Starting with polynomial:
P : -1/20397882081197443358640281739902897356800000000*t^39 + 1/13410836345297464404102749335899340800000000*t^38 - 1/18574565575204244327012118193766400000000*t^37 + 37/1506045857448992783271252826521600000000*t^36 - 37/4648289683484545627380409958400000000*t^35 + 37/18972610952998145417879224320000000*t^34 - 37/98473759271616671719096320000000*t^33 + 37/632981005419023601500160000000*t^32 - 37/4945164104836121886720000000*t^31 + 1147/1435692804629841838080000000*t^30 - 1147/15952142273664909312000000*t^29 + 33263/6050812586562551808000000*t^28 - 33263/92614478365753344000000*t^27 + 33263/1651561342599168000000*t^26 - 33263/34203933130752000000*t^25 + 33263/820894395138048000*t^24 - 33263/22802622087168000*t^23 + 765049/16854111977472000*t^22 - 765049/626805817344000*t^21 + 765049/27005239296000*t^20 - 765049/1350261964800*t^19 + 14535931/1492394803200*t^18 - 14535931/101335449600*t^17 + 10743949/5960908800*t^16 - 10743949/558835200*t^15 + 10743949/62092800*t^14 - 10743949/8236800*t^13 + 139671337/17107200*t^12 - 139671337/3326400*t^11 + 52978783/302400*t^10 - 52978783/90720*t^9 + 1708993/1120*t^8 - 1708993/560*t^7 + 1087541/240*t^6 - 191919/40*t^5 + 27417/8*t^4 - 9139/6*t^3 + 741/2*t^2 - 39*t + 1
Extension levels are: 39
-------------------------------------------------
Ending with final polynomial:
P : -1/20397882081197443358640281739902897356800000000*t^39 + 1/13410836345297464404102749335899340800000000*t^38 - 1/18574565575204244327012118193766400000000*t^37 + 37/1506045857448992783271252826521600000000*t^36 - 37/4648289683484545627380409958400000000*t^35 + 37/18972610952998145417879224320000000*t^34 - 37/98473759271616671719096320000000*t^33 + 37/632981005419023601500160000000*t^32 - 37/4945164104836121886720000000*t^31 + 1147/1435692804629841838080000000*t^30 - 1147/15952142273664909312000000*t^29 + 33263/6050812586562551808000000*t^28 - 33263/92614478365753344000000*t^27 + 33263/1651561342599168000000*t^26 - 33263/34203933130752000000*t^25 + 33263/820894395138048000*t^24 - 33263/22802622087168000*t^23 + 765049/16854111977472000*t^22 - 765049/626805817344000*t^21 + 765049/27005239296000*t^20 - 765049/1350261964800*t^19 + 14535931/1492394803200*t^18 - 14535931/101335449600*t^17 + 10743949/5960908800*t^16 - 10743949/558835200*t^15 + 10743949/62092800*t^14 - 10743949/8236800*t^13 + 139671337/17107200*t^12 - 139671337/3326400*t^11 + 52978783/302400*t^10 - 52978783/90720*t^9 + 1708993/1120*t^8 - 1708993/560*t^7 + 1087541/240*t^6 - 191919/40*t^5 + 27417/8*t^4 - 9139/6*t^3 + 741/2*t^2 - 39*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 roots: 424
 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: 0
  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
-------------------------------------------------
The nodes are:
| (113.5443739641761282 - 5.8266730926469628736e-1142j)  +/-  (4.75e-494, 4.75e-494j)
| (138.45237953106137032 + 7.1192592056807860817e-1151j)  +/-  (1.3e-496, 1.3e-496j)
| (124.50918289601379234 + 1.1224160344240101974e-1147j)  +/-  (3.85e-495, 3.85e-495j)
| (104.19926132320354856 + 4.027317004012944554e-1158j)  +/-  (2.83e-493, 2.83e-493j)
| (81.723153393237976844 - 5.3762134765463967354e-1180j)  +/-  (1.28e-491, 1.28e-491j)
