Starting with polynomial:
P : -1/25852016738884976640000*t^23 + 23/1124000727777607680000*t^22 - 23/4644631106519040000*t^21 + 23/31596129976320000*t^20 - 23/315961299763200*t^19 + 437/83147710464000*t^18 - 437/1539772416000*t^17 + 7429/634023936000*t^16 - 7429/19813248000*t^15 + 7429/792529920*t^14 - 7429/40435200*t^13 + 96577/34214400*t^12 - 96577/2851200*t^11 + 81719/259200*t^10 - 81719/36288*t^9 + 81719/6720*t^8 - 81719/1680*t^7 + 33649/240*t^6 - 33649/120*t^5 + 8855/24*t^4 - 1771/6*t^3 + 253/2*t^2 - 23*t + 1
Extension levels are: 23
-------------------------------------------------
Ending with final polynomial:
P : -1/25852016738884976640000*t^23 + 23/1124000727777607680000*t^22 - 23/4644631106519040000*t^21 + 23/31596129976320000*t^20 - 23/315961299763200*t^19 + 437/83147710464000*t^18 - 437/1539772416000*t^17 + 7429/634023936000*t^16 - 7429/19813248000*t^15 + 7429/792529920*t^14 - 7429/40435200*t^13 + 96577/34214400*t^12 - 96577/2851200*t^11 + 81719/259200*t^10 - 81719/36288*t^9 + 81719/6720*t^8 - 81719/1680*t^7 + 33649/240*t^6 - 33649/120*t^5 + 8855/24*t^4 - 1771/6*t^3 + 253/2*t^2 - 23*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: 0
  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:   23 out of 23
Indefinite weights: 0 out of 23
Negative weights:   0 out of 23
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (77.743227284712324617 - 4.4400315597897086404e-363j)  +/-  (1.59e-118, 1.59e-118j)
| (44.06980781487121377 - 8.1136790645444977579e-360j)  +/-  (6.19e-116, 6.19e-116j)
| (66.402873068345171385 + 3.1375500199543988035e-366j)  +/-  (1.94e-117, 1.94e-117j)
| (33.564896563116417073 + 1.2088843711855878437e-363j)  +/-  (1.21e-115, 1.21e-115j)
| (57.668304350434123593 - 1.1923886949693940373e-369j)  +/-  (1.04e-116, 1.04e-116j)
| (10.367009043445766501 - 1.5650401727588530777e-375j)  +/-  (8.94e-118, 8.94e-118j)
| (4.8705603687334524498 - 3.1438865083235168769e-386j)  +/-  (5.33e-120, 5.33e-120j)
| (3.5177974425035332235 - 1.572365166818766135e-389j)  +/-  (6.53e-121, 6.53e-121j)
| (21.521727850814163458 - 9.5179953612887966248e-392j)  +/-  (4.69e-116, 4.69e-116j)
| (29.125175108751015319 - 4.5027461426237386687e-405j)  +/-  (1.12e-115, 1.12e-115j)
| (1.4868863342221972166 - 1.5564754341128456263e-419j)  +/-  (5.39e-123, 5.39e-123j)
| (6.4569913067677399088 + 1.6394496285581059227e-415j)  +/-  (3.59e-119, 3.59e-119j)
| (50.375226603043749053 + 1.488333346936809924e-411j)  +/-  (3.18e-116, 3.18e-116j)
| (38.514459677180714452 - 6.2722123133468784001e-413j)  +/-  (1.01e-115, 1.01e-115j)
| (8.2856518925980025062 - 2.3292562988692599971e-418j)  +/-  (1.84e-118, 1.84e-118j)
| (0.7988739686929836942 - 2.0771866269600602012e-428j)  +/-  (2.88e-124, 2.88e-124j)
| (15.341687572888509221 + 5.4366892821957863798e-429j)  +/-  (9.81e-117, 9.81e-117j)
| (25.127477130115497228 - 3.5197900827343073362e-446j)  +/-  (8.07e-116, 8.07e-116j)
| (12.713825028162594491 - 6.4613328664909552259e-464j)  +/-  (3.18e-117, 3.18e-117j)
| (18.269742393895989941 + 9.8010995471760638314e-475j)  +/-  (2.5e-116, 2.5e-116j)
| (2.3917558297927677788 + 4.7668005470416330388e-486j)  +/-  (7.52e-122, 7.52e-122j)
| (0.32451132915455278205 - 6.312384490986758562e-489j)  +/-  (1.19e-125, 1.19e-125j)
| (0.06153203775752033807 + 1.5001146245227501322e-493j)  +/-  (2.7e-127, 2.7e-127j)
-------------------------------------------------
The weights are:
| (2.3446147663116609593e-33 - 9.9155835965357746479e-387j)  +/-  (9.72e-42, 3.57e-98j)
| (4.281846844983518274e-19 + 1.7072673794250732822e-378j)  +/-  (6.62e-37, 2.43e-93j)
