Starting with polynomial:
P : t^50 - 1225*t^48 + 690900*t^46 - 238360500*t^44 + 56372258250*t^42 - 9707302870650*t^40 + 1261949373184500*t^38 - 126735772764100500*t^36 + 9980442105172914375*t^34 - 622114224555778329375*t^32 + 30856865537966605137000*t^30 - 1220248773546861203145000*t^28 + 38437836366726127899067500*t^26 - 960945909168153197476687500*t^24 + 18944362209315020178826125000*t^22 - 291743178023451310753922325000*t^20 + 3464450239028484315202827609375*t^18 - 31180052151256358836825448484375*t^16 + 207867014341709058912169656562500*t^14 - 995573595005027597947759934062500*t^12 + 3285392863516591073227607782406250*t^10 - 7040127564678409442630588105156250*t^8 + 8960162355045248381529839406562500*t^6 - 5843584144594727205345547439062500*t^4 + 1460896036148681801336386859765625*t^2 - 58435841445947272053455474390625
Extension levels are: 50
-------------------------------------------------
Ending with final polynomial:
P : t^50 - 1225*t^48 + 690900*t^46 - 238360500*t^44 + 56372258250*t^42 - 9707302870650*t^40 + 1261949373184500*t^38 - 126735772764100500*t^36 + 9980442105172914375*t^34 - 622114224555778329375*t^32 + 30856865537966605137000*t^30 - 1220248773546861203145000*t^28 + 38437836366726127899067500*t^26 - 960945909168153197476687500*t^24 + 18944362209315020178826125000*t^22 - 291743178023451310753922325000*t^20 + 3464450239028484315202827609375*t^18 - 31180052151256358836825448484375*t^16 + 207867014341709058912169656562500*t^14 - 995573595005027597947759934062500*t^12 + 3285392863516591073227607782406250*t^10 - 7040127564678409442630588105156250*t^8 + 8960162355045248381529839406562500*t^6 - 5843584144594727205345547439062500*t^4 + 1460896036148681801336386859765625*t^2 - 58435841445947272053455474390625
-------------------------------------------------
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:   50 out of 50
Indefinite weights: 0 out of 50
Negative weights:   0 out of 50
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (9.9480357096375083617 - 7.2216441935236767037e-927j)  +/-  (1.22e-243, 1.22e-243j)
| (-9.9480357096375083617 - 3.8663390946382193823e-930j)  +/-  (1.24e-243, 1.24e-243j)
| (6.1673473886599247262 + 7.6657680899871360319e-929j)  +/-  (8.22e-244, 8.22e-244j)
| (8.7722995795145978758 + 4.0075324050735098956e-931j)  +/-  (3.38e-243, 3.38e-243j)
| (-11.279233321482634037 + 8.4599792701119000666e-940j)  +/-  (1.31e-244, 1.31e-244j)
| (11.279233321482634037 - 5.24098117315392727e-938j)  +/-  (1.57e-244, 1.57e-244j)
| (-9.3460395935757239712 - 2.7290585611528211762e-937j)  +/-  (2.51e-243, 2.51e-243j)
| (-2.8935827277077385478 + 8.4146593673507100901e-943j)  +/-  (5.19e-248, 5.19e-248j)
| (9.3460395935757239712 - 5.9306657830469836229e-937j)  +/-  (2.26e-243, 2.26e-243j)
| (12.985884455415557341 + 7.7825794842651317976e-944j)  +/-  (1.14e-246, 1.14e-246j)
| (-5.2024349933999118485 - 2.0192797498068393305e-941j)  +/-  (1.13e-244, 1.13e-244j)
| (2.4434874526540172203 + 1.4948274533045037246e-945j)  +/-  (5.57e-249, 5.57e-249j)
| (-8.7722995795145978758 + 4.2270259533736390464e-940j)  +/-  (3.92e-243, 3.92e-243j)
| (1.9959047097951235451 + 7.177742659628424419e-947j)  +/-  (6.15e-250, 6.15e-250j)
| (-2.4434874526540172203 - 1.6719045660909697664e-945j)  +/-  (6e-249, 6e-249j)
| (10.587381749191773642 - 1.7204314417203485214e-940j)  +/-  (5.17e-244, 5.17e-244j)
| (12.053018380924483665 + 6.5692474200021283507e-942j)  +/-  (2.09e-245, 2.09e-245j)
| (8.2208159079821258325 - 3.3345120185904107113e-938j)  +/-  (5.02e-243, 5.02e-243j)
| (5.2024349933999118485 - 2.9980246808604040077e-947j)  +/-  (9.97e-245, 9.97e-245j)
