Starting with polynomial:
P : 3/2*t^2 - 1/2
Extension levels are: 2 4 42
-------------------------------------------------
Trying to find an order 4 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^6 - 25/14*t^4 + 45/98*t^2 - 1/98
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 3/2*t^48 - 57390053754844371717624076504072556945141774987/3198085752699181907101131185999209621103205010*t^46 + 13060591299648405562811893224808375937808588369501/129842281559586785428305926151567910616790123406*t^44 - 3874072088471280174330858915728516651760293618229297/11036593932564876761406003722883272402427160489510*t^42 + 22369269292007072278830258404007524098160240739032175/26172494182939564891334237399980331697184409160838*t^40 - 3105084983255671431403194965383903048716757535001923/2013268783303043453179556723075410130552646858526*t^38 + 15306221741985291279893739023857463693513257473123755993/7157170524642319476053324150533083014114659582059930*t^36 - 158923926389683740590987380109112876822289675446670289/68163528806117328343364991909838885848711043638666*t^34 + 237190915527739611570347221793479657659583655097554971/116947230794809141765577192002174559054161104282025*t^32 - 10187918655597146763526210766519885024133931024643381155/7171204192337696573065193413573343961201158914573773*t^30 + 212052563338745563055216679519777182492828467135488439279/263356291891022305183256240877779700644111525655898905*t^28 - 7728358762830798207037237788733643932954889411450946501/20901293007223992474861606418871404813024724258404675*t^26 + 7692486581122165295932799632023971849652967770173091413/56015465259360299832629105202575364898906261012524529*t^24 - 11497469652485552469894338389802504556176927175245369777/280077326296801499163145526012876824494531305062622645*t^22 + 1019168154051609793303304771356961722885399997021804895/104028721195954842546311195376211391955111627594688411*t^20 - 245836646871419287643623874996073533307495420030194611295/133260791852018153301824641276926793094497994948795854491*t^18 + 49470753235129260597806450227132597573102334523428781959623/183455690116278324378845256157902551826758906379508959682610*t^16 - 1098272181589968945102209486457286935738729898676845448571/36691138023255664875769051231580510365351781275901791936522*t^14 + 4936891058647218879108067901685837783998303443030445757/2015996594684377190976321496240687382711636333840757798710*t^12 - 171388468950283028002598100592259177998620695344583995/1209597956810626314585792897744412429626981800304454679226*t^10 + 37464950321375838871829088503391702734548974869279439/6854388421926882449319493087218337101219563535058576515614*t^8 - 233539666222920053958984261589324165465399440498580991/1816412931810623849069665668112859331823184336790522776637710*t^6 + 4043715836404046766821842447902009727877002578251573/2542978104534873388697531935358003064552458071506731887292794*t^4 - 687498118402237793206870810621680518203286555804703/89004233658720568604413617737530107259336032502735616055247790*t^2 + 163781501139515446201574409760327516578673067380/26701270097616170581324085321259032177800809750820684816574337
-------------------------------------------------
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:
| (0.98772667438787143277 + 1.016651036932015818e-890j)  +/-  (2.27e-238, 2.27e-238j)
| (-0.9956442451847219142 - 7.5339730820195241375e-903j)  +/-  (2.46e-238, 2.46e-238j)
| (-0.93770416208652045297 - 1.4216333694434750019e-905j)  +/-  (7.33e-239, 7.33e-239j)
| (0.99934463929056535478 - 3.7393970396145026835e-902j)  +/-  (9.21e-239, 9.21e-239j)
| (0.91248695683407599658 - 4.0812689888926393008e-912j)  +/-  (3.39e-239, 3.39e-239j)
| (0.93770416208652045297 + 4.8860103841819659428e-921j)  +/-  (6.77e-239, 6.77e-239j)
| (-0.98772667438787143277 - 1.6329867437543431205e-931j)  +/-  (2.37e-238, 2.37e-238j)
| (-0.91248695683407599658 + 3.7907945854394720107e-933j)  +/-  (3e-239, 3e-239j)
