Starting with polynomial:
P : 1/304888344611713860501504000000*t^28 - 1/388888194657798291456000000*t^27 + 1/1066908627319062528000000*t^26 - 1/4734801600528384000000*t^25 + 1/30302730243381657600*t^24 - 1/263044533362688000*t^23 + 23/68620313051136000*t^22 - 23/992442544128000*t^21 + 23/18003492864000*t^20 - 23/405078589440*t^19 + 437/213199257600*t^18 - 437/7238246400*t^17 + 7429/5109350400*t^16 - 7429/259459200*t^15 + 7429/16144128*t^14 - 7429/1235520*t^13 + 96577/1520640*t^12 - 5681/10560*t^11 + 62491/17280*t^10 - 16445/864*t^9 + 9867/128*t^8 - 3289/14*t^7 + 2093/4*t^6 - 819*t^5 + 6825/8*t^4 - 546*t^3 + 189*t^2 - 28*t + 1
Extension levels are: 28
-------------------------------------------------
Ending with final polynomial:
P : 1/304888344611713860501504000000*t^28 - 1/388888194657798291456000000*t^27 + 1/1066908627319062528000000*t^26 - 1/4734801600528384000000*t^25 + 1/30302730243381657600*t^24 - 1/263044533362688000*t^23 + 23/68620313051136000*t^22 - 23/992442544128000*t^21 + 23/18003492864000*t^20 - 23/405078589440*t^19 + 437/213199257600*t^18 - 437/7238246400*t^17 + 7429/5109350400*t^16 - 7429/259459200*t^15 + 7429/16144128*t^14 - 7429/1235520*t^13 + 96577/1520640*t^12 - 5681/10560*t^11 + 62491/17280*t^10 - 16445/864*t^9 + 9867/128*t^8 - 3289/14*t^7 + 2093/4*t^6 - 819*t^5 + 6825/8*t^4 - 546*t^3 + 189*t^2 - 28*t + 1
-------------------------------------------------
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: 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 roots: 848
 current precision for weights: 212
Linear system for weights solvable: 1
  current precision for roots: 424
  current precision for roots: 848
  current precision for roots: 1696
 current precision for weights: 424
Linear system for weights solvable: 1
Sufficient bits for target precision reached
Positive weights:   28 out of 28
Indefinite weights: 0 out of 28
Negative weights:   0 out of 28
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (96.582420627527319077 - 1.751170091962781755e-1104j)  +/-  (6.27e-500, 6.27e-500j)
| (59.748796084641240822 + 3.0547138688006924001e-1105j)  +/-  (9.46e-497, 9.46e-497j)
| (74.786778152339161835 - 4.0238774315816127361e-1115j)  +/-  (7.97e-498, 7.97e-498j)
| (84.317837107227043056 + 7.0896183090592229719e-1128j)  +/-  (1.11e-498, 1.11e-498j)
| (66.756977283906469554 - 1.6488777418905018346e-1154j)  +/-  (2.96e-497, 2.96e-497j)
| (5.2837360628434425628 + 6.4412592813779738102e-1196j)  +/-  (1.1e-501, 1.1e-501j)
| (47.892071633622743673 + 6.6489090437809809017e-1274j)  +/-  (3.2e-496, 3.2e-496j)
| (53.511297959664294205 + 1.8384812445049820601e-1365j)  +/-  (2.21e-496, 2.21e-496j)
| (38.132254410194646779 + 6.6089181089204536908e-1422j)  +/-  (5.12e-496, 5.12e-496j)