| (4.2645578430381078619 + 9.5913229004937842419e-953j)  +/-  (8.08e-246, 8.08e-246j)
| (-10.587381749191773642 - 1.2474239034107180664e-962j)  +/-  (5.2e-244, 5.2e-244j)
| (-12.985884455415557341 + 6.687878828715128082e-965j)  +/-  (1.11e-246, 1.11e-246j)
| (7.6873624067125014821 - 7.6413824344416781224e-959j)  +/-  (3.26e-243, 3.26e-243j)
| (-12.053018380924483665 + 1.643093186446951453e-978j)  +/-  (2.01e-245, 2.01e-245j)
| (-3.803505741742010663 - 2.0040190594169396171e-980j)  +/-  (1.87e-246, 1.87e-246j)
| (-8.2208159079821258325 - 1.7143262527283884063e-975j)  +/-  (4.31e-243, 4.31e-243j)
| (-5.6809922910332821994 + 9.6489643819022608014e-978j)  +/-  (3.47e-244, 3.47e-244j)
| (7.1688148378539031032 - 8.3853704374848313707e-978j)  +/-  (2.76e-243, 2.76e-243j)
| (2.8935827277077385478 + 3.7995863290409606723e-991j)  +/-  (4.88e-248, 4.88e-248j)
| (-1.9959047097951235451 + 1.1166022624889826395e-1002j)  +/-  (6.6e-250, 6.6e-250j)
| (-6.1673473886599247262 - 7.0872084995079346949e-996j)  +/-  (6.98e-244, 6.98e-244j)
| (-6.6627753990187212348 - 5.8543464047922885371e-995j)  +/-  (1.35e-243, 1.35e-243j)
| (-7.6873624067125014821 - 2.4161371577038471612e-997j)  +/-  (3.83e-243, 3.83e-243j)
| (-4.7305985502285964385 + 2.0583616909056023956e-1001j)  +/-  (3.3e-245, 3.3e-245j)
| (-3.346727774732427644 + 7.1908325530808926604e-1004j)  +/-  (3.88e-247, 3.88e-247j)
| (0.22104518164454322214 + 4.7611628730289817169e-1008j)  +/-  (2.26e-254, 2.26e-254j)
| (1.5503332143387701711 - 2.3178824468996032256e-1003j)  +/-  (7.23e-251, 7.23e-251j)
| (5.6809922910332821994 + 2.1081800812488450527e-1000j)  +/-  (3.03e-244, 3.03e-244j)
| (-0.66334967950829175505 + 8.806733583041084005e-1027j)  +/-  (3.65e-253, 3.65e-253j)
| (4.7305985502285964385 + 1.7154973702569215785e-1017j)  +/-  (3.23e-245, 3.23e-245j)
| (-1.5503332143387701711 - 9.905305104906056744e-1044j)  +/-  (5.98e-251, 5.98e-251j)
| (6.6627753990187212348 - 3.0204184940793552922e-1038j)  +/-  (1.48e-243, 1.48e-243j)
| (3.346727774732427644 - 1.3079063662308459538e-1050j)  +/-  (3.59e-247, 3.59e-247j)
| (1.1062992893971829866 + 2.5808870841488409854e-1057j)  +/-  (3.85e-252, 3.85e-252j)
| (-7.1688148378539031032 + 1.9105379506551539699e-1051j)  +/-  (3.03e-243, 3.03e-243j)
| (-0.22104518164454322214 - 2.2514222510390878694e-1063j)  +/-  (1.74e-254, 1.74e-254j)
| (-1.1062992893971829866 - 5.3979589218208660846e-1061j)  +/-  (4.41e-252, 4.41e-252j)
| (-4.2645578430381078619 + 6.2098319106886604756e-1059j)  +/-  (7.82e-246, 7.82e-246j)
| (0.66334967950829175505 + 3.3480313634227395897e-1066j)  +/-  (3.65e-253, 3.65e-253j)
| (3.803505741742010663 + 8.1032687399097930758e-1061j)  +/-  (1.93e-246, 1.93e-246j)
-------------------------------------------------
The weights are:
| (7.9950944779150836836e-23 - 5.9471182086805590351e-945j)  +/-  (5.45e-71, 3.54e-191j)
| (7.9950944779150836836e-23 - 1.3959065109302107568e-945j)  +/-  (5.2e-72, 3.38e-192j)
| (1.0770607893890171765e-09 - 2.5460401404544811459e-937j)  +/-  (9.17e-62, 5.96e-182j)
| (4.3681718162015651521e-18 - 2.0183795486002567595e-942j)  +/-  (1e-68, 6.51e-189j)
| (6.8562807589244336589e-29 - 1.1940395569400836716e-948j)  +/-  (1.43e-75, 9.31e-196j)
| (6.8562807589244336589e-29 - 4.0755050285430108407e-948j)  +/-  (1.33e-74, 8.64e-195j)
| (2.5224828071680072898e-20 + 2.5756820909130843427e-944j)  +/-  (6.85e-72, 4.45e-192j)
| (0.0027381608969353410999 - 1.4529151285967679075e-935j)  +/-  (2.48e-51, 1.61e-171j)
| (2.5224828071680072898e-20 + 1.2568450815680658453e-943j)  +/-  (2.28e-70, 1.48e-190j)
