Starting with polynomial:
P : 1/24*t^4 - 2/3*t^3 + 3*t^2 - 4*t + 1
Extension levels are: 4 11
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Trying to find an order 11 Kronrod extension for:
P1 : 1/24*t^4 - 2/3*t^3 + 3*t^2 - 4*t + 1
Solvable: 1
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Ending with final polynomial:
P : 1/24*t^15 - 2582685385518509/342153039075864*t^14 + 50572983713511755/85538259768966*t^13 - 1130462181125218829/42769129884483*t^12 + 74864723642114561651/99794636397127*t^11 - 1420042046675839732871/99794636397127*t^10 + 18460663150990015998460/99794636397127*t^9 - 165990490853443547940000/99794636397127*t^8 + 1028856920195827994586480/99794636397127*t^7 - 618309799772068099135440/14256376628161*t^6 + 1713014779541963586575040/14256376628161*t^5 - 2972690419430647704412800/14256376628161*t^4 + 2979133428781164249936000/14256376628161*t^3 - 1504412072863215900278400/14256376628161*t^2 + 296735875510868927654400/14256376628161*t - 12326755351750243430400/14256376628161
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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:
| (32.307097117857015348 + 3.5941649146888979953e-278j)  +/-  (9.05e-121, 9.05e-121j)
| (25.694321723330669361 - 5.1466605096201184409e-277j)  +/-  (2.55e-120, 2.55e-120j)
| (20.397552359217984805 - 1.6692395936109057305e-282j)  +/-  (3.47e-120, 3.47e-120j)
| (41.228135136244468458 + 1.0065350370983943157e-285j)  +/-  (1.27e-121, 1.27e-121j)
| (4.5366202969211279833 - 1.3707709132239104584e-292j)  +/-  (1.87e-121, 1.87e-121j)
| (1.7457611011583465757 - 4.3184233445907764443e-304j)  +/-  (1.23e-123, 1.23e-123j)
| (7.1313689249580078034 - 7.8616041768272488507e-317j)  +/-  (2.09e-120, 2.09e-120j)
| (16.03077102797732905 - 1.0756362647852641454e-330j)  +/-  (4.01e-120, 4.01e-120j)
| (2.9702557719113650073 + 2.7450027184410350006e-350j)  +/-  (1.76e-122, 1.76e-122j)
| (6.0767535956187316056 - 3.5210347456554373281e-365j)  +/-  (1.26e-120, 1.26e-120j)
| (0.87144548374952918999 - 6.4772003217468841681e-376j)  +/-  (9.78e-125, 9.78e-125j)
| (0.055563802645548363525 - 5.0250313531838304924e-377j)  +/-  (2.07e-127, 2.07e-127j)
| (9.3950709123011331292 - 1.0569518890014938288e-383j)  +/-  (2.92e-120, 2.92e-120j)
| (12.396748773920318264 + 4.1723664856944692084e-395j)  +/-  (3.03e-120, 3.03e-120j)
| (0.3225476896193923118 + 5.9608574635513995975e-405j)  +/-  (6e-126, 6e-126j)
-------------------------------------------------
The weights are:
| (6.9868269690089271845e-14 + 8.643096567537713963e-290j)  +/-  (3.42e-54, 2.78e-113j)
| (4.0676512858504091797e-11 + 1.1942597509251356141e-287j)  +/-  (5.1e-53, 4.14e-112j)
| (6.6321637721856112135e-09 - 7.7442776233106659196e-287j)  +/-  (3.64e-52, 2.96e-111j)
| (1.3545853259247829007e-17 - 3.4759250428034747276e-292j)  +/-  (2.45e-56, 1.99e-115j)
| (0.018218812145458729143 - 4.2206303039189358517e-283j)  +/-  (9.78e-47, 7.94e-106j)
| (0.18265677507254644572 - 6.4351513985365299716e-283j)  +/-  (1.73e-43, 1.41e-102j)
| (0.0013071764784289754244 - 2.1048226006168395803e-283j)  +/-  (7.61e-49, 6.18e-108j)
| (4.3395062449744459231e-07 + 5.5562459013416664985e-286j)  +/-  (4.36e-52, 3.54e-111j)
| (0.071949310754388612546 + 5.0513588120631994566e-283j)  +/-  (5.45e-47, 4.42e-106j)
| (0.00244639831167509074 + 3.8758694872883173905e-283j)  +/-  (1.22e-48, 9.93e-108j)
| (0.29541193431618261911 + 7.264835267088496252e-283j)  +/-  (2.46e-47, 1.92e-106j)
| (0.13901138875411003615 + 2.4197284076659531931e-283j)  +/-  (8.14e-48, 6.37e-107j)
| (0.00022375106737820609923 + 2.9454291365647208044e-284j)  +/-  (1.1e-50, 8.91e-110j)
| (1.3670741796275101223e-05 - 4.0543362591725804301e-285j)  +/-  (9.43e-52, 7.67e-111j)
| (0.28876034173450034565 - 6.1100893270462419891e-283j)  +/-  (4.34e-48, 3.1e-107j)
