Starting with polynomial:
P : t
Extension levels are: 1 2 10 26
-------------------------------------------------
Trying to find an order 2 Kronrod extension for:
P1 : t
Solvable: 1
-------------------------------------------------
Trying to find an order 10 Kronrod extension for:
P2 : t^3 - 3*t
Solvable: 1
-------------------------------------------------
Trying to find an order 26 Kronrod extension for:
P3 : t^13 - 629/8*t^11 + 17435/8*t^9 - 105435/4*t^7 + 557865/4*t^5 - 2248785/8*t^3 + 1133055/8*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^39 - 62344019653739501860494948964782623868150229/107107765571014895711482237366976081467608*t^37 + 1233581744529904314609470513581742737711841497885/8140190183397132074072650039890182191538208*t^35 - 190450052906489912692065749584619996195644106830795/8140190183397132074072650039890182191538208*t^33 + 41419600209009034562007305677067523168083740727107195/17297904139718905657404381334766637157018692*t^31 - 175066301769333140233457169580343514664197399121933145/1017523772924641509259081254986272773942276*t^29 + 32656934164920136616048366645889400400865811375206961495/3641664029414506454190396070477186769898672*t^27 - 7967956141139620793661276449581133932940071002880897514625/23063872186291874209872508446355516209358256*t^25 + 114538386211271892544993287568588998740273341104219398430375/11531936093145937104936254223177758104679128*t^23 - 2464033845779568995421369434389334031520340661118437410515875/11531936093145937104936254223177758104679128*t^21 + 1040382453979074178554596810680070099133177055887319055650125/303472002451208871182533005873098897491556*t^19 - 725689826603055442029691917171482693431296825322208578362375/17851294261835815951913706227829346911268*t^17 + 3131054153930636782252718342535849163501155239635446349149375/8925647130917907975956853113914673455634*t^15 - 19212891260161469094091188875725761643023079648839047881258125/8925647130917907975956853113914673455634*t^13 + 648813938120183219863668890785526731072718353449065117001294375/71405177047343263807654824911317387645072*t^11 - 1796402629495949352845955540848191923720541892375483071865570625/71405177047343263807654824911317387645072*t^9 + 1519959679967665559326370237295005468949299028008415630493385625/35702588523671631903827412455658693822536*t^7 - 702987496567067711634926914145594171816637244913003162088965625/17851294261835815951913706227829346911268*t^5 + 2331205017591749907313626444424796214669956704613057825904496875/142810354094686527615309649822634775290144*t^3 - 274956935804831972811860612795367023122114018353806821174378125/142810354094686527615309649822634775290144*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
Positive weights:   39 out of 39
Indefinite weights: 0 out of 39
Negative weights:   0 out of 39
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (-7.7662920523750588234 - 6.8654200334390251136e-849j)  +/-  (2.13e-246, 2.13e-246j)
| (9.3388678141970788101 - 6.8584013961253526828e-848j)  +/-  (1.82e-247, 1.82e-247j)
| (7.7662920523750588234 + 2.4810849584461120893e-851j)  +/-  (2.05e-246, 2.05e-246j)
| (-8.5091998538526122613 + 9.9766047380867269454e-867j)  +/-  (7.82e-247, 7.82e-247j)
| (7.0795648317678558272 - 1.2806173317634475102e-866j)  +/-  (4.12e-246, 4.12e-246j)
