Starting with polynomial:
P : 3/2*t^2 - 1/2
Extension levels are: 2 3 42
-------------------------------------------------
Trying to find an order 3 Kronrod extension for:
P1 : 3/2*t^2 - 1/2
Solvable: 1
-------------------------------------------------
Trying to find an order 42 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^47 - 419757505899975397972370036053758346919375/23742308300227482407777430419893170688408*t^45 + 67213429085150289851175207321186931769569815/688526940706596989825545482176901949963832*t^43 - 70125799592829610682497632222478387760970033/209017107000216943339897735660845234810449*t^41 + 55816233622067572464097630325347009990914700725/69393679524072025188846048239400617957069068*t^39 - 198287470915277901295384240854896410068170405787/138787359048144050377692096478801235914138136*t^37 + 21372290588851834980885568884350265236791672154805/10964201364803379979837675621825297637216912744*t^35 - 2021927696912791041140682764639298161708400671065/967429532188533527632736084278702732695609948*t^33 + 5042102642488576542065993308183272296952659811686/2821669468883222788928813579146216303695529015*t^31 - 607666626247824471974878242381433632007750326013285/494356490948340632620328139066417096407456683428*t^29 + 1772549652225501712909379553177972689469765545010851/2593545137241294451924381616284404963911041220940*t^27 - 56076573635047430179206964160923362116568596991/182387140452974293384274375266132557237063377*t^25 + 215590025904072794694298660474283508660205527101205/1930750268835185869765928536567279250911552908922*t^23 - 125728572241339902470428591421559786242094421476449/3861500537670371739531857073134558501823105817844*t^21 + 29173434498107480731409431367182083922204289408025/3861500537670371739531857073134558501823105817844*t^19 - 1135235155007855648107575334640059083303674819145219/824430364792624366390051485114228240139233092109694*t^17 + 9418567731089059881057753846073048076646078164231305/48641391522764837617013037621739466168214752434471946*t^15 - 569744709015480662940408616289624852502174077846595/27795080870151335781150307212422552096122715676841112*t^13 + 555651184839555373340653665000031432707860176601/351836466710776402293041863448386735393958426289128*t^11 - 46646089212417675909926493963509456102723138068250/552427232294257798650362355846898222910438974077217101*t^9 + 36571359552173136624555429943680030996469167184977/12521683932003176769408213399196359719303283412416920956*t^7 - 10252588659037341282053435103477767534575386072645/175303575048044474771714987588749036070245967773836893384*t^5 + 681914383622955789474583634937795570712041830995/1227125025336311323402004913121243252491721774416858253688*t^3 - 972278741126383990987645646175414596497779873/613562512668155661701002456560621626245860887208429126844*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:
| (0.98256051976543094059 + 2.6052402846558796198e-908j)  +/-  (5.88e-239, 5.88e-239j)
| (-0.99287902253491320602 - 4.1395086842837292244e-928j)  +/-  (4.52e-239, 4.52e-239j)
| (-0.92582009977255146157 + 2.2852207363403808687e-928j)  +/-  (3.69e-239, 3.69e-239j)
| (0.13672421657525195307 - 9.8125991902586686903e-943j)  +/-  (4.79e-253, 4.79e-253j)
| (0.96779613025246020351 + 1.0159203860636689489e-926j)  +/-  (6.17e-239, 6.17e-239j)
| (0.92582009977255146157 - 1.8771231659743586421e-945j)  +/-  (3.62e-239, 3.62e-239j)
| (-0.98256051976543094059 + 4.3586253188291228583e-956j)  +/-  (6.37e-239, 6.37e-239j)
| (-0.89953428332451963077 - 5.0819441061210137976e-957j)  +/-  (2.38e-239, 2.38e-239j)
| (-0.99864596961390006453 - 1.9486242176439636076e-956j)  +/-  (1.38e-239, 1.38e-239j)
| (0.99864596961390006453 - 2.4527898230041512158e-953j)  +/-  (1.35e-239, 1.35e-239j)
