Starting with polynomial:
P : 3/2*t^2 - 1/2
Extension levels are: 2 6 39
-------------------------------------------------
Trying to find an order 6 Kronrod extension for:
P1 : 3/2*t^2 - 1/2
Solvable: 1
-------------------------------------------------
Trying to find an order 39 Kronrod extension for:
P2 : 3/2*t^8 - 161/52*t^6 + 105/52*t^4 - 245/572*t^2 + 25/1716
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 3/2*t^47 - 12085604879212642500508495564069472085330342395182695066755756587983377/679952931579439683395895285116044556949008937608580102032880981764164*t^45 + 2292919297197187551753815495271272800829472905395453689117020581839832455/23238391367509085650177362391318934563963187808857943487123755906175252*t^43 - 12450609003328803294384061987582206619186969194524909233963843231397073155/36517472148942848878850140900644040029085009413919625479765902138275396*t^41 + 120915980341384939403715013343823430231792105945375188004069224469776152771555/147128895288090738132887217688694837277183502928682171057976819715111570484*t^39 - 19379350879127042472583659883455410895918690580185112345578055486909326539807/13203875218161989319618083638729023858208775903856092274433817153920269146*t^37 + 104432620236673671019885688446778623967830350802462758241128511995419670359763/51872366928493529469928185723578308014391619622291791078132853104686771645*t^35 - 580059368716517726119519061640041596113781657806963278334904982787893087373013/267295255466825481268571121728556457768276816406632994026143407762974188006*t^33 + 536312817005772553307666565223119924661419419925254685529195882253245177529312/287544896032494078334371964283750128811328090376832463270548211381381323461*t^31 - 15574318734327737068712911591985278526514986285119294644900406387332189722720971/12076885633364751290043622499917505410075779795826963457363024878018015585362*t^29 + 1249436224826230817958938419510046055109971283319232476530362339703912063567191407/1733895723075939292356262944631013276732308384972299753521405714629729380469830*t^27 - 62752629498408226000859033078975872487158217080957269459284482250798324988847107/192655080341771032484029216070112586303589820552477750391267301625525486718870*t^25 + 32052114482397541114595567428250454742320659631720691685971888414460685719979285/269717112478479445477640902498157620825025748773468850547774222275735681406418*t^23 - 3717997295427016499722921833641530353431652140256089927026443357561877134681940/106835999098618481650234383457062434222899809579101297944248230901427769907737*t^21 + 7307813158668064002287330911460611905035349702373377600778954250402854917059108595/901375324395044129683027493227235757538605693418877650755622324115346094711577069*t^19 - 1336827730328303889025387603779723803193412385585524700506953922665743453930885394/901375324395044129683027493227235757538605693418877650755622324115346094711577069*t^17 + 2640410309976858949453613830740993988261347382389586624653272947822834079828737091/12619254541530617815562384905181300605540479707864287110578712537614845325962078966*t^15 - 