Starting with polynomial:
P : 8796093022208*t^44 - 96757023244288*t^42 + 495879744126976*t^40 - 1572301627719680*t^38 + 3454150138396672*t^36 - 5579780992794624*t^34 + 6864598984556544*t^32 - 6573052309536768*t^30 + 4964023879598080*t^28 - 2978414327758848*t^26 + 1423506847825920*t^24 - 541167892561920*t^22 + 162773155184640*t^20 - 38370843033600*t^18 + 6988974981120*t^16 - 963996549120*t^14 + 97905899520*t^12 - 7038986240*t^10 + 338412800*t^8 - 9974272*t^6 + 155848*t^4 - 968*t^2 + 1
Extension levels are: 44
-------------------------------------------------
Ending with final polynomial:
P : 8796093022208*t^44 - 96757023244288*t^42 + 495879744126976*t^40 - 1572301627719680*t^38 + 3454150138396672*t^36 - 5579780992794624*t^34 + 6864598984556544*t^32 - 6573052309536768*t^30 + 4964023879598080*t^28 - 2978414327758848*t^26 + 1423506847825920*t^24 - 541167892561920*t^22 + 162773155184640*t^20 - 38370843033600*t^18 + 6988974981120*t^16 - 963996549120*t^14 + 97905899520*t^12 - 7038986240*t^10 + 338412800*t^8 - 9974272*t^6 + 155848*t^4 - 968*t^2 + 1
-------------------------------------------------
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
  current precision for roots: 424
  current precision for roots: 848
 current precision for weights: 424
Linear system for weights solvable: 1
Sufficient bits for target precision reached
Positive weights:   44 out of 44
Indefinite weights: 0 out of 44
Negative weights:   0 out of 44
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (-0.99936282565699169131 - 2.5347185960572299502e-876j)  +/-  (1.04e-240, 1.04e-240j)
| (0.98411120433611610614 - 1.7692403597654519424e-879j)  +/-  (3.48e-240, 3.48e-240j)
| (-0.92387953251128675613 - 4.4672499816084977141e-894j)  +/-  (9.63e-241, 9.63e-241j)
| (0.99936282565699169131 + 1.2971882783946540282e-903j)  +/-  (1.08e-240, 1.08e-240j)
| (0.96893730178150732995 - 5.2749549050308050593e-923j)  +/-  (2.95e-240, 2.95e-240j)
| (0.92387953251128675613 - 7.2835653380597642237e-941j)  +/-  (1.12e-240, 1.12e-240j)
| (-0.8600142402077005234 + 3.1075036979601008502e-950j)  +/-  (1.45e-241, 1.45e-241j)
| (-0.8942252698597112824 + 2.7445105340568481708e-949j)  +/-  (4.5e-241, 4.5e-241j)
| (0.8942252698597112824 + 9.9396409216406185607e-953j)  +/-  (4.85e-241, 4.85e-241j)
| (-0.98411120433611610614 - 1.0472204737739325221e-952j)  +/-  (3.18e-240, 3.18e-240j)
| (0.8600142402077005234 - 3.1422688372389791355e-962j)  +/-  (1.7e-241, 1.7e-241j)
| (-0.99427030177189731837 + 9.1972712797845938672e-960j)  +/-  (2.89e-240, 2.89e-240j)
| (-0.96893730178150732995 + 6.6097280650708880554e-966j)  +/-  (2.91e-240, 2.91e-240j)
| (-0.82142077512049156131 - 6.7644778031900703968e-974j)  +/-  (4.58e-242, 4.58e-242j)
| (0.99427030177189731837 - 1.6070465674942978476e-971j)  +/-  (2.7e-240, 2.7e-240j)
| (0.82142077512049156131 + 5.073367117512780915e-980j)  +/-  (4.62e-242, 4.62e-242j)
| (0.31579958761502491553 - 1.8513570681134709537e-995j)  +/-  (3.65e-250, 3.65e-250j)
| (-0.51027003306089961332 + 9.5392135523808088522e-992j)  +/-  (1.03e-246, 1.03e-246j)
