Starting with polynomial:
P : 256*t^8 - 3584*t^6 + 13440*t^4 - 13440*t^2 + 1680
Extension levels are: 8 19
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Trying to find an order 19 Kronrod extension for:
P1 : 256*t^8 - 3584*t^6 + 13440*t^4 - 13440*t^2 + 1680
Solvable: 1
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Ending with final polynomial:
P : 256*t^27 - 103979191936/2980019*t^25 + 5986878345600/2980019*t^23 - 355849670846400/5534321*t^21 + 77167934332544400/60877531*t^19 - 982207262395135800/60877531*t^17 + 8235782950037677200/60877531*t^15 - 45621315787167603000/60877531*t^13 + 12686440347454676625/4682887*t^11 - 5280959871173476125/851434*t^9 + 7236328321833148125/851434*t^7 - 10713703347387691875/1702868*t^5 + 14093817146384810625/6811472*t^3 - 2605992197474649375/13622944*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
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The nodes are:
| (5.9133739440660476393 + 6.5281609839972095132e-480j)  +/-  (7.02e-123, 7.02e-123j)
| (-4.526235089362088434 - 2.8212591653587617433e-478j)  +/-  (1.19e-121, 1.19e-121j)
| (-5.9133739440660476393 + 5.1800189993728362485e-483j)  +/-  (7.07e-123, 7.07e-123j)
| (-3.4297526672439691429 + 2.1080075992876405629e-484j)  +/-  (1.66e-121, 1.66e-121j)
| (5.1578071743686593352 - 7.427092857900150315e-486j)  +/-  (4.52e-122, 4.52e-122j)
| (4.526235089362088434 - 6.4992435229463184404e-485j)  +/-  (1.14e-121, 1.14e-121j)
| (-5.1578071743686593352 + 1.4239085404929483337e-484j)  +/-  (4.58e-122, 4.58e-122j)
| (-1.5717545971730697689 + 3.1332697405773151549e-484j)  +/-  (6.54e-123, 6.54e-123j)
| (2.4540554471383068846 - 6.4253693170594428696e-484j)  +/-  (8.37e-122, 8.37e-122j)
| (2.9306374202572440192 - 3.3477865395432849879e-484j)  +/-  (1.15e-121, 1.15e-121j)
| (1.9327984480635749771 - 4.8756362578029246975e-483j)  +/-  (1.87e-121, 1.87e-121j)
| (3.9578373553374509139 + 4.0195926409169177034e-488j)  +/-  (1.78e-121, 1.78e-121j)
| (-3.9578373553374509139 + 4.7552262706667986297e-487j)  +/-  (1.65e-121, 1.65e-121j)
| (-1.9327984480635749771 - 2.2442239422748156858e-489j)  +/-  (1.83e-121, 1.83e-121j)
| (1.5717545971730697689 + 2.4566703889830940963e-510j)  +/-  (6.52e-123, 6.52e-123j)
| (1.9816567566958429259 - 9.5729127095899356329e-509j)  +/-  (2.12e-121, 2.12e-121j)
| (1.1571937124467801947 + 1.5931618058068650433e-511j)  +/-  (4.53e-124, 4.53e-124j)
| (-1.9816567566958429259 + 2.5147256263256124024e-507j)  +/-  (2.07e-121, 2.07e-121j)
| (-0.76380492148557780194 - 8.3755021971459652044e-525j)  +/-  (3.53e-125, 3.53e-125j)
| (-0.38118699020732211685 + 8.4623571595178854544e-527j)  +/-  (2.54e-126, 2.54e-126j)
| (9.7959978711685833053e-529 + 7.9300935147555198186e-529j)  +/-  (3.4e-527, 3.4e-527j)
| (0.76380492148557780194 - 1.2520410592805513013e-526j)  +/-  (3.69e-125, 3.69e-125j)
