Starting with polynomial:
P : 3/2*t^2 - 1/2
Extension levels are: 2 4 35
-------------------------------------------------
Trying to find an order 4 Kronrod extension for:
P1 : 3/2*t^2 - 1/2
Solvable: 1
-------------------------------------------------
Trying to find an order 35 Kronrod extension for:
P2 : 3/2*t^6 - 25/14*t^4 + 45/98*t^2 - 1/98
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 3/2*t^41 - 278074484073877457407598558951733167/18059221705995355685115679767929350*t^39 + 20959821151084128936128475668493619066281/286076131044672429407917483203768833350*t^37 - 4355726904159273474823523591887725430455663/20311405304171742487962141307467587167850*t^35 + 125376118606874465724573379453854009157281/290162932916739178399459161535251245255*t^33 - 12354689306043704051392935817706263941255858/19440916505421524952763763822861833432085*t^31 + 50910268949956263619713537356908151148771726/72119528971725011921542994826745511119025*t^29 - 6227745320530364602270515264029361677540914/10302789853103573131648999260963644445575*t^27 + 1776090769121173641870419054878388444984116269/4399291267275225727214122684431476178260525*t^25 - 15367638104761577534875346547611140597684447083/72676291735386729013577306746807986464863873*t^23 + 274491024197562436381326454494161530378015827/3159838771103770826677274206382955933254951*t^21 - 62891058953590121119012955166015389366158473/2257027693645550590483767290273539952324965*t^19 + 826968799760042184021439378909219376021439612/119622467763214181295639666384497617473223145*t^17 - 156321399776295945037465157684720109043940946/119622467763214181295639666384497617473223145*t^15 + 4404723323680619667145807073589159750348702/23924493552642836259127933276899523494644629*t^13 - 147448096612436079032193405284431949041108734/7871158378819493129253090048099943229738082941*t^11 + 724688617667089820940185380629481876451432901/550981086517364519047716303366996026081665805870*t^9 - 1410426730635422985495865649547705597610225689/23692186720246674319051801044780829121511629652410*t^7 + 5271978558025595537478975097477105144654761/3384598102892382045578828720682975588787375664630*t^5 - 13099991635643024201826001590340766334309/676919620578476409115765744136595117757475132926*t^3 + 462225101452904384173502769173031099/6386034156400720840714771171099953941108255971*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:
| (0.9825083862617839907 - 3.462442129682389139e-860j)  +/-  (5.21e-241, 5.21e-241j)
| (-0.99902395175578015731 - 1.8573194416392936012e-872j)  +/-  (2.16e-241, 2.16e-241j)
| (-0.96514755812383282516 - 2.2740952438368339358e-877j)  +/-  (3.92e-241, 3.92e-241j)
| (0.99902395175578015731 + 3.428783167581993646e-889j)  +/-  (1.98e-241, 1.98e-241j)
| (0.96514755812383282516 + 4.2914317655115181726e-911j)  +/-  (4.09e-241, 4.09e-241j)
| (0.83770632943528517312 - 3.3169691153901196296e-923j)  +/-  (1.8e-242, 1.8e-242j)
| (-0.91248695683407599658 - 3.2285870745397981276e-926j)  +/-  (1.19e-241, 1.19e-241j)
| (-0.87768526921320238124 - 6.5084833841818854505e-927j)  +/-  (4.97e-242, 4.97e-242j)
| (-0.9825083862617839907 + 8.8552543942038100615e-925j)  +/-  (5.3e-241, 5.3e-241j)
