Starting with polynomial:
P : 35/8*t^4 - 15/4*t^2 + 3/8
Extension levels are: 4 41
-------------------------------------------------
Trying to find an order 41 Kronrod extension for:
P1 : 35/8*t^4 - 15/4*t^2 + 3/8
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 35/8*t^45 - 355007147150647258821752481855/7277148538047608236822550828*t^43 + 260927342118465613508357162049962943/1028013665375833425182974465268248*t^41 - 630984609656923052131908590356784095/771010249031875068887230848951186*t^39 + 7829569018378049165568113982529010695/4274372608667938978392367513483768*t^37 - 174509742079468076637265309575936475/57761792009026202410707669101132*t^35 + 77558288406591876539558375883232823/20386514826715130262602706741576*t^33 - 1159316816570127779228163306543918182/310044912989625939410416165028135*t^31 + 51213670017895389978561497838526971659/17610551057810753358511638173598068*t^29 - 3287873493882978329122200424646106501023/1822692034483412972605954550967400038*t^27 + 24297279484561807456668257842710705964449/27137859180086370925466434425514622788*t^25 - 2411137104783452758660493931879835113045/6784464795021592731366608606378655697*t^23 + 132552478604447847953837095457086673063/1179906920873320475020279757631070556*t^21 - 12779970460377956110337353068783744585/455533684640965499849601678579084202*t^19 + 23218013532864959972023360589672952384015/4246485008223080389597986847714222931044*t^17 - 867581078941069254435191072568747102490/1061621252055770097399496711928555732761*t^15 + 776662475629294187013362764841491676775/8492970016446160779195973695428445862088*t^13 - 1667530861111337283417611887067378819877/225063705435823260648693302928853815345332*t^11 + 9516165319442041078506311585317047987295/22956497954453972586166716898743089165223864*t^9 - 199975943746341118412451541356557140365/13391290473431484008597251524266802013047254*t^7 + 31620016375504801794457456711703384415/101990809320036803579337702440684470768880152*t^5 - 10388677008659762901112701017518948485/3416692112221232919907813031762929770757485092*t^3 + 426234984999273938019004051995681213/47833689571097260878709382444681016790604791288*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:
| (0.40427345269739975878 - 3.7049503730273296095e-932j)  +/-  (3.89e-248, 3.89e-248j)
| (0.98210424780887051108 - 2.0229871521328156226e-920j)  +/-  (8.9e-240, 8.9e-240j)
| (-0.92273247971231820886 - 1.0597994136519203054e-918j)  +/-  (3.26e-240, 3.26e-240j)
| (0.99861418948301154121 + 6.8760819955234964288e-928j)  +/-  (2.11e-240, 2.11e-240j)
| (0.94703689714299337657 - 1.6627943386482749481e-930j)  +/-  (6.25e-240, 6.25e-240j)
| (0.92273247971231820886 - 5.0928845450748360228e-934j)  +/-  (3.55e-240, 3.55e-240j)
| (-0.99270541877186767603 - 1.3375505767723906692e-933j)  +/-  (5.69e-240, 5.69e-240j)
| (-0.82412290263972005612 - 1.2096837163385396985e-953j)  +/-  (2.26e-241, 2.26e-241j)
| (-0.98210424780887051108 + 1.4017872693206775333e-955j)  +/-  (8.6e-240, 8.6e-240j)
| (-0.99861418948301154121 - 1.6199716325304198557e-972j)  +/-  (2.13e-240, 2.13e-240j)
| (0.86113631159405257522 - 2.9869008270403891285e-993j)  +/-  (6.64e-241, 6.64e-241j)
| (-0.20670589733048573221 + 1.463470566568650852e-1002j)  +/-  (8.57e-252, 8.57e-252j)
| (-0.94703689714299337657 + 2.1280104575033583194e-993j)  +/-  (6.01e-240, 6.01e-240j)
| (-0.78318176445721246007 + 1.0443398177849687815e-1010j)  +/-  (5.91e-242, 5.91e-242j)
