Starting with polynomial:
P : t^38 - 703*t^36 + 221445*t^34 - 41410215*t^32 + 5134866660*t^30 - 446733399420*t^28 + 28144204163460*t^26 - 1306695193303500*t^24 + 45080984168970750*t^22 - 1157078593670249250*t^20 + 21984493279734735750*t^18 - 305784315618128597250*t^16 + 3057843156181285972500*t^14 - 21404902093269001807500*t^12 + 100908824153982437092500*t^10 - 302726472461947311277500*t^8 + 529771326808407794735625*t^6 - 467445288360359818884375*t^4 + 155815096120119939628125*t^2 - 8200794532637891559375
Extension levels are: 38
-------------------------------------------------
Ending with final polynomial:
P : t^38 - 703*t^36 + 221445*t^34 - 41410215*t^32 + 5134866660*t^30 - 446733399420*t^28 + 28144204163460*t^26 - 1306695193303500*t^24 + 45080984168970750*t^22 - 1157078593670249250*t^20 + 21984493279734735750*t^18 - 305784315618128597250*t^16 + 3057843156181285972500*t^14 - 21404902093269001807500*t^12 + 100908824153982437092500*t^10 - 302726472461947311277500*t^8 + 529771326808407794735625*t^6 - 467445288360359818884375*t^4 + 155815096120119939628125*t^2 - 8200794532637891559375
-------------------------------------------------
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:   38 out of 38
Indefinite weights: 0 out of 38
Negative weights:   0 out of 38
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (-11.123868434949870717 + 5.3367994643930865501e-392j)  +/-  (9.72e-121, 9.72e-121j)
| (11.123868434949870717 - 8.0372027742081812915e-393j)  +/-  (9.09e-121, 9.09e-121j)
| (-9.3265847573955630211 - 1.1305046653537093598e-389j)  +/-  (3.85e-119, 3.85e-119j)
| (4.9437900298022665601 - 1.0629624816103551049e-394j)  +/-  (2.97e-119, 2.97e-119j)
| (-10.142787661129668848 - 1.1071001079129890019e-393j)  +/-  (9.01e-120, 9.01e-120j)
| (-6.0743660420595618136 + 8.7914558443384571122e-396j)  +/-  (1.13e-118, 1.13e-118j)
| (6.0743660420595618136 + 9.7319743430642854491e-404j)  +/-  (1.22e-118, 1.22e-118j)
| (8.5947641363861120929 + 2.371208834612706854e-404j)  +/-  (8.47e-119, 8.47e-119j)
| (-5.5019607568110190479 - 1.0456058639082704588e-404j)  +/-  (6.99e-119, 6.99e-119j)
| (-7.9166169284803578694 - 7.2745218381338234915e-406j)  +/-  (1.69e-118, 1.69e-118j)
| (-3.8603617381632557525 - 3.4312554003169899866e-409j)  +/-  (2.45e-120, 2.45e-120j)
| (2.8087664139019159508 - 3.4659864216503549101e-416j)  +/-  (9.69e-122, 9.69e-122j)
| (10.142787661129668848 - 6.6036449403134058528e-414j)  +/-  (8.08e-120, 8.08e-120j)
| (-6.6643288644147137093 - 2.8572012287123858098e-411j)  +/-  (1.68e-118, 1.68e-118j)
| (7.2763116655551420252 - 5.6275930430252283929e-417j)  +/-  (1.63e-118, 1.63e-118j)
| (-8.5947641363861120929 + 5.4256705303813147015e-417j)  +/-  (8.55e-119, 8.55e-119j)
| (-4.3972783099327125986 + 4.0680337285215337314e-421j)  +/-  (1.01e-119, 1.01e-119j)
| (-7.2763116655551420252 - 1.4059291711949724204e-429j)  +/-  (1.57e-118, 1.57e-118j)
| (-0.7599132481367387184 - 1.3944812881162418442e-445j)  +/-  (1.23e-125, 1.23e-125j)
| (2.291397563624212716 + 2.110613153361719216e-443j)  +/-  (1.42e-122, 1.42e-122j)
| (6.6643288644147137093 - 2.2127628338205985697e-438j)  +/-  (1.96e-118, 1.96e-118j)
| (1.7781234251365620845 - 5.6281640398547280183e-444j)  +/-  (1.7e-123, 1.7e-123j)
| (9.3265847573955630211 - 6.8821403906893654863e-440j)  +/-  (4.02e-119, 4.02e-119j)
| (-4.9437900298022665601 + 4.4676548227976889467e-439j)  +/-  (2.81e-119, 2.81e-119j)
| (-1.7781234251365620845 + 1.6302199194896049246e-449j)  +/-  (1.6e-123, 1.6e-123j)
| (3.8603617381632557525 + 1.8858827432673293347e-446j)  +/-  (2.61e-120, 2.61e-120j)
| (5.5019607568110190479 - 1.9069643433600650468e-445j)  +/-  (7.14e-119, 7.14e-119j)
| (4.3972783099327125986 + 1.4905101711428307422e-447j)  +/-  (1.02e-119, 1.02e-119j)
| (0.2531636353359344267 - 4.5976313594150767937e-454j)  +/-  (6.2e-127, 6.2e-127j)
| (-1.267939114780749254 + 4.6175417966944893998e-452j)  +/-  (1.15e-124, 1.15e-124j)
| (-3.3313380605440064768 - 8.3931496965401428871e-449j)  +/-  (5.25e-121, 5.25e-121j)