| (8.4412163282713244886 - 3.8844155182969516075e-1441j)  +/-  (4.73e-500, 4.73e-500j)
| (1.2239718083849077187 + 2.9339303326084873546e-1456j)  +/-  (3.59e-506, 3.59e-506j)
| (14.714085164135748813 + 1.298911371073227711e-1464j)  +/-  (3.76e-498, 3.76e-498j)
| (20.023783329951712751 - 1.0001987501967736208e-1494j)  +/-  (3.59e-497, 3.59e-497j)
| (33.866605516584459212 - 9.8801489203036528694e-1525j)  +/-  (3.77e-496, 3.77e-496j)
| (12.407903414460671739 - 5.3696142421009981296e-1541j)  +/-  (1.1e-498, 1.1e-498j)
| (0.65813662835479151933 + 3.1688062569504533571e-1558j)  +/-  (2.01e-507, 2.01e-507j)
| (6.7646034042435051552 - 6.7098221082465458824e-1552j)  +/-  (8.12e-501, 8.12e-501j)
| (3.9933116592501141362 - 8.7601420429388062329e-1553j)  +/-  (1.18e-502, 1.18e-502j)
| (42.78967237077257627 - 7.7981260847960814809e-1547j)  +/-  (4.35e-496, 4.35e-496j)
| (0.050734624849873887593 - 1.4933744249947694608e-1569j)  +/-  (3.31e-510, 3.31e-510j)
| (17.248663415608056266 - 3.2721961314311949424e-1556j)  +/-  (1.25e-497, 1.25e-497j)
| (0.26748726864074108429 + 2.4713593801940518797e-1578j)  +/-  (9.67e-509, 9.67e-509j)
| (10.319850462993260104 + 9.1804542734149270654e-1567j)  +/-  (2.66e-499, 2.66e-499j)
| (26.35629737440131762 - 4.3968904315912933646e-1567j)  +/-  (1.65e-496, 1.65e-496j)
| (29.951966833596182109 - 2.1858514682430365535e-1581j)  +/-  (2.85e-496, 2.85e-496j)
| (23.05389013503029597 - 4.0288074189140678681e-1593j)  +/-  (8.67e-497, 8.67e-497j)
| (1.9667676124737776998 - 2.4355603556936708235e-1613j)  +/-  (7.25e-505, 7.25e-505j)
| (2.8888833260303218929 - 4.077728490782218278e-1612j)  +/-  (9.41e-504, 9.41e-504j)
-------------------------------------------------
The weights are:
| (1.661375878029033961e-41 + 1.170716024132352041e-1139j)  +/-  (1.17e-94, 1.78e-469j)
| (7.4201565888674851324e-26 - 1.1143546307183903498e-1130j)  +/-  (1.56e-89, 2.37e-464j)
| (2.8739103179403958143e-32 + 1.049474686642930643e-1134j)  +/-  (3.51e-92, 5.33e-467j)
| (2.5418229038893180043e-36 - 6.4144100426573681589e-1137j)  +/-  (1.09e-93, 1.65e-468j)
| (7.6004132058017376938e-29 - 1.0941430625048183264e-1132j)  +/-  (3.66e-91, 5.57e-466j)
| (0.0070258876355838677331 - 3.8081640244536228008e-1121j)  +/-  (2.46e-70, 3.75e-445j)
| (8.4885933676865431996e-21 - 5.7889184945234328999e-1129j)  +/-  (1.68e-89, 2.56e-464j)
| (3.4024553794255118473e-23 + 7.364122800551308731e-1130j)  +/-  (4.77e-90, 7.26e-465j)
| (1.2249225003240834109e-16 - 3.4035083005688376537e-1127j)  +/-  (9.96e-89, 1.51e-463j)
| (0.0003833443038571231766 - 1.1935152398805177146e-1121j)  +/-  (2.29e-78, 3.48e-453j)
| (0.19230711313238282667 - 8.9239214255190608321e-1121j)  +/-  (2.42e-65, 3.68e-440j)
| (9.84701225624928887e-07 + 9.09879685654335691e-1123j)  +/-  (5.56e-83, 8.45e-458j)