880982363073818794015246631525304990732575287646194929527273095314275014058322015/39660514273381941706053209701998373331698650510430616633247382261075228167309391036*t^13 + 88973708416830548750031193606606544953972832040918600569219878986629012553966305/51863749434422539154069581917997872818375158359793883289631192187559913757250742124*t^11 - 198574230915642704393724684284922589254943609619091649054664995928923527102742285/2160804662265165789033989907610275011379469833054300239088324162210049668891660598332*t^9 + 327534788698329853704145503133276261308726650858171584031261886163926217489389/102895460107865037573047138457632143399022373002585725670872579152859508042460028492*t^7 - 55801070115871136264686444485862440492376793945993838919317577672343555715555/874611410916852819370900676889873218891690170521978668202416922799305818360910242182*t^5 + 3357251079560204720965848672644368307364402630912637890170307674028802860/5535515258967422907410763777784007714504368167860624482293777992400669736461457229*t^3 - 10589024204798489147270259926272101673462801819017286785456903859000647525/6122279876417969735596304738229112532241831193653850677416918459595140728526371695274*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:
| (0.9927156086719214682 - 3.8549778253506735372e-875j)  +/-  (5.34e-239, 5.34e-239j)
| (-0.96722756079140619804 - 1.8559476763328131322e-878j)  +/-  (9.7e-239, 9.7e-239j)
| (-0.903961349205221144 + 2.0245864992532843635e-878j)  +/-  (5.43e-239, 5.43e-239j)
| (0.13669843625018375233 + 1.77981398782355529e-892j)  +/-  (4.72e-253, 4.72e-253j)
| (0.94825033627150817192 - 1.5464584523557337274e-877j)  +/-  (8.52e-239, 8.52e-239j)
| (0.903961349205221144 + 3.5435789700869925782e-877j)  +/-  (5.11e-239, 5.11e-239j)
| (-0.98219129046748981137 + 3.0817473601184145525e-882j)  +/-  (8.09e-239, 8.09e-239j)
| (-0.88054439726820519948 + 7.3474432651889399477e-884j)  +/-  (2.6e-239, 2.6e-239j)
| (-0.99861378253564184076 + 1.3641363733492209923e-883j)  +/-  (1.92e-239, 1.92e-239j)
| (0.99861378253564184076 + 8.0188872124919969634e-881j)  +/-  (1.7e-239, 1.7e-239j)
| (0.85110112875893547946 - 2.2754349971858457641e-882j)  +/-  (7.51e-240, 7.51e-240j)
| (-0.2041968861768067152 - 2.0700659434944010312e-901j)  +/-  (9.24e-252, 9.24e-252j)
| (-0.92636664006123565409 - 6.3119753201703579722e-889j)  +/-  (8.09e-239, 8.09e-239j)
| (-0.85110112875893547946 - 1.2157298364210157112e-889j)  +/-  (7.44e-240, 7.44e-240j)
| (0.98219129046748981137 + 1.8880517765358240378e-886j)  +/-  (8.84e-239, 8.84e-239j)
| (0.81549503306480411251 + 8.5265630076684279697e-894j)  +/-  (1.66e-240, 1.66e-240j)
| (0.92636664006123565409 - 2.7610812410258701935e-902j)  +/-  (7.61e-239, 7.61e-239j)
| (0.96722756079140619804 + 8.5173165483889210411e-914j)  +/-  (9.96e-239, 9.96e-239j)
| (-0.7307642246685694696 + 2.8862165368618184299e-927j)  +/-  (5.93e-242, 5.93e-242j)
| (-0.94825033627150817192 + 2.4959651800589585689e-923j)  +/-  (8.61e-239, 8.61e-239j)
| (0.68280348585124448874 - 2.2421562808909441003e-939j)  +/-  (8.13e-243, 8.13e-243j)
| (0.7307642246685694696 - 1.6788734979107725318e-970j)  +/-  (5.32e-242, 5.32e-242j)
| (-0.9927156086719214682 + 3.6709254315663785706e-990j)  +/-  (5.68e-239, 5.68e-239j)