| (0.99270541877186767603 + 1.1226187711579138823e-1008j)  +/-  (5.98e-240, 5.98e-240j)
| (0.89405562740424758966 - 1.4814472181877878785e-1012j)  +/-  (1.69e-240, 1.69e-240j)
| (0.78318176445721246007 - 6.4055350174742729673e-1014j)  +/-  (5.9e-242, 5.9e-242j)
| (-0.96685789811927238765 - 5.8408893941813912316e-1010j)  +/-  (7.79e-240, 7.79e-240j)
| (-0.73849701495353198766 + 8.1071688685377827208e-1023j)  +/-  (1.35e-242, 1.35e-242j)
| (-0.86113631159405257522 - 1.3231619666163815646e-1020j)  +/-  (7.15e-241, 7.15e-241j)
| (0.82412290263972005612 + 7.8881594578419179303e-1030j)  +/-  (2.09e-241, 2.09e-241j)
| (0.73849701495353198766 - 1.9926454684895228906e-1030j)  +/-  (1.27e-242, 1.27e-242j)
| (0.20670589733048573221 - 6.4386832075881633381e-1041j)  +/-  (9.45e-252, 9.45e-252j)
| (-0.89405562740424758966 - 3.7494856028004781797e-1030j)  +/-  (1.72e-240, 1.72e-240j)
| (-0.69027038643688075046 + 7.0693211286436653428e-1042j)  +/-  (2.4e-243, 2.4e-243j)
| (6.8925112920523839079e-1054 - 7.3452989724503443592e-1052j)  +/-  (3.31e-1050, 3.31e-1050j)
| (0.69027038643688075046 + 5.439747223592275052e-1040j)  +/-  (2.33e-243, 2.33e-243j)
| (0.96685789811927238765 - 2.8189376505852077632e-1045j)  +/-  (8.86e-240, 8.86e-240j)
| (-0.46658486913005328659 + 6.3991423385968150467e-1053j)  +/-  (4.87e-247, 4.87e-247j)
| (-0.63872108800866317795 - 9.4494760890935659296e-1050j)  +/-  (4.17e-244, 4.17e-244j)
| (-0.27401817136141172431 - 4.270728887464826856e-1058j)  +/-  (1.44e-250, 1.44e-250j)
| (0.3399810435848562648 - 2.9145500028161751132e-1056j)  +/-  (2.64e-249, 2.64e-249j)
| (0.63872108800866317795 + 2.9390599008937573737e-1052j)  +/-  (3.89e-244, 3.89e-244j)
| (0.069358377427648167752 - 1.3697506550371346134e-1061j)  +/-  (2.37e-254, 2.37e-254j)
| (-0.58408556290422437969 + 4.1886390642285272689e-1052j)  +/-  (5.09e-245, 5.09e-245j)
| (-0.40427345269739975878 - 6.5944579348383083824e-1056j)  +/-  (4.39e-248, 4.39e-248j)
| (0.13837389073031277551 - 1.6015258467831695392e-1062j)  +/-  (4.28e-253, 4.28e-253j)
| (0.58408556290422437969 - 9.6359223631090342172e-1054j)  +/-  (4.85e-245, 4.85e-245j)
| (0.27401817136141172431 - 1.4667387725616784946e-1059j)  +/-  (1.53e-250, 1.53e-250j)
| (-0.3399810435848562648 + 1.6873450577303968729e-1057j)  +/-  (2.53e-249, 2.53e-249j)
| (-0.52661704759384410382 + 2.2871817659584472799e-1055j)  +/-  (5.09e-246, 5.09e-246j)
| (-0.13837389073031277551 + 8.6664293598613290211e-1063j)  +/-  (4.28e-253, 4.28e-253j)
| (0.46658486913005328659 - 3.9382731669119900278e-1055j)  +/-  (4.86e-247, 4.86e-247j)
| (0.52661704759384410382 - 2.6836525605531413794e-1057j)  +/-  (5.74e-246, 5.74e-246j)
| (-0.069358377427648167752 - 3.4701256985420371229e-1065j)  +/-  (2.1e-254, 2.1e-254j)
-------------------------------------------------
The weights are:
| (0.063352699138177192383 + 7.1237325983880626852e-920j)  +/-  (1.91e-73, 4.88e-189j)
| (0.012933727391338382202 + 1.2293710092819054871e-920j)  +/-  (9.2e-74, 2.35e-189j)
| (0.026510736964093553388 - 1.6678830478357202306e-919j)  +/-  (4.73e-75, 1.21e-190j)
| (0.0035556180931508865482 - 1.585267717887854729e-921j)  +/-  (3.86e-74, 9.85e-190j)
| (0.022079588297140325019 + 2.7970651687955540903e-920j)  +/-  (3.88e-74, 9.9e-190j)
| (0.026510736964093553388 - 2.7928316191886001998e-920j)  +/-  (1.46e-74, 3.72e-190j)