| (-2.9306374202572440192 - 6.4878546765594724858e-522j)  +/-  (1.1e-121, 1.1e-121j)
| (3.4297526672439691429 + 8.1622044424681467963e-532j)  +/-  (1.52e-121, 1.52e-121j)
| (-1.1571937124467801947 + 4.4813396863350294533e-535j)  +/-  (4.72e-124, 4.72e-124j)
| (-2.4540554471383068846 + 8.0827620442452631948e-541j)  +/-  (8.65e-122, 8.65e-122j)
| (0.38118699020732211685 - 3.4738026991411763633e-549j)  +/-  (2.54e-126, 2.54e-126j)
-------------------------------------------------
The weights are:
| (3.1898719071092846654e-16 - 3.1943258577968300856e-492j)  +/-  (1.2e-47, 6.03e-108j)
| (4.249444027707216079e-10 - 6.5817099568965221434e-487j)  +/-  (5.67e-45, 2.86e-105j)
| (3.1898719071092846654e-16 + 2.3933980708290017569e-491j)  +/-  (3.46e-48, 1.74e-108j)
| (2.2501303088312381591e-06 - 2.7981983189295314261e-485j)  +/-  (1.68e-42, 8.48e-103j)
| (1.0678573251268047386e-12 + 3.537836523065659876e-490j)  +/-  (2.19e-47, 1.11e-107j)
| (4.249444027707216079e-10 - 1.325066163814786545e-488j)  +/-  (2.23e-46, 1.12e-106j)
| (1.0678573251268047386e-12 - 5.4195982766536761995e-489j)  +/-  (3.6e-47, 1.82e-107j)
| (0.020431904091079096405 + 2.427259515227409484e-482j)  +/-  (5.3e-38, 2.67e-98j)
| (0.00063869114993306427128 - 4.6334792912004849386e-484j)  +/-  (2.83e-42, 1.43e-102j)
| (5.1163635112435920874e-05 + 4.3258071570165256002e-485j)  +/-  (9.49e-44, 4.79e-104j)
| (-0.0026865909033372170927 - 3.0061382963695071365e-482j)  +/-  (3.09e-41, 1.56e-101j)
| (4.846253694201269453e-08 + 2.7361630807320449713e-487j)  +/-  (2.76e-46, 1.4e-106j)
| (4.846253694201269453e-08 + 4.0825210257722372088e-486j)  +/-  (6.18e-47, 3.12e-107j)
| (-0.0026865909033372170927 - 7.5424422602435637121e-482j)  +/-  (6.35e-43, 3.21e-103j)
| (0.020431904091079096405 + 1.1769621550959370338e-482j)  +/-  (8.15e-42, 4.1e-102j)
| (0.0070361680744121285632 + 2.4760253436600379302e-482j)  +/-  (8.92e-42, 4.5e-102j)
| (0.059530848350755077962 - 1.5362164931832022467e-482j)  +/-  (7.89e-42, 3.94e-102j)
| (0.0070361680744121285632 + 6.3931921315323043839e-482j)  +/-  (2.37e-43, 1.2e-103j)
| (0.1215104004252658175 + 3.2309637580679383313e-482j)  +/-  (1.76e-42, 8.52e-103j)
| (0.18589151529044846188 - 3.6607015952530019812e-482j)  +/-  (3.54e-42, 1.7e-102j)
| (0.2151872017349455645 + 3.6092565117482412079e-482j)  +/-  (1.92e-42, 9.3e-103j)
| (0.1215104004252658175 + 2.2976231751395571676e-482j)  +/-  (4.54e-43, 2.2e-103j)
| (5.1163635112435920874e-05 + 2.0139923903701588286e-484j)  +/-  (1.12e-46, 5.67e-107j)
| (2.2501303088312381591e-06 - 3.8574993144148496759e-486j)  +/-  (1.93e-47, 9.43e-108j)
| (0.059530848350755077962 - 2.592522207174564244e-482j)  +/-  (6.06e-44, 2.97e-104j)
| (0.00063869114993306427128 - 1.567482506359966177e-483j)  +/-  (1.02e-45, 5.19e-106j)
| (0.18589151529044846188 - 3.0918284445700866631e-482j)  +/-  (9.26e-44, 3.49e-104j)