| (3.3313380605440064768 + 2.1672287682111097732e-452j)  +/-  (5.09e-121, 5.09e-121j)
| (7.9166169284803578694 + 3.8919800998509060061e-455j)  +/-  (1.39e-118, 1.39e-118j)
| (1.267939114780749254 + 1.3098886403070370964e-462j)  +/-  (1.57e-124, 1.57e-124j)
| (-0.2531636353359344267 + 4.2031505923831076146e-463j)  +/-  (6.2e-127, 6.2e-127j)
| (-2.8087664139019159508 + 1.1995435019469054271e-458j)  +/-  (8.41e-122, 8.41e-122j)
| (-2.291397563624212716 + 6.6600663038019523914e-460j)  +/-  (1.73e-122, 1.73e-122j)
| (0.7599132481367387184 - 6.4581644618366248582e-463j)  +/-  (1.02e-125, 1.02e-125j)
-------------------------------------------------
The weights are:
| (6.0860195684248572435e-28 + 2.0290804011822539505e-412j)  +/-  (2.38e-34, 2.06e-93j)
| (6.0860195684248572435e-28 + 4.4533361478372748066e-412j)  +/-  (1.65e-35, 1.42e-94j)
| (3.9537522102357508077e-20 - 5.1594722160671676741e-409j)  +/-  (5.52e-32, 4.78e-91j)
| (1.0851993047659445254e-06 + 2.8493601754424274526e-400j)  +/-  (4.53e-24, 3.92e-83j)
| (1.6015868349741150637e-23 - 4.0805879898428132135e-410j)  +/-  (4.15e-33, 3.59e-92j)
| (2.2514847896604813359e-09 - 3.8395386111926337207e-403j)  +/-  (4.35e-27, 3.76e-86j)
| (2.2514847896604813359e-09 - 4.6559269223920314426e-402j)  +/-  (5.81e-28, 5.02e-87j)
| (2.5486537893761919475e-17 - 1.5389236479461107268e-406j)  +/-  (3.5e-33, 3.02e-92j)
| (6.0175703299469123165e-08 + 2.2774698861171366581e-402j)  +/-  (2e-26, 1.73e-85j)
| (6.4479065248543082682e-15 + 5.8155972496368210636e-406j)  +/-  (3.81e-31, 3.29e-90j)
| (0.0001234207566124393763 - 1.3306485904515258824e-400j)  +/-  (7.94e-24, 6.87e-83j)
| (0.0040143425017802059325 + 3.2713614496013752667e-399j)  +/-  (1.23e-21, 1.06e-80j)
| (1.6015868349741150637e-23 - 8.5802035806756085857e-410j)  +/-  (5.27e-37, 4.56e-96j)
| (5.4314696473971017924e-11 + 6.9290606800289807477e-404j)  +/-  (2.55e-29, 2.21e-88j)
| (7.941720700519844437e-13 - 4.2454730076222783584e-404j)  +/-  (5.08e-33, 4.39e-92j)
| (2.5486537893761919475e-17 - 2.6619622229695356128e-407j)  +/-  (1.07e-32, 9.28e-92j)
| (1.3666598489184858266e-05 + 4.1218034618823786553e-401j)  +/-  (4.38e-27, 3.79e-86j)
| (7.941720700519844437e-13 - 7.407464871992091598e-405j)  +/-  (1.34e-30, 1.16e-89j)
| (0.15161114626010783565 - 7.4265607404809110667e-399j)  +/-  (2.25e-23, 1.95e-82j)
| (0.01488362222069110628 - 5.0634941840520500593e-399j)  +/-  (2.55e-24, 2.2e-83j)
| (5.4314696473971017924e-11 + 4.7559237576318666774e-403j)  +/-  (4.06e-33, 3.52e-92j)
| (0.042000519974162715999 + 7.1162355823411891113e-399j)  +/-  (1.98e-23, 1.72e-82j)
| (3.9537522102357508077e-20 + 5.0530780411679675108e-408j)  +/-  (1.65e-37, 1.43e-96j)
| (1.0851993047659445254e-06 - 1.0747751102238592336e-401j)  +/-  (2.72e-29, 2.35e-88j)
| (0.042000519974162715999 - 3.2951069378286768586e-399j)  +/-  (1.55e-25, 1.34e-84j)
| (0.0001234207566124393763 + 1.1330861071972067268e-399j)  +/-  (5.46e-30, 4.72e-89j)
| (6.0175703299469123165e-08 + 4.8710969544610525053e-401j)  +/-  (3.52e-32, 3.05e-91j)
| (1.3666598489184858266e-05 - 7.4828447879881179145e-400j)  +/-  (6.62e-31, 5.73e-90j)
| (0.19565198704136345898 - 1.0309053827129299521e-398j)  +/-  (1.72e-27, 1.49e-86j)
| (0.090884155552588242262 + 5.2638242796827916809e-399j)  +/-  (2.37e-27, 2.05e-86j)
| (0.0008159914125966136063 + 3.6718933835337471583e-400j)  +/-  (1.16e-30, 1e-89j)
| (0.0008159914125966136063 - 1.9553425887723263836e-399j)  +/-  (4.16e-30, 3.59e-89j)
| (6.4479065248543082682e-15 + 3.0038348694828387421e-405j)  +/-  (3.22e-36, 2.78e-95j)
| (0.090884155552588242262 - 9.0004347350365585782e-399j)  +/-  (5.94e-29, 5.12e-88j)
| (0.19565198704136345898 + 9.2833846814398618208e-399j)  +/-  (1.01e-28, 8.73e-88j)
| (0.0040143425017802059325 - 8.7502657686844982437e-400j)  +/-  (4.96e-31, 4.29e-90j)
| (0.01488362222069110628 + 1.8147073223149546464e-399j)  +/-  (1.15e-30, 9.97e-90j)
| (0.15161114626010783565 + 1.0194726877292044567e-398j)  +/-  (4.92e-30, 3.96e-89j)
