Starting with polynomial:
P : 35/8*t^4 - 15/4*t^2 + 3/8
Extension levels are: 4 38
-------------------------------------------------
Trying to find an order 38 Kronrod extension for:
P1 : 35/8*t^4 - 15/4*t^2 + 3/8
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 35/8*t^42 - 97243042869838832791731069/2062620448608929012285768*t^40 + 81088366321701546613009626615/343487328967014163652452732*t^38 - 206063406991591662229163852943/282616156745011653638094020*t^36 + 1983710360454479681322639376323/1275810079020338322137681576*t^34 - 85867582673563272944466312368529/35361088981617184618393602184*t^32 + 63534916388094443146172176434519/22100680613510740386496001365*t^30 - 17944325540801452623893765055689889/6811429765084010187118067620693*t^28 + 3350402855594690405141416924761733719/1770971738921842648650697581380180*t^26 - 204282525484520127008316676786221735/190720033422352285239305893379404*t^24 + 11004712791161890582814347855389105/22991940788070137153355058292774*t^22 - 32600719333053098402270811839424747/193789215213734013149706919896238*t^20 + 196703176409922948995159095129274655/4263362734702148289293552237717236*t^18 - 457076301879227625464656049063339859/46896990081723631182229074614889596*t^16 + 12567768630299743021265620274089861845/8078006541576895471138958102414732911*t^14 - 8730041489100158485523606004843675/47798855275602931781887326049791319*t^12 + 335951080225325536998536035160687127/22143906044042958214590710322703323784*t^10 - 18666605821358096562720155413835745/22143906044042958214590710322703323784*t^8 + 45463252326974113036764400929471/1581707574574497015327907880193094556*t^6 - 358007942028421941631239371569155/687882622020961948805328241010052527348*t^4 + 408116908879792409490394786880265/108685454279311987911241862079588299320984*t^2 - 82941385181609738083764709503/18349492280922803153846028662787634950296
-------------------------------------------------
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:
| (0.97290423467251717547 + 1.3335969459204709162e-867j)  +/-  (3.26e-240, 3.26e-240j)
| (-0.99598513134970901804 - 1.9239816554912930337e-878j)  +/-  (5.19e-240, 5.19e-240j)
| (-0.9531779842548471047 + 3.1839182018103534734e-893j)  +/-  (1.87e-240, 1.87e-240j)
| (0.99972828532683215523 + 9.7734688590993249105e-903j)  +/-  (2.41e-240, 2.41e-240j)
| (0.8971902891292156082 - 1.7897317626121642777e-920j)  +/-  (3.17e-241, 3.17e-241j)
| (0.92791709550749614496 - 7.4703039651660518745e-924j)  +/-  (8.69e-241, 8.69e-241j)
| (-0.41134741431388242616 + 1.4379362931893095468e-937j)  +/-  (1.21e-248, 1.21e-248j)
| (-0.86113631159405257522 - 1.8477637129850224444e-931j)  +/-  (1.05e-241, 1.05e-241j)
| (-0.99972828532683215523 + 3.7099171204458268345e-928j)  +/-  (2.43e-240, 2.43e-240j)
| (0.99598513134970901804 + 2.9069478906993547974e-931j)  +/-  (5.33e-240, 5.33e-240j)
| (0.86113631159405257522 - 9.6746291549867301008e-953j)  +/-  (1.04e-241, 1.04e-241j)
| (-0.26657194994861754305 + 6.6332298425244103049e-964j)  +/-  (3.91e-251, 3.91e-251j)
| (-0.92791709550749614496 + 4.7190930576632726215e-953j)  +/-  (9.83e-241, 9.83e-241j)