| (95.946323568541830645 - 1.8370925343585761781e-1200j)  +/-  (1.4e-492, 1.4e-492j)
| (38.402675557525423705 - 3.8204244845803393047e-1220j)  +/-  (3.75e-491, 3.75e-491j)
| (75.474429567805443617 + 1.2698092167120284296e-1245j)  +/-  (3.09e-491, 3.09e-491j)
| (31.702202788744929046 + 2.612743404191856562e-1269j)  +/-  (1.06e-491, 1.06e-491j)
| (23.098886403465166436 - 7.0149442442217625877e-1282j)  +/-  (6.29e-493, 6.29e-493j)
| (18.233701853349192344 - 4.8168673512020113081e-1285j)  +/-  (6.56e-494, 6.56e-494j)
| (20.583690127440614672 - 1.3552673764398169172e-1299j)  +/-  (2.21e-493, 2.21e-493j)
| (7.3339184964215967333 - 1.4131605532112117099e-1316j)  +/-  (3.14e-498, 3.14e-498j)
| (54.550956176108401965 - 1.0482962344234298486e-1343j)  +/-  (1.06e-490, 1.06e-490j)
| (1.415153402964435068 + 6.7712249471926795605e-1385j)  +/-  (2.18e-504, 2.18e-504j)
| (4.8333778104884625389 - 2.1691428809995375989e-1383j)  +/-  (4.8e-500, 4.8e-500j)
| (12.122874592146699962 - 8.2687988756208103075e-1380j)  +/-  (7.04e-496, 7.04e-496j)
| (42.074128674236114599 + 6.0140015419135522817e-1414j)  +/-  (6.14e-491, 6.14e-491j)
| (59.263442771504351443 - 2.6806776993636359828e-1463j)  +/-  (9.83e-491, 9.83e-491j)
| (34.9493970550971913 + 4.833748516622662425e-1482j)  +/-  (2.16e-491, 2.16e-491j)
| (45.977817557450932708 - 1.6649253892429888788e-1504j)  +/-  (7.93e-491, 7.93e-491j)
| (2.075900054441475363 + 3.817497324529619279e-1538j)  +/-  (3.14e-503, 3.14e-503j)
| (25.785514374838579583 - 1.2072992312461884146e-1525j)  +/-  (1.85e-492, 1.85e-492j)
| (64.296297777645466068 + 7.067998943340723575e-1548j)  +/-  (8.1e-491, 8.1e-491j)
| (28.650618908103995768 + 2.7970384560350123976e-1563j)  +/-  (4.67e-492, 4.67e-492j)
| (14.007915384768099867 + 8.4712940964574881176e-1576j)  +/-  (3.69e-495, 3.69e-495j)
| (0.8816185217504255774 - 2.3377936630829546919e-1596j)  +/-  (1.17e-505, 1.17e-505j)
| (6.0161301557274294076 + 1.1801834960082309755e-1589j)  +/-  (3.91e-499, 3.91e-499j)
| (50.13024018849515474 - 9.9138976429759603128e-1580j)  +/-  (9.48e-491, 9.48e-491j)
| (69.684981277416199586 + 1.3811194631844861725e-1606j)  +/-  (5.31e-491, 5.31e-491j)
| (0.19292946677486190875 - 1.2717307652942225309e-1642j)  +/-  (1.41e-508, 1.41e-508j)
| (3.7835828044507915713 + 8.8072453460437945015e-1636j)  +/-  (4.77e-501, 4.77e-501j)
| (2.8649400871242441816 + 1.7942308360595302923e-1637j)  +/-  (3.8e-502, 3.8e-502j)
| (16.043408191605697429 - 1.5984720156313907607e-1629j)  +/-  (1.49e-494, 1.49e-494j)
| (88.510023667782516312 + 7.7301829787552307063e-1625j)  +/-  (4.95e-492, 4.95e-492j)
| (10.384419922696526398 - 6.5665342405579016676e-1643j)  +/-  (1.31e-496, 1.31e-496j)
| (8.7891167619757293027 - 4.7468174898752394406e-1643j)  +/-  (2.05e-497, 2.05e-497j)
| (0.47443065146260347738 + 7.0614183948990659678e-1653j)  +/-  (3.95e-507, 3.95e-507j)
| (0.036604291956600413971 - 1.793925805927854057e-1655j)  +/-  (3.02e-510, 3.02e-510j)
-------------------------------------------------
The weights are:
| (4.8943584509291588975e-49 + 1.4133333272067097024e-1190j)  +/-  (3.08e-75, 8.6e-448j)
| (1.2295294484185288804e-59 - 6.3367483569600038557e-1197j)  +/-  (5.53e-79, 1.55e-451j)
| (1.0202390702404189318e-53 + 1.2434728513359016887e-1193j)  +/-  (4.9e-77, 1.37e-449j)
