Starting with polynomial:
P : 3/2*t^2 - 1/2
Extension levels are: 2 4 43
-------------------------------------------------
Trying to find an order 4 Kronrod extension for:
P1 : 3/2*t^2 - 1/2
Solvable: 1
-------------------------------------------------
Trying to find an order 43 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^49 - 908149681658035872139456197541857048997507/50605053622889588835325225376652592018160*t^47 + 689452996968413862469028624655413559275379903/6853684436317437792262525089055340179850800*t^45 - 13955178364871055511104778010320525545757803567/39751369730641139195122645516520973043134640*t^43 + 412617131132246669832860812290979310288597464557/482695203872070975940774981272040386952349200*t^41 - 2472108989417308845763450357274941801547428542945/1602548076855275640123372937823174084681799344*t^39 + 11866138309974096902742861099169804006515081632569/5547281804499031061965521707849448754667766960*t^37 - 243341515710327668950353099378272690162468080352311/104341729179862727117922908314311059909227045200*t^35 + 5811178838010108590332905667169639208577046881991/2864282761800153293433177875294813409272899280*t^33 - 1068560439075886365379753786494521984099725018068697/751874224972540239526209192264888519934136061000*t^31 + 1061111202347571281379279231851810791729976187022423/1317283642151890499649918504848084686924606378872*t^29 - 473431349612610465232224312621498864472919070348011/1279791168483637458608979390314915336229434221400*t^27 + 20221884627491761099333994106356132540641724112725041/147175984375618307740032629886215263666384935461000*t^25 - 16201032117223402856856162295789341820415474238730433/394431638126657064743287448095056906625911627035480*t^23 + 1561043388914676887004707852681665814364144450714681/159242586821321175206917292709184465407976743834200*t^21 - 3382439463876793179130692767153809015321991746381/1832380451094654618819322272270067821132883079736*t^19 + 5137123329896875857167107618726666158350730035327257/19039043680357159707739031516310094684177699492816952*t^17 - 1681985636320920389514545122582391119885933770025986741/56165178857053621137830142973114779318324213503810008400*t^15 + 3930453771362534006164693001699425356971670724478751/1604719395915817746795146942088993694809263242966000240*t^13 - 262235309122372621908816236482223153525741538034157/1851599302979789707840554163948838878626072972653077200*t^11 + 134697072177002763278284378409956576647755767431/24687990706397196104540722185984518381680972968707696*t^9 - 2033080996131263063988532488583160645029141326127/15888485447474195492993707635408607901353254746289738640*t^7 + 6116384811221820178054360962035872427079830207779/3892678934631177895783458370675108935831547412840985966800*t^5 - 40698952223113953493731893325300021572346484737/5449750508483649054096841718945152510164166377977380353520*t^3 + 9658291342907778163700688662121762663739835969/1880163925426858923663410393036077616006637400402196221964400*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:
| (-0.99937968958118697401 + 1.2032624484466962167e-888j)  +/-  (9.68e-239, 9.68e-239j)
| (-0.99572006023855850275 - 2.1556296675616109513e-886j)  +/-  (2.25e-238, 2.25e-238j)
| (-0.91248695683407599658 + 2.3584064729335544616e-887j)  +/-  (3.42e-239, 3.42e-239j)
| (0.99937968958118697401 + 1.9709146867686725971e-883j)  +/-  (9.8e-239, 9.8e-239j)
| (0.95875649003604807013 + 4.4494702850830736995e-899j)  +/-  (1.43e-238, 1.43e-238j)
| (0.9377284751396981437 + 2.3464112976235891229e-907j)  +/-  (7.02e-239, 7.02e-239j)
| (-0.9377284751396981437 - 3.287894584768108535e-921j)  +/-  (7.49e-239, 7.49e-239j)
| (-0.88315115362457108704 + 3.3291597866086603922e-921j)  +/-  (1.21e-239, 1.21e-239j)
| (0.9754731398386546031 - 2.6129009087487176687e-918j)  +/-  (2.12e-238, 2.12e-238j)
| (-0.98780501235740280008 - 3.5746240456412705663e-935j)  +/-  (2.34e-238, 2.34e-238j)
| (0.84986064891360897307 - 4.0269115641315084071e-935j)  +/-  (3.86e-240, 3.86e-240j)
| (0.99572006023855850275 + 6.4713461900274997446e-949j)  +/-  (2.23e-238, 2.23e-238j)
| (-0.81277486368178747991 + 1.9738026982036081117e-977j)  +/-  (1.05e-240, 1.05e-240j)
| (-0.84986064891360897307 - 1.0926637687402454396e-976j)  +/-  (3.74e-240, 3.74e-240j)
| (0.98780501235740280008 - 1.4134224595888549275e-974j)  +/-  (2.56e-238, 2.56e-238j)
| (0.88315115362457108704 - 2.4089634097049621317e-986j)  +/-  (1.17e-239, 1.17e-239j)
| (0.91248695683407599658 + 2.1827396017869906317e-995j)  +/-  (3.14e-239, 3.14e-239j)
| (-0.9754731398386546031 + 4.7942075344457591598e-1000j)  +/-  (2.11e-238, 2.11e-238j)
| (-0.72795223847401933177 + 2.2598755300553940997e-1004j)  +/-  (5.31e-242, 5.31e-242j)
| (-0.95875649003604807013 + 2.8313462692926511664e-1004j)  +/-  (1.3e-238, 1.3e-238j)
| (0.81277486368178747991 - 5.7203730438177993891e-1006j)  +/-  (1.15e-240, 1.15e-240j)
| (0.77207268944441237568 - 1.9761047769244550778e-1010j)  +/-  (2.58e-241, 2.58e-241j)
| (0.15655801081562154215 - 1.8336635725461928704e-1023j)  +/-  (1.82e-252, 1.82e-252j)
| (-0.63034469465099996953 + 2.0186871038556028363e-1013j)  +/-  (1.31e-243, 1.31e-243j)
| (-0.77207268944441237568 + 1.8908783456228546258e-1012j)  +/-  (2.49e-241, 2.49e-241j)
| (0.09331242359596709002 - 8.4867080602345978276e-1026j)  +/-  (8.54e-254, 8.54e-254j)
| (0.68063074561276276804 + 1.7223369468872457313e-1013j)  +/-  (9.43e-243, 9.43e-243j)
| (0.72795223847401933177 + 3.5777624138372063193e-1016j)  +/-  (4.93e-242, 4.93e-242j)
| (-0.15655801081562154215 + 1.1044650381218309058e-1026j)  +/-  (1.73e-252, 1.73e-252j)
| (-0.68063074561276276804 - 9.4993865045820405888e-1018j)  +/-  (8.17e-243, 8.17e-243j)
| (-0.21958666559816872258 - 1.2861574240871079934e-1028j)  +/-  (3.19e-251, 3.19e-251j)
| (0.46436530839952417421 - 4.3087390294750029713e-1022j)  +/-  (1.61e-246, 1.61e-246j)