| (-0.8971902891292156082 - 1.8701727710664236361e-953j)  +/-  (3.55e-241, 3.55e-241j)
| (0.98712410889125726175 + 8.2859643302018077541e-952j)  +/-  (5.3e-240, 5.3e-240j)
| (0.81994607713034625448 - 5.2783111097245965788e-968j)  +/-  (2.68e-242, 2.68e-242j)
| (0.66805736729973675222 + 3.5762455355453934651e-970j)  +/-  (1.6e-244, 1.6e-244j)
| (0.41134741431388242616 + 8.4155590861831817531e-974j)  +/-  (1.19e-248, 1.19e-248j)
| (-0.77385222910026989757 + 8.6811890842589795211e-970j)  +/-  (5.75e-243, 5.75e-243j)
| (-0.98712410889125726175 - 2.1330167710533654696e-965j)  +/-  (5.36e-240, 5.36e-240j)
| (0.48024256141269197882 - 1.4856175025367000299e-974j)  +/-  (1.66e-247, 1.66e-247j)
| (0.77385222910026989757 - 1.434215686012924618e-969j)  +/-  (6.02e-243, 6.02e-243j)
| (0.9531779842548471047 + 1.8532627080357559472e-970j)  +/-  (1.95e-240, 1.95e-240j)
| (-0.72312286836568058606 - 1.583136120259366632e-981j)  +/-  (1.01e-243, 1.01e-243j)
| (-0.81994607713034625448 + 6.9699651080835926715e-983j)  +/-  (2.61e-242, 2.61e-242j)
| (0.11539905328268449455 - 1.2223756655449939748e-995j)  +/-  (1.07e-253, 1.07e-253j)
| (0.72312286836568058606 - 6.5626236802707533737e-987j)  +/-  (1e-243, 1e-243j)
| (0.19156106559362508057 + 2.9766767530035323503e-994j)  +/-  (2.01e-252, 2.01e-252j)
| (-0.97290423467251717547 - 1.5961742325897687546e-988j)  +/-  (3.69e-240, 3.69e-240j)
| (-0.66805736729973675222 - 1.2997199267321654936e-1000j)  +/-  (1.62e-244, 1.62e-244j)
| (-0.3399810435848562648 + 2.0675264150669925007e-1005j)  +/-  (7.3e-250, 7.3e-250j)
| (0.3399810435848562648 + 2.6487491193291777432e-1003j)  +/-  (7.49e-250, 7.49e-250j)
| (0.54625306389755454887 + 6.9786855215651858698e-1000j)  +/-  (2.11e-246, 2.11e-246j)
| (-0.038543560481209533807 - 2.1243780442868116033e-1006j)  +/-  (5.83e-255, 5.83e-255j)
| (-0.60898317440906569214 + 3.7964579918938641805e-1001j)  +/-  (1.79e-245, 1.79e-245j)
| (-0.48024256141269197882 - 3.4415412010514072033e-1004j)  +/-  (1.73e-247, 1.73e-247j)
| (0.038543560481209533807 + 6.8361279044429041508e-1008j)  +/-  (5.83e-255, 5.83e-255j)
| (0.60898317440906569214 - 4.8784009062989529173e-1003j)  +/-  (1.72e-245, 1.72e-245j)
| (0.26657194994861754305 + 2.1859590703593132699e-1009j)  +/-  (4e-251, 4e-251j)
| (-0.11539905328268449455 + 7.3772132117922255843e-1012j)  +/-  (1.02e-253, 1.02e-253j)
| (-0.54625306389755454887 - 6.7596870899792348475e-1006j)  +/-  (2.07e-246, 2.07e-246j)
| (-0.19156106559362508057 - 6.9806760489008402797e-1012j)  +/-  (1.94e-252, 1.94e-252j)
-------------------------------------------------
The weights are:
| (0.016958745417016373233 + 1.8237448981990197629e-868j)  +/-  (2.85e-77, 5.47e-193j)
| (0.0062572674637652644118 + 8.7677517369889809502e-870j)  +/-  (8.28e-78, 1.59e-193j)
| (0.022497965485868993423 - 1.1791484838390561854e-869j)  +/-  (7.96e-78, 1.53e-193j)
| (0.0013130736694323624834 - 2.6901494356653023355e-868j)  +/-  (3.95e-78, 7.58e-194j)
| (0.033418308730714100653 + 2.8415341503563838358e-868j)  +/-  (2.57e-78, 4.93e-194j)
| (0.028011890439429929301 - 4.9397415532295268136e-868j)  +/-  (3.59e-78, 6.9e-194j)
