Starting with polynomial:
P : t^10 - 45*t^8 + 630*t^6 - 3150*t^4 + 4725*t^2 - 945
Extension levels are: 10 17
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Trying to find an order 17 Kronrod extension for:
P1 : t^10 - 45*t^8 + 630*t^6 - 3150*t^4 + 4725*t^2 - 945
Solvable: 1
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Ending with final polynomial:
P : t^27 - 2133931887/7930307*t^25 + 242558486550/7930307*t^23 - 312514703550/161843*t^21 + 84889912926375/1132901*t^19 - 2117887772942115/1132901*t^17 + 34552661259406140/1132901*t^15 - 52576727127297300/161843*t^13 + 2514139075042589475/1132901*t^11 - 965847906202330125/102991*t^9 + 339133387971906450/14713*t^7 - 436596584756769450/14713*t^5 + 242427777674779125/14713*t^3 - 36876618764051625/14713*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
Positive weights:   27 out of 27
Indefinite weights: 0 out of 27
Negative weights:   0 out of 27
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (4.8594628283323121502 + 3.6644459409279677441e-443j)  +/-  (2.38e-121, 2.38e-121j)
| (5.5761327373741432446 - 2.8761191179084933132e-452j)  +/-  (2.47e-121, 2.47e-121j)
| (-6.3578362042129091111 + 3.5470503392956416033e-464j)  +/-  (1.88e-121, 1.88e-121j)
| (-5.5761327373741432446 + 5.2963270703318033007e-479j)  +/-  (2.59e-121, 2.59e-121j)
| (8.2893132876774067443 - 9.9058104518909535824e-488j)  +/-  (1.27e-122, 1.27e-122j)
| (-4.8594628283323121502 + 5.3038011712846084676e-485j)  +/-  (2.22e-121, 2.22e-121j)
| (-8.2893132876774067443 + 8.6390346005115750147e-489j)  +/-  (1.11e-122, 1.11e-122j)
| (4.1958653119257106465 - 2.6608985872510686159e-488j)  +/-  (1.65e-121, 1.65e-121j)
| (-7.2342076046422425759 + 5.4415346653567045798e-490j)  +/-  (5.89e-122, 5.89e-122j)
| (-2.4843258416389545809 + 3.0523231367799254248e-494j)  +/-  (1.19e-122, 1.19e-122j)
| (7.2342076046422425759 - 4.3243907895950147642e-493j)  +/-  (6.23e-122, 6.23e-122j)
| (6.3578362042129091111 + 1.7076597305113961385e-497j)  +/-  (1.76e-121, 1.76e-121j)
| (3.0151071137397646369 + 2.5680124999211967133e-498j)  +/-  (3.58e-122, 3.58e-122j)
| (-1.4659890943911581833 - 4.8830338574169224151e-499j)  +/-  (3.95e-124, 3.95e-124j)
| (2.4843258416389545809 + 2.9932205043591871483e-499j)  +/-  (1.27e-122, 1.27e-122j)
| (-3.0151071137397646369 + 6.817958884063777814e-497j)  +/-  (3.6e-122, 3.6e-122j)
| (-4.1958653119257106465 + 3.6705623770201526464e-500j)  +/-  (1.61e-121, 1.61e-121j)
| (1.9706725020134815124 - 5.1615312561268055563e-506j)  +/-  (2.64e-123, 2.64e-123j)
| (-0.97166894826197596651 - 2.0211909617884798245e-508j)  +/-  (3.51e-125, 3.51e-125j)
| (3.5818234835519269228 - 1.4979523128041362834e-506j)  +/-  (9.21e-122, 9.21e-122j)
| (1.4659890943911581833 - 1.2557926288218802842e-508j)  +/-  (3.92e-124, 3.92e-124j)
| (0.97166894826197596651 + 1.7586064618370270383e-508j)  +/-  (3.58e-125, 3.58e-125j)
