584254117604096934 + 2.2412941041783554838e-909j)  +/-  (2.76e-72, 2.5e-185j)
| (0.033331293323278613079 - 1.1340288038074148453e-908j)  +/-  (1.96e-74, 1.78e-187j)
| (0.043661375321890820805 - 3.7953693391596685912e-909j)  +/-  (1.16e-75, 1.05e-188j)
| (0.076583845737698090995 + 1.4261464946756142005e-909j)  +/-  (9.2e-79, 8.36e-192j)
| (0.043661375321890820805 - 3.7259329663978039193e-910j)  +/-  (6.39e-76, 5.8e-189j)
| (0.048452287843965916419 + 3.1722943035768318881e-910j)  +/-  (1.11e-76, 1.01e-189j)
| (0.075662168850049121326 - 9.6815079427026796855e-910j)  +/-  (2.29e-79, 2.08e-192j)
| (0.048452287843965916419 + 2.5033628085803230699e-909j)  +/-  (1.22e-77, 1.11e-190j)
| (0.011023155871683362247 - 6.7244990737669919742e-907j)  +/-  (9.29e-75, 8.44e-188j)
| (0.070208052481936046876 + 3.0916528405937170784e-910j)  +/-  (8.44e-81, 7.67e-194j)
| (0.057134748462446613424 + 2.6418303399147720702e-910j)  +/-  (2.64e-79, 2.4e-192j)
| (0.072464822730636880199 - 3.6503824235904024144e-910j)  +/-  (5.36e-81, 4.87e-194j)
| (0.064445132779271016488 + 8.9213963405914767681e-910j)  +/-  (1.19e-81, 1.08e-194j)
| (0.060973283468348351258 - 1.061326163962607772e-909j)  +/-  (2.73e-81, 2.48e-194j)
| (0.077046046534580064115 - 3.8712797409572061329e-909j)  +/-  (3.99e-82, 3.63e-195j)
| (0.060973283468348351258 - 2.5714746946649700468e-910j)  +/-  (1.24e-81, 1.12e-194j)
| (0.067529517444496535869 - 2.7729892202938142216e-910j)  +/-  (2.37e-82, 2.15e-195j)
| (1.3324907094545519118e-10 + 5.8342014984136393417e-909j)  +/-  (1.19e-82, 1.08e-195j)
| (0.057134748462446613424 + 1.3325902311982595727e-909j)  +/-  (1.94e-82, 1.76e-195j)
| (0.070208052481936046876 + 7.4236463345981337829e-910j)  +/-  (5.61e-84, 5.1e-197j)
| (0.074286453023451687855 + 4.63903766886641301e-910j)  +/-  (1.41e-83, 1.28e-196j)
| (0.064445132779271016488 + 2.6116850348088568665e-910j)  +/-  (3.87e-83, 3.51e-196j)
| (0.077046046534580064115 - 3.5835232803768485142e-909j)  +/-  (1.38e-83, 1.25e-196j)
| (0.072464822730636880199 - 7.4196221307135752811e-910j)  +/-  (9.07e-85, 8.28e-198j)
| (0.067529517444496535869 - 7.9124353879997885736e-910j)  +/-  (7.35e-85, 6.72e-198j)
| (0.076583845737698090995 + 1.1306593409159899001e-909j)  +/-  (1.98e-84, 1.78e-197j)