| (0.79301580768306047188 - 7.7384141585905075029e-927j)  +/-  (4.65e-243, 4.65e-243j)
| (0.87768526921320238124 - 6.9857719651957193354e-932j)  +/-  (5.3e-242, 5.3e-242j)
| (-0.99371871623687572033 + 3.689269857071970926e-936j)  +/-  (4.76e-241, 4.76e-241j)
| (-0.4495612369192149487 - 4.9361357958695205799e-942j)  +/-  (4.94e-248, 4.94e-248j)
| (-0.83770632943528517312 + 3.0516867345593761071e-939j)  +/-  (1.71e-242, 1.71e-242j)
| (0.99371871623687572033 - 2.4774207170439025062e-935j)  +/-  (4.62e-241, 4.62e-241j)
| (0.91248695683407599658 + 1.5006895470413244331e-945j)  +/-  (1.15e-241, 1.15e-241j)
| (0.9417375093167541866 + 6.7061388292014719804e-958j)  +/-  (2.36e-241, 2.36e-241j)
| (-0.9417375093167541866 - 1.5734907401787273111e-970j)  +/-  (2.46e-241, 2.46e-241j)
| (-0.74416233978870339285 + 6.8864202765236037922e-972j)  +/-  (1.21e-243, 1.21e-243j)
| (-0.15655801081562154215 - 2.1922697129748989133e-978j)  +/-  (4.49e-253, 4.49e-253j)
| (0.30807767302019550248 - 2.7163473946728956404e-980j)  +/-  (2.2e-250, 2.2e-250j)
| (0.74416233978870339285 - 1.3619617778891939379e-972j)  +/-  (1.11e-243, 1.11e-243j)
| (0.15655801081562154215 - 5.2794411858213533752e-980j)  +/-  (4.49e-253, 4.49e-253j)
| (-0.79301580768306047188 + 4.350383334002590674e-975j)  +/-  (4.51e-243, 4.51e-243j)
| (-0.69171264638771845626 + 1.6302165082834367615e-977j)  +/-  (2.28e-244, 2.28e-244j)
| (6.599121546835957152e-983 + 1.1423741962941699824e-983j)  +/-  (2.75e-981, 2.75e-981j)
| (0.69171264638771845626 - 1.1686992023027485697e-977j)  +/-  (2.3e-244, 2.3e-244j)
| (0.51525256721355755621 + 9.5022537795028150175e-982j)  +/-  (5.23e-247, 5.23e-247j)
| (-0.23326508925676187602 + 1.1588156111194246342e-984j)  +/-  (1.01e-251, 1.01e-251j)
| (-0.63608545704528209137 + 9.1756763958045328623e-982j)  +/-  (3.54e-245, 3.54e-245j)
| (-0.078592542065825245477 + 3.4627698949993351047e-988j)  +/-  (2.07e-254, 2.07e-254j)
| (0.4495612369192149487 - 1.5995769909059835071e-983j)  +/-  (4.57e-248, 4.57e-248j)
| (0.63608545704528209137 + 4.0630838114690464408e-983j)  +/-  (3.76e-245, 3.76e-245j)
| (0.078592542065825245477 - 9.9602468023310253597e-988j)  +/-  (2.07e-254, 2.07e-254j)
| (-0.57735026918962576451 + 2.2454421870211442973e-985j)  +/-  (4.91e-246, 4.91e-246j)
| (-0.38036742016952953622 + 3.7364859529255424329e-988j)  +/-  (3.19e-249, 3.19e-249j)
| (0.23326508925676187602 + 5.3635284835896005457e-989j)  +/-  (1.12e-251, 1.12e-251j)
| (0.57735026918962576451 + 1.0084477565887372322e-987j)  +/-  (4.99e-246, 4.99e-246j)
| (0.38036742016952953622 - 7.7603164711940710831e-991j)  +/-  (3.53e-249, 3.53e-249j)
| (-0.30807767302019550248 - 1.2932659844849818241e-990j)  +/-  (2.24e-250, 2.24e-250j)
| (-0.51525256721355755621 + 6.9687063038970556735e-1000j)  +/-  (5.67e-247, 5.67e-247j)
-------------------------------------------------
The weights are:
| (0.014289337578414770946 + 2.9103617972074433241e-861j)  +/-  (2.02e-77, 1.27e-193j)
| (0.0027065263705837749091 + 6.034657434030507223e-863j)  +/-  (6.17e-78, 3.87e-194j)
| (0.020413210068139584726 - 3.2706428730051936575e-862j)  +/-  (4.92e-78, 3.08e-194j)
| (0.0027065263705837749091 - 7.240362954786434194e-861j)  +/-  (2.84e-78, 1.78e-194j)