| (-0.81549503306480411251 + 3.6388018254268384315e-993j)  +/-  (1.52e-240, 1.52e-240j)
| (-0.77513640107548973193 - 1.320043771784018066e-993j)  +/-  (3.06e-241, 3.06e-241j)
| (-2.6566732390095131426e-1003 - 2.6587063992110970676e-1003j)  +/-  (1.77e-1001, 1.77e-1001j)
| (0.77513640107548973193 + 2.1522086344813351323e-993j)  +/-  (3.17e-241, 3.17e-241j)
| (0.88054439726820519948 + 1.0210991411504023423e-1001j)  +/-  (2.61e-239, 2.61e-239j)
| (0.2041968861768067152 + 6.0012323157414954288e-1015j)  +/-  (9.6e-252, 9.6e-252j)
| (-0.68280348585124448874 - 1.929254015880295942e-1006j)  +/-  (8.09e-243, 8.09e-243j)
| (-0.27068610906547321733 - 1.9153803730268578046e-1015j)  +/-  (1.89e-250, 1.89e-250j)
| (0.52040181188867789087 - 4.542096160941071425e-1010j)  +/-  (1.13e-245, 1.13e-245j)
| (0.57735026918962576451 - 6.5574800573681777811e-1008j)  +/-  (1.14e-244, 1.14e-244j)
| (0.068520228507126693138 - 4.2213892984152168565e-1019j)  +/-  (1.89e-254, 1.89e-254j)
| (-0.63157243565817505573 - 4.3350031055277628495e-1009j)  +/-  (1.01e-243, 1.01e-243j)
| (-0.57735026918962576451 + 4.959896229043445697e-1011j)  +/-  (1.13e-244, 1.13e-244j)
| (0.27068610906547321733 + 1.0639014964488497375e-1015j)  +/-  (1.83e-250, 1.83e-250j)
| (0.63157243565817505573 - 5.1788922375111185247e-1013j)  +/-  (1.02e-243, 1.02e-243j)
| (0.3358482230623023461 - 1.2429880260624744828e-1017j)  +/-  (3.67e-249, 3.67e-249j)
| (-0.3358482230623023461 + 2.6849390830755924668e-1017j)  +/-  (3.6e-249, 3.6e-249j)
| (-0.52040181188867789087 + 3.150587624657079096e-1014j)  +/-  (1.13e-245, 1.13e-245j)
| (-0.13669843625018375233 - 6.7327756867359956008e-1022j)  +/-  (4.72e-253, 4.72e-253j)
| (0.39937913961605856095 + 1.7415530958131896524e-1015j)  +/-  (6.6e-248, 6.6e-248j)
| (0.46098918747505052646 - 1.464341709156683468e-1015j)  +/-  (9.61e-247, 9.61e-247j)
| (-0.068520228507126693138 + 1.8394257054456152719e-1023j)  +/-  (1.94e-254, 1.94e-254j)
| (-0.46098918747505052646 + 1.0388942707974147061e-1015j)  +/-  (9.74e-247, 9.74e-247j)
| (-0.39937913961605856095 - 2.7034887881105890273e-1017j)  +/-  (5.8e-248, 5.8e-248j)
-------------------------------------------------
The weights are:
| (0.0082309699159050142748 + 2.5254200406551417391e-875j)  +/-  (3.1e-66, 3.36e-181j)
| (0.017074477282156422458 + 6.6557380254182627178e-877j)  +/-  (1.31e-66, 1.42e-181j)
| (0.022116181679217114875 - 3.4005731027132592744e-876j)  +/-  (1.06e-66, 1.15e-181j)
| (0.067894054019477751544 + 2.8452027584104490035e-876j)  +/-  (3.04e-67, 3.29e-182j)
| (0.020714366975381423697 - 5.3992138904830276619e-875j)  +/-  (1.54e-67, 1.67e-182j)
| (0.022116181679217114875 - 7.3194784016982830197e-875j)  +/-  (1.06e-67, 1.15e-182j)
| (0.012788116223916648774 - 3.647442078961520807e-877j)  +/-  (7.35e-68, 7.98e-183j)
| (0.02591341222341571936 + 3.6863845133454400269e-876j)  +/-  (4.66e-68, 5.05e-183j)
| (0.0035553149672078333342 - 4.3600981451326750458e-878j)  +/-  (1.58e-68, 1.72e-183j)
| (0.0035553149672078333342 + 1.4478993828987481176e-875j)  +/-  (4.86e-69, 5.27e-184j)
| (0.032815788564520360549 - 4.088966275021760799e-875j)  +/-  (6.7e-70, 7.26e-185j)
