Starting with polynomial:
P : 8589934592*t^33 - 2267742732288*t^31 + 263625092628480*t^29 - 17838631267860480*t^27 + 782669946877378560*t^25 - 23480098406321356800*t^23 + 495038741399941939200*t^21 - 7425581120999129088000*t^19 + 79360898230678192128000*t^17 - 599615675520679673856000*t^15 + 3147982296483568287744000*t^13 - 11161028142078105747456000*t^11 + 25577356158928992337920000*t^9 - 35414800835440143237120000*t^7 + 26561100626580107427840000*t^5 - 8853700208860035809280000*t^3 + 830034394580628357120000*t
Extension levels are: 33
-------------------------------------------------
Ending with final polynomial:
P : 8589934592*t^33 - 2267742732288*t^31 + 263625092628480*t^29 - 17838631267860480*t^27 + 782669946877378560*t^25 - 23480098406321356800*t^23 + 495038741399941939200*t^21 - 7425581120999129088000*t^19 + 79360898230678192128000*t^17 - 599615675520679673856000*t^15 + 3147982296483568287744000*t^13 - 11161028142078105747456000*t^11 + 25577356158928992337920000*t^9 - 35414800835440143237120000*t^7 + 26561100626580107427840000*t^5 - 8853700208860035809280000*t^3 + 830034394580628357120000*t
-------------------------------------------------
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:   33 out of 33
Indefinite weights: 0 out of 33
Negative weights:   0 out of 33
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (-2.7384458243513549069 - 1.4133678831665551041e-463j)  +/-  (4.5e-121, 4.5e-121j)
| (-6.541655445738077261 + 4.4785882777474126548e-467j)  +/-  (8.8e-121, 8.8e-121j)
| (5.9480711820871444798 + 3.3562895047689124508e-465j)  +/-  (3.04e-120, 3.04e-120j)
| (-4.4519111488328271901 - 9.161397274254100813e-472j)  +/-  (6.77e-120, 6.77e-120j)
| (6.541655445738077261 + 2.2891155738697733443e-470j)  +/-  (9.38e-121, 9.38e-121j)
| (7.2538518220152006461 - 2.7272766891217187476e-474j)  +/-  (9.67e-122, 9.67e-122j)
| (-5.4149290026141925399 - 2.4810671290623894217e-475j)  +/-  (6.04e-120, 6.04e-120j)
| (5.4149290026141925399 + 6.6348098770559773556e-475j)  +/-  (5.89e-120, 5.89e-120j)
| (-7.2538518220152006461 + 1.5765118828675943329e-485j)  +/-  (8.31e-122, 8.31e-122j)
| (4.9200285205950082924 + 3.4532030062567458289e-482j)  +/-  (7.85e-120, 7.85e-120j)
| (-4.9200285205950082924 - 1.7432126062373081129e-493j)  +/-  (8.02e-120, 8.02e-120j)
| (4.0036716099569314145 - 5.0074679470700772635e-494j)  +/-  (5.23e-120, 5.23e-120j)
| (-4.0036716099569314145 - 3.1912698956735844853e-498j)  +/-  (4.87e-120, 4.87e-120j)
| (-1.9371545818222066164 + 2.537129792105587459e-500j)  +/-  (1.67e-122, 1.67e-122j)
| (-3.1497966817038253846 + 1.4714111532606710003e-498j)  +/-  (1.1e-120, 1.1e-120j)
| (3.1497966817038253846 - 1.2708899546624103452e-497j)  +/-  (1.25e-120, 1.25e-120j)
| (1.5443482612431218091 - 3.885208245269869624e-509j)  +/-  (2.2e-123, 2.2e-123j)
| (-3.5707219802327182856 - 8.4123734952352419801e-507j)  +/-  (2.97e-120, 2.97e-120j)
| (-1.1552002041267896136 + 4.1926333732482939982e-511j)  +/-  (2.8e-124, 2.8e-124j)
| (-1.5443482612431218091 - 5.1898002295884287869e-510j)  +/-  (2.26e-123, 2.26e-123j)
| (3.5707219802327182856 + 1.1155050855032223666e-507j)  +/-  (2.74e-120, 2.74e-120j)
| (0.76870137975886859811 + 4.4100288463141760083e-516j)  +/-  (3.19e-125, 3.19e-125j)
| (-5.9480711820871444798 + 1.1933001374712644102e-511j)  +/-  (3.25e-120, 3.25e-120j)
| (2.7384458243513549069 + 1.003181270174702993e-510j)  +/-  (4.1e-121, 4.1e-121j)
| (-0.76870137975886859811 - 1.2072375685720279766e-518j)  +/-  (3.42e-125, 3.42e-125j)
| (-4.2019396661326761654e-526 - 4.5672818155056154259e-527j)  +/-  (1.39e-524, 1.39e-524j)