| (1.0346075005769982122e-37 - 1.1868536591863513334e-952j)  +/-  (1.01e-78, 6.59e-199j)
| (2.5146098808388233911e-07 + 1.10960192814786181e-937j)  +/-  (9.86e-64, 6.4e-184j)
| (0.0090450541548496417153 - 6.4253010424574331949e-935j)  +/-  (3.56e-51, 2.31e-171j)
| (4.3681718162015651521e-18 - 3.5196068476281503502e-943j)  +/-  (5.42e-72, 3.52e-192j)
| (0.024304812864243064987 + 9.4024580689929442054e-935j)  +/-  (2.93e-48, 1.9e-168j)
| (0.0090450541548496417153 + 2.778713379957915495e-935j)  +/-  (6.07e-52, 3.95e-172j)
| (1.2060445507610766364e-25 + 1.977008411574366142e-946j)  +/-  (1.34e-73, 8.7e-194j)
| (9.443414659584385685e-33 + 4.1540836576307563208e-950j)  +/-  (6.55e-77, 4.26e-197j)
| (4.5666982468005818064e-16 + 2.6180393989315170358e-941j)  +/-  (3.17e-70, 2.06e-190j)
| (2.5146098808388233911e-07 - 1.307451042248566665e-936j)  +/-  (2.33e-65, 1.51e-185j)
| (2.0784851757345459401e-05 - 6.0278462314564781952e-936j)  +/-  (4.56e-63, 2.96e-183j)
| (1.2060445507610766364e-25 + 5.2146943915990576218e-947j)  +/-  (1.2e-78, 7.8e-199j)
| (1.0346075005769982122e-37 - 4.225038534815018487e-953j)  +/-  (1.34e-84, 8.68e-205j)
| (3.0838286870053813556e-14 - 2.906469263749268828e-940j)  +/-  (5.74e-72, 3.73e-192j)
| (9.443414659584385685e-33 + 1.3418138690476490476e-950j)  +/-  (2.19e-82, 1.42e-202j)
| (0.00013217263286689880727 - 2.9008295654876504392e-936j)  +/-  (1.3e-67, 8.45e-188j)
| (4.5666982468005818064e-16 + 3.7366320860979633535e-942j)  +/-  (1.6e-76, 1.04e-196j)
| (1.888225976835228001e-08 - 2.9177872381236661819e-938j)  +/-  (7.08e-73, 4.6e-193j)
| (1.4142289361266409117e-12 + 2.987410335099154123e-939j)  +/-  (9.37e-74, 6.09e-194j)
| (0.0027381608969353410999 + 4.0212669453062637658e-935j)  +/-  (5.42e-66, 3.52e-186j)
| (0.024304812864243064987 - 4.8046995067041389177e-935j)  +/-  (8.41e-64, 5.46e-184j)
| (1.0770607893890171765e-09 + 6.6938490840458383359e-939j)  +/-  (2.53e-74, 1.64e-194j)
| (4.5766367123104493014e-11 - 1.3265594098761807859e-939j)  +/-  (1.43e-75, 9.28e-196j)
| (3.0838286870053813556e-14 - 3.1888357122914148294e-941j)  +/-  (3.22e-77, 2.09e-197j)
| (2.5849376589493844886e-06 - 3.7116271562690547196e-937j)  +/-  (7.47e-73, 4.86e-193j)
| (0.00067082806197870789999 + 6.8489293972420853135e-936j)  +/-  (1.75e-70, 1.14e-190j)
| (0.17212585199244318261 + 1.7553291927839810773e-934j)  +/-  (6.37e-68, 4.14e-188j)
| (0.053343524531700962173 - 1.2585239031807354642e-934j)  +/-  (4.48e-68, 2.91e-188j)
| (1.888225976835228001e-08 + 7.1080511462755557879e-937j)  +/-  (5.28e-76, 3.43e-196j)
| (0.1416854132499438741 + 1.3863739986788431012e-934j)  +/-  (2.73e-69, 1.78e-189j)
| (2.5849376589493844886e-06 + 2.8152890117195607896e-936j)  +/-  (4.8e-75, 3.12e-195j)
| (0.053343524531700962173 + 7.5289985886035091639e-935j)  +/-  (2.08e-70, 1.35e-190j)
| (4.5766367123104493014e-11 - 3.4353168548590274674e-938j)  +/-  (2.07e-77, 1.35e-197j)
| (0.00067082806197870789999 - 2.3101573547972731349e-935j)  +/-  (4.96e-74, 3.2e-194j)
| (0.095930540358101494727 + 1.5396430741977245e-934j)  +/-  (1.02e-71, 6.45e-192j)
| (1.4142289361266409117e-12 + 2.2434343568272641852e-940j)  +/-  (8.11e-79, 5.18e-199j)
| (0.17212585199244318261 - 1.6338573785555901248e-934j)  +/-  (9.58e-72, 6.03e-192j)
| (0.095930540358101494727 - 1.0712954529398239848e-934j)  +/-  (1.67e-72, 1.05e-192j)
| (2.0784851757345459401e-05 + 1.0994961017991530406e-936j)  +/-  (4.92e-75, 3.14e-195j)
| (0.1416854132499438741 - 1.7205473273960166719e-934j)  +/-  (1.28e-72, 7.36e-193j)
| (0.00013217263286689880727 + 1.2235800730513063748e-935j)  +/-  (6.92e-75, 4.56e-195j)