| (0.067047877876964311954 - 2.0589038515998019131e-876j)  +/-  (3.9e-71, 4.23e-186j)
| (0.022610283506061668597 + 2.2378526607174476693e-876j)  +/-  (1.42e-68, 1.54e-183j)
| (0.032815788564520360549 - 3.1167734699104012778e-876j)  +/-  (8.2e-70, 8.89e-185j)
| (0.012788116223916648774 - 6.6253902652604073917e-875j)  +/-  (4.68e-69, 5.08e-184j)
| (0.038151170953147287157 + 2.6254877876750346778e-875j)  +/-  (6.96e-71, 7.55e-186j)
| (0.022610283506061668597 + 6.4589353316586204806e-875j)  +/-  (1.17e-69, 1.27e-184j)
| (0.017074477282156422458 + 5.1841338296440135271e-875j)  +/-  (1.91e-69, 2.07e-184j)
| (0.046224885736141738372 + 2.0364517072652861468e-876j)  +/-  (1.64e-73, 1.77e-188j)
| (0.020714366975381423697 - 1.2134187428915347541e-876j)  +/-  (9.13e-71, 9.9e-186j)
| (0.049644486055368403566 - 1.0445619013962179413e-875j)  +/-  (9.57e-74, 1.04e-188j)
| (0.046224885736141738372 + 1.3434906328370456038e-875j)  +/-  (3.41e-73, 3.69e-188j)
| (0.0082309699159050142748 + 1.6303664021611670943e-877j)  +/-  (1.13e-71, 1.23e-186j)
| (0.038151170953147287157 + 2.5604229974318843452e-876j)  +/-  (2.42e-73, 2.62e-188j)
| (0.042451543641227747247 - 2.227131800229029452e-876j)  +/-  (4.49e-74, 4.87e-189j)
| (0.068577376777114349156 + 2.4291504076426015837e-876j)  +/-  (3.02e-78, 3.28e-193j)
| (0.042451543641227747247 - 1.8160557570046513638e-875j)  +/-  (1.5e-74, 1.62e-189j)
| (0.02591341222341571936 + 6.2455135570445987026e-875j)  +/-  (2.65e-73, 2.87e-188j)
| (0.067047877876964311954 - 3.1262376857814817925e-876j)  +/-  (1.51e-78, 1.64e-193j)
| (0.049644486055368403566 - 1.9280014165017071024e-876j)  +/-  (6.92e-77, 7.5e-192j)
| (0.065877549647398726401 + 1.982558208958245249e-876j)  +/-  (7.49e-79, 8.13e-194j)
| (0.058224409632862312853 + 5.8979582704895649136e-876j)  +/-  (1e-78, 1.09e-193j)
| (0.055628935837680047801 - 6.9754863203529524508e-876j)  +/-  (3.04e-78, 3.3e-193j)
| (0.068406004697347848072 - 2.6158581385966755533e-876j)  +/-  (2.33e-79, 2.53e-194j)
| (0.052771437714282506503 + 1.8693262960775850267e-876j)  +/-  (3.73e-79, 4.05e-194j)
| (0.055628935837680047801 - 1.842895723252626229e-876j)  +/-  (5.77e-80, 6.26e-195j)
| (0.065877549647398726401 + 3.4705564686229813089e-876j)  +/-  (2.1e-80, 2.28e-195j)
| (0.052771437714282506503 + 8.421648427473320882e-876j)  +/-  (2.63e-79, 2.86e-194j)
| (0.064395985635721342982 - 3.8934967519600910823e-876j)  +/-  (7.6e-81, 8.24e-196j)
| (0.064395985635721342982 - 1.9239406694894767708e-876j)  +/-  (1.88e-82, 2.04e-197j)
| (0.058224409632862312853 + 1.8390155158243997735e-876j)  +/-  (3.58e-82, 3.88e-197j)
| (0.067894054019477751544 + 2.1560269487883019683e-876j)  +/-  (2.13e-82, 2.31e-197j)
| (0.062617590424383494772 + 4.4161797933556238154e-876j)  +/-  (5.19e-82, 5.63e-197j)
| (0.060556468401657100276 - 5.0690306173877528088e-876j)  +/-  (5.98e-82, 6.49e-197j)
| (0.068406004697347848072 - 2.2778362544960813303e-876j)  +/-  (5.24e-83, 5.68e-198j)
| (0.060556468401657100276 - 1.8524789222400028176e-876j)  +/-  (4.02e-84, 4.38e-199j)
| (0.062617590424383494772 + 1.8809225241007320348e-876j)  +/-  (3.96e-84, 4.28e-199j)