| (2.3347511515295151771 + 7.7115218063302493665e-514j)  +/-  (1.07e-121, 1.07e-121j)
| (1.9371545818222066164 - 6.6785211576979996326e-518j)  +/-  (1.75e-122, 1.75e-122j)
| (-2.3347511515295151771 + 1.3246599725592732366e-520j)  +/-  (1.14e-121, 1.14e-121j)
| (-0.38392601450840908377 - 2.8059198001440325677e-528j)  +/-  (1.93e-126, 1.93e-126j)
| (4.4519111488328271901 + 1.4292870651410684137e-525j)  +/-  (6.71e-120, 6.71e-120j)
| (1.1552002041267896136 + 4.1542253937646357209e-533j)  +/-  (3.11e-124, 3.11e-124j)
| (0.38392601450840908377 - 1.8638628135258496278e-535j)  +/-  (2.79e-126, 2.79e-126j)
-------------------------------------------------
The weights are:
| (0.00012719246285659432081 - 4.9228969876955925361e-467j)  +/-  (2.87e-26, 7.03e-86j)
| (9.349155921250696923e-20 + 1.2815095542941450327e-475j)  +/-  (1.49e-38, 3.64e-98j)
| (1.3584475998220762444e-16 + 2.1387554399555985221e-474j)  +/-  (5.49e-38, 1.35e-97j)
| (6.3692617245384664514e-10 + 2.3477677682019199105e-470j)  +/-  (5e-34, 1.22e-93j)
| (9.349155921250696923e-20 - 5.2519376215430660871e-476j)  +/-  (1.72e-39, 4.2e-99j)
| (6.50688997040275675e-24 + 4.0691842760186221407e-478j)  +/-  (2.83e-41, 6.93e-101j)
| (5.3230238712251332273e-14 + 1.3740438668950458729e-472j)  +/-  (7.15e-38, 1.75e-97j)
| (5.3230238712251332273e-14 - 4.5105296546387171005e-473j)  +/-  (7.83e-38, 1.92e-97j)
| (6.50688997040275675e-24 - 9.0048365947084557634e-478j)  +/-  (2.16e-42, 5.3e-102j)
| (8.3160469105554274411e-12 + 6.0020834690291260368e-472j)  +/-  (2.07e-37, 5.08e-97j)
| (8.3160469105554274411e-12 - 2.1070395807791701332e-471j)  +/-  (4.79e-37, 1.17e-96j)
| (2.7124800309283070126e-08 + 3.8937927466610094906e-470j)  +/-  (1.24e-36, 3.04e-96j)
| (2.7124800309283070126e-08 - 2.0749190046759775237e-469j)  +/-  (1.25e-35, 3.05e-95j)
| (0.0052276057658435239362 - 1.4382915319344532643e-466j)  +/-  (2.26e-31, 5.55e-91j)
| (1.1522829799483730523e-05 - 1.315385572013861989e-467j)  +/-  (2.23e-34, 5.45e-94j)
| (1.1522829799483730523e-05 + 9.1892437124225156535e-469j)  +/-  (9.96e-37, 2.44e-96j)
| (0.020304044757041959937 + 5.3033462556453737904e-467j)  +/-  (1.55e-32, 3.8e-92j)
| (6.9829370540107094689e-07 + 1.6004330772905822497e-468j)  +/-  (1.91e-35, 4.68e-95j)
| (0.057586311735787181462 - 2.4160017303997289115e-466j)  +/-  (6.49e-31, 1.59e-90j)
| (0.020304044757041959937 + 1.9021176436903332032e-466j)  +/-  (4.71e-32, 1.15e-91j)
| (6.9829370540107094689e-07 - 2.1112169480704595642e-469j)  +/-  (1.45e-37, 3.56e-97j)
| (0.12045105210565650457 + 1.5773831732217998118e-466j)  +/-  (7.92e-33, 1.94e-92j)
| (1.3584475998220762444e-16 - 5.7883263972145495955e-474j)  +/-  (4.16e-41, 1.02e-100j)
| (0.00012719246285659432081 - 3.2823314022985844354e-468j)  +/-  (1.12e-36, 2.73e-96j)
| (0.12045105210565650457 + 2.8085445566684936333e-466j)  +/-  (4.89e-34, 1.19e-93j)
| (0.21652764968960661187 + 2.7085598046423332147e-466j)  +/-  (1.95e-34, 4.7e-94j)
| (0.00096953420642404635467 + 9.7833081949855986798e-468j)  +/-  (1.94e-36, 4.75e-96j)
| (0.0052276057658435239362 - 2.4649034958760981409e-467j)  +/-  (4.78e-36, 1.17e-95j)
| (0.00096953420642404635467 + 1.229460147506458546e-466j)  +/-  (5.31e-36, 1.3e-95j)
| (0.18705818522798610386 - 2.9280056629668573725e-466j)  +/-  (7.27e-35, 1.75e-94j)
| (6.3692617245384664514e-10 - 5.5947405469155368618e-471j)  +/-  (6.61e-40, 1.64e-99j)
| (0.057586311735787181462 - 9.8240160374128181013e-467j)  +/-  (8.7e-36, 2.16e-95j)
| (0.18705818522798610386 - 2.2079520507327815799e-466j)  +/-  (2.65e-35, 5.73e-95j)
