Starting with polynomial:
P : t^8 - 28*t^6 + 210*t^4 - 420*t^2 + 105
Extension levels are: 8 19
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Trying to find an order 19 Kronrod extension for:
P1 : t^8 - 28*t^6 + 210*t^4 - 420*t^2 + 105
Solvable: 1
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Ending with final polynomial:
P : t^27 - 812337437/2980019*t^25 + 93544974150/2980019*t^23 - 11120302213950/5534321*t^21 + 4822995895784025/60877531*t^19 - 122775907799391975/60877531*t^17 + 2058945737509419300/60877531*t^15 - 22810657893583801500/60877531*t^13 + 12686440347454676625/4682887*t^11 - 5280959871173476125/425717*t^9 + 14472656643666296250/425717*t^7 - 21427406694775383750/425717*t^5 + 14093817146384810625/425717*t^3 - 2605992197474649375/425717*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:
| (4.1445471861258943321 - 3.1234802478778829728e-347j)  +/-  (1.74e-121, 1.74e-121j)
| (0.53907981135137510807 + 4.8297705078689913002e-350j)  +/-  (3.28e-126, 3.28e-126j)
| (-4.8504027376017180633 + 1.2152863270536635328e-351j)  +/-  (2.09e-121, 2.09e-121j)
| (-8.3627736310818845355 + 7.6067438377333156928e-361j)  +/-  (1.17e-122, 1.17e-122j)
| (8.3627736310818845355 - 1.3662112569778921155e-370j)  +/-  (1.29e-122, 1.29e-122j)
| (-7.294240858097409139 + 2.6800876168587923304e-368j)  +/-  (5.72e-122, 5.72e-122j)
| (-2.8024858612875416991 - 1.6652863581187916867e-382j)  +/-  (3.23e-121, 3.23e-121j)
| (-1.6365190424351079992 - 8.795918269546018972e-403j)  +/-  (6.47e-124, 6.47e-124j)
| (6.4010630498648632936 - 8.6344753830014169052e-411j)  +/-  (1.6e-121, 1.6e-121j)
| (5.5972272655850856902 + 4.6963784757340740398e-409j)  +/-  (2.26e-121, 2.26e-121j)
| (-2.7333897785851779022 + 7.5471187476872071063e-413j)  +/-  (2.69e-121, 2.69e-121j)
| (2.7333897785851779022 + 1.4169339638154627212e-427j)  +/-  (2.49e-121, 2.49e-121j)
| (-3.4705584961585636227 + 1.7528705046233800903e-431j)  +/-  (1.05e-121, 1.05e-121j)
| (-5.5972272655850856902 - 1.732028064724476763e-441j)  +/-  (2.51e-121, 2.51e-121j)
| (3.4705584961585636227 + 2.1368071505300252456e-443j)  +/-  (1.03e-121, 1.03e-121j)
| (7.294240858097409139 - 8.7201556222266089444e-444j)  +/-  (5.67e-122, 5.67e-122j)
| (2.2227966680444159865 - 1.8580826134491169914e-442j)  +/-  (9.34e-123, 9.34e-123j)
| (-0.53907981135137510807 - 5.955752313230622672e-445j)  +/-  (3.28e-126, 3.28e-126j)
| (-2.2227966680444159865 + 4.0537069053532939118e-446j)  +/-  (9.79e-123, 9.79e-123j)
| (1.987460192502647951e-458 + 5.3782239411010199395e-458j)  +/-  (1.55e-456, 1.55e-456j)
| (4.8504027376017180633 + 4.8018270290315305463e-454j)  +/-  (2.15e-121, 2.15e-121j)
| (1.0801832789722211494 - 1.823829952872753923e-457j)  +/-  (5.77e-125, 5.77e-125j)
| (-6.4010630498648632936 + 3.3817358733084468008e-457j)  +/-  (1.46e-121, 1.46e-121j)
