Starting with polynomial:
P : -1/121645100408832000*t^19 + 19/6402373705728000*t^18 - 19/39520825344000*t^17 + 323/6974263296000*t^16 - 323/108972864000*t^15 + 323/2421619200*t^14 - 323/74131200*t^13 + 4199/39916800*t^12 - 4199/2217600*t^11 + 46189/1814400*t^10 - 46189/181440*t^9 + 4199/2240*t^8 - 4199/420*t^7 + 2261/60*t^6 - 969/10*t^5 + 323/2*t^4 - 323/2*t^3 + 171/2*t^2 - 19*t + 1
Extension levels are: 19
-------------------------------------------------
Ending with final polynomial:
P : -1/121645100408832000*t^19 + 19/6402373705728000*t^18 - 19/39520825344000*t^17 + 323/6974263296000*t^16 - 323/108972864000*t^15 + 323/2421619200*t^14 - 323/74131200*t^13 + 4199/39916800*t^12 - 4199/2217600*t^11 + 46189/1814400*t^10 - 46189/181440*t^9 + 4199/2240*t^8 - 4199/420*t^7 + 2261/60*t^6 - 969/10*t^5 + 323/2*t^4 - 323/2*t^3 + 171/2*t^2 - 19*t + 1
-------------------------------------------------
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:   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:
| (62.802423153500375841 + 1.4464367109447659364e-253j)  +/-  (7.57e-120, 7.57e-120j)
| (27.160669327411448879 - 7.6342294998808138224e-253j)  +/-  (1.44e-117, 1.44e-117j)
| (37.712905801219649477 + 2.5046155680536672297e-260j)  +/-  (7.29e-118, 7.29e-118j)
| (32.069122251862242322 - 4.1103158523123509118e-269j)  +/-  (1.25e-117, 1.25e-117j)
| (44.31736279583149612 - 8.8540646842229681612e-285j)  +/-  (3.23e-118, 3.23e-118j)
| (22.850849760829482932 + 2.1455193413309685265e-303j)  +/-  (1.03e-117, 1.03e-117j)
| (52.312902457404383166 - 3.3854249189588960493e-315j)  +/-  (7.24e-119, 7.24e-119j)
| (15.691278339835888545 - 3.1551836973565467017e-325j)  +/-  (3.27e-118, 3.27e-118j)
| (7.8686189153347337311 - 3.7549528029212051239e-334j)  +/-  (1.18e-119, 1.18e-119j)
| (1.7961755820683281256 - 3.1025623305749836046e-344j)  +/-  (3.1e-123, 3.1e-123j)
| (0.96395734399795805862 + 7.0096082651487076397e-345j)  +/-  (1.43e-124, 1.43e-124j)
| (5.9181415616440485582 + 1.5873520982400779058e-338j)  +/-  (2.43e-120, 2.43e-120j)
| (0.39126861331999460734 + 3.1947434298741846899e-348j)  +/-  (6.41e-126, 6.41e-126j)
| (4.2642155396277664744 + 1.3763608227894387923e-340j)  +/-  (3.45e-121, 3.45e-121j)
| (0.074158783757205087713 - 1.0625141298231795804e-348j)  +/-  (1.76e-127, 1.76e-127j)
| (2.8936513818737839912 + 2.7443473116112857675e-341j)  +/-  (3.99e-122, 3.99e-122j)
| (19.048993209823550153 + 1.5546454186763403465e-344j)  +/-  (7.18e-118, 7.18e-118j)
| (10.132423716815265925 + 4.2025483359776913615e-357j)  +/-  (4.71e-119, 4.71e-119j)
| (12.730881463842398005 - 1.3043837930717125313e-367j)  +/-  (1.4e-118, 1.4e-118j)
-------------------------------------------------
The weights are:
| (6.71506464990818996e-27 + 7.2350478013705636668e-273j)  +/-  (1.51e-49, 1.89e-107j)
| (7.3482588395511443768e-12 + 2.7016435279301399309e-264j)  +/-  (1.82e-43, 2.27e-101j)
