Starting with polynomial:
P : 3/2*t^2 - 1/2
Extension levels are: 2 3 40
-------------------------------------------------
Trying to find an order 3 Kronrod extension for:
P1 : 3/2*t^2 - 1/2
Solvable: 1
-------------------------------------------------
Trying to find an order 40 Kronrod extension for:
P2 : 3/2*t^5 - 25/14*t^3 + 3/7*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 3/2*t^45 - 3798738450570985823085951780981501473313/227961392259805374529635366690340009766*t^43 + 2712870981854339293027912237252970937480/31429892952763863930165673480561828589*t^41 - 78307453294562635246289673320824630454815/282869036574874775371491061325056457301*t^39 + 9173146600073455622199425292964502995953655/14897769259610071502898529229786306751186*t^37 - 35042918248600874282516205395874606036266023/34761461605756833506763234869501382419434*t^35 + 2757153518707949367845273664609090748270337/2190848420530892868073313122027398051645*t^33 - 165258203856675360081662725077257080235620/134963657973633062758946715534177263941*t^31 + 4987154575078850395909408806622748277745717753/5299078103018754943104524892018401914115483*t^29 - 10025094879758919279198826157939985832579602169/17411256624204480527343438930917606289236587*t^27 + 1640332623926796717913526094724662926877762056748/5832770969108500976660052041857398106894256645*t^25 - 127799386774157685524495952345345091509672270306/1166554193821700195332010408371479621378851329*t^23 + 36082932225472754801526820586937583447569683945/1065114698706769743564009503295698784737212083*t^21 - 25507053592326859412059838403358445143444406605/3093904601005378778924027604811315517569997003*t^19 + 284485042198076835020569273634343285106604561790/182540371459317347956517628683867615536629823177*t^17 - 287075056969561541203004449134428401955063084044/1277782600215221435695623400787073308756408762239*t^15 + 8790042256012545199776410186777369572497836607/365080742918634695913035257367735231073259646354*t^13 - 35828669280106389383699469546887111730078010995/19349279374687638883390868640489967246882761256762*t^11 + 15989270467110752124778874543084834308687167620/164468874684844930508822383444164721598503470682477*t^9 - 26087477482395685644010143039801686723834692935/8058974859557401594932296788764071358326670063441373*t^7 + 6584272781850684067372894383817859257449372567/108220519542627964274805128306260386811815283709069866*t^5 - 2790906354994559904550813617714377343108109/5322320633243998243023203031455428859597472969298518*t^3 + 21018204962286838691250125554552810298732245/16287188191165508623358171810092188215178200198215014833*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:
| (0.45602503276591046247 - 1.6290690039859665555e-944j)  +/-  (2.66e-247, 2.66e-247j)
| (0.98379866320997716242 - 6.6173813856363435224e-935j)  +/-  (1.08e-239, 1.08e-239j)
| (-0.94997131415289343196 - 3.1691036841074827758e-946j)  +/-  (6.56e-240, 6.56e-240j)
| (0.99879689537787841368 - 5.3359537935361446727e-949j)  +/-  (3.42e-240, 3.42e-240j)
| (0.94997131415289343196 - 1.1668280100054838435e-967j)  +/-  (6.42e-240, 6.42e-240j)
| (0.92582009977255146157 - 3.6608947438992714466e-978j)  +/-  (3.56e-240, 3.56e-240j)
| (-0.99355051257660271205 - 3.2273667860385274061e-980j)  +/-  (9.05e-240, 9.05e-240j)
| (-0.92582009977255146157 + 2.2508473842079442893e-985j)  +/-  (3.26e-240, 3.26e-240j)
| (-0.98379866320997716242 + 5.7745389470985489278e-986j)  +/-  (1.13e-239, 1.13e-239j)
| (-0.99879689537787841368 - 3.2076630648408665291e-987j)  +/-  (3.23e-240, 3.23e-240j)
