Starting with polynomial:
P : t^2 - 1
Extension levels are: 2 3 6 20
-------------------------------------------------
Trying to find an order 3 Kronrod extension for:
P1 : t^2 - 1
Solvable: 1
-------------------------------------------------
Trying to find an order 6 Kronrod extension for:
P2 : t^5 - 7*t^3 + 6*t
Solvable: 1
-------------------------------------------------
Trying to find an order 20 Kronrod extension for:
P3 : t^11 - 6923/164*t^9 + 97479/164*t^7 - 566685/164*t^5 + 1313235/164*t^3 - 418635/82*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^31 - 121921938457464510034469253163056449697836728231/261532353574196499978585172820869754275211148*t^29 + 46721345774014034094114901782926188977659229853481/523064707148392999957170345641739508550422296*t^27 - 7671336076773682666951258788997282210217001072248115/813656211119722444377820537664928124411768016*t^25 + 929263510475282351885815567247020275074277395423463225/1511075820650913110987380998520580802478997744*t^23 - 277433414685348288781589388900373518765355616033832188925/10577530744556391776911666989644065617352984208*t^21 + 1137620377287397238822112648626688114672403182510008805975/1511075820650913110987380998520580802478997744*t^19 - 2781209059042065986072630989654046194029486376889037714975/188884477581364138873422624815072600309874718*t^17 + 148339151584349410226503876051374268756948982602247441719125/755537910325456555493690499260290401239498872*t^15 - 1335337535407712069995177645993009407403524315341953063631625/755537910325456555493690499260290401239498872*t^13 + 152791988285748761332482382324727177349994343611564893873375/14529575198566472221032509601159430793067286*t^11 - 4635584095347505642223792677587578908012764570708037999279125/116236601588531777768260076809275446344538288*t^9 + 10556175685090291234201524157913883859275654096455353941608625/116236601588531777768260076809275446344538288*t^7 - 13063732950334203429399596854206267330900742447866011205541875/116236601588531777768260076809275446344538288*t^5 + 7332115608620337099121646950355075119657811815644263925211875/116236601588531777768260076809275446344538288*t^3 - 613534018006080977160851631739772482956498672166138016604375/58118300794265888884130038404637723172269144*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: 1
  current precision for roots: 212
  current precision for roots: 424
 current precision for weights: 212
Linear system for weights solvable: 1
Sufficient bits for target precision reached
-------------------------------------------------
The nodes are:
| (2.7774922272315637741 - 6.0181078280381401459e-374j)  +/-  (1.09e-121, 1.09e-121j)
| (-12.538691004639930526 - 6.0108640630913767687e-377j)  +/-  (1.33e-123, 1.33e-123j)
| (8.6568931161583564745 + 1.0842072441041552103e-374j)  +/-  (6.89e-122, 6.89e-122j)
| (2.4494897427831780982 - 1.310849436374515339e-374j)  +/-  (4.73e-122, 4.73e-122j)
| (5.9647277735900030785 + 2.0482264238009274107e-373j)  +/-  (9.25e-121, 9.25e-121j)
| (-8.6568931161583564745 + 4.4742972990113314513e-373j)  +/-  (6.32e-122, 6.32e-122j)
| (-4.5448979391212497356 - 3.3215281723032696894e-378j)  +/-  (5.74e-121, 5.74e-121j)
| (-1.4520548644586134844 + 8.8869225925461201812e-389j)  +/-  (6.6e-124, 6.6e-124j)
| (6.749260010075933742 + 1.4806622109784237708e-388j)  +/-  (7.21e-121, 7.21e-121j)
| (5.2349036925197808702 + 2.5556631499868743344e-388j)  +/-  (8.21e-121, 8.21e-121j)
| (3.2728782272458314193 - 6.1556456512843220323e-389j)  +/-  (1.91e-121, 1.91e-121j)
| (4.5448979391212497356 - 7.4540652445276646654e-389j)  +/-  (5.81e-121, 5.81e-121j)
| (-3.2728782272458314193 + 2.4452703827008484159e-392j)  +/-  (1.73e-121, 1.73e-121j)
| (-6.749260010075933742 - 1.1735486810404662618e-403j)  +/-  (6.97e-121, 6.97e-121j)
| (-1.961016437141193946 - 3.3444191210932015532e-412j)  +/-  (6.29e-123, 6.29e-123j)
| (1.961016437141193946 - 1.836721888911561664e-419j)  +/-  (6.13e-123, 6.13e-123j)
| (12.538691004639930526 + 7.4311309368644592568e-424j)  +/-  (1.37e-123, 1.37e-123j)