| (-10.336744786887891352 - 6.0832618378484886002e-883j)  +/-  (1.83e-248, 1.83e-248j)
| (-5.2629794541638639486 + 1.0419830568831753146e-879j)  +/-  (1.25e-245, 1.25e-245j)
| (10.336744786887891352 + 1.4792392384613601181e-881j)  +/-  (1.88e-248, 1.88e-248j)
| (-3.0919067736119443475 - 1.9028452787078784162e-893j)  +/-  (4.65e-248, 4.65e-248j)
| (-9.3388678141970788101 - 8.1472292237002621264e-892j)  +/-  (1.91e-247, 1.91e-247j)
| (2.1805341248582534995 - 6.8662691067768652043e-890j)  +/-  (1.27e-249, 1.27e-249j)
| (1.7320508075688772935 + 6.1167212225209119103e-890j)  +/-  (1.58e-250, 1.58e-250j)
| (-2.1805341248582534995 + 4.0676033501142065401e-894j)  +/-  (1.41e-249, 1.41e-249j)
| (5.8238536767427603773 - 5.1329009158754388873e-895j)  +/-  (7.72e-246, 7.72e-246j)
| (-4.9552567202732027226 + 8.1346484174410043154e-911j)  +/-  (1.13e-245, 1.13e-245j)
| (-5.8238536767427603773 - 4.7476285550216175265e-911j)  +/-  (8.35e-246, 8.35e-246j)
| (5.2629794541638639486 + 8.8924738856942324515e-917j)  +/-  (1.31e-245, 1.31e-245j)
| (-1.2903835467548838988 + 9.7029035107346848119e-934j)  +/-  (1.77e-251, 1.77e-251j)
| (-1.7320508075688772935 - 1.9559730677778446878e-932j)  +/-  (1.73e-250, 1.73e-250j)
| (8.5091998538526122613 - 3.6237068965957897657e-928j)  +/-  (8.1e-247, 8.1e-247j)
| (0.85995874045067267595 - 1.5124888363870539223e-937j)  +/-  (1.64e-252, 1.64e-252j)
| (3.5773982809904283695 + 6.3719716042337437769e-931j)  +/-  (1.98e-247, 1.98e-247j)
| (-4.6096758921816875609 + 6.5438390836376962591e-936j)  +/-  (4.75e-246, 4.75e-246j)
| (-6.4341746493458385534 - 3.2810387416524275495e-934j)  +/-  (6.22e-246, 6.22e-246j)
| (-4.08895114162132361 - 2.826311938346739506e-936j)  +/-  (8.88e-247, 8.88e-247j)
| (-2.6308380841127442917 - 2.5820728830962887486e-937j)  +/-  (9.38e-249, 9.38e-249j)
| (3.0919067736119443475 - 1.2552901894844922234e-935j)  +/-  (4.42e-248, 4.42e-248j)
| (0.43248820373582011404 - 5.8412046499762727447e-945j)  +/-  (1.01e-253, 1.01e-253j)
| (-3.5773982809904283695 + 4.1147393251561810527e-937j)  +/-  (2.1e-247, 2.1e-247j)
| (-0.85995874045067267595 - 4.5158492569409430571e-944j)  +/-  (1.73e-252, 1.73e-252j)
| (-7.0795648317678558272 - 6.7669292013432591599e-938j)  +/-  (4.24e-246, 4.24e-246j)
| (4.08895114162132361 - 6.1950079201359420852e-937j)  +/-  (8.9e-247, 8.9e-247j)
| (1.2903835467548838988 + 2.5707024211967402752e-954j)  +/-  (1.79e-251, 1.79e-251j)
| (6.4341746493458385534 - 3.1903799034952788398e-948j)  +/-  (6.24e-246, 6.24e-246j)
| (-0.43248820373582011404 + 4.5483048537368563338e-963j)  +/-  (1.01e-253, 1.01e-253j)
| (2.6308380841127442917 - 8.4164021803212211749e-958j)  +/-  (8.5e-249, 8.5e-249j)
| (4.9552567202732027226 - 7.1517297007020925467e-960j)  +/-  (1.24e-245, 1.24e-245j)
| (1.4943504891810959722e-992 + 8.8591792966236281338e-993j)  +/-  (6.78e-991, 6.78e-991j)
| (4.6096758921816875609 - 2.0162891464070561159e-977j)  +/-  (4.87e-246, 4.87e-246j)
-------------------------------------------------
The weights are:
| (2.2686464302295133322e-14 - 7.5544839059740958373e-862j)  +/-  (3.28e-94, 3.98e-216j)
| (4.0994110572300105079e-20 + 1.2074388930520599061e-866j)  +/-  (1.16e-97, 1.41e-219j)