| (0.86345229817332822548 + 3.4763324103629477725e-989j)  +/-  (5.44e-241, 5.44e-241j)
| (-0.19295466862645680272 - 5.8032570752659712754e-1011j)  +/-  (4.96e-252, 4.96e-252j)
| (-0.89693610670527040585 + 1.1187853850072989281e-997j)  +/-  (1.46e-240, 1.46e-240j)
| (-0.78338823319794908055 + 4.9864512016975139536e-1000j)  +/-  (4.05e-242, 4.05e-242j)
| (0.99355051257660271205 - 1.3248109324074641987e-996j)  +/-  (8.7e-240, 8.7e-240j)
| (0.89693610670527040585 + 8.0668093016136304472e-1014j)  +/-  (1.47e-240, 1.47e-240j)
| (0.82553695034210628946 + 2.6663888804825040383e-1023j)  +/-  (1.74e-241, 1.74e-241j)
| (-0.96930322336369854382 - 3.1143653924786182867e-1029j)  +/-  (9.99e-240, 9.99e-240j)
| (-0.82553695034210628946 - 1.0210465229886365114e-1031j)  +/-  (1.65e-241, 1.65e-241j)
| (-0.86345229817332822548 + 3.7421359876827842354e-1031j)  +/-  (5.26e-241, 5.26e-241j)
| (0.78338823319794908055 + 3.8495255725166542923e-1031j)  +/-  (3.94e-242, 3.94e-242j)
| (0.73723144389431457554 + 1.3302178214673107104e-1037j)  +/-  (9.32e-243, 9.32e-243j)
| (0.19295466862645680272 + 4.9419088393050254659e-1050j)  +/-  (5.69e-252, 5.69e-252j)
| (-0.73723144389431457554 - 2.785693074572034827e-1041j)  +/-  (8.97e-243, 8.97e-243j)
| (-0.68731761895496321609 + 4.9460587565026907678e-1042j)  +/-  (1.53e-243, 1.53e-243j)
| (8.5172213066553258581e-1051 + 2.1934915265930822974e-1050j)  +/-  (1.06e-1048, 1.06e-1048j)
| (0.68731761895496321609 - 7.3494544894503511119e-1042j)  +/-  (1.63e-243, 1.63e-243j)
| (0.96930322336369854382 + 2.2303096328759659063e-1048j)  +/-  (1.06e-239, 1.06e-239j)
| (-0.45602503276591046247 - 1.257697215843731655e-1069j)  +/-  (2.85e-247, 2.85e-247j)
| (-0.633923118011879036 - 4.7565616495912399713e-1068j)  +/-  (2.26e-244, 2.26e-244j)
| (-0.25984509307920656244 + 1.2238450685523300395e-1074j)  +/-  (7.8e-251, 7.8e-251j)
| (0.25984509307920656244 + 1.8476211761193250832e-1072j)  +/-  (7.98e-251, 7.98e-251j)
| (0.51792962223584562884 + 1.7050600501616656678e-1066j)  +/-  (2.98e-246, 2.98e-246j)
| (0.062435425649932677909 - 9.585003951595222723e-1077j)  +/-  (1.79e-254, 1.79e-254j)
| (-0.57735026918962576451 + 6.7597736845329400114e-1069j)  +/-  (3.07e-245, 3.07e-245j)
| (-0.39204406362290903475 + 2.5370310989956422986e-1071j)  +/-  (2e-248, 2e-248j)
| (0.12678997759091780718 + 4.9777157061009610552e-1076j)  +/-  (3.12e-253, 3.12e-253j)
| (0.57735026918962576451 - 1.3431954664464683318e-1065j)  +/-  (3.23e-245, 3.23e-245j)
| (0.32645864332483180038 - 6.5913351256414698128e-1071j)  +/-  (1.28e-249, 1.28e-249j)
| (-0.32645864332483180038 + 2.2315394958097350768e-1073j)  +/-  (1.29e-249, 1.29e-249j)
| (-0.51792962223584562884 + 5.0660576878243057447e-1069j)  +/-  (3.06e-246, 3.06e-246j)
| (-0.12678997759091780718 - 5.6419688502424935397e-1076j)  +/-  (3.1e-253, 3.1e-253j)
| (0.39204406362290903475 + 1.6037748826496653523e-1069j)  +/-  (1.83e-248, 1.83e-248j)
| (0.633923118011879036 + 2.1280319825807395924e-1069j)  +/-  (2.16e-244, 2.16e-244j)
| (-0.062435425649932677909 + 1.6339159439461465608e-1080j)  +/-  (1.47e-254, 1.47e-254j)
-------------------------------------------------
The weights are:
| (0.063015142094999863339 - 1.0362722322303501383e-935j)  +/-  (7.61e-68, 7.43e-184j)
| (0.012096487401763237904 + 1.4154994662471468924e-935j)  +/-  (3.65e-68, 3.56e-184j)
| (0.021751242153953339451 + 7.2110914540727365283e-937j)  +/-  (8.83e-70, 8.62e-186j)
| (0.0031019472431608417485 - 9.5703794112395229592e-936j)  +/-  (1.67e-68, 1.63e-184j)
