Starting with polynomial:
P : -1/51090942171709440000*t^21 + 1/115852476579840000*t^20 - 1/579262382899200*t^19 + 19/91462481510400*t^18 - 19/1129166438400*t^17 + 323/332107776000*t^16 - 323/7783776000*t^15 + 323/242161920*t^14 - 323/9884160*t^13 + 4199/6842880*t^12 - 4199/475200*t^11 + 4199/43200*t^10 - 4199/5184*t^9 + 323/64*t^8 - 323/14*t^7 + 2261/30*t^6 - 6783/40*t^5 + 1995/8*t^4 - 665/3*t^3 + 105*t^2 - 21*t + 1
Extension levels are: 21
-------------------------------------------------
Ending with final polynomial:
P : -1/51090942171709440000*t^21 + 1/115852476579840000*t^20 - 1/579262382899200*t^19 + 19/91462481510400*t^18 - 19/1129166438400*t^17 + 323/332107776000*t^16 - 323/7783776000*t^15 + 323/242161920*t^14 - 323/9884160*t^13 + 4199/6842880*t^12 - 4199/475200*t^11 + 4199/43200*t^10 - 4199/5184*t^9 + 323/64*t^8 - 323/14*t^7 + 2261/30*t^6 - 6783/40*t^5 + 1995/8*t^4 - 665/3*t^3 + 105*t^2 - 21*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:   21 out of 21
Indefinite weights: 0 out of 21
Negative weights:   0 out of 21
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (70.255688628018936999 + 5.8102303092546392302e-308j)  +/-  (3.95e-119, 3.95e-119j)
| (32.751497410560833306 - 6.7545190464073765778e-317j)  +/-  (1.33e-116, 1.33e-116j)
| (50.947351189939920974 - 1.7823009277716773225e-327j)  +/-  (1.83e-117, 1.83e-117j)
| (59.325994120229994368 + 1.0682338751150020031e-333j)  +/-  (3.8e-118, 3.8e-118j)
| (28.107528600944306245 + 2.1402237854658852412e-340j)  +/-  (1.23e-116, 1.23e-116j)
| (5.3423692806224341299 + 1.408133211891019359e-350j)  +/-  (3.24e-120, 3.24e-120j)
| (37.997187819260953854 - 7.8819489718453530159e-351j)  +/-  (9.79e-117, 9.79e-117j)
| (14.036270697873757765 - 3.8050243495485928874e-356j)  +/-  (1.3e-117, 1.3e-117j)
| (11.421771762378382508 + 1.2387451398517447016e-367j)  +/-  (4.01e-118, 4.01e-118j)
| (20.278509414993741305 + 6.3686153933132260546e-381j)  +/-  (6.24e-117, 6.24e-117j)
| (1.6268699419292102463 + 4.3098722152289023678e-393j)  +/-  (4.01e-123, 4.01e-123j)
| (9.1127788542697046704 - 3.4222905408500652801e-391j)  +/-  (8.88e-119, 8.88e-119j)
| (23.97184558715147629 + 3.4391131231560385282e-396j)  +/-  (1.01e-116, 1.01e-116j)
| (43.985245757142216124 + 1.9539309424866960081e-405j)  +/-  (5.16e-117, 5.16e-117j)
| (0.87366016677864235687 - 5.4804546783993024352e-417j)  +/-  (2.32e-124, 2.32e-124j)
| (2.6186264105455439088 + 1.8789769124002767586e-414j)  +/-  (4.56e-122, 4.56e-122j)
| (3.8546521381097596585 + 2.5445299223117274965e-414j)  +/-  (4.39e-121, 4.39e-121j)
| (7.0911688132196751422 + 6.4673950103195034529e-412j)  +/-  (1.76e-119, 1.76e-119j)
| (0.35477289532351182708 - 5.4666767583282744714e-419j)  +/-  (9.93e-126, 9.93e-126j)
| (16.97895269278383719 - 8.8088495668572047737e-417j)  +/-  (3.21e-117, 3.21e-117j)
| (0.067257817923161130962 + 5.2961224785017394718e-431j)  +/-  (2.75e-127, 2.75e-127j)
-------------------------------------------------
The weights are:
| (4.0441339271159212262e-30 - 1.1490453490702990891e-337j)  +/-  (1.12e-47, 1.26e-104j)
| (2.9425193540719438027e-14 + 1.3283115926441323276e-330j)  +/-  (1.06e-41, 1.19e-98j)
| (5.6597208703242377328e-22 - 1.0370268371066811714e-334j)  +/-  (2.16e-45, 2.43e-102j)