| (-3.5818234835519269228 + 5.9931718518649418616e-507j)  +/-  (9.03e-122, 9.03e-122j)
| (-0.48493570751549765305 + 2.7538088551146819048e-513j)  +/-  (3.9e-126, 3.9e-126j)
| (-1.9706725020134815124 + 4.8707872298849508586e-511j)  +/-  (2.71e-123, 2.71e-123j)
| (5.0189980240658323943e-524 + 5.2241702509836883999e-523j)  +/-  (1.42e-521, 1.42e-521j)
| (0.48493570751549765305 + 3.906553458445228066e-514j)  +/-  (3.42e-126, 3.42e-126j)
-------------------------------------------------
The weights are:
| (2.0481148790083926706e-06 - 2.5605369823979167963e-448j)  +/-  (1.08e-37, 9.61e-98j)
| (5.2715576094220125922e-08 - 8.6488715813758408663e-450j)  +/-  (2.8e-39, 2.5e-99j)
| (5.471577503690254574e-10 - 2.9611810891527979532e-452j)  +/-  (3.38e-42, 3.02e-102j)
| (5.2715576094220125922e-08 + 5.9396571819106989397e-451j)  +/-  (5.76e-41, 5.15e-101j)
| (5.820958835535344004e-16 + 2.6912889938094105693e-455j)  +/-  (4.77e-46, 4.26e-106j)
| (2.0481148790083926706e-06 - 7.7222591485712495312e-450j)  +/-  (4.24e-40, 3.79e-100j)
| (5.820958835535344004e-16 - 7.0202113941960962556e-456j)  +/-  (2.56e-46, 2.29e-106j)
| (3.8302929956645834439e-05 + 9.7177963585766849872e-448j)  +/-  (4.01e-40, 3.59e-100j)
| (1.626052745428577976e-12 + 7.9187726885499396121e-454j)  +/-  (1.95e-44, 1.74e-104j)
| (0.0094679032866500273953 - 8.5988061894571862531e-447j)  +/-  (3.28e-37, 2.93e-97j)
| (1.626052745428577976e-12 - 4.0327292471913100086e-453j)  +/-  (1.21e-45, 1.08e-105j)
| (5.471577503690254574e-10 + 2.2168342223086038746e-451j)  +/-  (3.46e-44, 3.09e-104j)
| (0.0023110815295750717127 + 1.0139549488963163843e-446j)  +/-  (3.97e-40, 3.55e-100j)
| (0.068064661839057213209 - 5.3406665142901923564e-446j)  +/-  (5.33e-37, 4.76e-97j)
| (0.0094679032866500273953 - 2.6587020378610334782e-446j)  +/-  (1.67e-39, 1.49e-99j)
| (0.0023110815295750717127 + 2.374851729279423953e-447j)  +/-  (5.68e-41, 5.07e-101j)
| (3.8302929956645834439e-05 + 7.1214487529506490872e-449j)  +/-  (7.7e-43, 6.88e-103j)
| (0.029136923980472883669 + 5.6543079723735939306e-446j)  +/-  (6.53e-40, 5.83e-100j)
| (0.12179584814768533502 + 9.7057319151001124215e-446j)  +/-  (4.23e-39, 3.77e-99j)
| (0.00038510535765318313367 - 3.1804051938061683793e-447j)  +/-  (7.45e-42, 6.65e-102j)
| (0.068064661839057213209 - 9.9550289524732984792e-446j)  +/-  (1.32e-39, 1.18e-99j)
| (0.12179584814768533502 + 1.4557202241282966832e-445j)  +/-  (9.82e-40, 8.75e-100j)
| (0.00038510535765318313367 - 4.8137341373071143788e-448j)  +/-  (1.57e-42, 1.41e-102j)
| (0.1720680840298137572 - 1.4366633747339203092e-445j)  +/-  (3.64e-40, 3.27e-100j)
| (0.029136923980472883669 + 2.3914767984850583979e-446j)  +/-  (4.24e-41, 3.79e-101j)
| (0.19345997503979279002 + 1.7461639189333006933e-445j)  +/-  (1.51e-40, 1.35e-100j)
| (0.1720680840298137572 - 1.7551843717814629965e-445j)  +/-  (1.11e-40, 9.47e-101j)