| (5.8368387631383442907e-09 + 9.264251762725041982e-1124j)  +/-  (1.65e-85, 2.5e-460j)
| (7.9987905759689096525e-15 + 2.1647584693692195768e-1126j)  +/-  (7.43e-89, 1.13e-463j)
| (8.9713620534107683443e-06 - 2.3991335666183599985e-1122j)  +/-  (1.19e-82, 1.8e-457j)
| (0.24751189603647721187 + 7.3527484304928943063e-1121j)  +/-  (5.69e-72, 8.65e-447j)
| (0.0018206078926958548675 + 2.2547351446503828106e-1121j)  +/-  (1.71e-79, 2.6e-454j)
| (0.022066364326258807858 + 5.7313492864621107929e-1121j)  +/-  (9.81e-78, 1.49e-452j)
| (1.2711242950306737363e-18 + 4.6813656620541980447e-1128j)  +/-  (2.62e-90, 3.98e-465j)
| (0.12377884395428642661 + 1.4289850438064661621e-1121j)  +/-  (3.16e-76, 4.8e-451j)
| (8.5640758526730424462e-08 - 3.0785071555938022806e-1123j)  +/-  (3.85e-85, 5.86e-460j)
| (0.23227927690090116145 - 4.51116538308865474e-1121j)  +/-  (1.06e-76, 1.62e-451j)
| (6.5350870806943983079e-05 + 5.655793191237509745e-1122j)  +/-  (9.45e-83, 1.44e-457j)
| (1.2325909527244228202e-11 + 5.8105233123223774653e-1125j)  +/-  (1.44e-88, 2.18e-463j)
| (3.6821736741083120028e-13 - 1.1997955158942191792e-1125j)  +/-  (2.42e-89, 3.69e-464j)
| (3.0756388778423022836e-10 - 2.4702816906730800253e-1124j)  +/-  (7.29e-88, 1.11e-462j)
| (0.11640536172113000646 + 8.9142068392694668647e-1121j)  +/-  (5.9e-84, 9.03e-459j)
| (0.056345905364477306517 - 7.6384012346252755777e-1121j)  +/-  (3.51e-84, 5.3e-459j)
Starting with polynomial:
P : 1/304888344611713860501504000000*t^28 - 1/388888194657798291456000000*t^27 + 1/1066908627319062528000000*t^26 - 1/4734801600528384000000*t^25 + 1/30302730243381657600*t^24 - 1/263044533362688000*t^23 + 23/68620313051136000*t^22 - 23/992442544128000*t^21 + 23/18003492864000*t^20 - 23/405078589440*t^19 + 437/213199257600*t^18 - 437/7238246400*t^17 + 7429/5109350400*t^16 - 7429/259459200*t^15 + 7429/16144128*t^14 - 7429/1235520*t^13 + 96577/1520640*t^12 - 5681/10560*t^11 + 62491/17280*t^10 - 16445/864*t^9 + 9867/128*t^8 - 3289/14*t^7 + 2093/4*t^6 - 819*t^5 + 6825/8*t^4 - 546*t^3 + 189*t^2 - 28*t + 1
Extension levels are: 28
-------------------------------------------------
Ending with final polynomial:
P : 1/304888344611713860501504000000*t^28 - 1/388888194657798291456000000*t^27 + 1/1066908627319062528000000*t^26 - 1/4734801600528384000000*t^25 + 1/30302730243381657600*t^24 - 1/263044533362688000*t^23 + 23/68620313051136000*t^22 - 23/992442544128000*t^21 + 23/18003492864000*t^20 - 23/405078589440*t^19 + 437/213199257600*t^18 - 437/7238246400*t^17 + 7429/5109350400*t^16 - 7429/259459200*t^15 + 7429/16144128*t^14 - 7429/1235520*t^13 + 96577/1520640*t^12 - 5681/10560*t^11 + 62491/17280*t^10 - 16445/864*t^9 + 9867/128*t^8 - 3289/14*t^7 + 2093/4*t^6 - 819*t^5 + 6825/8*t^4 - 546*t^3 + 189*t^2 - 28*t + 1
-------------------------------------------------
