Starting with polynomial:
P : 1073741824*t^30 - 233538846720*t^28 + 22069421015040*t^26 - 1195426971648000*t^24 + 41242230521856000*t^22 - 952695525054873600*t^20 + 15084345813368832000*t^18 - 164850350674673664000*t^16 + 1236377630060052480000*t^14 - 6250575796414709760000*t^12 + 20626900128168542208000*t^10 - 42191386625799290880000*t^8 + 49223284396765839360000*t^6 - 28398048690441830400000*t^4 + 6085296147951820800000*t^2 - 202843204931727360000
Extension levels are: 30
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Ending with final polynomial:
P : 1073741824*t^30 - 233538846720*t^28 + 22069421015040*t^26 - 1195426971648000*t^24 + 41242230521856000*t^22 - 952695525054873600*t^20 + 15084345813368832000*t^18 - 164850350674673664000*t^16 + 1236377630060052480000*t^14 - 6250575796414709760000*t^12 + 20626900128168542208000*t^10 - 42191386625799290880000*t^8 + 49223284396765839360000*t^6 - 28398048690441830400000*t^4 + 6085296147951820800000*t^2 - 202843204931727360000
-------------------------------------------------
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
-------------------------------------------------
The nodes are:
| (4.9889189685899439445 + 5.0218110794994837203e-437j)  +/-  (1.24e-120, 1.24e-120j)
| (6.1382792201239346204 + 2.7429278471019164732e-439j)  +/-  (2.6e-121, 2.6e-121j)
| (3.5444438731553498869 - 4.0194913652285896533e-439j)  +/-  (6.96e-121, 6.96e-121j)
| (-6.8633452935298915811 - 1.6061587487720167483e-438j)  +/-  (3.78e-122, 3.78e-122j)
| (-5.5331471515674957251 + 1.1405746811199985753e-441j)  +/-  (7.29e-121, 7.29e-121j)
| (5.5331471515674957251 + 1.0164700557270404054e-450j)  +/-  (7.86e-121, 7.86e-121j)
| (-4.0039086038612288152 - 3.8338731098874059098e-456j)  +/-  (1.17e-120, 1.17e-120j)
| (6.8633452935298915811 + 1.361254828927546985e-467j)  +/-  (3.17e-122, 3.17e-122j)
| (-1.4155278001981885119 + 3.4885807591908387438e-469j)  +/-  (7.42e-124, 7.42e-124j)
| (2.2433914677615040725 + 5.5460991519995567427e-467j)  +/-  (2.23e-122, 2.23e-122j)
| (4.4830553570925183419 + 8.2697679822891618229e-466j)  +/-  (1.7e-120, 1.7e-120j)
| (3.0999705295864417487 - 2.4937972087098218692e-466j)  +/-  (2.68e-121, 2.68e-121j)
| (-2.6671321245356172006 + 6.3548151204768079035e-467j)  +/-  (1.09e-121, 1.09e-121j)
| (-1.8267411436036880388 + 1.0129817398297124614e-473j)  +/-  (5.57e-123, 5.57e-123j)
| (1.8267411436036880388 + 2.7088233511115660304e-474j)  +/-  (5.48e-123, 5.48e-123j)
| (2.6671321245356172006 + 1.2267949536233801073e-472j)  +/-  (1.18e-121, 1.18e-121j)
| (1.4155278001981885119 + 2.3977104360695700888e-475j)  +/-  (7.3e-124, 7.3e-124j)
| (-4.4830553570925183419 - 1.0192838201888480286e-470j)  +/-  (1.83e-120, 1.83e-120j)
| (0.20112857654887148555 + 1.4138744307550387962e-485j)  +/-  (4.78e-127, 4.78e-127j)
| (-3.5444438731553498869 - 2.5129439952405956844e-478j)  +/-  (7.65e-121, 7.65e-121j)
| (-6.1382792201239346204 - 4.0540323598510212405e-483j)  +/-  (2.26e-121, 2.26e-121j)
| (1.0083382710467234618 + 4.2839249751760165654e-489j)  +/-  (8.03e-125, 8.03e-125j)
| (4.0039086038612288152 + 2.0711427610373302573e-486j)  +/-  (1.2e-120, 1.2e-120j)
| (-0.20112857654887148555 + 9.2246691085121795206e-495j)  +/-  (7.31e-127, 7.31e-127j)