| (1.410767108895228277e-28 + 3.3975777910010069233e-384j)  +/-  (1.49e-40, 5.48e-97j)
| (1.2397411693143502477e-14 + 4.184071518400680426e-377j)  +/-  (1.44e-35, 5.27e-92j)
| (7.1293967953174463113e-25 - 3.7092849473964514594e-382j)  +/-  (1.57e-39, 5.77e-96j)
| (6.9566498942439339078e-05 - 6.1037432389420611947e-373j)  +/-  (2.99e-28, 1.1e-84j)
| (0.011260589222543518103 + 4.5884795759560382792e-372j)  +/-  (2.92e-23, 1.07e-79j)
| (0.036735792594759592493 - 6.8117817785244964118e-372j)  +/-  (2.49e-21, 9.15e-78j)
| (1.540551240061136014e-09 - 6.1072016745970400073e-375j)  +/-  (1.26e-33, 4.63e-90j)
| (9.4469123741313741337e-13 - 2.5325999889111302664e-376j)  +/-  (2.41e-35, 8.85e-92j)
| (0.17991491403828521368 - 9.3394341623937830817e-372j)  +/-  (1.78e-20, 6.53e-77j)
| (0.0026775401431269916664 - 2.6831328715626251304e-372j)  +/-  (2.99e-27, 1.1e-83j)
| (8.9432388362971850802e-22 + 2.6628492704724790872e-380j)  +/-  (2.28e-39, 8.38e-96j)
| (9.8211682680116023005e-17 - 9.1428036832002971266e-378j)  +/-  (3.06e-37, 1.12e-93j)
| (0.00049238967286655793964 + 1.368841854422789196e-372j)  +/-  (3.31e-30, 1.21e-86j)
| (0.26123706746535064581 + 8.1195889174669865192e-372j)  +/-  (3.82e-26, 1.4e-82j)
| (6.0306324124629508742e-07 - 8.0800651446533386957e-374j)  +/-  (9.44e-34, 3.46e-90j)
| (4.6390775303490565988e-11 + 1.3475035658009859692e-375j)  +/-  (9.26e-36, 3.4e-92j)
| (7.4763615231340992846e-06 + 2.3780799370430585083e-373j)  +/-  (2.05e-33, 7.52e-90j)
| (3.5883396900215093992e-08 + 2.3869026546427923687e-374j)  +/-  (1.23e-34, 4.52e-91j)
| (0.092807882163988973932 + 8.689648986379784208e-372j)  +/-  (2.86e-31, 1.05e-87j)
| (0.2662763422220290251 - 5.1687277198274890714e-372j)  +/-  (6.29e-32, 2.34e-88j)
| (0.14851979908204655867 + 1.6709936798406562882e-372j)  +/-  (2.7e-32, 9.75e-89j)
Starting with polynomial:
P : -1/25852016738884976640000*t^23 + 23/1124000727777607680000*t^22 - 23/4644631106519040000*t^21 + 23/31596129976320000*t^20 - 23/315961299763200*t^19 + 437/83147710464000*t^18 - 437/1539772416000*t^17 + 7429/634023936000*t^16 - 7429/19813248000*t^15 + 7429/792529920*t^14 - 7429/40435200*t^13 + 96577/34214400*t^12 - 96577/2851200*t^11 + 81719/259200*t^10 - 81719/36288*t^9 + 81719/6720*t^8 - 81719/1680*t^7 + 33649/240*t^6 - 33649/120*t^5 + 8855/24*t^4 - 1771/6*t^3 + 253/2*t^2 - 23*t + 1
Extension levels are: 23
-------------------------------------------------
Ending with final polynomial:
P : -1/25852016738884976640000*t^23 + 23/1124000727777607680000*t^22 - 23/4644631106519040000*t^21 + 23/31596129976320000*t^20 - 23/315961299763200*t^19 + 437/83147710464000*t^18 - 437/1539772416000*t^17 + 7429/634023936000*t^16 - 7429/19813248000*t^15 + 7429/792529920*t^14 - 7429/40435200*t^13 + 96577/34214400*t^12 - 96577/2851200*t^11 + 81719/259200*t^10 - 81719/36288*t^9 + 81719/6720*t^8 - 81719/1680*t^7 + 33649/240*t^6 - 33649/120*t^5 + 8855/24*t^4 - 1771/6*t^3 + 253/2*t^2 - 23*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: 0
  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:   23 out of 23
Indefinite weights: 0 out of 23
Negative weights:   0 out of 23
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (77.743227284712324617 - 4.4400315597897086404e-363j)  +/-  (1.59e-118, 1.59e-118j)
| (44.06980781487121377 - 8.1136790645444977579e-360j)  +/-  (6.19e-116, 6.19e-116j)
| (66.402873068345171385 + 3.1375500199543988035e-366j)  +/-  (1.94e-117, 1.94e-117j)
| (33.564896563116417073 + 1.2088843711855878437e-363j)  +/-  (1.21e-115, 1.21e-115j)
| (57.668304350434123593 - 1.1923886949693940373e-369j)  +/-  (1.04e-116, 1.04e-116j)