| (1.6062609247992960042e-25 + 3.7020218773168115286e-336j)  +/-  (1.3e-46, 1.46e-103j)
| (2.7178831180589082606e-12 - 6.7012166116966017511e-330j)  +/-  (9.76e-42, 1.1e-98j)
| (0.0077342394261187264652 - 5.8667100248370299405e-326j)  +/-  (8.94e-33, 1.01e-89j)
| (1.759074035797716089e-16 - 3.775676807988579356e-333j)  +/-  (1.36e-43, 1.53e-100j)
| (2.224790793645046512e-06 - 1.990161478459827462e-327j)  +/-  (4.76e-39, 5.36e-96j)
| (2.6930073439686183289e-05 + 5.8202089381346701028e-327j)  +/-  (3.31e-38, 3.72e-95j)
| (5.4439522906464423896e-09 - 1.4660790736006580877e-328j)  +/-  (2.92e-41, 3.28e-98j)
| (0.17131939639002142843 + 1.4157657356604611803e-325j)  +/-  (1.87e-32, 2.1e-89j)
| (0.0002384226587634135542 - 1.4619403430735492941e-326j)  +/-  (3.76e-38, 4.23e-95j)
| (1.5163662051980612686e-10 + 3.2062042050403247556e-329j)  +/-  (4.49e-42, 5.05e-99j)
| (5.0738022271720229565e-19 + 1.6553908124043460711e-333j)  +/-  (4.2e-46, 4.72e-103j)
| (0.26525457551389979161 - 1.272950755950741779e-325j)  +/-  (1.73e-35, 1.93e-92j)
| (0.081126625892353214254 - 1.2596287827820013233e-325j)  +/-  (9.6e-37, 1.07e-93j)
| (0.028816301767769421865 + 9.3319139592465034081e-326j)  +/-  (1.24e-37, 1.39e-94j)
| (0.0015674813904211877532 + 3.1585971794421103544e-326j)  +/-  (8.4e-39, 9.38e-96j)
| (0.28249356458299533678 + 8.2917937145940656998e-326j)  +/-  (2.07e-37, 2.21e-94j)
| (1.3173344974323331686e-07 + 5.8329230601026517632e-328j)  +/-  (4.18e-41, 4.74e-98j)
| (0.16142010018163800893 - 2.7148583321447640904e-326j)  +/-  (9.16e-38, 9.68e-95j)
Starting with polynomial:
P : -1/51090942171709440000*t^21 + 1/115852476579840000*t^20 - 1/579262382899200*t^19 + 19/91462481510400*t^18 - 19/1129166438400*t^17 + 323/332107776000*t^16 - 323/7783776000*t^15 + 323/242161920*t^14 - 323/9884160*t^13 + 4199/6842880*t^12 - 4199/475200*t^11 + 4199/43200*t^10 - 4199/5184*t^9 + 323/64*t^8 - 323/14*t^7 + 2261/30*t^6 - 6783/40*t^5 + 1995/8*t^4 - 665/3*t^3 + 105*t^2 - 21*t + 1
Extension levels are: 21
-------------------------------------------------
Ending with final polynomial:
P : -1/51090942171709440000*t^21 + 1/115852476579840000*t^20 - 1/579262382899200*t^19 + 19/91462481510400*t^18 - 19/1129166438400*t^17 + 323/332107776000*t^16 - 323/7783776000*t^15 + 323/242161920*t^14 - 323/9884160*t^13 + 4199/6842880*t^12 - 4199/475200*t^11 + 4199/43200*t^10 - 4199/5184*t^9 + 323/64*t^8 - 323/14*t^7 + 2261/30*t^6 - 6783/40*t^5 + 1995/8*t^4 - 665/3*t^3 + 105*t^2 - 21*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:   21 out of 21
Indefinite weights: 0 out of 21
Negative weights:   0 out of 21
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (70.255688628018936999 + 5.8102303092546392302e-308j)  +/-  (3.95e-119, 3.95e-119j)
| (32.751497410560833306 - 6.7545190464073765778e-317j)  +/-  (1.33e-116, 1.33e-116j)
| (50.947351189939920974 - 1.7823009277716773225e-327j)  +/-  (1.83e-117, 1.83e-117j)
| (59.325994120229994368 + 1.0682338751150020031e-333j)  +/-  (3.8e-118, 3.8e-118j)
| (28.107528600944306245 + 2.1402237854658852412e-340j)  +/-  (1.23e-116, 1.23e-116j)
| (5.3423692806224341299 + 1.408133211891019359e-350j)  +/-  (3.24e-120, 3.24e-120j)
