Starting with polynomial:
P : t^8 - 28*t^6 + 210*t^4 - 420*t^2 + 105
Extension levels are: 8
-------------------------------------------------
Ending with final polynomial:
P : t^8 - 28*t^6 + 210*t^4 - 420*t^2 + 105
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Computing nodes and weights
  current precision for roots: 53
  current precision for roots: 106
  current precision for roots: 212
 current precision for weights: 53
Linear system for weights solvable: 1
  current precision for roots: 106
  current precision for roots: 212
  current precision for roots: 424
 current precision for weights: 106
Linear system for weights solvable: 1
Sufficient bits for target precision reached
Positive weights:   8 out of 8
Indefinite weights: 0 out of 8
Negative weights:   0 out of 8
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (-4.1445471861258943321 + 4.4501477170144027662e-308j)  +/-  (4.36e-126, 4.36e-126j)
| (0.53907981135137510807 + 1.0118464426828729225e-320j)  +/-  (4.12e-127, 4.12e-127j)
| (4.1445471861258943321 - 4.044150784985703374e-335j)  +/-  (4.36e-126, 4.36e-126j)
| (-2.8024858612875416991 - 3.1179925809354366044e-353j)  +/-  (5.75e-126, 5.75e-126j)
| (-0.53907981135137510807 - 1.0817709856140433221e-370j)  +/-  (4.12e-127, 4.12e-127j)
| (1.6365190424351079992 - 2.0149554789327891955e-379j)  +/-  (2.5e-126, 2.5e-126j)
| (2.8024858612875416991 - 2.8634239568714139004e-393j)  +/-  (3.97e-126, 3.97e-126j)
| (-1.6365190424351079992 + 0j)  +/-  (1.8e-126, 1.8e-126j)
-------------------------------------------------
The weights are:
| (0.00011261453837536777039 + 1.0385226690552273047e-311j)  +/-  (1.25e-30, 2.35e-125j)
| (0.37301225767907734993 + 6.1581591511216825579e-311j)  +/-  (1.05e-28, 1.91e-123j)
| (0.00011261453837536777039 - 6.0459117529953964762e-313j)  +/-  (4.69e-31, 8.87e-126j)
| (0.0096352201207882671869 - 3.4540619038962450041e-311j)  +/-  (7.81e-30, 1.47e-124j)
| (0.37301225767907734993 - 7.9996620288301178807e-311j)  +/-  (4.98e-29, 8.99e-124j)
| (0.11723990766175901512 - 2.7970578368588333559e-311j)  +/-  (2.75e-29, 5.25e-124j)
| (0.0096352201207882671869 + 6.6727232523431961285e-312j)  +/-  (3.22e-30, 6.08e-125j)
| (0.11723990766175901512 + 6.4472867417039207299e-311j)  +/-  (1.54e-29, 2.64e-124j)
