Starting with polynomial:
P : t^8 - 28*t^6 + 210*t^4 - 420*t^2 + 105
Extension levels are: 8 13
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Trying to find an order 13 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^21 - 773122/5011*t^19 + 47735037/5011*t^17 - 1535354520/5011*t^15 + 28094703630/5011*t^13 - 300310739820/5011*t^11 + 1855395712170/5011*t^9 - 6327289888920/5011*t^7 + 10822722285375/5011*t^5 - 7689142310850/5011*t^3 + 1463173536825/5011*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:   21 out of 21
Indefinite weights: 0 out of 21
Negative weights:   0 out of 21
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (3.4215630331028556842 + 3.6221341838069057714e-439j)  +/-  (6.75e-123, 6.75e-123j)
| (4.1445471861258943321 - 2.5659548684070352734e-450j)  +/-  (1.02e-122, 1.02e-122j)
| (5.8918730094612552215 - 4.6766518207763043195e-454j)  +/-  (4.68e-123, 4.68e-123j)
| (7.0083416616804912679 + 1.1215807419012939138e-457j)  +/-  (1.36e-123, 1.36e-123j)
| (2.8024858612875416991 - 7.8986474066018395629e-456j)  +/-  (3.15e-123, 3.15e-123j)
| (-5.8918730094612552215 - 6.0539869591263023758e-459j)  +/-  (5.02e-123, 5.02e-123j)
| (-7.0083416616804912679 - 3.8733308577452174881e-463j)  +/-  (1.28e-123, 1.28e-123j)
| (-2.8024858612875416991 + 6.3053045474539693681e-465j)  +/-  (3.08e-123, 3.08e-123j)
| (-4.9639840200927492835 + 8.4040001502055483749e-470j)  +/-  (9.02e-123, 9.02e-123j)
| (-1.6365190424351079992 + 3.3090491173775256105e-475j)  +/-  (1.94e-124, 1.94e-124j)
| (2.2288115845706893975 + 5.4289041020600901241e-473j)  +/-  (1.16e-123, 1.16e-123j)
| (-1.7042708427473336246e-477 + 6.7652643250949898948e-478j)  +/-  (3.85e-476, 3.85e-476j)
| (-0.53907981135137510807 + 5.9016135601892465039e-479j)  +/-  (2.78e-126, 2.78e-126j)
| (-3.4215630331028556842 - 6.9834261068550344492e-480j)  +/-  (7.09e-123, 7.09e-123j)
| (4.9639840200927492835 - 1.053179353753531121e-487j)  +/-  (9.51e-123, 9.51e-123j)
| (1.0668273675044222989 - 1.677339457782308757e-491j)  +/-  (3.06e-125, 3.06e-125j)
| (0.53907981135137510807 + 5.4718085970337511281e-493j)  +/-  (3.35e-126, 3.35e-126j)
| (-4.1445471861258943321 + 1.185771606016075741e-493j)  +/-  (8.75e-123, 8.75e-123j)
| (-1.0668273675044222989 - 1.1033583819245987787e-496j)  +/-  (3.06e-125, 3.06e-125j)
| (-2.2288115845706893975 + 4.1980679595150929487e-497j)  +/-  (1.06e-123, 1.06e-123j)
| (1.6365190424351079992 - 2.8469269547168969752e-506j)  +/-  (2.3e-124, 2.3e-124j)
-------------------------------------------------
The weights are:
| (0.00076736418514429442108 - 8.266544212899245618e-442j)  +/-  (5.63e-41, 6.98e-102j)
| (5.738904607017558934e-05 - 4.4154077823318700448e-443j)  +/-  (8.73e-43, 1.08e-103j)
| (1.1542582172751011351e-08 - 3.7748205057768292733e-446j)  +/-  (1.88e-46, 2.33e-107j)
| (1.1064421304059559745e-11 + 3.8119659659433380796e-448j)  +/-  (3.14e-48, 3.89e-109j)
| (0.0045462401071627363175 + 2.2732375218381640749e-441j)  +/-  (3.67e-41, 4.56e-102j)
| (1.1542582172751011351e-08 + 1.0012391465131681967e-446j)  +/-  (1.69e-49, 2.1e-110j)
| (1.1064421304059559745e-11 - 1.3109111213959053112e-448j)  +/-  (5.04e-51, 6.25e-112j)
| (0.0045462401071627363175 + 2.2610835482915684445e-442j)  +/-  (1.97e-45, 2.44e-106j)
| (1.5441211674964070927e-06 - 2.7458251976460119013e-445j)  +/-  (8.61e-49, 1.07e-109j)
| (0.061836573738308210082 + 2.2204213382842699778e-441j)  +/-  (1.32e-43, 1.63e-104j)
| (0.019404777711096435721 - 3.7600782138846990483e-441j)  +/-  (1.4e-44, 1.73e-105j)
| (0.21848588479374270548 - 1.1222155141166071385e-440j)  +/-  (6.86e-43, 8.47e-104j)
| (0.18155561746728341926 + 8.6236533081988264967e-441j)  +/-  (4.59e-43, 5.66e-104j)
| (0.00076736418514429442108 - 4.0617343879988113998e-443j)  +/-  (4.11e-47, 5.09e-108j)
| (1.5441211674964070927e-06 + 1.4927990859193205691e-444j)  +/-  (6.54e-49, 8.02e-110j)
| (0.1225875396732492854 - 9.7088866718880426613e-441j)  +/-  (4.82e-44, 5.92e-105j)
| (0.18155561746728341926 + 1.1849231423248585636e-440j)  +/-  (1.23e-43, 1.52e-104j)
| (5.738904607017558934e-05 + 4.2191691150558745047e-444j)  +/-  (3.37e-48, 4.19e-109j)
| (0.1225875396732492854 - 5.0935546329626291545e-441j)  +/-  (4.8e-45, 6.1e-106j)
| (0.019404777711096435721 - 7.9372414037518091803e-442j)  +/-  (3.99e-46, 4.95e-107j)
| (0.061836573738308210082 + 6.2917627968977491022e-441j)  +/-  (9.05e-46, 8.98e-107j)
