Starting with polynomial:
P : 35/8*t^4 - 15/4*t^2 + 3/8
Extension levels are: 4 37
-------------------------------------------------
Trying to find an order 37 Kronrod extension for:
P1 : 35/8*t^4 - 15/4*t^2 + 3/8
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 35/8*t^41 - 3054385351742732032870925925/71372062536601267556954872*t^39 + 48337689337715640299007036297/249802218878104436449342052*t^37 - 19569900031505495532599476492599/36471123956203247721603939592*t^35 + 22214601486904736600229083042745/21760082360423786455746888328*t^33 - 9569551840381551837707262621/6774620909222847588962294*t^31 + 24356378346250876807392170074545/16567335433504473778807289977*t^29 - 894844947744507929760487709362809/762097429941205793825135338942*t^27 + 1109329822909068002551025235264681/1524194859882411587650270677884*t^25 - 228971139124439066879853696850968225/650831205169789747926665579456468*t^23 + 110663932144664071814301062275797495/834761763152556415818984112781122*t^21 - 9239560843891369896509680275814575/238503360900730404519709746508892*t^19 + 22800698874666468435434951751116445/2623536969908034449716807211597812*t^17 - 102444216861819292189478595788975235/69523729702562912917495391107342018*t^15 + 6417470467902377378419180520334525/34761864851281456458747695553671009*t^13 - 8058398336485616972549956565473245/486666107917940390422467737751394126*t^11 + 59176227143646698246325212584205475/58222963456364504890542503898257697256*t^9 - 2325780761455226123717111749331415/58222963456364504890542503898257697256*t^7 + 2750055170405314610520157081010145/3040070449043032362499040739259026906724*t^5 - 59324238372469303094165865998775/6080140898086064724998081478518053813448*t^3 + 195193820611763725051056763485/6080140898086064724998081478518053813448*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:
| (-0.99037016045108105218 + 7.5956041465471935524e-865j)  +/-  (5.41e-242, 5.41e-242j)
| (0.97639222378840376842 + 7.6296927336979281485e-864j)  +/-  (7.11e-242, 7.11e-242j)
| (-0.93030417494014471 + 8.5336525159216125039e-883j)  +/-  (4.57e-242, 4.57e-242j)
| (-0.97639222378840376842 - 2.2543914580462064173e-882j)  +/-  (8.11e-242, 8.11e-242j)
| (0.89850237540524299387 + 3.054997815141866913e-883j)  +/-  (2.34e-242, 2.34e-242j)
| (0.99037016045108105218 - 7.6339945911758384606e-899j)  +/-  (5.6e-242, 5.6e-242j)
| (-0.99816981403777082918 - 2.0821616836444458778e-920j)  +/-  (1.89e-242, 1.89e-242j)
| (-0.86113631159405257522 + 1.3625968213801085783e-920j)  +/-  (1.02e-242, 1.02e-242j)
| (-0.074184708318281580068 + 6.3676024879425411421e-928j)  +/-  (2.08e-254, 2.08e-254j)
| (0.95632572175562874702 + 2.3467685252117231282e-920j)  +/-  (6.98e-242, 6.98e-242j)
| (0.86113631159405257522 + 1.9211257504975830662e-932j)  +/-  (1.09e-242, 1.09e-242j)
| (0.93030417494014471 + 3.5131353747560010998e-938j)  +/-  (4.57e-242, 4.57e-242j)
| (-0.77078666167911538462 - 1.3031453393794149767e-955j)  +/-  (9.91e-244, 9.91e-244j)
| (-0.89850237540524299387 - 1.8819471751486482522e-954j)  +/-  (2.61e-242, 2.61e-242j)
