Starting with polynomial:
P : 1/720*t^6 - 1/20*t^5 + 5/8*t^4 - 10/3*t^3 + 15/2*t^2 - 6*t + 1
Extension levels are: 6 13
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Trying to find an order 13 Kronrod extension for:
P1 : 1/720*t^6 - 1/20*t^5 + 5/8*t^4 - 10/3*t^3 + 15/2*t^2 - 6*t + 1
Solvable: 1
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Ending with final polynomial:
P : 1/720*t^19 - 2286434967412543381698203/5970348408543309061223760*t^18 + 5849456343990687065595562/124382258511318938775495*t^17 - 847908484302821798965262207/248764517022637877550990*t^16 + 162123688827942683723157278557/995058068090551510203960*t^15 - 360730221080970330739301101145/66337204539370100680264*t^14 + 30386896982390070590041693094345/232180215887795352380924*t^13 - 537150388482224193924400441358265/232180215887795352380924*t^12 + 1759454773523524147009310038307055/58045053971948838095231*t^11 - 17121436174804205008441650192135345/58045053971948838095231*t^10 + 123223916236206782073010427174456490/58045053971948838095231*t^9 - 649055722482856851386633505068891490/58045053971948838095231*t^8 + 2458445161056951321303508038521994480/58045053971948838095231*t^7 - 931691972026284024742062346042063920/8292150567421262585033*t^6 + 1666024496708391612853058902519867680/8292150567421262585033*t^5 - 1898921466748823942188900403746221600/8292150567421262585033*t^4 + 1267712742786099581424861774066729600/8292150567421262585033*t^3 - 432369923760559889325890275599907200/8292150567421262585033*t^2 + 58790981144542395208371623357817600/8292150567421262585033*t - 1786486736609286078350328915398400/8292150567421262585033
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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
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The nodes are:
| (52.207759563521540563 + 6.0858472827900695569e-366j)  +/-  (1.91e-120, 1.91e-120j)
| (29.097483149698538823 + 2.2029143784632417684e-364j)  +/-  (1.3e-118, 1.3e-118j)
| (42.450525992102121954 + 3.2528941431306863836e-365j)  +/-  (1.62e-119, 1.62e-119j)
| (19.712220464353030802 + 6.2180953492785139983e-363j)  +/-  (2.43e-118, 2.43e-118j)
| (15.982873980601701783 - 3.3556243478296801694e-369j)  +/-  (2.87e-118, 2.87e-118j)
| (9.793460914960124835 + 6.1375589694321893353e-393j)  +/-  (6.61e-117, 6.61e-117j)
| (0.59176464896653972498 - 1.284541560617453935e-424j)  +/-  (1.28e-124, 1.28e-124j)
| (35.097411370169313126 - 2.9322409949021912047e-419j)  +/-  (6.1e-119, 6.1e-119j)
| (24.040541984657521219 - 3.702711944652371586e-418j)  +/-  (2.18e-118, 2.18e-118j)
| (1.1889321016726230307 - 2.5021833595614854262e-425j)  +/-  (1.45e-123, 1.45e-123j)
| (2.9927363260593140777 - 1.1740466838642283779e-423j)  +/-  (1.55e-121, 1.55e-121j)
| (5.7751435691045105018 + 6.7238340118631697828e-428j)  +/-  (6.43e-120, 6.43e-120j)
| (9.8374674183825899177 - 3.5880660451226310205e-447j)  +/-  (7e-117, 7e-117j)
| (0.22284660417926068946 + 6.1135233973964526682e-477j)  +/-  (5.15e-126, 5.15e-126j)
| (7.7198900810955323919 + 7.7027227599102316862e-468j)  +/-  (5.26e-119, 5.26e-119j)
| (1.9990632763588860294 - 1.2430454082785943108e-481j)  +/-  (1.7e-122, 1.7e-122j)
| (4.2178145339457695365 + 4.9669582164415855193e-477j)  +/-  (1.05e-120, 1.05e-120j)
| (0.041712463545761441838 - 2.4396640912131140761e-485j)  +/-  (2e-127, 2e-127j)
| (12.765210544309039242 - 4.4274847719177784372e-476j)  +/-  (2.24e-118, 2.24e-118j)
-------------------------------------------------
The weights are:
| (2.5067310882052791742e-22 - 1.626212009381041143e-380j)  +/-  (1.25e-51, 3.03e-110j)
| (1.2649582578921483303e-12 + 2.158157128279804793e-374j)  +/-  (1.41e-47, 3.44e-106j)
| (3.0312297990502900078e-18 + 4.5708472652257345888e-378j)  +/-  (3.07e-50, 7.49e-109j)
| (1.1026070795665913367e-08 - 4.6715044817445982147e-371j)  +/-  (1.47e-45, 3.59e-104j)
| (3.962240215648450302e-07 + 2.4622091518724805531e-370j)  +/-  (1.34e-44, 3.26e-103j)
| (-0.00062941401353006794887 - 5.9936237271937388226e-367j)  +/-  (1.03e-42, 2.5e-101j)
| (0.26627347265020550405 + 5.2567134476196572065e-367j)  +/-  (1.72e-36, 4.19e-95j)
| (3.7643037697765893109e-15 - 4.1335681858657013539e-376j)  +/-  (7.22e-50, 1.76e-108j)
| (1.6914677332263600939e-10 - 9.9661318211993542189e-373j)  +/-  (2.65e-47, 6.46e-106j)
| (0.21619811749600417123 - 4.7942673658712994496e-367j)  +/-  (1.72e-36, 4.19e-95j)
| (0.054778152900883421726 - 2.6108530889600165882e-367j)  +/-  (4e-40, 9.74e-99j)
| (0.0054161527585056984233 - 7.2255042180982109837e-368j)  +/-  (9.84e-43, 2.4e-101j)
| (0.00073443588235133028656 + 5.8144641489559410552e-367j)  +/-  (6.52e-43, 1.59e-101j)
| (0.21152197455587816784 - 4.3587198971754481203e-367j)  +/-  (5.96e-40, 1.45e-98j)
| (0.00095659280898726360266 + 4.3660855069302423207e-368j)  +/-  (7.54e-44, 1.84e-102j)
| (0.12237468930666262254 + 3.8280684846091755466e-367j)  +/-  (7.57e-42, 1.85e-100j)
| (0.020289535393057833513 + 1.4584299731836656048e-367j)  +/-  (3.88e-43, 9.51e-102j)
| (0.10207734613550287171 + 1.7017856729317530876e-367j)  +/-  (2.63e-42, 6.94e-101j)
| (8.5367049833236003066e-06 - 1.8041081282459968542e-369j)  +/-  (7.96e-46, 1.93e-104j)
