Starting with polynomial:
P : -1/119622220865480194561963161495657715064383733760000000000*t^45 + 1/59072701661965528178747240244769242007103078400000000*t^44 - 1/61025518245832157209449628352034340916428800000000*t^43 + 43/4257594296220848177403462443165186575564800000000*t^42 - 43/9654408834967909699327579236202237132800000000*t^41 + 1763/1177366931093647524308241370268565504000000000*t^40 - 1763/4415125991601178216155905138507120640000000*t^39 + 1763/20319449008026461218337498993786880000000*t^38 - 1763/112573124698207541375831019356160000000*t^37 + 65231/27382651953618050604931869573120000000*t^36 - 65231/211285894703842983062745907200000000*t^35 + 65231/1897261095299814541787922432000000*t^34 - 65231/19694751854323334343819264000000*t^33 + 65231/235107230584208766271488000000*t^32 - 65231/3214356668143479226368000000*t^31 + 2022161/1555333871682328657920000000*t^30 - 2022161/27650379941019176140800000*t^29 + 58642669/16208843413700896358400000*t^28 - 58642669/372141813069663436800000*t^27 + 58642669/9699169339264204800000*t^26 - 58642669/286957672759296000000*t^25 + 58642669/9641777804712345600*t^24 - 58642669/368262346707763200*t^23 + 58642669/16011406378598400*t^22 - 58642669/793954035302400*t^21 + 58642669/45008732160000*t^20 - 58642669/2925567590400*t^19 + 1114210711/4157385523200*t^18 - 1114210711/359280230400*t^17 + 653158003/21134131200*t^16 - 653158003/2476656000*t^15 + 21069613/11007360*t^14 - 21069613/1797120*t^13 + 273904969/4561920*t^12 - 16112057/63360*t^11 + 177232627/201600*t^10 - 177232627/72576*t^9 + 4790071/896*t^8 - 252109/28*t^7 + 135751/12*t^6 - 407253/40*t^5 + 49665/8*t^4 - 2365*t^3 + 495*t^2 - 45*t + 1
Extension levels are: 45
-------------------------------------------------
Ending with final polynomial:
P : -1/119622220865480194561963161495657715064383733760000000000*t^45 + 1/59072701661965528178747240244769242007103078400000000*t^44 - 1/61025518245832157209449628352034340916428800000000*t^43 + 43/4257594296220848177403462443165186575564800000000*t^42 - 43/9654408834967909699327579236202237132800000000*t^41 + 1763/1177366931093647524308241370268565504000000000*t^40 - 1763/4415125991601178216155905138507120640000000*t^39 + 1763/20319449008026461218337498993786880000000*t^38 - 1763/112573124698207541375831019356160000000*t^37 + 65231/27382651953618050604931869573120000000*t^36 - 65231/211285894703842983062745907200000000*t^35 + 65231/1897261095299814541787922432000000*t^34 - 65231/19694751854323334343819264000000*t^33 + 65231/235107230584208766271488000000*t^32 - 65231/3214356668143479226368000000*t^31 + 2022161/1555333871682328657920000000*t^30 - 2022161/27650379941019176140800000*t^29 + 58642669/16208843413700896358400000*t^28 - 58642669/372141813069663436800000*t^27 + 58642669/9699169339264204800000*t^26 - 58642669/286957672759296000000*t^25 + 58642669/9641777804712345600*t^24 - 