| (0.99816981403777082918 - 5.2796735266600460135e-955j)  +/-  (2.19e-242, 2.19e-242j)
| (0.71845464895300619817 - 2.014413050753479198e-972j)  +/-  (2.5e-244, 2.5e-244j)
| (0.81846385055857360972 + 8.585273753858478943e-973j)  +/-  (3.47e-243, 3.47e-243j)
| (-0.95632572175562874702 + 1.6779464220602284856e-976j)  +/-  (7.16e-242, 7.16e-242j)
| (-0.6618756469678823958 - 1.4036983975790909994e-981j)  +/-  (4.52e-245, 4.52e-245j)
| (-0.81846385055857360972 + 2.2937352656578499404e-981j)  +/-  (3.47e-243, 3.47e-243j)
| (0.47227408324693184291 + 4.0841481694728487776e-986j)  +/-  (1.25e-247, 1.25e-247j)
| (0.77078666167911538462 - 5.3120468117896662751e-983j)  +/-  (9.9e-244, 9.9e-244j)
| (0.14636780220938547625 - 1.6812788967483102325e-992j)  +/-  (4.91e-253, 4.91e-253j)
| (-0.5380518436120006096 + 1.2657813354408381116e-987j)  +/-  (9.25e-247, 9.25e-247j)
| (-0.60153666609275201815 - 3.5614428648510508927e-987j)  +/-  (8.48e-246, 8.48e-246j)
| (0.21421425536824183715 - 1.6147233234029016677e-992j)  +/-  (1.01e-251, 1.01e-251j)
| (0.6618756469678823958 - 2.9526993034999124401e-987j)  +/-  (4.58e-245, 4.58e-245j)
| (0.40554253094583655843 - 4.4102916831160965724e-993j)  +/-  (1.21e-248, 1.21e-248j)
| (-0.14636780220938547625 - 2.0096122263912597874e-996j)  +/-  (4.76e-253, 4.76e-253j)
| (-0.71845464895300619817 - 3.4605532882551331241e-989j)  +/-  (2.25e-244, 2.25e-244j)
| (-0.21421425536824183715 + 2.429585525907952467e-996j)  +/-  (9.94e-252, 9.94e-252j)
| (0.27723606894235341918 - 5.6972702005209426477e-994j)  +/-  (1.24e-250, 1.24e-250j)
| (0.5380518436120006096 - 2.2543015751751284169e-991j)  +/-  (9.92e-247, 9.92e-247j)
| (-4.2630728617532587233e-1001 - 2.8540288854850854414e-1002j)  +/-  (1.75e-999, 1.75e-999j)
| (-0.40554253094583655843 + 2.4084234098928995678e-996j)  +/-  (1.35e-248, 1.35e-248j)
| (-0.3399810435848562648 - 3.1930983246709276121e-997j)  +/-  (1.31e-249, 1.31e-249j)
| (0.074184708318281580068 - 6.3939920182400097354e-1001j)  +/-  (2.08e-254, 2.08e-254j)
| (0.60153666609275201815 + 5.2237468908634122087e-998j)  +/-  (7.54e-246, 7.54e-246j)
| (0.3399810435848562648 + 8.3389002857388368088e-1003j)  +/-  (1.31e-249, 1.31e-249j)
| (-0.27723606894235341918 - 6.9563642310913803237e-1004j)  +/-  (1.29e-250, 1.29e-250j)
| (-0.47227408324693184291 - 1.6497683536537660086e-1001j)  +/-  (1.16e-247, 1.16e-247j)
-------------------------------------------------
The weights are:
| (0.010899677515422142756 + 4.7836109559365076884e-865j)  +/-  (3.9e-77, 2.06e-194j)
| (0.017041000969219408685 - 3.0116620754422845258e-864j)  +/-  (3.63e-78, 1.91e-195j)
| (0.028944229129494823387 - 8.4691441216937531024e-865j)  +/-  (1.08e-77, 5.68e-195j)
| (0.017041000969219408685 - 1.2573906239301936279e-864j)  +/-  (1.43e-77, 7.53e-195j)
| (0.034623382023815079027 + 5.802923503782784121e-864j)  +/-  (1.11e-78, 5.84e-196j)
| (0.010899677515422142756 - 4.6222877128074316206e-864j)  +/-  (9.9e-79, 5.23e-196j)