| (0.8709296577148032401 - 4.121655055184827534e-965j)  +/-  (1.33e-239, 1.33e-239j)
| (-0.3996135626718536969 + 1.9573310920787435988e-979j)  +/-  (6.12e-248, 6.12e-248j)
| (-0.94877333619597980038 - 2.6314612862636314026e-970j)  +/-  (5.36e-239, 5.36e-239j)
| (-0.8709296577148032401 - 1.47045842389441645e-970j)  +/-  (1.23e-239, 1.23e-239j)
| (0.99287902253491320602 - 2.9922209621913249037e-968j)  +/-  (4.29e-239, 4.29e-239j)
| (0.84086956349999911183 - 5.4819586309636995296e-975j)  +/-  (5.45e-240, 5.45e-240j)
| (0.80821215790252711185 - 2.1330965380325495531e-979j)  +/-  (1.76e-240, 1.76e-240j)
| (0.33602650940049245674 + 6.9847330571025128628e-1000j)  +/-  (3.96e-249, 3.96e-249j)
| (-0.7708424786322375574 + 5.382136534569840749e-992j)  +/-  (3.5e-241, 3.5e-241j)
| (-0.96779613025246020351 + 3.7091878662858982625e-989j)  +/-  (6.52e-239, 6.52e-239j)
| (0.89953428332451963077 - 1.1629766621485948713e-988j)  +/-  (2.34e-239, 2.34e-239j)
| (0.72844980189944171066 + 5.8821455278352319049e-1003j)  +/-  (6.92e-242, 6.92e-242j)
| (0.94877333619597980038 - 2.3671088225654310492e-1009j)  +/-  (6.18e-239, 6.18e-239j)
| (-0.63117266258682944091 - 1.5805203266606474221e-1027j)  +/-  (1.14e-243, 1.14e-243j)
| (-0.80821215790252711185 + 1.9299213601210959802e-1024j)  +/-  (1.66e-240, 1.66e-240j)
| (0.06852801475491600387 - 5.4064222995859412011e-1040j)  +/-  (2e-254, 2e-254j)
| (0.7708424786322375574 + 1.2180971829173762831e-1026j)  +/-  (3.6e-241, 3.6e-241j)
| (0.52059515072219585487 - 4.0146831438521921336e-1035j)  +/-  (1.13e-245, 1.13e-245j)
| (-0.84086956349999911183 - 2.1686772983862075458e-1030j)  +/-  (5.1e-240, 5.1e-240j)
| (-0.72844980189944171066 + 1.3186922119771623693e-1033j)  +/-  (7.14e-242, 7.14e-242j)
| (-0.2042579101096971977 + 4.5677955657479793996e-1045j)  +/-  (1.03e-251, 1.03e-251j)
| (0.68169076340587233883 + 2.2975643999694807417e-1035j)  +/-  (1.04e-242, 1.04e-242j)
| (0.63117266258682944091 - 9.2797045056705979246e-1039j)  +/-  (1.15e-243, 1.15e-243j)
| (-0.46124245185583986547 - 7.1760463136689364439e-1040j)  +/-  (9.71e-247, 9.71e-247j)
| (-0.68169076340587233883 - 1.6797681901624740239e-1039j)  +/-  (9.9e-243, 9.9e-243j)
| (-0.57735026918962576451 - 5.5441001818696909099e-1043j)  +/-  (1.2e-244, 1.2e-244j)
| (0.2708005418591786523 + 2.8860674171824664305e-1050j)  +/-  (2.01e-250, 2.01e-250j)
| (0.57735026918962576451 - 6.5434842182700383311e-1046j)  +/-  (1.27e-244, 1.27e-244j)
| (0.2042579101096971977 + 1.2042983316987307997e-1052j)  +/-  (1.03e-251, 1.03e-251j)
| (-0.13672421657525195307 + 4.2292357086455341376e-1054j)  +/-  (4.64e-253, 4.64e-253j)
| (-0.52059515072219585487 - 3.0666807804090715164e-1046j)  +/-  (1.1e-245, 1.1e-245j)
| (-0.06852801475491600387 - 3.6338223855594723285e-1055j)  +/-  (2e-254, 2e-254j)
| (0.3996135626718536969 - 2.2282400887628300498e-1047j)  +/-  (6.49e-248, 6.49e-248j)
| (0.46124245185583986547 - 2.5968442785211594732e-1047j)  +/-  (9.07e-247, 9.07e-247j)
| (-6.5068882901216408653e-1067 + 9.4560484642156167303e-1067j)  +/-  (5.39e-1065, 5.39e-1065j)
| (-0.33602650940049245674 + 8.1964293700510625986e-1050j)  +/-  (3.62e-249, 3.62e-249j)
| (-0.2708005418591786523 - 3.5178822664338189778e-1051j)  +/-  (1.95e-250, 1.95e-250j)
-------------------------------------------------
The weights are:
| (0.012564759810141628257 - 1.141914905582957913e-908j)  +/-  (5.52e-67, 1.37e-181j)
| (0.0080548477449811610362 + 7.962938242807930214e-911j)  +/-  (1.94e-67, 4.83e-182j)
| (0.024751121445098889949 + 7.4017742213838404441e-910j)  +/-  (1.12e-67, 2.79e-182j)
| (0.067919916676717261093 + 1.9231917145420280211e-909j)  +/-  (5.28e-69, 1.32e-183j)
