Starting with polynomial:
P : t^34 - 561*t^32 + 139128*t^30 - 20173560*t^28 + 1906401420*t^26 - 123916092300*t^24 + 5700140245800*t^22 - 188104628111400*t^20 + 4467484917645750*t^18 - 75947243599977750*t^16 + 911366923199733000*t^14 - 7539490001015973000*t^12 + 41467195005587851500*t^10 - 143540290403957947500*t^8 + 287080580807915895000*t^6 - 287080580807915895000*t^4 + 107655217802968460625*t^2 - 6332659870762850625
Extension levels are: 34
-------------------------------------------------
Ending with final polynomial:
P : t^34 - 561*t^32 + 139128*t^30 - 20173560*t^28 + 1906401420*t^26 - 123916092300*t^24 + 5700140245800*t^22 - 188104628111400*t^20 + 4467484917645750*t^18 - 75947243599977750*t^16 + 911366923199733000*t^14 - 7539490001015973000*t^12 + 41467195005587851500*t^10 - 143540290403957947500*t^8 + 287080580807915895000*t^6 - 287080580807915895000*t^4 + 107655217802968460625*t^2 - 6332659870762850625
-------------------------------------------------
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:   34 out of 34
Indefinite weights: 0 out of 34
Negative weights:   0 out of 34
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (4.0957589719541636814 - 6.0309440623915631669e-450j)  +/-  (1.18e-120, 1.18e-120j)
| (7.1563392591348442233 + 1.3754003665982293036e-447j)  +/-  (1.54e-119, 1.54e-119j)
| (-7.1563392591348442233 + 1.3450450870941033939e-450j)  +/-  (1.65e-119, 1.65e-119j)
| (-10.436741871005049765 + 1.9303223715040957057e-457j)  +/-  (1.77e-121, 1.77e-121j)
| (-8.6007052339834314064 - 1.4701020132454711235e-461j)  +/-  (6.01e-120, 6.01e-120j)
| (-9.4351508337608006095 + 1.4820164471778856782e-467j)  +/-  (1.52e-120, 1.52e-120j)
| (2.9736296503039889495 + 3.1306275058556480834e-474j)  +/-  (6.93e-122, 6.93e-122j)
| (10.436741871005049765 - 2.1347582862235721725e-473j)  +/-  (2e-121, 2e-121j)
| (9.4351508337608006095 - 5.7989335449824260684e-473j)  +/-  (1.64e-120, 1.64e-120j)
| (4.672290691400980565 + 1.7054962595446430857e-471j)  +/-  (3.56e-120, 3.56e-120j)
| (-7.8515175906990722937 + 3.4940233416785599757e-470j)  +/-  (1.38e-119, 1.38e-119j)
| (7.8515175906990722937 + 2.7385530892755047371e-474j)  +/-  (1.02e-119, 1.02e-119j)
| (-2.4240505097562307671 - 1.8339231807611662886e-477j)  +/-  (9.72e-123, 9.72e-123j)
| (-5.2625364817346304193 - 5.977787557653933071e-474j)  +/-  (8.41e-120, 8.41e-120j)
| (5.8699275885967788594 + 4.7894411026829080285e-477j)  +/-  (1.41e-119, 1.41e-119j)
| (-2.9736296503039889495 + 1.4117216215595666617e-480j)  +/-  (7.14e-122, 7.14e-122j)
| (-4.0957589719541636814 - 2.9462608058535666535e-477j)  +/-  (1.47e-120, 1.47e-120j)
| (-1.3399906255226187504 - 1.243723479728862096e-487j)  +/-  (1.76e-124, 1.76e-124j)
| (8.6007052339834314064 + 1.3985926894113781718e-483j)  +/-  (6.37e-120, 6.37e-120j)
| (-1.879964366420187224 - 2.2837842388509223328e-486j)  +/-  (1.42e-123, 1.42e-123j)
| (-6.4990463539279639338 - 1.127508445984670707e-482j)  +/-  (2.25e-119, 2.25e-119j)
| (5.2625364817346304193 + 4.9751475056419889457e-494j)  +/-  (9.15e-120, 9.15e-120j)
| (2.4240505097562307671 + 2.9901968029942947719e-496j)  +/-  (1.13e-122, 1.13e-122j)
| (-5.8699275885967788594 + 5.17433724691065396e-494j)  +/-  (1.78e-119, 1.78e-119j)
| (-3.5302616340741692926 - 1.17968409087865324e-500j)  +/-  (3.75e-121, 3.75e-121j)
| (-0.26743918395155704722 + 2.709690736434203638e-509j)  +/-  (9.04e-127, 9.04e-127j)
| (1.3399906255226187504 + 3.7389681952124473544e-508j)  +/-  (1.35e-124, 1.35e-124j)
| (3.5302616340741692926 + 1.2022352696864847921e-503j)  +/-  (2.92e-121, 2.92e-121j)