| (0.004695330295012387988 + 2.9006307714232784233e-865j)  +/-  (6.52e-78, 3.44e-195j)
| (0.040065797060942207581 - 9.4181240208067213991e-865j)  +/-  (6.53e-79, 3.45e-196j)
| (0.073550204746974079638 + 1.450001140906673641e-863j)  +/-  (3.27e-80, 1.73e-197j)
| (0.023069732000875726898 + 1.0675625538299999336e-863j)  +/-  (6.27e-79, 3.31e-196j)
| (0.040065797060942207581 - 5.3664665847160134144e-864j)  +/-  (5.81e-80, 3.07e-197j)
| (0.028944229129494823387 - 6.9404093361031129479e-864j)  +/-  (3.37e-79, 1.78e-196j)
| (0.050067294076366413955 - 1.263288108954254704e-864j)  +/-  (1.53e-81, 8.09e-199j)
| (0.034623382023815079027 + 8.6636615445266513697e-865j)  +/-  (3.18e-80, 1.68e-197j)
| (0.004695330295012387988 + 8.3613485117355807662e-865j)  +/-  (4.58e-80, 2.42e-197j)
| (0.054529081635603200278 + 5.7470573457250820581e-864j)  +/-  (8.91e-83, 4.7e-200j)
| (0.04522891477981896055 + 5.2654586448253843299e-864j)  +/-  (2.02e-81, 1.07e-198j)
| (0.023069732000875726898 + 9.1520028919923898929e-865j)  +/-  (4.81e-81, 2.54e-198j)
| (0.058548475026129298473 - 1.9500210344888623705e-864j)  +/-  (3.18e-84, 1.68e-201j)
| (0.04522891477981896055 + 1.0706191522139654229e-864j)  +/-  (2.78e-82, 1.47e-199j)
| (0.066537032569490292683 + 1.1032635663424478893e-863j)  +/-  (6.11e-86, 3.23e-203j)
| (0.050067294076366413955 - 5.3974514224481124094e-864j)  +/-  (1.78e-83, 9.38e-201j)
| (0.070400803758055738712 - 1.9040654468204741231e-863j)  +/-  (9.47e-87, 5e-204j)
| (0.064802613744137940317 - 3.4941807118920003406e-864j)  +/-  (2.1e-86, 1.11e-203j)
| (0.062028807207357536582 + 2.5572885604593390378e-864j)  +/-  (8.43e-86, 4.45e-203j)
| (0.06509619083161625519 + 2.2033303095630741046e-863j)  +/-  (2.6e-87, 1.37e-204j)
| (0.058548475026129298473 - 6.3503705874208443451e-864j)  +/-  (2.22e-86, 1.17e-203j)
| (0.066564211967597638852 - 1.4505186178969116166e-863j)  +/-  (1.35e-87, 7.15e-205j)
| (0.070400803758055738712 - 1.5065179911947392762e-863j)  +/-  (3.07e-88, 1.62e-205j)
| (0.054529081635603200278 + 1.542754545189672068e-864j)  +/-  (8.78e-87, 4.64e-204j)
| (0.06509619083161625519 + 1.5610283258426859877e-863j)  +/-  (1.12e-88, 5.92e-206j)
| (0.061882437190589420582 - 2.2437412228001315144e-863j)  +/-  (2.44e-88, 1.29e-205j)
| (0.064802613744137940317 - 8.7604023793149247348e-864j)  +/-  (2.18e-88, 1.15e-205j)
| (0.074495916313412846286 - 1.48286679885962678e-863j)  +/-  (6.45e-89, 3.41e-206j)
| (0.066564211967597638852 - 7.4161356873218314456e-864j)  +/-  (3.21e-90, 1.69e-207j)
| (0.064176825314775024725 + 1.0927678428886094066e-863j)  +/-  (2.96e-90, 1.56e-207j)
| (0.073550204746974079638 + 1.6320624295481007673e-863j)  +/-  (1.09e-89, 5.75e-207j)
| (0.062028807207357536582 + 7.2978326578568593628e-864j)  +/-  (2.41e-90, 1.27e-207j)
| (0.064176825314775024725 + 1.9051062617357028962e-863j)  +/-  (5.65e-90, 2.98e-207j)
| (0.061882437190589420582 - 1.4318600923711007907e-863j)  +/-  (9.67e-91, 5.16e-208j)
| (0.066537032569490292683 + 4.9932105943322814687e-864j)  +/-  (3.1e-91, 1.6e-208j)