| (2.5414308430154227237e-16 - 3.6840611582145261169e-267j)  +/-  (4.25e-46, 5.31e-104j)
| (6.2022753875726163989e-14 + 1.140936908122559962e-265j)  +/-  (5.21e-45, 6.5e-103j)
| (4.0788612968257123501e-19 + 9.8403383098552881769e-269j)  +/-  (9.84e-48, 1.23e-105j)
| (4.8166846309280615577e-10 - 9.6661470006113573467e-264j)  +/-  (2.69e-44, 3.36e-102j)
| (1.707750187593837061e-22 - 1.4922006528287755955e-270j)  +/-  (2.23e-49, 2.78e-107j)
| (4.8305667247307725394e-07 - 9.5318027948607985783e-263j)  +/-  (1.33e-43, 1.66e-101j)
| (0.00080491274738136676659 + 1.638070056901098623e-261j)  +/-  (1.21e-41, 1.51e-99j)
| (0.15991337213558021679 + 8.3903057500575834167e-261j)  +/-  (5.42e-37, 6.76e-95j)
| (0.26759954703817503077 - 7.6986045289198894396e-261j)  +/-  (1e-36, 1.25e-94j)
| (0.0048416273511483959673 - 3.1642395960363200591e-261j)  +/-  (6.07e-41, 7.58e-99j)
| (0.30047814360725437948 + 5.0861890852299072574e-261j)  +/-  (3.7e-37, 4.62e-95j)
| (0.021239307606544324924 + 5.2192575573968602009e-261j)  +/-  (2.72e-40, 3.4e-98j)
| (0.17676847491591250225 - 1.678486481195600417e-261j)  +/-  (9e-38, 1.12e-95j)
| (0.068249379976149113455 - 7.2718221488537392668e-261j)  +/-  (1.46e-39, 1.82e-97j)
| (1.9049913611232856999e-08 + 2.9488936992650171433e-263j)  +/-  (4.08e-45, 5.09e-103j)
| (9.6524720931535017084e-05 - 7.2927822064506798711e-262j)  +/-  (1.07e-43, 1.34e-101j)
| (8.2073052580510305441e-06 + 2.8129161394573516826e-262j)  +/-  (2.84e-44, 3.54e-102j)
Starting with polynomial:
P : -1/121645100408832000*t^19 + 19/6402373705728000*t^18 - 19/39520825344000*t^17 + 323/6974263296000*t^16 - 323/108972864000*t^15 + 323/2421619200*t^14 - 323/74131200*t^13 + 4199/39916800*t^12 - 4199/2217600*t^11 + 46189/1814400*t^10 - 46189/181440*t^9 + 4199/2240*t^8 - 4199/420*t^7 + 2261/60*t^6 - 969/10*t^5 + 323/2*t^4 - 323/2*t^3 + 171/2*t^2 - 19*t + 1
Extension levels are: 19
-------------------------------------------------
Ending with final polynomial:
P : -1/121645100408832000*t^19 + 19/6402373705728000*t^18 - 19/39520825344000*t^17 + 323/6974263296000*t^16 - 323/108972864000*t^15 + 323/2421619200*t^14 - 323/74131200*t^13 + 4199/39916800*t^12 - 4199/2217600*t^11 + 46189/1814400*t^10 - 46189/181440*t^9 + 4199/2240*t^8 - 4199/420*t^7 + 2261/60*t^6 - 969/10*t^5 + 323/2*t^4 - 323/2*t^3 + 171/2*t^2 - 19*t + 1
-------------------------------------------------
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:   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:
| (62.802423153500375841 + 1.4464367109447659364e-253j)  +/-  (7.57e-120, 7.57e-120j)
| (27.160669327411448879 - 7.6342294998808138224e-253j)  +/-  (1.44e-117, 1.44e-117j)
| (37.712905801219649477 + 2.5046155680536672297e-260j)  +/-  (7.29e-118, 7.29e-118j)
| (32.069122251862242322 - 4.1103158523123509118e-269j)  +/-  (1.25e-117, 1.25e-117j)
| (44.31736279583149612 - 8.8540646842229681612e-285j)  +/-  (3.23e-118, 3.23e-118j)
