Starting with polynomial:
P : 3/2*t^2 - 1/2
Extension levels are: 2 4 37
-------------------------------------------------
Trying to find an order 4 Kronrod extension for:
P1 : 3/2*t^2 - 1/2
Solvable: 1
-------------------------------------------------
Trying to find an order 37 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^43 - 33085872071813179331199056227371599/2143887683808745850772115948692658*t^41 + 1069530363776331564108745616464301022375/14526982945488061884831857668341450608*t^39 - 109897154274980375723373642501414970007081/508444403092082165969115018391950771280*t^37 + 3244207722013498516547969764926475070529399/7423288285144399623149079268522481260688*t^35 - 242965208329436628625668801643731329292824271/376466763032323123745417591475068692506320*t^33 + 141748692924458308889686807947255068112703809/196789444312350723776013740998331361991940*t^31 - 1635627649788861810139333870477872975177466755/2636978553785499698598584129377640250691996*t^29 + 785565425480650247725304887015257909036577131/1883556109846785498998988663841171607637140*t^27 - 580767230356481557074581047694583277434410589/2636978553785499698598584129377640250691996*t^25 + 205847484560440605610884068679862569898066167603/2251979684932816742603190846488504774090964584*t^23 - 15600669485101519258668288574209792913980048873/525165222968522481476633438509177002653624152*t^21 + 562550566609870571887501859806226060714596725/75023603281217497353804776929882428950517736*t^19 - 13173951219041775590497737063171340944924511377/9077855997027317179810378008515773903012646056*t^17 + 50861490581208818779171411594328101543591302165/240563183921223905264975017225668008429835120484*t^15 - 777025534818659536543874249582254716814841103/34366169131603415037853573889381144061405017212*t^13 + 2889077877002003483271251237415218081290054179/1683942287448567336854825120579676059008845843388*t^11 - 94569114233176628612723459316028393641733275/1071599637467270123453070531277975673914720082156*t^9 + 582429886687917481087613084405582904845580909/201460731843846783209177259880259426695967375445328*t^7 - 1586138437655751868165881689673023248481175/28780104549120969029882465697179918099423910777904*t^5 + 15069580880921855377120388958826547915541/28780104549120969029882465697179918099423910777904*t^3 - 48206250254517812482969623263251400697/28780104549120969029882465697179918099423910777904*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:
| (-0.9985033617835308753 - 2.5730076492975425665e-900j)  +/-  (1.73e-241, 1.73e-241j)
| (-0.99206935952458725579 - 1.1708320998004419471e-903j)  +/-  (4.95e-241, 4.95e-241j)
| (-0.94058083526894862902 - 4.3630329377632950453e-909j)  +/-  (3.43e-241, 3.43e-241j)
| (0.98035068300028038832 - 3.3129774951971392922e-916j)  +/-  (5.97e-241, 5.97e-241j)
| (0.87902558400256699957 - 3.1122657092814867072e-929j)  +/-  (7.34e-242, 7.34e-242j)
| (0.96320947642682331194 - 4.6658371149986450952e-938j)  +/-  (5.12e-241, 5.12e-241j)
| (-0.84035449227944888752 + 3.7739874914486076303e-952j)  +/-  (2.47e-242, 2.47e-242j)
| (-0.91248695683407599658 + 4.9404698733349348612e-951j)  +/-  (1.83e-241, 1.83e-241j)
| (-0.98035068300028038832 + 1.4654665213842176313e-951j)  +/-  (5.95e-241, 5.95e-241j)
| (0.9985033617835308753 - 2.1486237433064177624e-961j)  +/-  (1.88e-241, 1.88e-241j)
