Starting with polynomial:
P : 676039/1024*t^12 - 969969/512*t^10 + 2078505/1024*t^8 - 255255/256*t^6 + 225225/1024*t^4 - 9009/512*t^2 + 231/1024
Extension levels are: 12 13
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Trying to find an order 13 Kronrod extension for:
P1 : 676039/1024*t^12 - 969969/512*t^10 + 2078505/1024*t^8 - 255255/256*t^6 + 225225/1024*t^4 - 9009/512*t^2 + 231/1024
Solvable: 1
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Ending with final polynomial:
P : 676039/1024*t^25 - 113897875/27648*t^23 + 122428248475/10824192*t^21 - 162762848091025/9059848704*t^19 + 91911271910897075/5034353347584*t^17 - 52228553975713777025/4213753751927808*t^15 + 5391794000036513461625275/946094114590029073152*t^13 - 201966691589935661524681/114678074495761099776*t^11 + 13591251201800897201395/38226024831920366592*t^9 - 636076610214703187075/14334759311970137472*t^7 + 59273215415530548341/19113012415960183296*t^5 - 3842874456522219755/38226024831920366592*t^3 + 110677163924317627/114678074495761099776*t
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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
-------------------------------------------------
The nodes are:
| (-0.24850574832046927627 - 1.1697755298688964217e-432j)  +/-  (1.49e-125, 1.49e-125j)
| (-0.5873179542866174473 - 8.2082025267153825227e-430j)  +/-  (3.3e-122, 3.3e-122j)
| (-0.90411725637047485668 - 6.6931690757420141249e-427j)  +/-  (1.11e-119, 1.11e-119j)
| (0.99693392252959542691 + 5.9903647597443998647e-425j)  +/-  (9.13e-120, 9.13e-120j)
| (0.90411725637047485668 + 8.8570510116192733488e-438j)  +/-  (1.07e-119, 1.07e-119j)
| (0.5873179542866174473 + 1.6913626940500805598e-446j)  +/-  (3.33e-122, 3.33e-122j)
| (0.24850574832046927627 - 9.4484680681381729711e-452j)  +/-  (1.51e-125, 1.51e-125j)
| (-0.84355812416115324479 - 3.4816402496533849211e-450j)  +/-  (4.44e-120, 4.44e-120j)
| (0.98156063424671925069 + 2.2686246740154185904e-448j)  +/-  (1.95e-119, 1.95e-119j)
| (-0.99693392252959542691 - 6.0971737878698984242e-459j)  +/-  (9.32e-120, 9.32e-120j)
| (0.84355812416115324479 + 1.9645386227035722493e-459j)  +/-  (4.82e-120, 4.82e-120j)
| (0.36783149899818019375 + 1.2120121326537952752e-468j)  +/-  (2.98e-124, 2.98e-124j)
| (-0.95053779594312129655 + 1.7979617416983712397e-465j)  +/-  (2.04e-119, 2.04e-119j)
| (-0.68405989547005589394 + 3.1762975545253175805e-469j)  +/-  (2.3e-121, 2.3e-121j)
| (-8.0258604968949450246e-474 - 1.9271992570206871277e-474j)  +/-  (2.06e-472, 2.06e-472j)
| (0.68405989547005589394 - 1.3197914724393417658e-467j)  +/-  (2.43e-121, 2.43e-121j)
| (0.95053779594312129655 - 1.4041095951715191129e-473j)  +/-  (1.89e-119, 1.89e-119j)
| (-0.12523340851146891547 + 1.6940257943512010945e-486j)  +/-  (7.38e-127, 7.38e-127j)