| (0.016933675947165785285 + 3.8455176142254009678e-908j)  +/-  (1.06e-67, 2.64e-182j)
| (0.024751121445098889949 + 2.4894779552314555911e-908j)  +/-  (5.14e-68, 1.28e-182j)
| (0.012564759810141628257 - 1.6657609259641762775e-910j)  +/-  (4.15e-68, 1.03e-182j)
| (0.027647440620891385941 - 1.1385784566434989927e-909j)  +/-  (1.23e-68, 3.06e-183j)
| (0.0034733782003790468069 - 2.1979385069161916618e-911j)  +/-  (2.16e-68, 5.39e-183j)
| (0.0034733782003790468069 + 2.7071484317695394544e-909j)  +/-  (5.03e-70, 1.25e-184j)
| (0.029372429337360272206 + 2.7552705288515212419e-908j)  +/-  (1.49e-70, 3.71e-185j)
| (0.062660985138778836733 + 1.3059819019213866007e-909j)  +/-  (3.28e-71, 8.17e-186j)
| (0.021059337576098864796 - 4.7165137798780701978e-910j)  +/-  (5.62e-69, 1.4e-183j)
| (0.029372429337360272206 + 1.6594273228710659912e-909j)  +/-  (6.86e-70, 1.71e-184j)
| (0.0080548477449811610362 - 1.52447534580907788e-908j)  +/-  (7.03e-70, 1.75e-184j)
| (0.030953404563607766803 - 2.7075809457832705908e-908j)  +/-  (1.11e-71, 2.76e-186j)
| (0.034787813994292290032 + 2.2707245972795968589e-908j)  +/-  (2.7e-72, 6.71e-187j)
| (0.064459939725262590215 - 2.6884327100390009417e-909j)  +/-  (1.21e-74, 3.01e-189j)
| (0.039968181194633782552 - 2.0279459622741002731e-909j)  +/-  (5.99e-74, 1.49e-188j)
| (0.016933675947165785285 + 2.9110942316572166649e-910j)  +/-  (7.28e-71, 1.81e-185j)
| (0.027647440620891385941 - 2.5810065444601828018e-908j)  +/-  (8.21e-72, 2.04e-186j)
| (0.044692390439354060122 + 1.204637917433363595e-908j)  +/-  (1.51e-74, 3.75e-189j)
| (0.021059337576098864796 - 2.6960408601275482415e-908j)  +/-  (1.04e-71, 2.59e-186j)
| (0.052237008132905848633 + 1.4721850884725889145e-909j)  +/-  (1.5e-76, 3.73e-191j)
| (0.034787813994292290032 + 2.2107614144139085007e-909j)  +/-  (1.1e-74, 2.74e-189j)
| (0.068417353726511115641 - 1.7639339716920703244e-909j)  +/-  (1.01e-77, 2.51e-192j)
| (0.039968181194633782552 - 1.6795009588261155288e-908j)  +/-  (2.05e-74, 5.11e-189j)
| (0.058108132859942922288 + 4.3507714663999884086e-909j)  +/-  (9.11e-78, 2.27e-192j)
| (0.030953404563607766803 - 2.1039453988115918726e-909j)  +/-  (9.45e-75, 2.35e-189j)
| (0.044692390439354060122 + 1.7890681434915320848e-909j)  +/-  (1.42e-76, 3.55e-191j)
| (0.067092697558328593621 - 1.3915443498982028763e-909j)  +/-  (1.44e-79, 3.59e-194j)
| (0.048724762581942064439 - 8.8579225829549309737e-909j)  +/-  (8.2e-77, 2.04e-191j)
| (0.052237008132905848633 + 6.7609448627728192044e-909j)  +/-  (1.42e-77, 3.53e-192j)
| (0.060543858900562280476 - 1.3113757312060747832e-909j)  +/-  (8.88e-80, 2.21e-194j)
| (0.048724762581942064439 - 1.601369358302103395e-909j)  +/-  (2.73e-78, 6.8e-193j)
| (0.0553465950099878847 - 1.3880804908064771309e-909j)  +/-  (2.16e-79, 5.38e-194j)
| (0.06593829142037861348 + 2.3715700275621408345e-909j)  +/-  (1.86e-81, 4.62e-196j)
| (0.0553465950099878847 - 5.3436005887565312056e-909j)  +/-  (2.71e-80, 6.75e-195j)
| (0.067092697558328593621 - 2.1219387677221113023e-909j)  +/-  (1.23e-81, 3.06e-196j)
| (0.067919916676717261093 + 1.4533436554066271574e-909j)  +/-  (3.44e-83, 8.56e-198j)
| (0.058108132859942922288 + 1.3371241485895004875e-909j)  +/-  (5.03e-82, 1.25e-196j)
| (0.068417353726511115641 - 1.5339269089778460101e-909j)  +/-  (2.27e-83, 5.64e-198j)
| (0.062660985138778836733 + 3.0964984292355275053e-909j)  +/-  (4.93e-83, 1.23e-197j)
| (0.060543858900562280476 - 3.6318867389719986037e-909j)  +/-  (5.96e-83, 1.48e-197j)
| (0.068583354789354109789 + 1.6360972040726360591e-909j)  +/-  (5.29e-84, 1.32e-198j)
| (0.064459939725262590215 - 1.3182013345886437114e-909j)  +/-  (5.86e-85, 1.47e-199j)
| (0.06593829142037861348 + 1.3467696437232417354e-909j)  +/-  (5.82e-85, 1.44e-199j)