58642669/368262346707763200*t^23 + 58642669/16011406378598400*t^22 - 58642669/793954035302400*t^21 + 58642669/45008732160000*t^20 - 58642669/2925567590400*t^19 + 1114210711/4157385523200*t^18 - 1114210711/359280230400*t^17 + 653158003/21134131200*t^16 - 653158003/2476656000*t^15 + 21069613/11007360*t^14 - 21069613/1797120*t^13 + 273904969/4561920*t^12 - 16112057/63360*t^11 + 177232627/201600*t^10 - 177232627/72576*t^9 + 4790071/896*t^8 - 252109/28*t^7 + 135751/12*t^6 - 407253/40*t^5 + 49665/8*t^4 - 2365*t^3 + 495*t^2 - 45*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 roots: 848
 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:
| (161.45944790908845989 + 5.4677553639311088871e-1414j)  +/-  (7.34e-495, 7.34e-495j)
| (116.35218467519681 + 1.1277261001883382977e-1409j)  +/-  (1.98e-490, 1.98e-490j)
| (135.11619015017160228 + 7.8605072560215478771e-1412j)  +/-  (3.85e-492, 3.85e-492j)
| (108.37460196797775735 + 1.1216809507609158949e-1406j)  +/-  (8.95e-490, 8.95e-490j)
| (101.06347092231989498 - 8.5167495598675145201e-1410j)  +/-  (2.95e-489, 2.95e-489j)
| (45.647640501793117951 - 4.6794418350772450407e-1421j)  +/-  (3.29e-488, 3.29e-488j)
| (125.17034745017208881 - 1.3150308699378823355e-1433j)  +/-  (3.36e-491, 3.36e-491j)
| (22.051620115564308515 - 1.5021388511960942755e-1443j)  +/-  (2.93e-491, 2.93e-491j)
| (146.73979649749683701 - 2.0473692658791631681e-1439j)  +/-  (2.54e-493, 2.54e-493j)
| (5.206107130165518563 - 5.9199243497517204437e-1460j)  +/-  (7.2e-499, 7.2e-499j)
| (6.3418686461714186534 - 2.0551034720154926771e-1461j)  +/-  (6.77e-498, 6.77e-498j)
| (4.1852949337854690246 - 9.3452259121341277801e-1463j)  +/-  (6.82e-500, 6.82e-500j)
| (49.381303694810929816 - 4.7830620244903093487e-1451j)  +/-  (5.12e-488, 5.12e-488j)
| (71.403201447971489027 - 3.9943326707278916081e-1470j)  +/-  (6.94e-488, 6.94e-488j)
| (57.474473058814141715 + 7.1638094132695935655e-1487j)  +/-  (8.75e-488, 8.75e-488j)
| (24.455391203193740067 + 1.0070040528199383594e-1507j)  +/-  (1.05e-490, 1.05e-490j)
| (3.2781154527749749007 + 1.5018436478958628975e-1524j)  +/-  (6.33e-501, 6.33e-501j)
| (17.661538267980240771 + 6.4662816604316611635e-1516j)  +/-  (2.09e-492, 2.09e-492j)
| (88.0109263746939159 + 7.0202123672811324333e-1510j)  +/-  (1.72e-488, 1.72e-488j)
| (94.302943609709913234 - 1.72836750015138141e-1530j)  +/-  (7.61e-489, 7.61e-489j)
| (1.8002069428945057169 - 1.2564222631767552715e-1555j)  +/-  (3.82e-503, 3.82e-503j)
| (1.2276394084198347379 + 4.4823664971321725709e-1557j)  +/-  (2.46e-504, 2.46e-504j)
| (2.4834175141915700703 + 1.4591353292295941911e-1554j)  +/-  (5.22e-502, 5.22e-502j)
| (32.555103986001469658 - 1.041682073745349469e-1541j)  +/-  (2.16e-489, 2.16e-489j)
| (10.454716247741847955 - 1.524760108965168176e-1547j)  +/-  (2.91e-495, 2.91e-495j)
| (12.067132515934922107 + 3.8168106591903525612e-1546j)  +/-  (1.8e-494, 1.8e-494j)