| (0.84035449227944888752 + 2.4803138016421962668e-980j)  +/-  (2.43e-242, 2.43e-242j)
| (0.99206935952458725579 - 2.0613787651903489799e-988j)  +/-  (4.6e-241, 4.6e-241j)
| (-0.96320947642682331194 + 9.7304575285962173157e-1002j)  +/-  (5.48e-241, 5.48e-241j)
| (-0.79667953649742200176 + 1.0835533430473445864e-1004j)  +/-  (6.24e-243, 6.24e-243j)
| (0.94058083526894862902 + 1.71526280215166525e-1001j)  +/-  (3.26e-241, 3.26e-241j)
| (0.79667953649742200176 + 2.5438110673572812881e-1013j)  +/-  (6.35e-243, 6.35e-243j)
| (0.91248695683407599658 - 2.1177739646090014769e-1020j)  +/-  (1.69e-241, 1.69e-241j)
| (-0.30290567277598982598 - 5.4916276522401460748e-1032j)  +/-  (2.89e-250, 2.89e-250j)
| (-0.74824654784780181402 - 2.4321660041428302732e-1023j)  +/-  (1.38e-243, 1.38e-243j)
| (-0.87902558400256699957 + 1.3845968393651333991e-1025j)  +/-  (6.87e-242, 6.87e-242j)
| (0.22844979333481706632 - 2.5273518030746870431e-1036j)  +/-  (2.63e-251, 2.63e-251j)
| (0.74824654784780181402 - 1.010634527388518815e-1027j)  +/-  (1.36e-243, 1.36e-243j)
| (0.16268981350277032876 + 9.4264327477744136528e-1037j)  +/-  (1.76e-251, 1.76e-251j)
| (-0.63825786066849826941 - 1.8847147829075653301e-1030j)  +/-  (3.75e-245, 3.75e-245j)
| (-0.69533579136017117188 + 4.8285318662268198e-1031j)  +/-  (2.55e-244, 2.55e-244j)
| (3.512872417548596387e-1042 - 1.5190382294174376883e-1043j)  +/-  (1.51e-1040, 1.51e-1040j)
| (0.69533579136017117188 + 5.6825809718850532073e-1030j)  +/-  (2.34e-244, 2.34e-244j)
| (0.51297422214928271025 - 4.2003028084944280425e-1034j)  +/-  (5.05e-247, 5.05e-247j)
| (-0.077159460936340872255 + 1.7009912972424668663e-1043j)  +/-  (3.42e-254, 3.42e-254j)
| (-0.57735026918962576451 - 2.6859478167180089479e-1036j)  +/-  (5.36e-246, 5.36e-246j)
| (-0.22844979333481706632 + 2.4032822135317191849e-1040j)  +/-  (2.71e-251, 2.71e-251j)
| (0.44551098658899530318 + 2.5740408484520234705e-1035j)  +/-  (4.84e-248, 4.84e-248j)
| (0.63825786066849826941 - 4.0380577217227691496e-1035j)  +/-  (3.91e-245, 3.91e-245j)
| (0.077159460936340872255 + 3.5146935844353894865e-1046j)  +/-  (3.42e-254, 3.42e-254j)
| (-0.44551098658899530318 - 6.6547730356795441204e-1039j)  +/-  (4.85e-248, 4.85e-248j)
| (-0.37535635160613926943 + 7.0248439979211260651e-1040j)  +/-  (3.96e-249, 3.96e-249j)
| (0.15655801081562154215 - 4.0593172507079669743e-1044j)  +/-  (1.17e-251, 1.17e-251j)
| (0.57735026918962576451 + 5.7258171756129492799e-1039j)  +/-  (5.11e-246, 5.11e-246j)
| (0.30290567277598982598 - 3.1630089333181873165e-1042j)  +/-  (3.18e-250, 3.18e-250j)
| (-0.16268981350277032876 - 1.6284845805480470031e-1042j)  +/-  (1.76e-251, 1.76e-251j)
| (-0.51297422214928271025 - 3.8467985078550463212e-1040j)  +/-  (5.21e-247, 5.21e-247j)
| (-0.15655801081562154215 - 2.5871303766799835097e-1044j)  +/-  (1.37e-251, 1.37e-251j)
| (0.37535635160613926943 + 1.4422775355525946495e-1041j)  +/-  (3.7e-249, 3.7e-249j)
-------------------------------------------------
The weights are:
| (0.0038464379241988277694 - 3.2261880566152797941e-900j)  +/-  (2.06e-68, 5.55e-185j)
| (0.0090495000713412469043 + 5.1738125825654669341e-900j)  +/-  (1.57e-68, 4.24e-185j)
| (0.025371803206479954114 - 2.1154747931545783424e-900j)  +/-  (1.86e-69, 5.02e-186j)
| (0.014411860112554477184 - 3.1102633047691684769e-902j)  +/-  (1.8e-70, 4.86e-187j)