| (0.070201006410440669378 + 1.2161501472380989547e-869j)  +/-  (6.32e-80, 1.21e-195j)
| (0.038657661572768069878 + 1.1319345385460801887e-869j)  +/-  (4.5e-80, 8.64e-196j)
| (0.0013130736694323624834 - 3.6580916244444347509e-870j)  +/-  (1.05e-79, 2.02e-195j)
| (0.0062572674637652644118 + 7.4792298574246976642e-868j)  +/-  (1.33e-78, 2.56e-194j)
| (0.038657661572768069878 - 1.8574326000060520258e-868j)  +/-  (4.5e-80, 8.65e-196j)
| (0.074284379423769882047 + 1.3264745391334680193e-869j)  +/-  (2.69e-81, 5.18e-197j)
| (0.028011890439429929301 + 1.1690990474632710641e-869j)  +/-  (2.97e-80, 5.7e-196j)
| (0.033418308730714100653 - 1.1504432484717730988e-869j)  +/-  (1.55e-80, 2.98e-196j)
| (0.011505970900500347598 - 1.4927819776280363481e-867j)  +/-  (4.55e-79, 8.75e-195j)
| (0.043683933688027374196 + 1.3099403899102840808e-868j)  +/-  (3.03e-81, 5.81e-197j)
| (0.057126619666575804158 - 5.9920813600758537894e-869j)  +/-  (2.86e-83, 5.5e-199j)
| (0.070201006410440669378 - 2.9978406204333414556e-869j)  +/-  (1.87e-84, 3.6e-200j)
| (0.048459011551436939144 + 1.1091883890158910408e-869j)  +/-  (2.19e-84, 4.2e-200j)
| (0.011505970900500347598 - 1.0830033144587473609e-869j)  +/-  (4.49e-83, 8.62e-199j)
| (0.067520341075826270333 + 3.4721555016212856544e-869j)  +/-  (2.12e-84, 4.08e-200j)
| (0.048459011551436939144 - 9.7335466808785378948e-869j)  +/-  (9.62e-83, 1.85e-198j)
| (0.022497965485868993423 + 1.1513272318978855365e-867j)  +/-  (4.98e-81, 9.56e-197j)
| (0.052949762462642529224 - 1.1075695555572863892e-869j)  +/-  (2.38e-85, 4.58e-201j)
| (0.043683933688027374196 - 1.1175839231951920267e-869j)  +/-  (2.42e-84, 4.64e-200j)
| (0.076585470648077402782 - 1.8926888713243275074e-869j)  +/-  (2.74e-87, 5.26e-203j)
| (0.052949762462642529224 + 7.5204488332292309824e-869j)  +/-  (2.17e-84, 4.16e-200j)
| (0.075662233034449498925 + 2.0879280455809083568e-869j)  +/-  (3.88e-87, 7.45e-203j)
| (0.016958745417016373233 + 1.1622999610589549306e-869j)  +/-  (2.74e-84, 5.27e-200j)
| (0.057126619666575804158 + 1.1131687843305348259e-869j)  +/-  (6.14e-87, 1.18e-202j)
| (0.072460274116673732051 - 1.2654630964948302981e-869j)  +/-  (4.43e-88, 8.51e-204j)
| (0.072460274116673732051 + 2.6249754993629934161e-869j)  +/-  (9e-88, 1.73e-203j)
| (0.064434663591854549436 - 4.0857976238440582445e-869j)  +/-  (3.39e-87, 6.51e-203j)
| (0.077048492852005722854 - 1.6004989045706406862e-869j)  +/-  (1.42e-89, 2.72e-205j)
| (0.06096292779872418449 - 1.1263372516505160318e-869j)  +/-  (7.74e-89, 1.49e-204j)
| (0.067520341075826270333 - 1.1771680217207137335e-869j)  +/-  (1.99e-89, 3.82e-205j)
| (0.077048492852005722854 + 1.7325441158755471699e-869j)  +/-  (7.72e-90, 1.48e-205j)
| (0.06096292779872418449 + 4.8959483562826338445e-869j)  +/-  (7.1e-89, 1.36e-204j)
| (0.074284379423769882047 - 2.327705580409620839e-869j)  +/-  (1.49e-89, 2.86e-205j)
| (0.076585470648077402782 + 1.491303510589997966e-869j)  +/-  (6.55e-91, 1.26e-206j)
| (0.064434663591854549436 + 1.1474850835826856463e-869j)  +/-  (4.24e-91, 9.17e-207j)
| (0.075662233034449498925 - 1.4009763241215016669e-869j)  +/-  (4.49e-91, 8.43e-207j)
