Starting with polynomial:
P : 8*t^4 - 8*t^2 + 1
Extension levels are: 4
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Ending with final polynomial:
P : 8*t^4 - 8*t^2 + 1
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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:   4 out of 4
Indefinite weights: 0 out of 4
Negative weights:   0 out of 4
Extension rule has valid weights: 1
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The nodes are:
| (0.92387953251128675613 - 5.096749823337506287e-73j)  +/-  (6.21e-64, 6.21e-64j)
| (-0.38268343236508977173 + 9.2225650054266650936e-87j)  +/-  (7.01e-64, 7.01e-64j)
| (-0.92387953251128675613 + 9.3144534765740800182e-107j)  +/-  (6.21e-64, 6.21e-64j)
| (0.38268343236508977173 + 1.8909140209225186879e-124j)  +/-  (7.01e-64, 7.01e-64j)
-------------------------------------------------
The weights are:
| (0.25 + 4.0191975621592767697e-73j)  +/-  (4.22e-30, 5.5e-62j)
| (0.25 + 2.3543914220560245038e-73j)  +/-  (1.94e-30, 2.58e-62j)
| (0.25 - 6.8958528195275156355e-74j)  +/-  (9.25e-31, 1.25e-62j)
| (0.25 - 5.68400370226254971e-73j)  +/-  (1.34e-30, 1.67e-62j)