| (-0.88317472704870307976 + 3.0277017243221924303e-934j)  +/-  (1.24e-239, 1.24e-239j)
| (0.95870932294967767065 - 1.6429409358502901106e-932j)  +/-  (1.29e-238, 1.29e-238j)
| (0.88317472704870307976 + 1.4221092401697433801e-943j)  +/-  (1.17e-239, 1.17e-239j)
| (-0.99934463929056535478 - 2.4396810668271394337e-948j)  +/-  (9.01e-239, 9.01e-239j)
| (-0.95870932294967767065 - 1.0309098475895041557e-952j)  +/-  (1.39e-238, 1.39e-238j)
| (-0.77214090234308301097 - 1.5549874699428612669e-956j)  +/-  (2.72e-241, 2.72e-241j)
| (0.9956442451847219142 + 1.699591568848374767e-955j)  +/-  (2.22e-238, 2.22e-238j)
| (0.77214090234308301097 - 6.9063434293478515292e-971j)  +/-  (2.5e-241, 2.5e-241j)
| (0.63037893579776753347 + 1.3001165117873790731e-975j)  +/-  (1.18e-243, 1.18e-243j)
| (-0.84990486621229774719 - 3.5360318094663722314e-971j)  +/-  (4.17e-240, 4.17e-240j)
| (-0.81283464154707637216 - 2.0670092945136450664e-972j)  +/-  (1.12e-240, 1.12e-240j)
| (-0.97540690655403729959 - 8.0258024555289012916e-971j)  +/-  (2.04e-238, 2.04e-238j)
| (0.84990486621229774719 + 4.5683929633610622098e-973j)  +/-  (3.94e-240, 3.94e-240j)
| (0.72801992815744523393 + 2.4446015923983236242e-981j)  +/-  (5.12e-242, 5.12e-242j)
| (0.97540690655403729959 + 1.7207846899689156266e-995j)  +/-  (2e-238, 2e-238j)
| (-0.68068745039433185052 - 5.3256801571843209624e-1016j)  +/-  (8.77e-243, 8.77e-243j)
| (-0.72801992815744523393 + 8.3608092280683085816e-1016j)  +/-  (4.96e-242, 4.96e-242j)
| (0.21940855261756467465 - 2.3720920365487397918e-1022j)  +/-  (3.28e-251, 3.28e-251j)
| (0.68068745039433185052 - 2.2804555723560735981e-1016j)  +/-  (8.59e-243, 8.59e-243j)
| (0.81283464154707637216 + 6.8224523693742797968e-1021j)  +/-  (1.01e-240, 1.01e-240j)
| (-0.15655801081562154215 - 1.0372023605393776945e-1027j)  +/-  (1.7e-252, 1.7e-252j)
| (-0.63037893579776753347 + 9.5335192753606436136e-1024j)  +/-  (1.24e-243, 1.24e-243j)
| (-0.28201079706809193157 - 3.5911362363616822261e-1028j)  +/-  (5.42e-250, 5.42e-250j)
| (0.46426647825903622183 - 3.9834202300389390427e-1028j)  +/-  (1.49e-246, 1.49e-246j)
| (0.5218790185193069337 - 4.8217913958709713663e-1027j)  +/-  (1.67e-245, 1.67e-245j)
| (0.15655801081562154215 - 1.2405869710874641457e-1031j)  +/-  (1.8e-252, 1.8e-252j)
| (-0.5218790185193069337 + 2.6123371852961235863e-1025j)  +/-  (1.59e-245, 1.59e-245j)
| (-0.46426647825903622183 - 3.1629215618436207393e-1027j)  +/-  (1.54e-246, 1.54e-246j)
| (-0.031224697471064979924 + 3.9611361958899730864e-1032j)  +/-  (4.61e-255, 4.61e-255j)
| (0.57735026918962576451 + 3.3886225690793266311e-1028j)  +/-  (1.46e-244, 1.46e-244j)
| (0.28201079706809193157 + 1.9323366378606411025e-1033j)  +/-  (5.56e-250, 5.56e-250j)
| (-0.21940855261756467465 - 3.4859712550027611577e-1033j)  +/-  (3.1e-251, 3.1e-251j)
| (-0.57735026918962576451 + 1.794464543519706662e-1029j)  +/-  (1.59e-244, 1.59e-244j)
| (-0.093784438623812992495 - 1.2253690595395301737e-1037j)  +/-  (8.53e-254, 8.53e-254j)
| (0.34395902984556538884 - 8.4483751242160954239e-1034j)  +/-  (8.77e-249, 8.77e-249j)
| (0.40484056051234727036 + 1.5236822432220804855e-1032j)  +/-  (1.18e-247, 1.18e-247j)
| (0.031224697471064979924 - 3.6654794952947810173e-1038j)  +/-  (4.61e-255, 4.61e-255j)
| (-0.34395902984556538884 + 2.8286799296372565166e-1034j)  +/-  (8.32e-249, 8.32e-249j)
| (-0.40484056051234727036 - 4.9806567483703700673e-1033j)  +/-  (1.24e-247, 1.24e-247j)
| (0.093784438623812992495 - 3.3132719080192696484e-1039j)  +/-  (8.53e-254, 8.53e-254j)
-------------------------------------------------
The weights are:
| (0.010116202679665658535 - 5.0501465225241235035e-892j)  +/-  (4.31e-65, 2.16e-179j)
| (0.005737125856901183451 - 3.5687635660427851294e-893j)  +/-  (1.22e-65, 6.13e-180j)
| (0.023128951252590347312 - 8.7938205458489681987e-893j)  +/-  (1.16e-65, 5.82e-180j)