| (0.63034469465099996953 + 2.8737501759153706868e-1022j)  +/-  (1.35e-243, 1.35e-243j)
| (0.028640813795433879981 - 2.6439252046891691488e-1032j)  +/-  (4.04e-255, 4.04e-255j)
| (-0.52192423554796389039 - 1.6020227137108749648e-1020j)  +/-  (1.7e-245, 1.7e-245j)
| (-0.57735026918962576451 - 3.4300733847510884592e-1023j)  +/-  (1.56e-244, 1.56e-244j)
| (2.2113859131252061668e-1038 + 2.381612242031275686e-1036j)  +/-  (1.17e-1034, 1.17e-1034j)
| (0.57735026918962576451 - 8.9079375587616322764e-1025j)  +/-  (1.56e-244, 1.56e-244j)
| (0.28223421644909581271 - 5.3009256339359646271e-1029j)  +/-  (5.96e-250, 5.96e-250j)
| (-0.28223421644909581271 + 4.8027237108061999256e-1030j)  +/-  (5.71e-250, 5.71e-250j)
| (-0.46436530839952417421 + 3.1382867941471095517e-1026j)  +/-  (1.68e-246, 1.68e-246j)
| (-0.09331242359596709002 + 1.9843403411649861388e-1033j)  +/-  (8.75e-254, 8.75e-254j)
| (0.34416256285904985521 - 1.1371603573280179687e-1027j)  +/-  (9.19e-249, 9.19e-249j)
| (0.40499579832783385628 + 8.3929807612844606241e-1026j)  +/-  (1.23e-247, 1.23e-247j)
| (-0.028640813795433879981 - 1.068790092045259578e-1034j)  +/-  (4.57e-255, 4.57e-255j)
| (-0.40499579832783385628 - 1.2907480486048456875e-1026j)  +/-  (1.34e-247, 1.34e-247j)
| (-0.34416256285904985521 + 3.8652026815981684444e-1028j)  +/-  (9.04e-249, 9.04e-249j)
| (0.21958666559816872258 + 9.3391594081529543341e-1030j)  +/-  (3.05e-251, 3.05e-251j)
| (0.52192423554796389039 + 2.2469444093995609444e-1025j)  +/-  (1.65e-245, 1.65e-245j)
-------------------------------------------------
The weights are:
| (0.0017811867941901447126 - 3.0075098768556312077e-886j)  +/-  (7.07e-61, 6.28e-175j)
| (0.0057212062910538970086 + 4.4225943053604141103e-886j)  +/-  (5.57e-61, 4.94e-175j)
| (0.027310249056529695099 - 1.3782237166787267683e-885j)  +/-  (3.4e-62, 3.02e-176j)
| (0.0017811867941901447126 - 1.8264212236611852647e-883j)  +/-  (4.4e-62, 3.9e-176j)
| (0.018886778140625545721 - 5.0312177386700940379e-884j)  +/-  (2.02e-62, 1.79e-176j)
| (0.023152903655767111958 + 3.846163506049416952e-884j)  +/-  (9.54e-63, 8.47e-177j)
| (0.023152903655767111958 + 1.1927717652247460197e-885j)  +/-  (1.5e-62, 1.33e-176j)
| (0.031338085164529320457 + 1.5878372174292168212e-885j)  +/-  (4.03e-63, 3.58e-177j)
| (0.014534119842828444986 + 7.1919113180374844309e-884j)  +/-  (8.87e-63, 7.88e-177j)
| (0.010123083628262501419 - 4.6730184946062011533e-886j)  +/-  (7.17e-63, 6.37e-177j)
| (0.03521634803266448213 - 2.3690030324796929801e-884j)  +/-  (9.11e-65, 8.09e-179j)
| (0.0057212062910538970086 + 2.5805362717746508565e-883j)  +/-  (3.66e-63, 3.25e-177j)
| (0.038925402923491884141 + 2.1982096403966499117e-885j)  +/-  (3.55e-65, 3.15e-179j)
| (0.03521634803266448213 - 1.8704242289910803034e-885j)  +/-  (1.45e-64, 1.29e-178j)
| (0.010123083628262501419 - 1.1844604960343922516e-883j)  +/-  (3.28e-63, 2.91e-177j)