| (2.8024858612875416991 - 5.4373690570651382861e-453j)  +/-  (3.22e-121, 3.22e-121j)
| (-1.0801832789722211494 - 3.7449750908560249433e-456j)  +/-  (4.72e-125, 4.72e-125j)
| (-4.1445471861258943321 - 1.2990017248509082195e-459j)  +/-  (1.62e-121, 1.62e-121j)
| (1.6365190424351079992 + 1.8425257154029136456e-471j)  +/-  (6.24e-124, 6.24e-124j)
-------------------------------------------------
The weights are:
| (5.1163635112435920874e-05 + 5.3498279240176594648e-351j)  +/-  (6.51e-41, 1.03e-100j)
| (0.18589151529044846188 - 2.1167448327247597336e-349j)  +/-  (2.99e-35, 4.72e-95j)
| (2.2501303088312381591e-06 - 1.7290309959751325965e-353j)  +/-  (4.79e-43, 7.56e-103j)
| (3.1898719071092846654e-16 - 1.3419975713173639516e-359j)  +/-  (2.04e-49, 3.22e-109j)
| (3.1898719071092846654e-16 + 3.9385490304205218014e-359j)  +/-  (2.27e-50, 3.58e-110j)
| (1.0678573251268047386e-12 + 1.5138527087328444097e-357j)  +/-  (6.66e-48, 1.05e-107j)
| (0.0070361680744121285632 + 1.1937848729219438695e-349j)  +/-  (2.72e-39, 4.3e-99j)
| (0.059530848350755077962 - 7.7440924602111784801e-350j)  +/-  (2.99e-35, 4.72e-95j)
| (4.249444027707216079e-10 + 2.6538732259041240174e-355j)  +/-  (6.67e-48, 1.05e-107j)
| (4.846253694201269453e-08 - 7.9698668193574876794e-354j)  +/-  (1.15e-46, 1.82e-106j)
| (-0.0026865909033372170927 - 1.4503564844252221634e-349j)  +/-  (1.4e-39, 2.21e-99j)
| (-0.0026865909033372170927 - 6.8440244483928813673e-349j)  +/-  (5.52e-42, 8.71e-102j)
| (0.00063869114993306427128 - 2.169085417477592241e-351j)  +/-  (1.44e-42, 2.27e-102j)
| (4.846253694201269453e-08 + 1.2070631007312996614e-354j)  +/-  (6.87e-47, 1.08e-106j)
| (0.00063869114993306427128 - 2.390243815520858306e-350j)  +/-  (5.83e-44, 9.19e-104j)
| (1.0678573251268047386e-12 - 5.4335165889907536921e-357j)  +/-  (3.69e-50, 5.83e-110j)
| (0.020431904091079096405 + 1.8303954107442064884e-349j)  +/-  (1.59e-42, 2.51e-102j)
| (0.18589151529044846188 - 1.6936034781840543053e-349j)  +/-  (1.71e-40, 2.72e-100j)
| (0.020431904091079096405 + 5.7539517742089255421e-350j)  +/-  (6.4e-42, 1.02e-101j)
| (0.2151872017349455645 + 2.1386153344230549817e-349j)  +/-  (1.55e-40, 2.46e-100j)
| (2.2501303088312381591e-06 + 2.165819985555133896e-352j)  +/-  (1.95e-46, 3.08e-106j)
| (0.1215104004252658175 + 1.8387201839224552584e-349j)  +/-  (2.49e-41, 3.95e-101j)
| (4.249444027707216079e-10 - 5.7556847638451239036e-356j)  +/-  (1.61e-49, 2.58e-109j)
| (0.0070361680744121285632 + 5.9880368281173067096e-349j)  +/-  (4.94e-43, 7.76e-103j)
| (0.1215104004252658175 + 1.200783256619794254e-349j)  +/-  (9.92e-43, 1.65e-102j)
| (5.1163635112435920874e-05 + 1.9681483602213029481e-352j)  +/-  (4.23e-46, 6.93e-106j)
| (0.059530848350755077962 - 1.6832710945116920645e-349j)  +/-  (2.3e-43, 3.25e-103j)