| (10.367009043445766501 - 1.5650401727588530777e-375j)  +/-  (8.94e-118, 8.94e-118j)
| (4.8705603687334524498 - 3.1438865083235168769e-386j)  +/-  (5.33e-120, 5.33e-120j)
| (3.5177974425035332235 - 1.572365166818766135e-389j)  +/-  (6.53e-121, 6.53e-121j)
| (21.521727850814163458 - 9.5179953612887966248e-392j)  +/-  (4.69e-116, 4.69e-116j)
| (29.125175108751015319 - 4.5027461426237386687e-405j)  +/-  (1.12e-115, 1.12e-115j)
| (1.4868863342221972166 - 1.5564754341128456263e-419j)  +/-  (5.39e-123, 5.39e-123j)
| (6.4569913067677399088 + 1.6394496285581059227e-415j)  +/-  (3.59e-119, 3.59e-119j)
| (50.375226603043749053 + 1.488333346936809924e-411j)  +/-  (3.18e-116, 3.18e-116j)
| (38.514459677180714452 - 6.2722123133468784001e-413j)  +/-  (1.01e-115, 1.01e-115j)
| (8.2856518925980025062 - 2.3292562988692599971e-418j)  +/-  (1.84e-118, 1.84e-118j)
| (0.7988739686929836942 - 2.0771866269600602012e-428j)  +/-  (2.88e-124, 2.88e-124j)
| (15.341687572888509221 + 5.4366892821957863798e-429j)  +/-  (9.81e-117, 9.81e-117j)
| (25.127477130115497228 - 3.5197900827343073362e-446j)  +/-  (8.07e-116, 8.07e-116j)
| (12.713825028162594491 - 6.4613328664909552259e-464j)  +/-  (3.18e-117, 3.18e-117j)
| (18.269742393895989941 + 9.8010995471760638314e-475j)  +/-  (2.5e-116, 2.5e-116j)
| (2.3917558297927677788 + 4.7668005470416330388e-486j)  +/-  (7.52e-122, 7.52e-122j)
| (0.32451132915455278205 - 6.312384490986758562e-489j)  +/-  (1.19e-125, 1.19e-125j)
| (0.06153203775752033807 + 1.5001146245227501322e-493j)  +/-  (2.7e-127, 2.7e-127j)
-------------------------------------------------
The weights are:
| (2.3446147663116609593e-33 - 9.9155835965357746479e-387j)  +/-  (9.72e-42, 3.57e-98j)
| (4.281846844983518274e-19 + 1.7072673794250732822e-378j)  +/-  (6.62e-37, 2.43e-93j)
| (1.410767108895228277e-28 + 3.3975777910010069233e-384j)  +/-  (1.49e-40, 5.48e-97j)
| (1.2397411693143502477e-14 + 4.184071518400680426e-377j)  +/-  (1.44e-35, 5.27e-92j)
| (7.1293967953174463113e-25 - 3.7092849473964514594e-382j)  +/-  (1.57e-39, 5.77e-96j)
| (6.9566498942439339078e-05 - 6.1037432389420611947e-373j)  +/-  (2.99e-28, 1.1e-84j)
| (0.011260589222543518103 + 4.5884795759560382792e-372j)  +/-  (2.92e-23, 1.07e-79j)
| (0.036735792594759592493 - 6.8117817785244964118e-372j)  +/-  (2.49e-21, 9.15e-78j)
| (1.540551240061136014e-09 - 6.1072016745970400073e-375j)  +/-  (1.26e-33, 4.63e-90j)
| (9.4469123741313741337e-13 - 2.5325999889111302664e-376j)  +/-  (2.41e-35, 8.85e-92j)
| (0.17991491403828521368 - 9.3394341623937830817e-372j)  +/-  (1.78e-20, 6.53e-77j)
| (0.0026775401431269916664 - 2.6831328715626251304e-372j)  +/-  (2.99e-27, 1.1e-83j)
| (8.9432388362971850802e-22 + 2.6628492704724790872e-380j)  +/-  (2.28e-39, 8.38e-96j)
| (9.8211682680116023005e-17 - 9.1428036832002971266e-378j)  +/-  (3.06e-37, 1.12e-93j)
| (0.00049238967286655793964 + 1.368841854422789196e-372j)  +/-  (3.31e-30, 1.21e-86j)
| (0.26123706746535064581 + 8.1195889174669865192e-372j)  +/-  (3.82e-26, 1.4e-82j)
| (6.0306324124629508742e-07 - 8.0800651446533386957e-374j)  +/-  (9.44e-34, 3.46e-90j)
| (4.6390775303490565988e-11 + 1.3475035658009859692e-375j)  +/-  (9.26e-36, 3.4e-92j)
| (7.4763615231340992846e-06 + 2.3780799370430585083e-373j)  +/-  (2.05e-33, 7.52e-90j)
| (3.5883396900215093992e-08 + 2.3869026546427923687e-374j)  +/-  (1.23e-34, 4.52e-91j)
| (0.092807882163988973932 + 8.689648986379784208e-372j)  +/-  (2.86e-31, 1.05e-87j)
| (0.2662763422220290251 - 5.1687277198274890714e-372j)  +/-  (6.29e-32, 2.34e-88j)
| (0.14851979908204655867 + 1.6709936798406562882e-372j)  +/-  (2.7e-32, 9.75e-89j)
