Starting with polynomial:
P : 4*t^2 - 2
Extension levels are: 2 12 29
-------------------------------------------------
Trying to find an order 12 Kronrod extension for:
P1 : 4*t^2 - 2
Solvable: 1
-------------------------------------------------
Trying to find an order 29 Kronrod extension for:
P2 : 4*t^14 - 248498/1555*t^12 + 3530769/1555*t^10 - 8883963/622*t^8 + 50229333/1244*t^6 - 114812775/2488*t^4 + 78937551/4976*t^2 - 6151761/9952
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 4*t^43 - 20888293171609213002444876374428885187889963853612865861683762415155608819792212869/15305977495150692794374540123605900207533615233478761709974758130746142038990240*t^41 + 6424745377939860744013626475553747570250101443679952820401616807116750115937448465763/30611954990301385588749080247211800415067230466957523419949516261492284077980480*t^39 - 393897761981906176659546105080849008931945008730461049640586268618130341725362890382401/20407969993534257059166053498141200276711486977971682279966344174328189385320320*t^37 + 920902214707019062877811721527788381932718605098216917060576053234601719909786095894946737/775502859754301768248310032929365610515036505162923926638721078624471196642172160*t^35 - 730544909197712473498117178141333092979094626780149701450219271977770028336851108769688809/14100051995532759422696546053261192918455209184780435029794928702263112666221312*t^33 + 794961308695682323048955898420073741568897665041473286116651144397785688411345030268182413637/479401767848113820371682565810880559227477112282534791013027575876945830651524608*t^31 - 38086749190576178936379992218326190871801131473200948387972887517726854671178011807360653233041/958803535696227640743365131621761118454954224565069582026055151753891661303049216*t^29 + 1381427120614593238356749520152991431201959072569799255476727795687949506563451654630587526620951/1917607071392455281486730263243522236909908449130139164052110303507783322606098432*t^27 - 19061622976807417625632546419899380013755783863179760313442445351048798258534829822149289858353549/1917607071392455281486730263243522236909908449130139164052110303507783322606098432*t^25 + 400180122425994306530548700543832593943573310731720770087545928326842245557468980617663530546076325/3835214142784910562973460526487044473819816898260278328104220607015566645212196864*t^23 - 6360072654013990121527443538546367321970912870177293288287043676404307304057671074027829484956294375/7670428285569821125946921052974088947639633796520556656208441214031133290424393728*t^21 + 75788290759797916378479177017151009905862660423280347285851107796936939289306885610725336733900202175/15340856571139642251893842105948177895279267593041113312416882428062266580848787456*t^19 - 70230054615679089046592173214262544321164720928086555017007125091123737863484136070105203329891987775/3229654014976766789872387811778563767427214230113918592087764721697319280178692096*t^17 + 26310165941392598172450304251945044675158110087573379210654998747829045005158867248769598341863740225/379959295879619622337927977856301619697319321189872775539737026082037562373963776*t^15 - 117780699458423437600116837174419157187181168440171298975519328727717447109405054053349133162693556125/759918591759239244675855955712603239394638642379745551079474052164075124747927552*t^13 + 356266195026598698354043423460127788482640948868205016031396989826561518958134033754293539352010952875/1519837183518478489351711911425206478789277284759491102158948104328150249495855104*t^11 - 1378204731257949605948913509266197779515247574994886451254373236033655475774405782830516878463810029875/6079348734073913957406847645700825915157109139037964408635792417312600997983420416*t^9 + 1573903161051848024798514244707540271721649126775496168043444174470149568969338123293902808925829146125/12158697468147827914813695291401651830314218278075928817271584834625201995966840832*t^7 - 938125640103756693976481797773148574253781894399659593538324166525927612618622383460722171594412767125/24317394936295655829627390582803303660628436556151857634543169669250403991933681664*t^5 + 234721513920989188232860963601600739203840680735451102659625659072362999844147993845168067552965699375/48634789872591311659254781165606607321256873112303715269086339338500807983867363328*t^3 - 3621946873720865440233249344145277261962350051959447637943940549849537352479975346647231041007126875/24317394936295655829627390582803303660628436556151857634543169669250403991933681664*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:
| (4.9408264586965861683 - 1.8694565998371528614e-904j)  +/-  (1.77e-245, 1.77e-245j)
| (2.5504966051126501465 - 1.2269487310638318811e-915j)  +/-  (3.15e-247, 3.15e-247j)
| (4.5151096502184581714 - 8.662472190349672779e-927j)  +/-  (2.55e-245, 2.55e-245j)
| (6.3880223293146376902 + 4.4072613733944114219e-938j)  +/-  (1.87e-246, 1.87e-246j)
| (-5.8698771058883392406 + 6.6600377077738333215e-938j)  +/-  (5.73e-246, 5.73e-246j)
| (-4.9408264586965861683 - 8.1652606489170422864e-938j)  +/-  (1.69e-245, 1.69e-245j)
| (-6.3880223293146376902 - 3.8700271731290268686e-939j)  +/-  (1.81e-246, 1.81e-246j)
| (-2.5504966051126501465 + 1.2397877119048823164e-937j)  +/-  (2.91e-247, 2.91e-247j)
| (7.6632090214179053853 - 9.5781071562142677586e-942j)  +/-  (4.22e-248, 4.22e-248j)
| (-3.6186831098228048752 - 1.3279458746326040503e-936j)  +/-  (2.25e-245, 2.25e-245j)
| (-7.6632090214179053853 - 3.1726317094244167301e-945j)  +/-  (3.9e-248, 3.9e-248j)
| (-5.3909477528474071769 - 5.2027024035236669716e-943j)  +/-  (1.05e-245, 1.05e-245j)
| (6.966807315070818071 + 8.7259035579579956984e-942j)  +/-  (4.01e-247, 4.01e-247j)
| (-6.966807315070818071 + 2.1876192211148834373e-945j)  +/-  (3.79e-247, 3.79e-247j)
| (5.3909477528474071769 - 8.1109997159103845591e-943j)  +/-  (1.1e-245, 1.1e-245j)
| (-4.1204787410992218738 + 3.628796842960456363e-951j)  +/-  (3.53e-245, 3.53e-245j)
| (1.8942430499246252602 - 9.3661947860757496191e-962j)  +/-  (1.41e-248, 1.41e-248j)
| (4.1204787410992218738 - 8.0335550504528904858e-962j)  +/-  (3.52e-245, 3.52e-245j)