| (0.036096860660691831372 - 1.0174803806504134546e-901j)  +/-  (7.06e-71, 1.91e-187j)
| (0.019881532258150625869 + 4.6665677809429247485e-902j)  +/-  (9.87e-71, 2.66e-187j)
| (0.041210882162021703261 + 1.4677356851439635054e-900j)  +/-  (1.85e-70, 5e-187j)
| (0.03079939124163405382 + 1.8043457732682826761e-900j)  +/-  (6.46e-70, 1.74e-186j)
| (0.014411860112554477184 - 3.3899612186231426464e-900j)  +/-  (1.77e-69, 4.76e-186j)
| (0.0038464379241988277694 - 4.9542919184576399447e-903j)  +/-  (2.75e-72, 7.42e-189j)
| (0.041210882162021703261 + 1.2623249435048464247e-901j)  +/-  (3.36e-73, 9.07e-190j)
| (0.0090495000713412469043 + 1.6719568018726328793e-902j)  +/-  (5.63e-72, 1.52e-188j)
| (0.019881532258150625869 + 2.5936010354553524844e-900j)  +/-  (2.3e-71, 6.2e-188j)
| (0.046097967851702355833 - 1.3939773361533024629e-900j)  +/-  (1.45e-73, 3.92e-190j)
| (0.025371803206479954114 - 6.3193950016638665336e-902j)  +/-  (6.02e-73, 1.62e-189j)
| (0.046097967851702355833 - 1.56719666677277144e-901j)  +/-  (4.12e-75, 1.11e-191j)
| (0.03079939124163405382 + 8.1218184495942105676e-902j)  +/-  (2.46e-73, 6.64e-190j)
| (0.073476720473924630589 - 5.1614351517736710771e-900j)  +/-  (2.56e-78, 6.9e-195j)
| (0.050721231878658630855 + 1.3696629132076819834e-900j)  +/-  (2.62e-76, 7.08e-193j)
| (0.036096860660691831372 - 1.5988884124360381187e-900j)  +/-  (1.37e-74, 3.71e-191j)
| (0.075532232385904928704 + 7.7498953635665370927e-900j)  +/-  (6.93e-80, 1.87e-196j)
| (0.050721231878658630855 + 1.9623298731937605661e-901j)  +/-  (5.1e-78, 1.38e-194j)
| (-0.04201970140269865242 - 1.0514478498445977532e-898j)  +/-  (5.39e-80, 1.46e-196j)
| (0.059051096704624902804 + 1.4734988068747858124e-900j)  +/-  (5.75e-79, 1.55e-195j)
| (0.055048459806855162581 - 1.3939350104671992404e-900j)  +/-  (3.38e-78, 9.13e-195j)
| (0.077190638830107767269 + 8.671530195361437527e-900j)  +/-  (3.24e-81, 8.75e-198j)
| (0.055048459806855162581 - 2.4949139577514376211e-901j)  +/-  (3.65e-80, 9.84e-197j)
| (0.065984640101126009027 + 6.0689193927576012115e-901j)  +/-  (1.1e-81, 2.96e-198j)
| (0.077122601715986580372 - 1.2003608790602382926e-899j)  +/-  (1.23e-81, 3.32e-198j)
| (0.062703827462119193106 - 1.6259956763139549682e-900j)  +/-  (3.92e-81, 1.06e-197j)
| (0.075532232385904928704 + 1.2348165646988656834e-899j)  +/-  (5.6e-82, 1.51e-198j)
| (0.068875683172449330823 - 8.9869438545209597031e-901j)  +/-  (8.34e-83, 2.25e-199j)
| (0.059051096704624902804 + 3.2431347645220064056e-901j)  +/-  (3.95e-82, 1.07e-198j)
| (0.077122601715986580372 - 1.0281526038871321505e-899j)  +/-  (1.78e-82, 4.8e-199j)
| (0.068875683172449330823 - 2.3467314040761340387e-900j)  +/-  (1.54e-83, 4.16e-200j)
| (0.07136689818040716212 + 3.2081625256746789444e-900j)  +/-  (2.03e-83, 5.47e-200j)
| (0.11677475461681316168 + 1.0534018296720544409e-898j)  +/-  (2.43e-82, 6.57e-199j)
| (0.062703827462119193106 - 4.3455533088366443588e-901j)  +/-  (3.33e-84, 8.98e-201j)
| (0.073476720473924630589 - 2.758769349311062014e-900j)  +/-  (1.99e-84, 5.38e-201j)
| (-0.04201970140269865242 - 1.46077222641775999e-898j)  +/-  (1.58e-84, 4.27e-201j)
| (0.065984640101126009027 + 1.8892808152505444972e-900j)  +/-  (2.36e-86, 6.35e-203j)
| (0.11677475461681316168 + 1.4451566823833377871e-898j)  +/-  (1.54e-84, 4.16e-201j)
| (0.07136689818040716212 + 1.4551416798513218583e-900j)  +/-  (2.36e-86, 6.29e-203j)