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: 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 roots: 848
 current precision for weights: 212
Linear system for weights solvable: 1
  current precision for roots: 424
  current precision for roots: 848
  current precision for roots: 1696
 current precision for weights: 424
Linear system for weights solvable: 1
Sufficient bits for target precision reached
Positive weights:   28 out of 28
Indefinite weights: 0 out of 28
Negative weights:   0 out of 28
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (96.582420627527319077 - 1.751170091962781755e-1104j)  +/-  (6.27e-500, 6.27e-500j)
| (59.748796084641240822 + 3.0547138688006924001e-1105j)  +/-  (9.46e-497, 9.46e-497j)
| (74.786778152339161835 - 4.0238774315816127361e-1115j)  +/-  (7.97e-498, 7.97e-498j)
| (84.317837107227043056 + 7.0896183090592229719e-1128j)  +/-  (1.11e-498, 1.11e-498j)
| (66.756977283906469554 - 1.6488777418905018346e-1154j)  +/-  (2.96e-497, 2.96e-497j)
| (5.2837360628434425628 + 6.4412592813779738102e-1196j)  +/-  (1.1e-501, 1.1e-501j)
| (47.892071633622743673 + 6.6489090437809809017e-1274j)  +/-  (3.2e-496, 3.2e-496j)
| (53.511297959664294205 + 1.8384812445049820601e-1365j)  +/-  (2.21e-496, 2.21e-496j)
| (38.132254410194646779 + 6.6089181089204536908e-1422j)  +/-  (5.12e-496, 5.12e-496j)
| (8.4412163282713244886 - 3.8844155182969516075e-1441j)  +/-  (4.73e-500, 4.73e-500j)
| (1.2239718083849077187 + 2.9339303326084873546e-1456j)  +/-  (3.59e-506, 3.59e-506j)
| (14.714085164135748813 + 1.298911371073227711e-1464j)  +/-  (3.76e-498, 3.76e-498j)
| (20.023783329951712751 - 1.0001987501967736208e-1494j)  +/-  (3.59e-497, 3.59e-497j)
| (33.866605516584459212 - 9.8801489203036528694e-1525j)  +/-  (3.77e-496, 3.77e-496j)
| (12.407903414460671739 - 5.3696142421009981296e-1541j)  +/-  (1.1e-498, 1.1e-498j)
| (0.65813662835479151933 + 3.1688062569504533571e-1558j)  +/-  (2.01e-507, 2.01e-507j)
| (6.7646034042435051552 - 6.7098221082465458824e-1552j)  +/-  (8.12e-501, 8.12e-501j)
| (3.9933116592501141362 - 8.7601420429388062329e-1553j)  +/-  (1.18e-502, 1.18e-502j)
| (42.78967237077257627 - 7.7981260847960814809e-1547j)  +/-  (4.35e-496, 4.35e-496j)
| (0.050734624849873887593 - 1.4933744249947694608e-1569j)  +/-  (3.31e-510, 3.31e-510j)
| (17.248663415608056266 - 3.2721961314311949424e-1556j)  +/-  (1.25e-497, 1.25e-497j)
| (0.26748726864074108429 + 2.4713593801940518797e-1578j)  +/-  (9.67e-509, 9.67e-509j)
| (10.319850462993260104 + 9.1804542734149270654e-1567j)  +/-  (2.66e-499, 2.66e-499j)
| (26.35629737440131762 - 4.3968904315912933646e-1567j)  +/-  (1.65e-496, 1.65e-496j)
| (29.951966833596182109 - 2.1858514682430365535e-1581j)  +/-  (2.85e-496, 2.85e-496j)