| (-0.76990267419430468704 - 2.6357067803208217867e-479j)  +/-  (1.23e-120, 1.23e-120j)
| (-0.98156063424671925069 + 4.814719760728730002e-482j)  +/-  (1.94e-119, 1.94e-119j)
| (0.48133945047815709294 - 9.4643085237428211205e-487j)  +/-  (3.41e-123, 3.41e-123j)
| (0.76990267419430468704 + 1.9065673272795404339e-491j)  +/-  (1.27e-120, 1.27e-120j)
| (0.12523340851146891547 + 7.7465648488297693608e-499j)  +/-  (7.38e-127, 7.38e-127j)
| (-0.36783149899818019375 + 9.2100015660193061739e-498j)  +/-  (2.97e-124, 2.97e-124j)
| (-0.48133945047815709294 - 1.7292806621617897896e-497j)  +/-  (3.76e-123, 3.76e-123j)
-------------------------------------------------
The weights are:
| (0.12162630352394838325 - 5.7245054869561122399e-426j)  +/-  (4.99e-41, 1.55e-98j)
| (0.10164973227906027772 + 3.6222306084921675369e-426j)  +/-  (3.55e-41, 1.1e-98j)
| (0.053697017607756251229 + 1.586337233181140418e-426j)  +/-  (6.86e-42, 2.13e-99j)
| (0.0082577114331683957577 - 6.3531138601166241702e-425j)  +/-  (2.48e-42, 7.69e-100j)
| (0.053697017607756251229 + 3.4342549415762434556e-425j)  +/-  (1.45e-42, 4.5e-100j)
| (0.10164973227906027772 + 1.4800278240658455891e-425j)  +/-  (8.85e-43, 2.75e-100j)
| (0.12162630352394838325 - 9.6635313159267230456e-426j)  +/-  (7.53e-43, 2.34e-100j)
| (0.067250907050839930305 - 1.4394487935818289681e-426j)  +/-  (6.68e-43, 2.07e-100j)
| (0.023036084038982232591 + 9.4052501932588570389e-425j)  +/-  (5.27e-43, 1.63e-100j)
| (0.0082577114331683957577 - 3.0816708437725778172e-427j)  +/-  (1.13e-44, 3.51e-102j)
| (0.067250907050839930305 - 2.6240024606474913475e-425j)  +/-  (2.44e-43, 7.56e-101j)
| (0.11671205350175682629 + 1.105785658374274176e-425j)  +/-  (3.3e-43, 1.02e-100j)
| (0.038915230469299477115 - 1.7630020834381812009e-426j)  +/-  (4.81e-44, 1.49e-101j)
| (0.091549468295049210528 - 2.9823898918828819594e-426j)  +/-  (5.28e-44, 1.64e-101j)
| (0.1255568939054743353 - 7.4505292344401307274e-426j)  +/-  (2.66e-44, 8.26e-102j)
| (0.091549468295049210528 - 1.7489320374328417613e-425j)  +/-  (1.75e-44, 5.43e-102j)
| (0.038915230469299477115 - 5.0230618639469506152e-425j)  +/-  (2.72e-44, 8.44e-102j)
| (0.12458416453615607344 + 6.5412531220955294045e-426j)  +/-  (1.19e-44, 3.69e-102j)
| (0.079920275333601701493 + 2.3149210087177752673e-426j)  +/-  (6.87e-45, 2.13e-102j)
| (0.023036084038982232591 + 9.4133294260186909989e-427j)  +/-  (3.54e-45, 1.1e-102j)
| (0.11002260497764407264 - 1.2729137290475017699e-425j)  +/-  (4.64e-45, 1.44e-102j)
| (0.079920275333601701493 + 2.1117843807618645087e-425j)  +/-  (4.57e-45, 1.42e-102j)
| (0.12458416453615607344 + 8.478186880645587743e-426j)  +/-  (1.65e-45, 5.11e-103j)
| (0.11671205350175682629 + 4.978413387544162114e-426j)  +/-  (1.43e-46, 4.44e-104j)
| (0.11002260497764407264 - 4.2818917611318667014e-426j)  +/-  (1.21e-46, 3.75e-104j)