| (35.569055951600568047 + 4.9405734333595669447e-1540j)  +/-  (4.73e-489, 4.73e-489j)
| (0.031776956867005243746 + 2.2850068504741920144e-1567j)  +/-  (2.77e-510, 2.77e-510j)
| (42.107299705811617091 + 1.4431172677920765663e-1545j)  +/-  (2.1e-488, 2.1e-488j)
| (82.126514283411425299 + 2.3106673835893702176e-1562j)  +/-  (3.06e-488, 3.06e-488j)
| (38.750609641045924384 + 2.3197794570360340219e-1577j)  +/-  (1.01e-488, 1.01e-488j)
| (19.78830061128360445 - 5.4646376628011995718e-1597j)  +/-  (8.55e-492, 8.55e-492j)
| (13.803972172016244759 - 5.8771007750280939579e-1605j)  +/-  (9.8e-494, 9.8e-494j)
| (29.7020560325842711 + 1.4719905897858570707e-1601j)  +/-  (8.31e-490, 8.31e-490j)
| (8.9643942355384919505 + 2.4849185411975168736e-1630j)  +/-  (4.27e-496, 4.27e-496j)
| (53.319341780002240081 + 1.7866645616039731617e-1658j)  +/-  (6.91e-488, 6.91e-488j)
| (7.5940714118217735297 + 1.2798702877258700001e-1710j)  +/-  (5.66e-497, 5.66e-497j)
| (0.41176935189346142362 + 4.4007778234657388917e-1733j)  +/-  (3.65e-507, 3.65e-507j)
| (66.497545839444643119 + 3.5761871882015247258e-1765j)  +/-  (8.4e-488, 8.4e-488j)
| (61.861450326356239998 + 3.9545392034089615688e-1833j)  +/-  (8.95e-488, 8.95e-488j)
| (27.003935367666315413 + 2.0461446915840467534e-1864j)  +/-  (3.1e-490, 3.1e-490j)
| (0.76501433412687708616 - 2.7184696574073482726e-1896j)  +/-  (1.04e-505, 1.04e-505j)
| (15.66781946769685039 + 7.3047016142121373046e-1879j)  +/-  (4.32e-493, 4.32e-493j)
| (0.16747251657589828304 - 1.4523660978856597344e-1903j)  +/-  (1.01e-508, 1.01e-508j)
| (76.602919389219769645 + 2.506821847712699448e-1890j)  +/-  (5.12e-488, 5.12e-488j)
-------------------------------------------------
The weights are:
| (1.3198453933537642534e-69 - 7.1270457845377627095e-1466j)  +/-  (1.92e-71, 4.65e-441j)
| (2.4615136785986681592e-50 - 1.8379933588277206812e-1455j)  +/-  (1.45e-65, 3.52e-435j)
| (2.2253609931215085063e-58 - 5.4660513303362540902e-1460j)  +/-  (1.55e-68, 3.74e-438j)
| (6.5394028187249256694e-47 - 3.6261025124589681028e-1453j)  +/-  (8.11e-65, 1.96e-434j)
| (9.0161728188217369479e-44 + 4.0656279451851375679e-1452j)  +/-  (3.73e-64, 9.03e-434j)
| (5.4452758145862728147e-20 + 1.019900948737899185e-1440j)  +/-  (2.05e-53, 4.96e-423j)
| (4.0609526541757688706e-54 + 1.1475348186700113851e-1457j)  +/-  (1.61e-67, 3.9e-437j)
| (6.1800526258521580377e-10 - 4.1628866764976386541e-1437j)  +/-  (1.42e-43, 3.43e-413j)
| (2.3909249277721373583e-63 + 1.2834818651785981716e-1462j)  +/-  (3.84e-71, 9.29e-441j)
| (0.005910940410591947044 - 8.2700870166779372711e-1434j)  +/-  (2.87e-22, 6.94e-392j)
| (0.0021021480717924899632 + 5.4222260771617183186e-1434j)  +/-  (2.2e-25, 5.33e-395j)
| (0.014666691055305094759 + 1.1712147080640093243e-1433j)  +/-  (1.56e-19, 3.77e-389j)
| (1.3728113526206403155e-21 + 1.5244225857932891991e-1441j)  +/-  (7.83e-56, 1.9e-425j)