| (22.850849760829482932 + 2.1455193413309685265e-303j)  +/-  (1.03e-117, 1.03e-117j)
| (52.312902457404383166 - 3.3854249189588960493e-315j)  +/-  (7.24e-119, 7.24e-119j)
| (15.691278339835888545 - 3.1551836973565467017e-325j)  +/-  (3.27e-118, 3.27e-118j)
| (7.8686189153347337311 - 3.7549528029212051239e-334j)  +/-  (1.18e-119, 1.18e-119j)
| (1.7961755820683281256 - 3.1025623305749836046e-344j)  +/-  (3.1e-123, 3.1e-123j)
| (0.96395734399795805862 + 7.0096082651487076397e-345j)  +/-  (1.43e-124, 1.43e-124j)
| (5.9181415616440485582 + 1.5873520982400779058e-338j)  +/-  (2.43e-120, 2.43e-120j)
| (0.39126861331999460734 + 3.1947434298741846899e-348j)  +/-  (6.41e-126, 6.41e-126j)
| (4.2642155396277664744 + 1.3763608227894387923e-340j)  +/-  (3.45e-121, 3.45e-121j)
| (0.074158783757205087713 - 1.0625141298231795804e-348j)  +/-  (1.76e-127, 1.76e-127j)
| (2.8936513818737839912 + 2.7443473116112857675e-341j)  +/-  (3.99e-122, 3.99e-122j)
| (19.048993209823550153 + 1.5546454186763403465e-344j)  +/-  (7.18e-118, 7.18e-118j)
| (10.132423716815265925 + 4.2025483359776913615e-357j)  +/-  (4.71e-119, 4.71e-119j)
| (12.730881463842398005 - 1.3043837930717125313e-367j)  +/-  (1.4e-118, 1.4e-118j)
-------------------------------------------------
The weights are:
| (6.71506464990818996e-27 + 7.2350478013705636668e-273j)  +/-  (1.51e-49, 1.89e-107j)
| (7.3482588395511443768e-12 + 2.7016435279301399309e-264j)  +/-  (1.82e-43, 2.27e-101j)
| (2.5414308430154227237e-16 - 3.6840611582145261169e-267j)  +/-  (4.25e-46, 5.31e-104j)
| (6.2022753875726163989e-14 + 1.140936908122559962e-265j)  +/-  (5.21e-45, 6.5e-103j)
| (4.0788612968257123501e-19 + 9.8403383098552881769e-269j)  +/-  (9.84e-48, 1.23e-105j)
| (4.8166846309280615577e-10 - 9.6661470006113573467e-264j)  +/-  (2.69e-44, 3.36e-102j)
| (1.707750187593837061e-22 - 1.4922006528287755955e-270j)  +/-  (2.23e-49, 2.78e-107j)
| (4.8305667247307725394e-07 - 9.5318027948607985783e-263j)  +/-  (1.33e-43, 1.66e-101j)
| (0.00080491274738136676659 + 1.638070056901098623e-261j)  +/-  (1.21e-41, 1.51e-99j)
| (0.15991337213558021679 + 8.3903057500575834167e-261j)  +/-  (5.42e-37, 6.76e-95j)
| (0.26759954703817503077 - 7.6986045289198894396e-261j)  +/-  (1e-36, 1.25e-94j)
| (0.0048416273511483959673 - 3.1642395960363200591e-261j)  +/-  (6.07e-41, 7.58e-99j)
| (0.30047814360725437948 + 5.0861890852299072574e-261j)  +/-  (3.7e-37, 4.62e-95j)
| (0.021239307606544324924 + 5.2192575573968602009e-261j)  +/-  (2.72e-40, 3.4e-98j)
| (0.17676847491591250225 - 1.678486481195600417e-261j)  +/-  (9e-38, 1.12e-95j)
| (0.068249379976149113455 - 7.2718221488537392668e-261j)  +/-  (1.46e-39, 1.82e-97j)
| (1.9049913611232856999e-08 + 2.9488936992650171433e-263j)  +/-  (4.08e-45, 5.09e-103j)
| (9.6524720931535017084e-05 - 7.2927822064506798711e-262j)  +/-  (1.07e-43, 1.34e-101j)
| (8.2073052580510305441e-06 + 2.8129161394573516826e-262j)  +/-  (2.84e-44, 3.54e-102j)