| (23.05389013503029597 - 4.0288074189140678681e-1593j)  +/-  (8.67e-497, 8.67e-497j)
| (1.9667676124737776998 - 2.4355603556936708235e-1613j)  +/-  (7.25e-505, 7.25e-505j)
| (2.8888833260303218929 - 4.077728490782218278e-1612j)  +/-  (9.41e-504, 9.41e-504j)
-------------------------------------------------
The weights are:
| (1.661375878029033961e-41 + 1.170716024132352041e-1139j)  +/-  (1.17e-94, 1.78e-469j)
| (7.4201565888674851324e-26 - 1.1143546307183903498e-1130j)  +/-  (1.56e-89, 2.37e-464j)
| (2.8739103179403958143e-32 + 1.049474686642930643e-1134j)  +/-  (3.51e-92, 5.33e-467j)
| (2.5418229038893180043e-36 - 6.4144100426573681589e-1137j)  +/-  (1.09e-93, 1.65e-468j)
| (7.6004132058017376938e-29 - 1.0941430625048183264e-1132j)  +/-  (3.66e-91, 5.57e-466j)
| (0.0070258876355838677331 - 3.8081640244536228008e-1121j)  +/-  (2.46e-70, 3.75e-445j)
| (8.4885933676865431996e-21 - 5.7889184945234328999e-1129j)  +/-  (1.68e-89, 2.56e-464j)
| (3.4024553794255118473e-23 + 7.364122800551308731e-1130j)  +/-  (4.77e-90, 7.26e-465j)
| (1.2249225003240834109e-16 - 3.4035083005688376537e-1127j)  +/-  (9.96e-89, 1.51e-463j)
| (0.0003833443038571231766 - 1.1935152398805177146e-1121j)  +/-  (2.29e-78, 3.48e-453j)
| (0.19230711313238282667 - 8.9239214255190608321e-1121j)  +/-  (2.42e-65, 3.68e-440j)
| (9.84701225624928887e-07 + 9.09879685654335691e-1123j)  +/-  (5.56e-83, 8.45e-458j)
| (5.8368387631383442907e-09 + 9.264251762725041982e-1124j)  +/-  (1.65e-85, 2.5e-460j)
| (7.9987905759689096525e-15 + 2.1647584693692195768e-1126j)  +/-  (7.43e-89, 1.13e-463j)
| (8.9713620534107683443e-06 - 2.3991335666183599985e-1122j)  +/-  (1.19e-82, 1.8e-457j)
| (0.24751189603647721187 + 7.3527484304928943063e-1121j)  +/-  (5.69e-72, 8.65e-447j)
| (0.0018206078926958548675 + 2.2547351446503828106e-1121j)  +/-  (1.71e-79, 2.6e-454j)
| (0.022066364326258807858 + 5.7313492864621107929e-1121j)  +/-  (9.81e-78, 1.49e-452j)
| (1.2711242950306737363e-18 + 4.6813656620541980447e-1128j)  +/-  (2.62e-90, 3.98e-465j)
| (0.12377884395428642661 + 1.4289850438064661621e-1121j)  +/-  (3.16e-76, 4.8e-451j)
| (8.5640758526730424462e-08 - 3.0785071555938022806e-1123j)  +/-  (3.85e-85, 5.86e-460j)
| (0.23227927690090116145 - 4.51116538308865474e-1121j)  +/-  (1.06e-76, 1.62e-451j)
| (6.5350870806943983079e-05 + 5.655793191237509745e-1122j)  +/-  (9.45e-83, 1.44e-457j)
| (1.2325909527244228202e-11 + 5.8105233123223774653e-1125j)  +/-  (1.44e-88, 2.18e-463j)
| (3.6821736741083120028e-13 - 1.1997955158942191792e-1125j)  +/-  (2.42e-89, 3.69e-464j)
| (3.0756388778423022836e-10 - 2.4702816906730800253e-1124j)  +/-  (7.29e-88, 1.11e-462j)
| (0.11640536172113000646 + 8.9142068392694668647e-1121j)  +/-  (5.9e-84, 9.03e-459j)
| (0.056345905364477306517 - 7.6384012346252755777e-1121j)  +/-  (3.51e-84, 5.3e-459j)