| (-7.6193269084567655214 + 1.9025901099949821474e-423j)  +/-  (3.11e-121, 3.11e-121j)
| (-3.8885076994910220805 + 2.6357403743170652756e-442j)  +/-  (2.99e-121, 2.99e-121j)
| (-2.7774922272315637741 + 2.0061507155638211913e-458j)  +/-  (1.04e-121, 1.04e-121j)
| (7.6193269084567655214 + 4.0049407612358854669e-468j)  +/-  (3.12e-121, 3.12e-121j)
| (0.52607400304926710414 + 1.4138262420438853299e-471j)  +/-  (6.16e-126, 6.16e-126j)
| (-0.52607400304926710414 + 1.1879344005424170405e-468j)  +/-  (5.1e-126, 5.1e-126j)
| (-5.2349036925197808702 - 7.1279976463554021189e-477j)  +/-  (8.66e-121, 8.66e-121j)
| (-1 + 4.3799997064603086114e-488j)  +/-  (7.93e-125, 7.93e-125j)
| (3.8885076994910220805 - 1.2544983156627582155e-485j)  +/-  (3.2e-121, 3.2e-121j)
| (1 - 6.1055156263276038755e-489j)  +/-  (6.53e-125, 6.53e-125j)
| (1.4520548644586134844 + 5.9411527237523306155e-488j)  +/-  (6.11e-124, 6.11e-124j)
| (-5.9647277735900030785 - 4.906667931916560563e-488j)  +/-  (1.03e-120, 1.03e-120j)
| (-1.1104939513754183888e-498 - 1.4548895743247907492e-499j)  +/-  (3.47e-497, 3.47e-497j)
| (-2.4494897427831780982 + 5.3129998997994552699e-493j)  +/-  (4.42e-122, 4.42e-122j)
-------------------------------------------------
The weights are:
| (0.0030794756938060059339 + 8.9690648497702504952e-376j)  +/-  (2.06e-24, 1.06e-84j)
| (7.4050344422321839669e-29 - 6.3054603558985037448e-393j)  +/-  (1.5e-44, 7.71e-105j)
| (2.5291679923743924957e-17 - 1.3260500350397976665e-386j)  +/-  (9.99e-40, 5.13e-100j)
| (0.0079216757889067689649 - 1.1442139726184834926e-375j)  +/-  (8.67e-24, 4.45e-84j)
| (5.6559921992320875826e-09 - 3.5310825361167474527e-381j)  +/-  (3.51e-35, 1.8e-95j)
| (2.5291679923743924957e-17 + 4.4987619197788604545e-387j)  +/-  (4.01e-41, 2.06e-101j)
| (8.7783865454721804058e-06 - 5.6710176003763061361e-380j)  +/-  (6.78e-34, 3.48e-94j)
| (0.066490568513662931539 - 2.2062603276776299947e-376j)  +/-  (5.7e-22, 2.93e-82j)
| (4.198810196518653544e-11 - 1.0737671994142066791e-382j)  +/-  (4.71e-37, 2.42e-97j)
| (3.1646970266369076293e-07 + 8.0807457139318229876e-381j)  +/-  (2.11e-34, 1.09e-94j)
| (0.0010979332779036407517 + 4.8543389990110522663e-377j)  +/-  (2.68e-30, 1.38e-90j)
| (8.7783865454721804058e-06 + 7.5834555831999334272e-380j)  +/-  (2.24e-33, 1.15e-93j)
| (0.0010979332779036407517 - 4.921843366172522913e-378j)  +/-  (9.92e-34, 5.09e-94j)
| (4.198810196518653544e-11 + 1.7069178880837696283e-383j)  +/-  (5.29e-41, 2.72e-101j)
| (0.03073258577415638431 + 1.1530367379864049629e-376j)  +/-  (3.01e-30, 1.54e-90j)
| (0.03073258577415638431 + 4.4637630000431288095e-376j)  +/-  (2.31e-29, 1.19e-89j)
| (7.4050344422321839669e-29 + 1.2374725520966867145e-392j)  +/-  (9.01e-49, 4.63e-109j)
| (9.2007616549074520819e-14 - 4.6189224908363403882e-385j)  +/-  (2.32e-42, 1.19e-102j)
| (0.00013280532864853856659 + 5.3969840206745967335e-379j)  +/-  (2.02e-36, 1.04e-96j)
| (0.0030794756938060059339 + 3.1429971866954235325e-377j)  +/-  (1.8e-34, 9.26e-95j)
| (9.2007616549074520819e-14 + 1.8009403370561139274e-384j)  +/-  (2.13e-42, 1.1e-102j)
| (0.17605209841741741463 - 5.7299548646365241193e-376j)  +/-  (6.42e-32, 3.29e-92j)
| (0.17605209841741741463 - 4.1462999893703382773e-376j)  +/-  (3.92e-32, 2.01e-92j)
| (3.1646970266369076293e-07 + 5.0994219531757967621e-381j)  +/-  (2.28e-39, 1.17e-99j)
| (0.10765358406947887892 + 3.4445559633097481694e-376j)  +/-  (1.34e-32, 6.9e-93j)
| (0.00013280532864853856659 - 1.9975513885120569122e-378j)  +/-  (1.09e-36, 5.6e-97j)
| (0.10765358406947887892 + 6.47713969273362971e-376j)  +/-  (1.74e-33, 8.91e-94j)
| (0.066490568513662931539 - 5.7401711030338522933e-376j)  +/-  (8.4e-34, 4.31e-94j)
| (5.6559921992320875826e-09 - 3.5619009586801556271e-382j)  +/-  (1.09e-40, 5.62e-101j)
| (0.2136603451633979328 + 4.6999342193909237872e-376j)  +/-  (1.37e-34, 7.27e-95j)
| (0.0079216757889067689649 - 6.7888839035146924377e-377j)  +/-  (2.55e-35, 1.3e-95j)