| (37.997187819260953854 - 7.8819489718453530159e-351j)  +/-  (9.79e-117, 9.79e-117j)
| (14.036270697873757765 - 3.8050243495485928874e-356j)  +/-  (1.3e-117, 1.3e-117j)
| (11.421771762378382508 + 1.2387451398517447016e-367j)  +/-  (4.01e-118, 4.01e-118j)
| (20.278509414993741305 + 6.3686153933132260546e-381j)  +/-  (6.24e-117, 6.24e-117j)
| (1.6268699419292102463 + 4.3098722152289023678e-393j)  +/-  (4.01e-123, 4.01e-123j)
| (9.1127788542697046704 - 3.4222905408500652801e-391j)  +/-  (8.88e-119, 8.88e-119j)
| (23.97184558715147629 + 3.4391131231560385282e-396j)  +/-  (1.01e-116, 1.01e-116j)
| (43.985245757142216124 + 1.9539309424866960081e-405j)  +/-  (5.16e-117, 5.16e-117j)
| (0.87366016677864235687 - 5.4804546783993024352e-417j)  +/-  (2.32e-124, 2.32e-124j)
| (2.6186264105455439088 + 1.8789769124002767586e-414j)  +/-  (4.56e-122, 4.56e-122j)
| (3.8546521381097596585 + 2.5445299223117274965e-414j)  +/-  (4.39e-121, 4.39e-121j)
| (7.0911688132196751422 + 6.4673950103195034529e-412j)  +/-  (1.76e-119, 1.76e-119j)
| (0.35477289532351182708 - 5.4666767583282744714e-419j)  +/-  (9.93e-126, 9.93e-126j)
| (16.97895269278383719 - 8.8088495668572047737e-417j)  +/-  (3.21e-117, 3.21e-117j)
| (0.067257817923161130962 + 5.2961224785017394718e-431j)  +/-  (2.75e-127, 2.75e-127j)
-------------------------------------------------
The weights are:
| (4.0441339271159212262e-30 - 1.1490453490702990891e-337j)  +/-  (1.12e-47, 1.26e-104j)
| (2.9425193540719438027e-14 + 1.3283115926441323276e-330j)  +/-  (1.06e-41, 1.19e-98j)
| (5.6597208703242377328e-22 - 1.0370268371066811714e-334j)  +/-  (2.16e-45, 2.43e-102j)
| (1.6062609247992960042e-25 + 3.7020218773168115286e-336j)  +/-  (1.3e-46, 1.46e-103j)
| (2.7178831180589082606e-12 - 6.7012166116966017511e-330j)  +/-  (9.76e-42, 1.1e-98j)
| (0.0077342394261187264652 - 5.8667100248370299405e-326j)  +/-  (8.94e-33, 1.01e-89j)
| (1.759074035797716089e-16 - 3.775676807988579356e-333j)  +/-  (1.36e-43, 1.53e-100j)
| (2.224790793645046512e-06 - 1.990161478459827462e-327j)  +/-  (4.76e-39, 5.36e-96j)
| (2.6930073439686183289e-05 + 5.8202089381346701028e-327j)  +/-  (3.31e-38, 3.72e-95j)
| (5.4439522906464423896e-09 - 1.4660790736006580877e-328j)  +/-  (2.92e-41, 3.28e-98j)
| (0.17131939639002142843 + 1.4157657356604611803e-325j)  +/-  (1.87e-32, 2.1e-89j)
| (0.0002384226587634135542 - 1.4619403430735492941e-326j)  +/-  (3.76e-38, 4.23e-95j)
| (1.5163662051980612686e-10 + 3.2062042050403247556e-329j)  +/-  (4.49e-42, 5.05e-99j)
| (5.0738022271720229565e-19 + 1.6553908124043460711e-333j)  +/-  (4.2e-46, 4.72e-103j)
| (0.26525457551389979161 - 1.272950755950741779e-325j)  +/-  (1.73e-35, 1.93e-92j)
| (0.081126625892353214254 - 1.2596287827820013233e-325j)  +/-  (9.6e-37, 1.07e-93j)
| (0.028816301767769421865 + 9.3319139592465034081e-326j)  +/-  (1.24e-37, 1.39e-94j)
| (0.0015674813904211877532 + 3.1585971794421103544e-326j)  +/-  (8.4e-39, 9.38e-96j)
| (0.28249356458299533678 + 8.2917937145940656998e-326j)  +/-  (2.07e-37, 2.21e-94j)
| (1.3173344974323331686e-07 + 5.8329230601026517632e-328j)  +/-  (4.18e-41, 4.74e-98j)
| (0.16142010018163800893 - 2.7148583321447640904e-326j)  +/-  (9.16e-38, 9.68e-95j)