| (4.8789620355537146858e-45 - 2.9187522290489551821e-1189j)  +/-  (9.42e-75, 2.63e-447j)
| (2.0949052412114022675e-35 + 4.9742046298790684781e-1185j)  +/-  (1.35e-72, 3.78e-445j)
| (1.6738095333344955975e-41 + 8.7114081468135163854e-1188j)  +/-  (2.72e-74, 7.62e-447j)
| (7.4714397915603449491e-17 - 2.7270155673005769398e-1176j)  +/-  (1.42e-64, 3.96e-437j)
| (1.0013738949252817781e-32 - 8.7357770495273429531e-1184j)  +/-  (5.15e-72, 1.44e-444j)
| (5.3692093587419097512e-14 - 6.0982957002547775014e-1175j)  +/-  (1.95e-62, 5.45e-435j)
| (2.4167002595719436265e-10 + 3.1601357849630768948e-1173j)  +/-  (3e-59, 8.38e-432j)
| (2.7358438359831648616e-08 + 2.8348316743805898438e-1172j)  +/-  (3.04e-57, 8.51e-430j)
| (2.7958394098502959367e-09 - 9.8719773706539466285e-1173j)  +/-  (2.88e-58, 8.06e-431j)
| (0.00090511841936780834562 + 2.9345343809429544792e-1170j)  +/-  (2.85e-49, 7.96e-422j)
| (9.2897804591571634953e-24 - 1.4597755429042217236e-1179j)  +/-  (6.21e-71, 1.74e-443j)
| (0.14499922361998282629 + 1.5454377890405999824e-1169j)  +/-  (1.9e-34, 5.32e-407j)
| (0.0088825097797072924864 + 7.2913085353609265299e-1170j)  +/-  (2.45e-46, 6.85e-419j)
| (9.8413506071601350863e-06 - 4.1198923075613200835e-1171j)  +/-  (3.81e-55, 1.06e-427j)
| (2.0207324212639931612e-18 + 4.9354008276211799756e-1177j)  +/-  (9.76e-68, 2.73e-440j)
| (8.902481021644908894e-26 + 1.6187784320625267395e-1180j)  +/-  (2.17e-72, 6.07e-445j)
| (2.2207653752454377582e-15 + 1.3560076013892616995e-1175j)  +/-  (4.63e-66, 1.29e-438j)
| (4.3337267248715197808e-20 - 7.9920627332869664009e-1178j)  +/-  (2.14e-69, 5.98e-442j)
| (0.090908191055554771033 - 1.4908652945295866853e-1169j)  +/-  (2.79e-48, 7.8e-421j)
| (1.7566955022031579768e-11 - 9.2774987692123869104e-1174j)  +/-  (2.61e-64, 7.29e-437j)
| (6.2061835307056086236e-28 - 1.5516785352629442761e-1181j)  +/-  (2.73e-74, 7.63e-447j)
| (1.0666803102389331758e-12 + 2.4911170346216635738e-1174j)  +/-  (1.72e-65, 4.81e-438j)
| (1.6166036545618917982e-06 + 1.8289089294210622573e-1171j)  +/-  (1.02e-62, 2.86e-435j)
| (0.19472992949107219782 - 1.406896241968683893e-1169j)  +/-  (8.94e-53, 2.5e-425j)
| (0.0030486191043798838549 - 4.8180729856385746478e-1170j)  +/-  (4.2e-59, 1.18e-431j)
| (7.2520873386581318149e-22 + 1.1502204193547004811e-1178j)  +/-  (4.82e-71, 1.35e-443j)
| (3.0400394863406010305e-30 + 1.2694988861999022991e-1182j)  +/-  (9.12e-76, 2.55e-448j)
| (0.18043580804346419749 - 6.2967915951607154213e-1170j)  +/-  (1.05e-56, 2.95e-429j)
| (0.022375843723617601909 - 1.0140977871439096354e-1169j)  +/-  (8.02e-60, 2.24e-432j)
| (0.048643919709767013911 + 1.2903004738405067526e-1169j)  +/-  (3.33e-59, 9.31e-432j)
| (2.2759149325497965688e-07 - 7.497269871769437651e-1172j)  +/-  (1.42e-64, 3.98e-437j)
| (2.577494120748522673e-38 - 2.3080460877223005476e-1186j)  +/-  (4.99e-80, 1.4e-452j)
| (5.1507133788566893026e-05 + 8.5762889510347352279e-1171j)  +/-  (5.14e-64, 1.44e-436j)
| (0.00023234877337334871514 - 1.6502612944504288218e-1170j)  +/-  (1.09e-63, 3.05e-436j)
| (0.2142062151333397874 + 1.0785516844339704047e-1169j)  +/-  (1.39e-62, 3.93e-435j)
| (0.09056905005219230624 + 1.9405107527475832263e-1170j)  +/-  (3.23e-63, 8.88e-436j)