| (0.46559009997215711698 - 9.5249790411044618983e-984j)  +/-  (5.92e-253, 5.92e-253j)
| (2.2123905082512458296 + 5.7361762404485573869e-978j)  +/-  (7.15e-248, 7.15e-248j)
| (-3.8364510911341272968 - 8.6132194263772618077e-976j)  +/-  (3.84e-245, 3.84e-245j)
| (3.6186831098228048752 - 1.4504286872859138133e-982j)  +/-  (2.43e-245, 2.43e-245j)
| (3.8364510911341272968 - 4.3807268300554812347e-1005j)  +/-  (3.86e-245, 3.86e-245j)
| (-1.8942430499246252602 - 3.0136793782678035681e-1015j)  +/-  (1.37e-248, 1.37e-248j)
| (-7.9298216769147886976e-1026 - 4.8855386183650988413e-1026j)  +/-  (4.01e-1024, 4.01e-1024j)
| (5.8698771058883392406 - 1.2048720744415722652e-1011j)  +/-  (5.5e-246, 5.5e-246j)
| (1.5874891944402508357 - 3.3436561671685399626e-1016j)  +/-  (2.32e-249, 2.32e-249j)
| (2.9057414886006588375 - 1.0116594597295719186e-1012j)  +/-  (1.18e-246, 1.18e-246j)
| (-2.9057414886006588375 + 1.2513616412765292456e-1013j)  +/-  (1.19e-246, 1.19e-246j)
| (-0.7071067811865475244 + 1.9202531344407231884e-1020j)  +/-  (4.84e-252, 4.84e-252j)
| (-0.21096799267853511108 - 2.0701929365263044179e-1022j)  +/-  (6.28e-254, 6.28e-254j)
| (0.97742072941086408045 - 1.2477515658402196855e-1019j)  +/-  (3.93e-251, 3.93e-251j)
| (1.2798739543845792198 - 3.066505836148577805e-1018j)  +/-  (3.62e-250, 3.62e-250j)
| (-4.5151096502184581714 - 4.3902246579615722325e-1015j)  +/-  (2.66e-245, 2.66e-245j)
| (-2.2123905082512458296 - 1.198483150199737633e-1016j)  +/-  (6.38e-248, 6.38e-248j)
| (-1.2798739543845792198 + 7.3606420372323930252e-1020j)  +/-  (3.51e-250, 3.51e-250j)
| (3.270676901126319117 + 2.631264345840234978e-1018j)  +/-  (4.83e-246, 4.83e-246j)
| (0.7071067811865475244 + 1.6525108521605444507e-1027j)  +/-  (4.53e-252, 4.53e-252j)
| (-0.97742072941086408045 - 9.3773435924009474771e-1027j)  +/-  (3.57e-251, 3.57e-251j)
| (-1.5874891944402508357 - 1.544663537196654997e-1029j)  +/-  (2.45e-249, 2.45e-249j)
| (-0.46559009997215711698 + 5.9837944238382059314e-1032j)  +/-  (5.92e-253, 5.92e-253j)
| (-3.270676901126319117 - 3.7676059579328776376e-1033j)  +/-  (5.23e-246, 5.23e-246j)
| (0.21096799267853511108 - 2.5323628707688678971e-1044j)  +/-  (5.72e-254, 5.72e-254j)
-------------------------------------------------
The weights are:
| (6.1756040344613506825e-12 + 8.0550526826659834336e-915j)  +/-  (4.83e-86, 2.84e-207j)
| (0.00029341318277992769607 - 1.4783853508814705488e-910j)  +/-  (6.52e-75, 3.84e-196j)
| (3.2657280093639252182e-10 - 5.2449007561867923956e-914j)  +/-  (1.49e-84, 8.76e-206j)
| (5.8125115767740308401e-19 + 2.4593442007176612632e-920j)  +/-  (1.8e-91, 1.06e-212j)
| (3.0426868733047603646e-16 + 1.5332422242360164339e-919j)  +/-  (2.7e-92, 1.59e-213j)
| (6.1756040344613506825e-12 + 1.1683292057718070432e-916j)  +/-  (9.63e-90, 5.67e-211j)
| (5.8125115767740308401e-19 - 3.1416720578400252387e-921j)  +/-  (3.99e-94, 2.35e-215j)
| (0.00029341318277992769607 - 4.717229037800475164e-911j)  +/-  (9e-81, 5.3e-202j)
| (1.4197521015204529973e-26 + 4.7958194541192611599e-925j)  +/-  (2.32e-98, 1.36e-219j)
