Starting with polynomial:
P : 2*t^2 - 1
Extension levels are: 2 12
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Trying to find an order 12 Kronrod extension for:
P1 : 2*t^2 - 1
Solvable: 1
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Ending with final polynomial:
P : 2*t^14 - 7*t^12 + 77/8*t^10 - 105/16*t^8 + 147/64*t^6 - 49/128*t^4 + 49/2048*t^2 - 1/4096
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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: 1
  current precision for roots: 106
  current precision for roots: 212
 current precision for weights: 106
Linear system for weights solvable: 1
Sufficient bits for target precision reached
Positive weights:   14 out of 14
Indefinite weights: 0 out of 14
Negative weights:   0 out of 14
Extension rule has valid weights: 1
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The nodes are:
| (0.99371220989324258353 + 8.2375481105557111419e-127j)  +/-  (3.41e-60, 3.41e-60j)
| (-0.99371220989324258353 + 3.4992988961407938609e-125j)  +/-  (3.1e-60, 3.1e-60j)
| (-0.9438833303083675629 - 6.5370209940377523838e-128j)  +/-  (6.78e-60, 6.78e-60j)
| (0.11196447610330785847 + 1.3221640067833799251e-132j)  +/-  (1.14e-63, 1.14e-63j)
| (0.84672419922828416835 + 3.4458636967769661786e-139j)  +/-  (3.46e-60, 3.46e-60j)
| (0.9438833303083675629 - 1.4915128252493922146e-138j)  +/-  (5.97e-60, 5.97e-60j)
| (-0.11196447610330785847 + 1.1029716021335124965e-140j)  +/-  (9.89e-64, 9.89e-64j)
| (-0.84672419922828416835 - 2.8817483551291758931e-144j)  +/-  (3.63e-60, 3.63e-60j)
| (-0.33027906195516708177 + 3.4642978362085517094e-148j)  +/-  (1.39e-62, 1.39e-62j)
| (0.53203207651533656356 + 1.6062282598712765242e-150j)  +/-  (2.31e-61, 2.31e-61j)
| (0.7071067811865475244 + 5.7394262658064090954e-155j)  +/-  (8.46e-61, 8.46e-61j)
| (0.33027906195516708177 + 1.3185080930516416499e-165j)  +/-  (1.11e-62, 1.11e-62j)
| (-0.53203207651533656356 + 3.5763210798126800307e-178j)  +/-  (1.74e-61, 1.74e-61j)
| (-0.7071067811865475244 + 5.9019796501009048599e-184j)  +/-  (9.7e-61, 9.7e-61j)
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The weights are:
| (0.071428571428571428571 - 3.5905362108344570595e-126j)  +/-  (7.79e-17, 3.79e-46j)
| (0.071428571428571428571 + 9.9063497757171405412e-125j)  +/-  (3.31e-17, 1.61e-46j)
| (0.071428571428571428571 - 1.4807943928824475425e-124j)  +/-  (2.91e-17, 1.41e-46j)
| (0.071428571428571428571 - 2.066898873004281181e-125j)  +/-  (7.94e-18, 3.86e-47j)
| (0.071428571428571428571 - 8.3597714405766899641e-126j)  +/-  (2.58e-18, 1.25e-47j)
| (0.071428571428571428571 + 7.2910786036982690541e-126j)  +/-  (3.59e-18, 1.74e-47j)
| (0.071428571428571428571 + 2.5647939951796348878e-125j)  +/-  (9.72e-19, 4.73e-48j)
| (0.071428571428571428571 + 8.1032550053703219056e-125j)  +/-  (1.75e-19, 8.5e-49j)
| (0.071428571428571428571 - 3.21573752906311157e-125j)  +/-  (2.39e-19, 1.16e-48j)
| (0.071428571428571428571 - 1.3360824622991471677e-125j)  +/-  (8.47e-20, 4.12e-49j)
| (0.071428571428571428571 + 1.0583712212765783483e-125j)  +/-  (8.85e-20, 4.3e-49j)
| (0.071428571428571428571 + 1.6673118378158574541e-125j)  +/-  (5.7e-20, 2.77e-49j)
| (0.071428571428571428571 + 4.1263129778160304646e-125j)  +/-  (4.83e-21, 2.41e-50j)
| (0.071428571428571428571 - 5.5338091152132604615e-125j)  +/-  (4.17e-21, 1.96e-50j)