| (0.0018459612826232833139 + 2.2498981316583358424e-891j)  +/-  (1.05e-65, 5.26e-180j)
| (0.027285940474457825757 - 2.5082236500628817656e-891j)  +/-  (3.41e-66, 1.71e-180j)
| (0.023128951252590347312 + 3.3848546324625817558e-891j)  +/-  (4.58e-66, 2.3e-180j)
| (0.010116202679665658535 + 5.2062216260431887506e-893j)  +/-  (3.78e-67, 1.9e-181j)
| (0.027285940474457825757 + 9.9314117052048107783e-893j)  +/-  (1.46e-67, 7.33e-182j)
| (0.031315612518658954833 - 1.1126004875898295185e-892j)  +/-  (4.91e-68, 2.47e-182j)
| (0.018865402152665406352 - 5.1455853563639947089e-891j)  +/-  (8.15e-68, 4.09e-182j)
| (0.031315612518658954833 + 1.9909393028304823974e-891j)  +/-  (1.56e-68, 7.82e-183j)
| (0.0018459612826232833139 + 1.3154654963439256324e-893j)  +/-  (5.02e-68, 2.52e-182j)
| (0.018865402152665406352 + 7.6710078754061633055e-893j)  +/-  (3.38e-68, 1.7e-182j)
| (0.042441686662309642558 + 1.5440664984084632539e-892j)  +/-  (8.22e-71, 4.13e-185j)
| (0.005737125856901183451 - 8.9398403337960172929e-891j)  +/-  (8.45e-69, 4.24e-183j)
| (0.042441686662309642558 - 1.2604507899938857138e-891j)  +/-  (1.13e-71, 5.67e-186j)
| (0.051712991167168253379 + 9.9116092937218846857e-892j)  +/-  (1.08e-72, 5.4e-187j)
| (0.035197893192343422921 + 1.2415633828737530133e-892j)  +/-  (1.91e-70, 9.57e-185j)
| (0.038913078634408741104 - 1.383931077443381112e-892j)  +/-  (4.49e-71, 2.25e-185j)
| (0.014517850993076596372 - 6.5067024378995767406e-893j)  +/-  (2.14e-69, 1.07e-183j)
| (0.035197893192343422921 - 1.655424538545770247e-891j)  +/-  (7.54e-72, 3.78e-186j)
| (0.045764310873468725584 + 1.141023366668332091e-891j)  +/-  (2.79e-73, 1.4e-187j)
| (0.014517850993076596372 + 1.0368317186317252797e-890j)  +/-  (1.24e-70, 6.21e-185j)
| (0.048861411130099471113 + 1.9394373590401150345e-892j)  +/-  (1.25e-74, 6.27e-189j)
| (0.045764310873468725584 - 1.7271283853444292195e-892j)  +/-  (1.09e-73, 5.49e-188j)
| (0.062790607258091329483 - 9.6675530042457291416e-892j)  +/-  (4.39e-78, 2.2e-192j)
| (0.048861411130099471113 - 1.0538668779370720013e-891j)  +/-  (1.93e-74, 9.69e-189j)
| (0.038913078634408741104 + 1.4247948985866762893e-891j)  +/-  (5.67e-73, 2.84e-187j)
| (0.062854246288521747497 - 7.1854610586486352841e-892j)  +/-  (3.02e-79, 1.52e-193j)
| (0.051712991167168253379 - 2.1889122345374835512e-892j)  +/-  (1.03e-76, 5.17e-191j)
| (0.062345050433523817373 - 5.230261797889884182e-892j)  +/-  (2.49e-79, 1.25e-193j)
| (0.058576266747672444691 - 9.0841803193635967445e-892j)  +/-  (9.22e-79, 4.63e-193j)
| (0.056594220091437827988 + 9.2105038222996962808e-892j)  +/-  (2.59e-78, 1.3e-192j)
| (0.062854246288521747497 + 9.8923520650990402055e-892j)  +/-  (4.54e-80, 2.28e-194j)
| (0.056594220091437827988 - 2.8422598266247880115e-892j)  +/-  (1.12e-79, 5.63e-194j)
| (0.058576266747672444691 + 3.2749512647370444059e-892j)  +/-  (3.88e-80, 1.95e-194j)
| (0.062470110707328612052 - 9.1328398367641587612e-892j)  +/-  (1.55e-81, 7.79e-196j)
| (0.054298114469072824632 - 9.4794686171399171052e-892j)  +/-  (3.43e-79, 1.72e-193j)
| (0.062345050433523817373 + 9.4103868195830679332e-892j)  +/-  (2.43e-81, 1.22e-195j)
| (0.062790607258091329483 + 6.1532096820397161327e-892j)  +/-  (1.43e-81, 7.15e-196j)
| (0.054298114469072824632 + 2.4855968074050983672e-892j)  +/-  (9.43e-81, 4.73e-195j)
| (0.06266881042025220087 + 8.2317228933212317166e-892j)  +/-  (9.09e-82, 4.56e-196j)
| (0.061482177626424705367 - 9.2021255383110319074e-892j)  +/-  (6.05e-82, 3.04e-196j)
| (0.060215977087236977464 + 9.0860561544752741254e-892j)  +/-  (7.49e-82, 3.76e-196j)
| (0.062470110707328612052 + 9.7291170381422942737e-892j)  +/-  (4.41e-83, 2.21e-197j)
| (0.061482177626424705367 + 4.4485201453722119785e-892j)  +/-  (2e-83, 9.94e-198j)
| (0.060215977087236977464 - 3.8031456073447731297e-892j)  +/-  (1.82e-83, 9.02e-198j)
| (0.06266881042025220087 - 9.9589206463082005117e-892j)  +/-  (1.96e-83, 1e-197j)