| (-0.77864153804975517562 + 2.1684271938057051226e-988j)  +/-  (1.18e-242, 1.18e-242j)
| (-0.94882591683731963814 + 3.3510485875129952938e-986j)  +/-  (2.23e-240, 2.23e-240j)
| (0.24730650055421550199 + 7.3615729406425522121e-998j)  +/-  (2.21e-251, 2.21e-251j)
| (0.68141793959389110718 + 1.4478684184479291093e-986j)  +/-  (4.66e-244, 4.66e-244j)
| (0.94882591683731963814 - 7.0045592492260524325e-990j)  +/-  (1.88e-240, 1.88e-240j)
| (-0.68141793959389110718 + 2.5125755152477313405e-1001j)  +/-  (4.67e-244, 4.67e-244j)
| (-0.731894522181725425 - 1.8680048814032369228e-1001j)  +/-  (2.67e-243, 2.67e-243j)
| (0.10689512156511278441 + 3.6384664349198245118e-1013j)  +/-  (6e-254, 6e-254j)
| (0.731894522181725425 - 2.0122425639783024682e-1001j)  +/-  (2.95e-243, 2.95e-243j)
| (0.77864153804975517562 - 3.3982168406374033939e-1007j)  +/-  (1.24e-242, 1.24e-242j)
| (-0.10689512156511278441 + 6.681765152910051743e-1018j)  +/-  (4.54e-254, 4.54e-254j)
| (-0.62746900738085196925 - 4.9749247399521152883e-1008j)  +/-  (7.14e-245, 7.14e-245j)
| (-0.31579958761502491553 + 5.7992123163383751167e-1015j)  +/-  (3.55e-250, 3.55e-250j)
| (0.51027003306089961332 + 1.5893154732118014399e-1011j)  +/-  (1.09e-246, 1.09e-246j)
| (0.62746900738085196925 + 1.6863264469728608161e-1009j)  +/-  (7.45e-245, 7.45e-245j)
| (0.03569233383898045576 - 1.3477265648202834545e-1022j)  +/-  (2.32e-255, 2.32e-255j)
| (-0.38268343236508977173 + 8.8101424317253596237e-1014j)  +/-  (5.44e-249, 5.44e-249j)
| (-0.44761721006271254934 + 1.1793892712006398214e-1011j)  +/-  (8.23e-248, 8.23e-248j)
| (-0.03569233383898045576 - 1.6800331999573755759e-1022j)  +/-  (2.32e-255, 2.32e-255j)
| (0.57032263693496406021 - 9.1322035377750316706e-1012j)  +/-  (8.56e-246, 8.56e-246j)
| (0.17755319625430326814 - 9.2746165307954748237e-1020j)  +/-  (1.08e-252, 1.08e-252j)
| (-0.24730650055421550199 + 8.5458162441632149719e-1017j)  +/-  (2.08e-251, 2.08e-251j)
| (-0.57032263693496406021 + 1.7215551572756924236e-1013j)  +/-  (9.99e-246, 9.99e-246j)
| (-0.17755319625430326814 + 2.0448412471197329421e-1021j)  +/-  (1.08e-252, 1.08e-252j)
| (0.38268343236508977173 + 6.5283129722770753026e-1017j)  +/-  (5.41e-249, 5.41e-249j)
| (0.44761721006271254934 + 9.6463091915860437414e-1017j)  +/-  (9.52e-248, 9.52e-248j)
-------------------------------------------------
The weights are:
| (0.022727272727272727273 - 2.259542190500796802e-875j)  +/-  (1.02e-70, 1.06e-186j)
| (0.022727272727272727273 + 1.4510640501598756116e-877j)  +/-  (4.24e-71, 4.42e-187j)
| (0.022727272727272727273 + 8.1826384159522367277e-876j)  +/-  (1.7e-71, 1.77e-187j)
| (0.022727272727272727273 + 2.8291998792834353646e-878j)  +/-  (1.57e-71, 1.64e-187j)
| (0.022727272727272727273 - 2.0648090754266416558e-877j)  +/-  (2.17e-71, 2.26e-187j)
| (0.022727272727272727273 - 3.2258875300442571151e-877j)  +/-  (4.32e-72, 4.51e-188j)
| (0.022727272727272727273 + 5.9102279633112801598e-876j)  +/-  (2.55e-73, 2.66e-189j)
| (0.022727272727272727273 - 6.8715456915463164073e-876j)  +/-  (4.23e-73, 4.42e-189j)
| (0.022727272727272727273 + 3.8265311175301918191e-877j)  +/-  (1.71e-73, 1.79e-189j)