| (0.021751242153953339451 + 4.1222834631985003684e-935j)  +/-  (1.35e-68, 1.32e-184j)
| (0.026536405655492405198 - 2.8551970360818022324e-935j)  +/-  (8.26e-69, 8.06e-185j)
| (0.0074477755475638674115 - 2.3334019424007112107e-937j)  +/-  (1.12e-70, 1.09e-186j)
| (0.026536405655492405198 - 8.6687576379286855557e-937j)  +/-  (7.31e-71, 7.13e-187j)
| (0.012096487401763237904 + 4.0682648574311178139e-937j)  +/-  (6.35e-71, 6.2e-187j)
| (0.0031019472431608417485 + 7.2399421917275460881e-938j)  +/-  (4.36e-71, 4.26e-187j)
| (0.035730238339189162696 - 1.7935187113279500348e-935j)  +/-  (6.08e-73, 5.93e-189j)
| (0.06671653164697901698 - 9.3339025460187878831e-936j)  +/-  (2.19e-74, 2.14e-190j)
| (0.031209248988042021731 + 1.0138333863329419226e-936j)  +/-  (2.23e-72, 2.18e-188j)
| (0.044192476902991131886 - 1.5268171691273145774e-936j)  +/-  (5.76e-74, 5.62e-190j)
| (0.0074477755475638674115 + 4.7313593906671885129e-935j)  +/-  (1.53e-72, 1.49e-188j)
| (0.031209248988042021731 + 2.1951365216562343964e-935j)  +/-  (3.36e-73, 3.28e-189j)
| (0.040067385571001287249 + 1.528701303573277277e-935j)  +/-  (2.37e-74, 2.31e-190j)
| (0.016909016890029194775 - 5.6973215083637473374e-937j)  +/-  (7.95e-73, 7.75e-189j)
| (0.040067385571001287249 + 1.3371476516235884648e-936j)  +/-  (4.21e-75, 4.11e-191j)
| (0.035730238339189162696 - 1.1684576809233597285e-936j)  +/-  (1.5e-74, 1.46e-190j)
| (0.044192476902991131886 - 1.3463227914348535839e-935j)  +/-  (2.31e-76, 2.26e-192j)
| (0.048079255119195544203 + 1.2184293950190982332e-935j)  +/-  (3.51e-77, 3.43e-193j)
| (0.06671653164697901698 - 1.3888581051229773702e-935j)  +/-  (6.16e-80, 6.01e-196j)
| (0.048079255119195544203 + 1.7456100650396584916e-936j)  +/-  (9.58e-78, 9.35e-194j)
| (0.05170234435769468289 - 2.0037908729803082579e-936j)  +/-  (1.12e-78, 1.09e-194j)
| (0.061992738066740707003 + 1.7154302248435730796e-935j)  +/-  (1.25e-81, 1.22e-197j)
| (0.05170234435769468289 - 1.1294373183728105018e-935j)  +/-  (1.04e-79, 1.02e-195j)
| (0.016909016890029194775 - 7.6765172369860716606e-935j)  +/-  (1.33e-77, 1.29e-193j)
| (0.063015142094999863339 - 3.7985008831295330776e-936j)  +/-  (8.09e-82, 7.89e-198j)
| (0.055036304359988267037 + 2.3149681697340931457e-936j)  +/-  (2.2e-80, 2.15e-196j)
| (0.066896374006274249676 + 7.2336419639784910683e-936j)  +/-  (3.9e-82, 3.8e-198j)
| (0.066896374006274249676 + 1.2426313000796510708e-935j)  +/-  (5.65e-83, 5.51e-199j)
| (0.06072643277090116851 + 1.0248627629558118854e-935j)  +/-  (6.89e-83, 6.72e-199j)
| (0.063243765892546641831 - 1.7169273092048513645e-935j)  +/-  (3.65e-83, 3.57e-199j)
| (0.058054380930016924465 - 2.6979074265055217307e-936j)  +/-  (1.18e-82, 1.15e-198j)
| (0.064868774728684880227 + 4.6141869263017425354e-936j)  +/-  (1.45e-83, 1.41e-199j)
| (0.06541491203724890077 + 1.5678234639575806291e-935j)  +/-  (1.87e-83, 1.82e-199j)
| (0.058054380930016924465 - 1.0362534000603285216e-935j)  +/-  (3.01e-84, 2.92e-200j)
| (0.066207188328913016522 - 1.1392568603487821225e-935j)  +/-  (2.87e-84, 2.8e-200j)
| (0.066207188328913016522 - 5.7155119377916797179e-936j)  +/-  (2.9e-84, 2.85e-200j)
| (0.06072643277090116851 + 3.1793489961902198842e-936j)  +/-  (3.89e-84, 3.8e-200j)
| (0.06541491203724890077 + 1.2098433901973614695e-935j)  +/-  (5.35e-85, 5.24e-201j)
| (0.064868774728684880227 + 1.0728088160540519704e-935j)  +/-  (2.54e-85, 2.38e-201j)
| (0.055036304359988267037 + 1.0703733041445296631e-935j)  +/-  (1.52e-85, 1.4e-201j)
| (0.063243765892546641831 - 1.5120074189915333239e-935j)  +/-  (3.73e-85, 3.73e-201j)
