Starting with polynomial:
P : 262144*t^19 - 1245184*t^17 + 2490368*t^15 - 2723840*t^13 + 1770496*t^11 - 695552*t^9 + 160512*t^7 - 20064*t^5 + 1140*t^3 - 19*t
Extension levels are: 19
-------------------------------------------------
Ending with final polynomial:
P : 262144*t^19 - 1245184*t^17 + 2490368*t^15 - 2723840*t^13 + 1770496*t^11 - 695552*t^9 + 160512*t^7 - 20064*t^5 + 1140*t^3 - 19*t
-------------------------------------------------
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
  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:   19 out of 19
Indefinite weights: 0 out of 19
Negative weights:   0 out of 19
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (0.99658449300666984982 + 6.5304652959637800704e-379j)  +/-  (2.56e-122, 2.56e-122j)
| (0.16459459028073389414 + 1.2074389808371204092e-394j)  +/-  (5.21e-127, 5.21e-127j)
| (-0.91577332665505743992 + 1.3948174311837152027e-396j)  +/-  (5.6e-122, 5.6e-122j)
| (4.7312790968669463745e-397 + 2.8362500259452555297e-396j)  +/-  (5.46e-395, 5.46e-395j)
| (0.96940026593933041674 - 3.1800076686856861928e-401j)  +/-  (6.72e-122, 6.72e-122j)
| (0.73572391067313162477 + 6.7954238374053790766e-414j)  +/-  (5.77e-123, 5.77e-123j)
| (-0.96940026593933041674 - 7.7041112569941740867e-423j)  +/-  (6.41e-122, 6.41e-122j)
| (-0.83716647826252857481 - 1.9953758450693751173e-422j)  +/-  (2.17e-122, 2.17e-122j)
| (-0.99658449300666984982 - 4.2957175831321488223e-423j)  +/-  (3.27e-122, 3.27e-122j)
| (0.32469946920468348741 + 2.0180690575407645421e-422j)  +/-  (8.86e-126, 8.86e-126j)
| (0.91577332665505743992 + 1.1715044408642928451e-429j)  +/-  (5.18e-122, 5.18e-122j)
| (0.61421271268966781744 + 2.2640617249560528834e-446j)  +/-  (8.41e-124, 8.41e-124j)
| (-0.47594739303707354443 + 3.4235827305346882593e-456j)  +/-  (1.21e-124, 1.21e-124j)
| (-0.61421271268966781744 + 3.0382783236755576726e-457j)  +/-  (1.04e-123, 1.04e-123j)
| (-0.32469946920468348741 + 3.0323039944395777689e-456j)  +/-  (8.18e-126, 8.18e-126j)
| (0.83716647826252857481 + 3.6809752492387204104e-466j)  +/-  (2.12e-122, 2.12e-122j)
| (0.47594739303707354443 - 1.319783705674273844e-486j)  +/-  (1.21e-124, 1.21e-124j)
| (-0.16459459028073389414 - 2.0040858553497776063e-494j)  +/-  (5.21e-127, 5.21e-127j)
| (-0.73572391067313162477 + 2.7679059832978520017e-496j)  +/-  (5.1e-123, 5.1e-123j)
-------------------------------------------------
The weights are:
| (0.052631578947368421053 - 2.5114919000995059535e-378j)  +/-  (3.13e-44, 3.51e-104j)
| (0.052631578947368421053 - 4.9344307544960035496e-379j)  +/-  (1.12e-44, 1.26e-104j)
| (0.052631578947368421053 - 8.7427249941808842304e-380j)  +/-  (2.89e-45, 3.24e-105j)
| (0.052631578947368421053 + 4.1764276602449084607e-379j)  +/-  (7.09e-45, 7.96e-105j)
| (0.052631578947368421053 + 3.7586156835843697084e-378j)  +/-  (5.21e-45, 5.84e-105j)
| (0.052631578947368421053 - 1.0806371363116356716e-378j)  +/-  (3.29e-45, 3.69e-105j)
| (0.052631578947368421053 + 5.1971441658682348654e-380j)  +/-  (6.79e-46, 7.62e-106j)
| (0.052631578947368421053 + 1.2414376027573184634e-379j)  +/-  (2.82e-46, 3.17e-106j)
| (0.052631578947368421053 - 1.7244333129778442303e-380j)  +/-  (2.83e-46, 3.17e-106j)
| (0.052631578947368421053 + 5.8591059910235713983e-379j)  +/-  (1.82e-46, 2.04e-106j)
| (0.052631578947368421053 - 2.0689242913569514814e-378j)  +/-  (5.85e-47, 6.56e-107j)
| (0.052631578947368421053 + 8.589889820632471389e-379j)  +/-  (5.26e-47, 5.9e-107j)
| (0.052631578947368421053 - 2.485863415722543951e-379j)  +/-  (2.15e-48, 2.41e-108j)
| (0.052631578947368421053 + 2.0390719898363921275e-379j)  +/-  (1.55e-48, 1.74e-108j)
| (0.052631578947368421053 + 2.9794091813910365912e-379j)  +/-  (1.17e-48, 1.31e-108j)
| (0.052631578947368421053 + 1.4279988453500676491e-378j)  +/-  (1.1e-48, 1.24e-108j)
| (0.052631578947368421053 - 7.0308342302437204771e-379j)  +/-  (1.14e-48, 1.28e-108j)
| (0.052631578947368421053 - 3.5355412636423361774e-379j)  +/-  (3.9e-49, 4.44e-109j)
| (0.052631578947368421053 - 1.6272831793154874253e-379j)  +/-  (1.9e-49, 2.01e-109j)