| (1.879964366420187224 - 5.7804074381204944418e-507j)  +/-  (1.54e-123, 1.54e-123j)
| (-0.8028734607837122872 - 6.6411534409702260253e-509j)  +/-  (1.37e-125, 1.37e-125j)
| (-4.672290691400980565 - 2.3194213076083423264e-506j)  +/-  (3.33e-120, 3.33e-120j)
| (0.26743918395155704722 + 9.8469135874951203959e-515j)  +/-  (9.04e-127, 9.04e-127j)
| (0.8028734607837122872 + 5.0808629542861191819e-514j)  +/-  (9.68e-126, 9.68e-126j)
| (6.4990463539279639338 + 7.5130630362255326208e-512j)  +/-  (2.33e-119, 2.33e-119j)
-------------------------------------------------
The weights are:
| (5.182712643366909242e-05 + 6.447167849944407705e-454j)  +/-  (2.78e-21, 1.1e-80j)
| (2.036657679770806884e-12 + 1.0221631143539800221e-458j)  +/-  (2.17e-29, 8.61e-89j)
| (2.036657679770806884e-12 + 5.7121920352658823734e-459j)  +/-  (2.76e-30, 1.09e-89j)
| (1.0233271298054581444e-24 + 3.1345241060760046099e-465j)  +/-  (5.79e-36, 2.29e-95j)
| (2.7080547092623234842e-17 + 1.8436816898953392519e-461j)  +/-  (1.9e-33, 7.52e-93j)
| (1.6681443755785366433e-20 - 4.2960345728836795999e-463j)  +/-  (1.29e-34, 5.1e-94j)
| (0.0026508242383101953263 + 2.0162724000055073099e-453j)  +/-  (2.63e-22, 1.04e-81j)
| (1.0233271298054581444e-24 + 7.5316972360088130482e-465j)  +/-  (7.6e-39, 3.01e-98j)
| (1.6681443755785366433e-20 - 1.1614749751369694803e-462j)  +/-  (2.06e-37, 8.16e-97j)
| (4.2277257483877443905e-06 + 1.5321882155126888301e-454j)  +/-  (4.67e-29, 1.85e-88j)
| (1.1779377906225182927e-14 - 4.0831261724009033697e-460j)  +/-  (1.03e-34, 4.08e-94j)
| (1.1779377906225182927e-14 - 1.5610953254327691537e-459j)  +/-  (3.98e-35, 1.58e-94j)
| (0.011550738946777123932 + 7.3776787560593278684e-454j)  +/-  (1.41e-25, 5.58e-85j)
| (2.3120342643228853594e-07 - 2.3073040613238434842e-456j)  +/-  (1.73e-32, 6.84e-92j)
| (8.1174090401222649454e-09 + 2.0673569759638492948e-456j)  +/-  (6.53e-33, 2.59e-92j)
| (0.0026508242383101953263 - 3.2620767600944939256e-454j)  +/-  (3.96e-28, 1.57e-87j)
| (5.182712643366909242e-05 - 3.9417687678601744004e-455j)  +/-  (6.68e-31, 2.65e-90j)
| (0.087511681358623896726 + 2.4312969516445855814e-453j)  +/-  (4.73e-24, 1.88e-83j)
| (2.7080547092623234842e-17 + 5.7225022055579980184e-461j)  +/-  (1.55e-37, 6.16e-97j)
| (0.036923462958044258767 - 1.4379354693331616087e-453j)  +/-  (2.24e-26, 8.87e-86j)
| (1.7243055667452884664e-10 - 5.5737726447362148159e-458j)  +/-  (1.48e-34, 5.89e-94j)
| (2.3120342643228853594e-07 - 1.7394136464541187851e-455j)  +/-  (2.7e-33, 1.08e-92j)
| (0.011550738946777123932 - 2.8359105420037644976e-453j)  +/-  (5.89e-30, 2.34e-89j)
| (8.1174090401222649454e-09 + 4.0623382112834124878e-457j)  +/-  (5.56e-34, 2.2e-93j)
| (0.00043996496677462378165 + 1.2328315135640359238e-454j)  +/-  (3.16e-31, 1.27e-90j)
| (0.20592493666911354384 + 4.6356873900808434604e-453j)  +/-  (6.62e-29, 2.64e-88j)
| (0.087511681358623896726 - 4.760631496020533405e-453j)  +/-  (1.48e-29, 6.05e-89j)
| (0.00043996496677462378165 - 1.621789901545228726e-453j)  +/-  (4.43e-32, 1.83e-91j)
| (0.036923462958044258767 + 3.8367025387695820743e-453j)  +/-  (1.72e-30, 6.84e-90j)
| (0.15494209651485980755 - 3.5859740260213648104e-453j)  +/-  (2.04e-29, 7.78e-89j)
| (4.2277257483877443905e-06 + 1.0524346033832462092e-455j)  +/-  (5.88e-33, 2.24e-92j)
| (0.20592493666911354384 - 5.275893696231372046e-453j)  +/-  (3.03e-30, 1.11e-89j)
| (0.15494209651485980755 + 5.3117577959811023483e-453j)  +/-  (1.53e-30, 5.17e-90j)
| (1.7243055667452884664e-10 - 1.9801222146571217788e-457j)  +/-  (2.95e-36, 1.5e-95j)