| (0.0082605529303588063552 + 7.1382911657350612416e-920j)  +/-  (8.6e-76, 2.19e-191j)
| (0.039006486087938767449 + 4.9362006921686322578e-919j)  +/-  (4.92e-76, 1.26e-191j)
| (0.012933727391338382202 - 1.6402555916416237023e-919j)  +/-  (5.6e-76, 1.43e-191j)
| (0.0035556180931508865482 - 1.8877189911331086045e-920j)  +/-  (3.59e-76, 9.17e-192j)
| (0.034992600671839617107 - 3.2706068568219809142e-920j)  +/-  (2.19e-77, 5.59e-193j)
| (0.067877701685556189555 - 1.356703496629337573e-919j)  +/-  (5.43e-79, 1.39e-194j)
| (0.022079588297140325019 - 8.8471616476534791668e-919j)  +/-  (1.23e-76, 3.14e-192j)
| (0.042845101875897888461 - 3.964331051984164862e-919j)  +/-  (3.12e-78, 7.96e-194j)
| (0.0082605529303588063552 + 1.0050494084917641508e-920j)  +/-  (1.02e-76, 2.6e-192j)
| (0.030821295843911742796 + 2.9860750016769388219e-920j)  +/-  (3.54e-77, 9.02e-193j)
| (0.042845101875897888461 - 3.9811399250593099422e-920j)  +/-  (5.64e-79, 1.44e-194j)
| (0.017547192717709460892 + 3.4716593529523990248e-919j)  +/-  (5.51e-77, 1.41e-192j)
| (0.046490773051077107252 + 3.347135490569004608e-919j)  +/-  (1.32e-79, 3.38e-195j)
| (0.034992600671839617107 - 6.791698364226327989e-919j)  +/-  (1.58e-78, 4.03e-194j)
| (0.039006486087938767449 + 3.6083249597962158881e-920j)  +/-  (3.19e-79, 8.13e-195j)
| (0.046490773051077107252 + 4.3790506158391573724e-920j)  +/-  (1.62e-80, 4.14e-196j)
| (0.067877701685556189555 - 8.7951675989398124977e-920j)  +/-  (2.5e-83, 6.37e-199j)
| (0.030821295843911742796 + 1.2179245308834760178e-918j)  +/-  (6.43e-79, 1.64e-194j)
| (0.049925945316045528279 - 2.9088183743032430684e-919j)  +/-  (1.58e-81, 4.04e-197j)
| (0.069415595684435519453 + 1.0857054524175258095e-919j)  +/-  (1.95e-84, 4.99e-200j)
| (0.049925945316045528279 - 4.7962436536702521403e-920j)  +/-  (2.27e-82, 5.79e-198j)
| (0.017547192717709460892 - 3.510152039508927703e-920j)  +/-  (3.17e-80, 8.09e-196j)
| (0.061220400480463591801 - 1.8968766813127404534e-919j)  +/-  (1.6e-84, 4.07e-200j)
| (0.053133237139605377914 + 2.5744009959946829768e-919j)  +/-  (5.63e-83, 1.44e-198j)
| (0.066691867222000426343 + 1.4679399984932392733e-919j)  +/-  (5.04e-85, 1.29e-200j)
| (0.06518033483896656707 - 7.6493324525026730291e-920j)  +/-  (1.78e-85, 4.55e-201j)
| (0.053133237139605377914 + 5.2295724784214700004e-920j)  +/-  (9.42e-85, 2.4e-200j)
| (0.069243978062433257294 - 1.0112759960315736331e-919j)  +/-  (7.28e-86, 1.86e-201j)
| (0.05609559534522866257 - 2.3066208215752571461e-919j)  +/-  (5.27e-85, 1.34e-200j)
| (0.063352699138177192383 + 1.7346915998415538509e-919j)  +/-  (4.39e-86, 1.12e-201j)
| (0.068730238126049644231 + 9.4285658620454392979e-920j)  +/-  (3.05e-86, 7.78e-202j)
| (0.05609559534522866257 - 5.6778693336247985748e-920j)  +/-  (7.96e-87, 2.03e-202j)
| (0.066691867222000426343 + 8.2044466910008816012e-920j)  +/-  (1.73e-86, 4.42e-202j)
| (0.06518033483896656707 - 1.5929852195818112398e-919j)  +/-  (9.88e-87, 2.52e-202j)
| (0.058796530878799265365 + 2.0848895200068170639e-919j)  +/-  (1.8e-86, 4.59e-202j)
| (0.068730238126049644231 + 1.2570573028334942105e-919j)  +/-  (1.43e-87, 3.66e-203j)
| (0.061220400480463591801 - 6.6225214486298001752e-920j)  +/-  (1.77e-88, 4.55e-204j)
| (0.058796530878799265365 + 6.1415781651860027901e-920j)  +/-  (1.65e-88, 4.25e-204j)
| (0.069243978062433257294 - 1.1672166647158706058e-919j)  +/-  (2e-88, 4.97e-204j)