| (0.031338085164529320457 + 2.6707209323390022182e-884j)  +/-  (1.64e-65, 1.45e-179j)
| (0.027310249056529695099 - 3.1295866299178309166e-884j)  +/-  (6.51e-65, 5.78e-179j)
| (0.014534119842828444986 + 7.6576000203824354043e-886j)  +/-  (2.12e-65, 1.88e-179j)
| (0.045758772970650450567 + 3.0943955129020245305e-885j)  +/-  (4.74e-69, 4.21e-183j)
| (0.018886778140625545721 - 9.8174683279015138907e-886j)  +/-  (1.21e-65, 1.07e-179j)
| (0.038925402923491884141 + 2.1719518575392634831e-884j)  +/-  (1.95e-68, 1.73e-182j)
| (0.04244592502608976076 - 2.0508265165796180772e-884j)  +/-  (1.9e-69, 1.69e-183j)
| (0.0631361266973996521 + 8.0835108929788791314e-884j)  +/-  (2.83e-73, 2.51e-187j)
| (0.051684613162113111369 + 4.5558093704629452607e-885j)  +/-  (1.13e-71, 1e-185j)
| (0.04244592502608976076 - 2.5968667350067281915e-885j)  +/-  (2.92e-69, 2.59e-183j)
| (0.06342528420079839336 - 1.3625315946995270403e-883j)  +/-  (7.96e-74, 7.07e-188j)
| (0.048844806024706289504 - 1.9821015272449790871e-884j)  +/-  (1.38e-72, 1.23e-186j)
| (0.045758772970650450567 + 1.9900055797894484651e-884j)  +/-  (1.03e-71, 9.11e-186j)
| (0.0631361266973996521 + 5.8878434752058242619e-884j)  +/-  (1.3e-75, 1.15e-189j)
| (0.048844806024706289504 - 3.7289951809163800895e-885j)  +/-  (1.16e-72, 1.03e-186j)
| (0.062887197349035618282 - 3.6194932384277038414e-884j)  +/-  (9.25e-76, 8.21e-190j)
| (0.058519980191408507929 - 2.5453831679674953761e-884j)  +/-  (2.79e-76, 2.48e-190j)
| (0.051684613162113111369 + 2.0258399638228418029e-884j)  +/-  (9.36e-75, 8.31e-189j)
| (0.069231527611057893554 + 4.6739146008192222415e-883j)  +/-  (3.93e-76, 3.49e-190j)
| (0.056544177737583422532 + 7.1603903788194865463e-885j)  +/-  (1.76e-76, 1.56e-190j)
| (0.054258133099804878054 - 5.6572384774660826948e-885j)  +/-  (9.21e-76, 8.18e-190j)
| (-0.015360987570552491758 - 7.4474111089725903599e-883j)  +/-  (6.33e-77, 5.61e-191j)
| (0.054258133099804878054 - 2.1255743405922257652e-884j)  +/-  (2.29e-77, 2.03e-191j)
| (0.062349752117648250512 + 4.3148364254153998564e-884j)  +/-  (1.17e-78, 1.04e-192j)
| (0.062349752117648250512 + 2.409692591102875315e-884j)  +/-  (1.39e-78, 1.23e-192j)
| (0.058519980191408507929 - 9.2681330877867565393e-885j)  +/-  (1.98e-78, 1.75e-192j)
| (0.06342528420079839336 - 1.1291415230469118877e-883j)  +/-  (2.88e-78, 2.55e-192j)
| (0.061443633391352096668 - 3.4730660883218074913e-884j)  +/-  (8.82e-80, 7.82e-194j)
| (0.060161200675684893056 + 2.9193386219888165205e-884j)  +/-  (7.12e-80, 6.32e-194j)
| (0.069231527611057893554 + 4.4126757871443089211e-883j)  +/-  (1.92e-78, 1.71e-192j)
| (0.060161200675684893056 + 1.2317263247950299923e-884j)  +/-  (2.07e-80, 1.83e-194j)
| (0.061443633391352096668 - 1.6895029321091072976e-884j)  +/-  (2.17e-80, 1.93e-194j)
| (0.062887197349035618282 - 5.6663140381460452333e-884j)  +/-  (9.99e-81, 8.95e-195j)
| (0.056544177737583422532 + 2.2921454060538390428e-884j)  +/-  (2e-81, 1.74e-195j)