| (3.5392819968137323671e-07 + 9.6930602133994396071e-913j)  +/-  (3.93e-86, 2.32e-207j)
| (1.4197521015204529973e-26 - 1.0358630985386737369e-925j)  +/-  (1.21e-98, 7.12e-220j)
| (6.247633641389723443e-14 - 4.8831138991914298468e-918j)  +/-  (9.83e-92, 5.79e-213j)
| (2.9255249528318182299e-22 - 1.9541488793772124653e-922j)  +/-  (1.14e-97, 6.72e-219j)
| (2.9255249528318182299e-22 + 3.3248152337782523384e-923j)  +/-  (1.44e-96, 8.51e-218j)
| (6.247633641389723443e-14 + 1.1208363383385092489e-916j)  +/-  (1.42e-93, 8.36e-215j)
| (8.7508343933955472532e-09 + 4.5000598603749863277e-914j)  +/-  (1.57e-89, 9.25e-211j)
| (0.0048346901992767964321 - 1.4736177248822367978e-909j)  +/-  (1.12e-82, 6.63e-204j)
| (8.7508343933955472532e-09 + 4.9706258718881885433e-913j)  +/-  (1e-90, 5.91e-212j)
| (0.11260224531825127737 + 9.0958025311936218561e-908j)  +/-  (3.77e-83, 2.22e-204j)
| (0.0013849186927707134151 + 4.9430477266546030323e-910j)  +/-  (8.85e-85, 5.22e-206j)
| (4.2569288886582680827e-08 - 3.5757446154765816598e-913j)  +/-  (4.2e-90, 2.47e-211j)
| (3.5392819968137323671e-07 + 6.2752531287464701369e-912j)  +/-  (3.22e-90, 1.9e-211j)
| (4.2569288886582680827e-08 - 2.8419053820460669745e-912j)  +/-  (1.48e-90, 8.7e-212j)
| (0.0048346901992767964321 - 6.5683301684569765601e-910j)  +/-  (1.31e-87, 7.74e-209j)
| (0.10347550059677415962 + 1.6751471479237735226e-907j)  +/-  (1.09e-83, 6.4e-205j)
| (3.0426868733047603646e-16 - 1.7841252515109207538e-918j)  +/-  (1.22e-96, 7.17e-218j)
| (0.013895682085657560901 + 3.8269257650566659112e-909j)  +/-  (1.02e-85, 6.01e-207j)
| (4.3939494480077838499e-05 + 4.3259234798490567626e-911j)  +/-  (2.34e-89, 1.38e-210j)
| (4.3939494480077838499e-05 + 1.1219710133756991509e-911j)  +/-  (6.42e-91, 3.78e-212j)
| (0.084676591205865666213 - 3.9893973474940428169e-908j)  +/-  (1.11e-84, 6.55e-206j)
| (0.13342043038660690998 - 1.2887237371742783366e-907j)  +/-  (5.03e-84, 2.97e-205j)
| (0.063322317760656833646 + 2.3534432458117183214e-908j)  +/-  (2.4e-85, 1.41e-206j)
| (0.033782955541554016503 - 9.3779399601694893345e-909j)  +/-  (9.87e-86, 5.82e-207j)
| (3.2657280093639252182e-10 - 2.3613129165140325476e-915j)  +/-  (3.29e-94, 1.94e-215j)
| (0.0013849186927707134151 + 1.8854159289069321109e-910j)  +/-  (1.14e-89, 6.73e-211j)
| (0.033782955541554016503 - 5.5190236704286875486e-909j)  +/-  (2.8e-88, 1.65e-209j)
| (4.6602525789926864454e-06 - 1.4018633770727577478e-911j)  +/-  (7.63e-91, 4.51e-212j)
| (0.084676591205865666213 - 5.3219985236110915475e-908j)  +/-  (1.04e-86, 6.17e-208j)
| (0.063322317760656833646 + 1.5760832820135347093e-908j)  +/-  (9e-88, 5.32e-209j)
| (0.013895682085657560901 + 1.9657402433105678823e-909j)  +/-  (4.72e-89, 2.78e-210j)
| (0.11260224531825127737 + 7.5291768165339180257e-908j)  +/-  (2.35e-87, 1.41e-208j)
| (4.6602525789926864454e-06 - 2.8512702089992332532e-912j)  +/-  (3.53e-92, 2.08e-213j)
| (0.13342043038660690998 - 1.40368677946158168e-907j)  +/-  (3e-87, 1.75e-208j)