| (4.9331123148055445476e-31 - 1.822020006114904865e-1446j)  +/-  (6.71e-62, 1.62e-431j)
| (4.6710984407366277701e-25 + 1.6252467294255004258e-1443j)  +/-  (1.09e-58, 2.63e-428j)
| (5.9265751381617852561e-11 + 1.1757256772280484502e-1437j)  +/-  (5.53e-48, 1.34e-417j)
| (0.032073009065684556084 - 1.5356798057574164274e-1433j)  +/-  (3.03e-23, 7.34e-393j)
| (4.4003996132626462638e-08 - 3.645322222911966982e-1436j)  +/-  (2.49e-44, 6.02e-414j)
| (3.6408456570754763079e-38 + 8.6909717777448249203e-1450j)  +/-  (5.2e-65, 1.26e-434j)
| (7.221766658476636768e-41 - 5.6945006030491315783e-1451j)  +/-  (1.31e-65, 3.17e-435j)
| (0.10374664065632619 - 2.050965458416741285e-1433j)  +/-  (3.36e-22, 8.14e-392j)
| (0.15161633179828397723 + 2.0484900574605343979e-1433j)  +/-  (1.89e-19, 4.57e-389j)
| (0.061658521650479345725 + 1.8555901080204581015e-1433j)  +/-  (5.86e-25, 1.42e-394j)
| (2.1317103204600729378e-14 + 4.0099850823922977989e-1440j)  +/-  (8.89e-54, 2.15e-423j)
| (4.4687548597413919704e-05 - 9.9134316066305465738e-1435j)  +/-  (6.61e-42, 1.6e-411j)
| (9.6188526495208205467e-06 + 4.8696769976694654819e-1435j)  +/-  (1.69e-43, 4.1e-413j)
| (1.105188416522013286e-15 - 7.2964603940811544258e-1440j)  +/-  (3.67e-55, 8.88e-425j)
| (0.079003863218577096004 + 2.3803709578044091803e-1434j)  +/-  (2.55e-27, 6.16e-397j)
| (1.7802221281288381343e-18 - 2.7767141738487353734e-1440j)  +/-  (2.56e-57, 6.2e-427j)
| (1.2262094662884912199e-35 - 1.236629523657666518e-1448j)  +/-  (1.54e-66, 3.72e-436j)
| (4.842595191226188018e-17 + 4.5531164004975861025e-1440j)  +/-  (1.55e-56, 3.75e-426j)
| (5.5894745239344662512e-09 + 1.2965842045737163775e-1436j)  +/-  (2.78e-51, 6.73e-421j)
| (1.8207784506475033482e-06 - 2.2205833086144570671e-1435j)  +/-  (3.56e-49, 8.61e-419j)
| (3.4975836508759965683e-13 + 4.176408240250579353e-1439j)  +/-  (7.59e-55, 1.84e-424j)
| (0.00018287173922646090771 + 1.876676417791317701e-1434j)  +/-  (2.61e-47, 6.32e-417j)
| (2.8219444221277577772e-23 - 1.4517337128152188831e-1442j)  +/-  (2.22e-61, 5.38e-431j)
| (0.00065997635763383282778 - 3.3064684396312620359e-1434j)  +/-  (1.18e-47, 2.86e-417j)
| (0.19788792774994047444 + 1.3559843033656516524e-1433j)  +/-  (2.8e-44, 6.77e-414j)
| (6.2913370569461149504e-29 + 1.8947331850446113101e-1445j)  +/-  (2.7e-65, 6.55e-435j)
| (6.136739815177040709e-27 - 1.8083241921617495665e-1444j)  +/-  (2.82e-64, 6.83e-434j)
| (4.9096834353215369505e-12 - 2.7431713601396234802e-1438j)  +/-  (1.14e-56, 2.76e-426j)
| (0.18978490012961408995 - 1.8097400775569494224e-1433j)  +/-  (7.45e-50, 1.8e-419j)
| (3.0249820529758365254e-07 + 9.3729415213682498708e-1436j)  +/-  (3.45e-54, 8.32e-424j)
| (0.16064969814261798036 - 7.7922445266780460983e-1434j)  +/-  (5.11e-51, 1.18e-420j)
| (2.8882104259709836511e-33 + 1.5844257243643588016e-1447j)  +/-  (1.54e-67, 3.74e-437j)