| (0.022727272727272727273 - 1.878949385517515646e-875j)  +/-  (3.78e-74, 3.94e-190j)
| (0.022727272727272727273 - 4.4386082186683771061e-877j)  +/-  (1.17e-74, 1.22e-190j)
| (0.022727272727272727273 + 3.3878727988515248232e-875j)  +/-  (4.06e-74, 4.23e-190j)
| (0.022727272727272727273 + 1.3118994344635350611e-875j)  +/-  (1.55e-74, 1.62e-190j)
| (0.022727272727272727273 - 5.1730914102796546051e-876j)  +/-  (4.81e-76, 5.02e-192j)
| (0.022727272727272727273 - 8.4156663497513772734e-878j)  +/-  (2.8e-75, 2.92e-191j)
| (0.022727272727272727273 + 5.0634423476389052294e-877j)  +/-  (2.58e-77, 2.69e-193j)
| (0.022727272727272727273 - 1.1647405111080894405e-876j)  +/-  (7.6e-80, 7.93e-196j)
| (0.022727272727272727273 - 2.8381572318239590672e-876j)  +/-  (1.23e-79, 1.28e-195j)
| (0.022727272727272727273 + 4.5883635065175220963e-876j)  +/-  (9.36e-78, 9.76e-194j)
| (0.022727272727272727273 - 1.0085713006694720034e-875j)  +/-  (3.58e-76, 3.73e-192j)
| (0.022727272727272727273 + 1.2547280997564095859e-876j)  +/-  (1.12e-80, 1.17e-196j)
| (0.022727272727272727273 - 7.0336021169760141336e-877j)  +/-  (2.74e-80, 2.86e-196j)
| (0.022727272727272727273 + 2.6365391693029601822e-877j)  +/-  (2.68e-77, 2.79e-193j)
| (0.022727272727272727273 + 3.7154413795007416863e-876j)  +/-  (1.4e-79, 1.46e-195j)
| (0.022727272727272727273 - 4.1119977300821594803e-876j)  +/-  (7.12e-79, 7.43e-195j)
| (0.022727272727272727273 + 1.4508651003687473879e-876j)  +/-  (3.11e-82, 3.24e-198j)
| (0.022727272727272727273 + 6.3587558248267461663e-877j)  +/-  (2.3e-80, 2.4e-196j)
| (0.022727272727272727273 - 5.7028058150949337247e-877j)  +/-  (7.02e-80, 7.32e-196j)
| (0.022727272727272727273 - 1.7983074036252322848e-876j)  +/-  (1.13e-83, 1.18e-199j)
| (0.022727272727272727273 - 3.3793626437987626236e-876j)  +/-  (2.2e-81, 2.3e-197j)
| (0.022727272727272727273 + 2.2404848514679078552e-876j)  +/-  (8.29e-84, 8.64e-200j)
| (0.022727272727272727273 + 9.1987863511222841654e-877j)  +/-  (9.14e-84, 9.53e-200j)
| (0.022727272727272727273 + 7.7299185096971260122e-877j)  +/-  (8.98e-83, 9.37e-199j)
| (0.022727272727272727273 - 1.5585772171644672996e-876j)  +/-  (1.99e-84, 2.08e-200j)
| (0.022727272727272727273 - 2.4181627736967891273e-876j)  +/-  (1.47e-84, 1.53e-200j)
| (0.022727272727272727273 + 2.6159754192810539013e-876j)  +/-  (2.13e-84, 2.22e-200j)
| (0.022727272727272727273 + 1.6739956988446303454e-876j)  +/-  (2.78e-85, 2.9e-201j)
| (0.022727272727272727273 - 8.4505753438413822429e-877j)  +/-  (2.12e-85, 2.22e-201j)
| (0.022727272727272727273 - 1.3498631446765485446e-876j)  +/-  (1.47e-85, 1.54e-201j)
| (0.022727272727272727273 - 2.0796231830575077237e-876j)  +/-  (4.33e-86, 4.52e-202j)
| (0.022727272727272727273 + 3.0902004759820702508e-876j)  +/-  (4.24e-86, 4.42e-202j)
| (0.022727272727272727273 + 1.9329391692472397356e-876j)  +/-  (3.73e-86, 3.89e-202j)
| (0.022727272727272727273 + 1.0792819253101171203e-876j)  +/-  (1.89e-87, 1.97e-203j)
| (0.022727272727272727273 - 9.9781689327119347935e-877j)  +/-  (1.71e-87, 1.78e-203j)