| (0.020413210068139584726 - 3.6692299371363497102e-860j)  +/-  (4.72e-78, 2.96e-194j)
| (0.042420101521030076787 - 9.1526316894225363626e-861j)  +/-  (2.47e-79, 1.55e-195j)
| (0.032081106411965555158 - 4.9331025811394283681e-862j)  +/-  (4.08e-79, 2.56e-195j)
| (0.037460113397784081894 + 5.9882817872174481115e-862j)  +/-  (1.98e-79, 1.24e-195j)
| (0.014289337578414770946 + 2.5178413297074768237e-862j)  +/-  (3.92e-79, 2.46e-195j)
| (0.046868574938149354415 + 8.3069931057017916751e-861j)  +/-  (1.11e-80, 6.98e-197j)
| (0.037460113397784081894 + 1.0626819828957343448e-860j)  +/-  (1.88e-80, 1.18e-196j)
| (0.0081548394582633344889 - 1.672008315221179975e-862j)  +/-  (2.89e-79, 1.81e-195j)
| (0.067488556412592096443 + 1.7199779553678429559e-861j)  +/-  (3.14e-83, 1.97e-199j)
| (0.042420101521030076787 - 7.2811184448093491349e-862j)  +/-  (4.16e-81, 2.61e-197j)
| (0.0081548394582633344889 + 2.9475208633487358866e-860j)  +/-  (1.77e-80, 1.11e-196j)
| (0.032081106411965555158 - 1.335049354856520379e-860j)  +/-  (1.61e-81, 1.01e-197j)
| (0.026371871173938396086 + 1.9113402040667001743e-860j)  +/-  (2.89e-81, 1.81e-197j)
| (0.026371871173938396086 + 4.0497431455122129265e-862j)  +/-  (5.14e-82, 3.23e-198j)
| (0.050741070955604987926 - 1.0746165228692236885e-861j)  +/-  (1.39e-84, 8.7e-201j)
| (0.077441991161733200229 + 1.7644466202730063402e-861j)  +/-  (5.81e-87, 3.64e-203j)
| (0.073653751524192947854 + 3.2648078129194679067e-861j)  +/-  (1.93e-87, 1.21e-203j)
| (0.050741070955604987926 - 7.7849367305666483763e-861j)  +/-  (2.54e-85, 1.59e-201j)
| (0.077441991161733200229 + 2.4333445620200243926e-861j)  +/-  (1.11e-87, 6.98e-204j)
| (0.046868574938149354415 + 8.8656271156301515006e-862j)  +/-  (4.83e-85, 3.03e-201j)
| (0.05408438445078777453 + 1.2806879469796836624e-861j)  +/-  (2.32e-86, 1.45e-202j)
| (0.078696894320457152844 + 1.9797192821360252517e-861j)  +/-  (1.38e-88, 8.64e-205j)
| (0.05408438445078777453 + 7.373404775556266737e-861j)  +/-  (2.4e-87, 1.51e-203j)
| (0.063878115764739493416 - 5.4496786307463924869e-861j)  +/-  (8.96e-89, 5.62e-205j)
| (0.075865989762494234512 - 1.7197446075239299188e-861j)  +/-  (4.03e-89, 2.53e-205j)
| (0.057158327732491621176 - 1.4757848037616219955e-861j)  +/-  (1.97e-88, 1.23e-204j)
| (0.078383755081175240889 - 1.8482975062115233013e-861j)  +/-  (5.75e-89, 3.61e-205j)
| (0.067488556412592096443 + 4.6217119004464628068e-861j)  +/-  (8.37e-90, 5.25e-206j)
| (0.057158327732491621176 - 6.8953178209693622805e-861j)  +/-  (2.66e-89, 1.67e-205j)
| (0.078383755081175240889 - 2.1697044169100091721e-861j)  +/-  (4.73e-90, 2.96e-206j)
| (0.060361554499972469282 + 1.622488915733310085e-861j)  +/-  (3.66e-90, 2.3e-206j)
| (0.070828374575718427912 - 1.7124258180363076161e-861j)  +/-  (1.04e-90, 6.5e-207j)
| (0.075865989762494234512 - 2.7905753536297467134e-861j)  +/-  (1.56e-90, 9.79e-207j)
| (0.060361554499972469282 + 6.2465819440401255242e-861j)  +/-  (1.49e-90, 9.36e-207j)
| (0.070828374575718427912 - 3.8758759977048309457e-861j)  +/-  (8.01e-91, 5.02e-207j)
| (0.073653751524192947854 + 1.7061137814302447166e-861j)  +/-  (1.28e-91, 8.1e-208j)
| (0.063878115764739493416 - 1.700133820585650386e-861j)  +/-  (1.16e-91, 7.11e-208j)