| (-1.0083382710467234618 + 2.3065654849423756873e-491j)  +/-  (7.3e-125, 7.3e-125j)
| (-4.9889189685899439445 - 5.9402281415146262209e-488j)  +/-  (1.18e-120, 1.18e-120j)
| (0.60392105862555230778 - 6.0356866490173082247e-500j)  +/-  (7.5e-126, 7.5e-126j)
| (-3.0999705295864417487 - 1.5041512170755046017e-496j)  +/-  (3.73e-121, 3.73e-121j)
| (-2.2433914677615040725 + 5.2666513541484517968e-504j)  +/-  (2.58e-122, 2.58e-122j)
| (-0.60392105862555230778 + 5.5051372680700356596e-508j)  +/-  (7.5e-126, 7.5e-126j)
-------------------------------------------------
The weights are:
| (4.573425871326203375e-12 - 5.8410873250780249456e-448j)  +/-  (3.1e-37, 4.6e-97j)
| (1.5855609449662979156e-17 + 9.5445705076787072027e-451j)  +/-  (4.25e-40, 6.3e-100j)
| (8.909088868621194354e-07 + 1.3394418098960261176e-444j)  +/-  (7.42e-34, 1.1e-93j)
| (1.6408070081178413677e-21 - 1.8436453767811419567e-453j)  +/-  (1.5e-43, 2.22e-103j)
| (1.6240801299723970104e-14 - 6.6268774537510003689e-450j)  +/-  (5.03e-41, 7.46e-101j)
| (1.6240801299723970104e-14 - 4.9459840950476412695e-449j)  +/-  (3.74e-39, 5.54e-99j)
| (2.8821751540476444461e-08 + 1.0560314846037606286e-446j)  +/-  (2.57e-38, 3.81e-98j)
| (1.6408070081178413677e-21 - 6.9513206394633765252e-453j)  +/-  (1.71e-42, 2.53e-102j)
| (0.031111770183501276848 + 1.6449606141803584898e-443j)  +/-  (3.95e-29, 5.86e-89j)
| (0.0015447073398660852068 - 1.2998210649917420153e-443j)  +/-  (9.84e-33, 1.46e-92j)
| (5.1784594671897099968e-10 - 4.3670484486215080417e-447j)  +/-  (1.01e-37, 1.5e-97j)
| (1.6579981630673451563e-05 - 3.7071366376744868515e-444j)  +/-  (3.88e-35, 5.75e-95j)
| (0.00019651294398482640497 - 1.0528537038714008651e-444j)  +/-  (6.99e-37, 1.04e-96j)
| (0.0082957475577232948228 - 7.8686441744879614802e-444j)  +/-  (1.08e-33, 1.59e-93j)
| (0.0082957475577232948228 + 2.3210525032668826649e-443j)  +/-  (4.36e-33, 6.47e-93j)
| (0.00019651294398482640497 + 6.7106090408656047725e-444j)  +/-  (9.12e-35, 1.35e-94j)
| (0.031111770183501276848 - 3.6734516793813538022e-443j)  +/-  (1.33e-32, 1.98e-92j)
| (5.1784594671897099968e-10 - 1.3335058800818249462e-447j)  +/-  (5.86e-42, 8.69e-102j)
| (0.21799997181557725417 + 6.3456409225225379758e-443j)  +/-  (1.25e-34, 1.85e-94j)
| (8.909088868621194354e-07 - 6.2394684538071420389e-446j)  +/-  (2.76e-40, 4.09e-100j)
| (1.5855609449662979156e-17 + 1.9445363777703163258e-451j)  +/-  (7.25e-46, 1.08e-105j)
| (0.082786836715621843839 + 5.0805657399076685493e-443j)  +/-  (7.52e-36, 1.11e-95j)
| (2.8821751540476444461e-08 + 1.2167329304904789592e-445j)  +/-  (6.72e-40, 9.97e-100j)
| (0.21799997181557725417 - 5.6954525866446761141e-443j)  +/-  (5.58e-36, 8.25e-96j)
| (0.082786836715621843839 - 2.9129249592547082727e-443j)  +/-  (8.37e-37, 1.24e-96j)
| (4.573425871326203375e-12 + 1.1809742704476115563e-448j)  +/-  (2.37e-43, 3.52e-103j)
| (0.15804695320902071341 - 6.1029399466784874676e-443j)  +/-  (4.76e-37, 6.97e-97j)
| (1.6579981630673451563e-05 + 2.8656139162760765914e-445j)  +/-  (2.49e-40, 3.67e-100j)
| (0.0015447073398660852068 + 3.1599096215867752654e-444j)  +/-  (2.21e-39, 3.36e-99j)
| (0.15804695320902071341 + 4.3992199811672869294e-443j)  +/-  (7.64e-38, 9.94e-98j)
