Starting with polynomial:
P : 256*t^8 - 3584*t^6 + 13440*t^4 - 13440*t^2 + 1680
Extension levels are: 8 13
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Trying to find an order 13 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^21 - 98959616/5011*t^19 + 3055042368/5011*t^17 - 49131344640/5011*t^15 + 449515258080/5011*t^13 - 2402485918560/5011*t^11 + 7421582848680/5011*t^9 - 12654579777840/5011*t^7 + 10822722285375/5011*t^5 - 3844571155425/5011*t^3 + 1463173536825/20044*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:
| (-2.9306374202572440192 + 1.8643265840769865659e-451j)  +/-  (6.29e-123, 6.29e-123j)
| (-4.1661833588800450479 + 3.3445673672677421031e-453j)  +/-  (3.47e-123, 3.47e-123j)
| (2.9306374202572440192 - 2.8929985682011556953e-455j)  +/-  (7.35e-123, 7.35e-123j)
| (3.5100667623092421974 + 1.4329043660169258002e-455j)  +/-  (6.61e-123, 6.61e-123j)
| (4.9556459138464720181 - 4.8856736863124545489e-459j)  +/-  (9.25e-124, 9.25e-124j)
| (2.4194104229642408382 + 7.7151160124725369224e-457j)  +/-  (4.88e-123, 4.88e-123j)
| (4.1661833588800450479 + 2.4003527241448146262e-458j)  +/-  (3.39e-123, 3.39e-123j)
| (-0.38118699020732211685 - 1.8183202936884613452e-457j)  +/-  (2e-126, 2e-126j)
| (-3.5100667623092421974 + 6.3938599112176035618e-458j)  +/-  (6.7e-123, 6.7e-123j)
| (2.3648386559087118655e-461 - 3.5265137851270264662e-461j)  +/-  (8.92e-460, 8.92e-460j)
| (1.1571937124467801947 + 2.5307922457970425228e-461j)  +/-  (1.5e-124, 1.5e-124j)
| (0.38118699020732211685 - 1.283547296792557427e-462j)  +/-  (2e-126, 2e-126j)
| (-1.5760077854370687303 - 1.0015249834175991443e-468j)  +/-  (7.67e-124, 7.67e-124j)
| (-1.1571937124467801947 - 6.5891324226817580476e-485j)  +/-  (1.59e-124, 1.59e-124j)
| (-4.9556459138464720181 - 2.9063393335721947118e-486j)  +/-  (9.12e-124, 9.12e-124j)
| (1.5760077854370687303 + 7.3730933277892393518e-487j)  +/-  (7.67e-124, 7.67e-124j)
| (1.9816567566958429259 + 5.9893291858373171226e-491j)  +/-  (2.2e-123, 2.2e-123j)
| (-1.9816567566958429259 - 7.3349142787066679773e-498j)  +/-  (1.98e-123, 1.98e-123j)
| (-0.75436086591777005941 + 4.360322074869529509e-507j)  +/-  (2.12e-125, 2.12e-125j)
| (-2.4194104229642408382 + 1.053659463636093391e-513j)  +/-  (4.54e-123, 4.54e-123j)
| (0.75436086591777005941 - 1.5181156361777464237e-520j)  +/-  (1.99e-125, 1.99e-125j)
-------------------------------------------------
The weights are:
| (5.738904607017558934e-05 + 4.8155067075974618643e-455j)  +/-  (1.71e-47, 5.25e-108j)
| (1.1542582172751011351e-08 - 2.5093207692790236455e-458j)  +/-  (1.3e-50, 3.99e-111j)
| (5.738904607017558934e-05 + 1.835123489424685477e-456j)  +/-  (1.02e-48, 3.13e-109j)
| (1.5441211674964070927e-06 - 1.1983646596956655809e-457j)  +/-  (2.21e-50, 6.79e-111j)
| (1.1064421304059559745e-11 - 5.812400745686991569e-461j)  +/-  (4.75e-54, 1.46e-114j)
| (0.00076736418514429442108 - 1.7463036923133900372e-455j)  +/-  (8.85e-49, 2.71e-109j)
| (1.1542582172751011351e-08 + 4.4030851077684994502e-459j)  +/-  (2.69e-52, 8.25e-113j)
| (0.18155561746728341926 + 4.494521760499932889e-453j)  +/-  (5.76e-46, 1.77e-106j)
| (1.5441211674964070927e-06 + 1.3303740073453873737e-456j)  +/-  (1.24e-52, 3.79e-113j)
| (0.21848588479374270548 - 4.3958078684415796664e-453j)  +/-  (3.98e-46, 1.22e-106j)
| (0.061836573738308210082 + 9.220909985741603612e-454j)  +/-  (1.99e-47, 6.13e-108j)
| (0.18155561746728341926 + 3.4604390426678303364e-453j)  +/-  (1.48e-46, 4.56e-107j)
| (0.019404777711096435721 - 1.1104116190305790279e-453j)  +/-  (7.15e-49, 2.19e-109j)
| (0.061836573738308210082 + 2.1242686611835672075e-453j)  +/-  (7.8e-48, 2.4e-108j)
| (1.1064421304059559745e-11 + 2.2700236202216564132e-460j)  +/-  (4.09e-56, 1.26e-116j)
| (0.019404777711096435721 - 3.3406453516139476151e-454j)  +/-  (3.2e-49, 9.9e-110j)
| (0.0045462401071627363175 + 9.6205883986574626102e-455j)  +/-  (3.17e-50, 9.95e-111j)
| (0.0045462401071627363175 + 4.9731674691936036359e-454j)  +/-  (1.6e-50, 4.92e-111j)
| (0.1225875396732492854 - 3.5240837067333694346e-453j)  +/-  (6.21e-49, 2.01e-109j)
| (0.00076736418514429442108 - 1.8229247646282271447e-454j)  +/-  (2.47e-51, 7.51e-112j)
| (0.1225875396732492854 - 2.0819000579410909471e-453j)  +/-  (2.93e-49, 8.65e-110j)