| (2.2686464302295133322e-14 - 7.7631601073186420128e-864j)  +/-  (8.88e-95, 1.08e-216j)
| (5.8831429424407611893e-17 - 5.4730935381883081077e-864j)  +/-  (1.87e-96, 2.26e-218j)
| (3.4660998644675557483e-12 + 1.9929324181037622281e-862j)  +/-  (6.91e-94, 8.38e-216j)
| (2.8829694358882658258e-24 - 9.1840836881238110186e-869j)  +/-  (1.92e-100, 2.33e-222j)
| (1.940978491598060731e-07 - 9.8720121987911906804e-858j)  +/-  (3.07e-91, 3.72e-213j)
| (2.8829694358882658258e-24 + 2.4493074686919331651e-869j)  +/-  (4.38e-101, 5.3e-223j)
| (0.0015802422327212488275 + 8.9816626547048631652e-856j)  +/-  (4.45e-85, 5.39e-207j)
| (4.0994110572300105079e-20 + 3.558252478209767738e-866j)  +/-  (1.58e-98, 1.91e-220j)
| (0.016631643221151782379 + 2.1418660011350292849e-855j)  +/-  (5.96e-82, 7.23e-204j)
| (0.039749694585546572318 - 4.2087602550833222138e-855j)  +/-  (3.13e-79, 3.79e-201j)
| (0.016631643221151782379 + 3.9820546926346839642e-855j)  +/-  (2.73e-82, 3.31e-204j)
| (1.0193716827880236299e-08 + 8.1311239011173516067e-860j)  +/-  (3.48e-94, 4.21e-216j)
| (3.2372870299540589205e-07 + 3.4833302702754544701e-857j)  +/-  (2.79e-91, 3.38e-213j)
| (1.0193716827880236299e-08 + 6.8112030024744920902e-859j)  +/-  (1.96e-93, 2.38e-215j)
| (1.940978491598060731e-07 - 1.6395873134984512324e-858j)  +/-  (5.82e-94, 7.05e-216j)
| (0.075612120173501171656 + 1.0517156289653702456e-854j)  +/-  (1.52e-80, 1.85e-202j)
| (0.039749694585546572318 - 6.8504767854020717465e-855j)  +/-  (7.66e-83, 9.29e-205j)
| (5.8831429424407611893e-17 - 1.7126763075002585498e-866j)  +/-  (2.06e-99, 2.5e-221j)
| (0.11763123469753732583 - 1.1046121251933906152e-854j)  +/-  (6.88e-82, 8.34e-204j)
| (0.00033141923472824957548 - 1.1794817562792005684e-856j)  +/-  (4.06e-91, 4.92e-213j)
| (4.8725200648561680686e-06 - 6.313334905913380913e-857j)  +/-  (1.27e-91, 1.54e-213j)
| (2.5641585872180455458e-10 - 5.7768104340650996793e-860j)  +/-  (1e-95, 1.21e-217j)
| (4.8721421566208093662e-05 + 1.2998846087986487711e-856j)  +/-  (1.83e-91, 2.22e-213j)
| (0.0056767835575515835062 - 2.0426900705385601341e-855j)  +/-  (4.51e-89, 5.47e-211j)
| (0.0015802422327212488275 + 3.6230884995331445161e-856j)  +/-  (5.3e-93, 6.42e-215j)
| (0.1561557961819257768 + 1.4181912576394598699e-854j)  +/-  (6.94e-87, 8.41e-209j)
| (0.00033141923472824957548 - 3.4554548392856801383e-856j)  +/-  (5.5e-91, 6.66e-213j)
| (0.11763123469753732583 - 1.4021927139893129817e-854j)  +/-  (5.37e-88, 6.5e-210j)
| (3.4660998644675557483e-12 + 5.7588980158473445348e-861j)  +/-  (1.6e-97, 1.94e-219j)
| (4.8721421566208093662e-05 + 3.6663028476355350339e-857j)  +/-  (9.6e-96, 1.16e-217j)
| (0.075612120173501171656 + 7.3379168127183397272e-855j)  +/-  (1.29e-90, 1.56e-212j)
| (2.5641585872180455458e-10 - 4.3084122561854802212e-861j)  +/-  (1.13e-99, 1.38e-221j)
| (0.1561557961819257768 + 1.5983194261871572335e-854j)  +/-  (6.45e-91, 7.83e-213j)
| (0.0056767835575515835062 - 9.5643715013210386132e-856j)  +/-  (5.84e-94, 7.09e-216j)
| (3.2372870299540589205e-07 + 6.7577786331288480688e-858j)  +/-  (1.76e-97, 2.14e-219j)
| (0.17315388778706307568 - 1.5934616626052617123e-854j)  +/-  (4.71e-94, 9.58e-216j)
| (4.8725200648561680686e-06 - 1.4355977919946289747e-857j)  +/-  (3.81e-97, 4.61e-219j)
