Starting with polynomial:
P : 35184372088832*t^45 - 17416264183971840*t^43 + 3931721639531642880*t^41 - 537335290735991193600*t^39 + 49770681304421184307200*t^37 - 3314727374874450874859520*t^35 + 164355232337524855878451200*t^33 - 6198540191015223135987302400*t^31 + 180145074301379922389630976000*t^29 - 4063272231464458249455009792000*t^27 + 71310427662201242277935421849600*t^25 - 972414922666380576517301207040000*t^23 + 10250873976441428577453216890880000*t^21 - 82795520578950000048660597964800000*t^19 + 505644072107158928868605794713600000*t^17 - 2292253126885787144204346269368320000*t^15 + 7521455572593989066920511196364800000*t^13 - 17255103960656798447641172744601600000*t^11 + 26361964384336775406118458359808000000*t^9 - 24974492574634839858428013182976000000*t^7 + 13111608601683290925674706921062400000*t^5 - 3121811571829354982303501647872000000*t^3 + 212850788988365112429784203264000000*t
Extension levels are: 45
-------------------------------------------------
Ending with final polynomial:
P : 35184372088832*t^45 - 17416264183971840*t^43 + 3931721639531642880*t^41 - 537335290735991193600*t^39 + 49770681304421184307200*t^37 - 3314727374874450874859520*t^35 + 164355232337524855878451200*t^33 - 6198540191015223135987302400*t^31 + 180145074301379922389630976000*t^29 - 4063272231464458249455009792000*t^27 + 71310427662201242277935421849600*t^25 - 972414922666380576517301207040000*t^23 + 10250873976441428577453216890880000*t^21 - 82795520578950000048660597964800000*t^19 + 505644072107158928868605794713600000*t^17 - 2292253126885787144204346269368320000*t^15 + 7521455572593989066920511196364800000*t^13 - 17255103960656798447641172744601600000*t^11 + 26361964384336775406118458359808000000*t^9 - 24974492574634839858428013182976000000*t^7 + 13111608601683290925674706921062400000*t^5 - 3121811571829354982303501647872000000*t^3 + 212850788988365112429784203264000000*t
-------------------------------------------------
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
-------------------------------------------------
The nodes are:
| (6.925582073277595149 - 9.7269790426918667995e-900j)  +/-  (4.82e-245, 4.82e-245j)
| (7.9836998162220029719 - 7.5091527730993413756e-909j)  +/-  (2.33e-246, 2.33e-246j)
| (-7.4253266258561949355 + 1.1737320050024508385e-910j)  +/-  (1.16e-245, 1.16e-245j)
| (-5.6119841218396651048 - 2.6804179767461076778e-911j)  +/-  (1.36e-244, 1.36e-244j)
| (5.6119841218396651048 + 1.2274866678882035631e-916j)  +/-  (1.66e-244, 1.66e-244j)
| (7.4253266258561949355 + 8.1689676188374635385e-934j)  +/-  (1.17e-245, 1.17e-245j)
| (-6.0276294722536947304 - 7.0329479081936022517e-938j)  +/-  (1.58e-244, 1.58e-244j)
| (-8.6561523259903277651 - 2.6928739404704458686e-943j)  +/-  (1.56e-247, 1.56e-247j)
| (-7.9836998162220029719 - 1.7519864634796235785e-941j)  +/-  (1.95e-246, 1.95e-246j)
| (8.6561523259903277651 + 3.0438799514206579859e-940j)  +/-  (1.56e-247, 1.56e-247j)
| (-6.925582073277595149 - 5.9164044492884728354e-942j)  +/-  (4.18e-245, 4.18e-245j)
| (-5.2120588631620083271 + 1.0762302397590144265e-943j)  +/-  (1.35e-244, 1.35e-244j)
| (4.8248063087032578863 + 1.3858141038871890224e-952j)  +/-  (9.76e-245, 9.76e-245j)
| (3.0148178197492258368 - 3.8485774050777518587e-962j)  +/-  (1.28e-246, 1.28e-246j)
| (-3.3642645958565403212 - 1.9227893882983942196e-965j)  +/-  (4.98e-246, 4.98e-246j)
| (3.7189496893415633288 - 2.0670210393518168438e-965j)  +/-  (1.06e-245, 1.06e-245j)
| (2.3285579714531896165 - 5.2708609536386956331e-973j)  +/-  (5.64e-248, 5.64e-248j)
| (6.0276294722536947304 - 1.0095596165433995669e-970j)  +/-  (1.16e-244, 1.16e-244j)
| (-1.3215117856392311609 - 3.0875689230724564441e-983j)  +/-  (1.17e-250, 1.17e-250j)
| (2.6698124652513463097 + 1.3885995062146552421e-979j)  +/-  (3.08e-247, 3.08e-247j)
| (-4.8248063087032578863 - 3.4323788924544327214e-977j)  +/-  (1.09e-244, 1.09e-244j)
| (-3.7189496893415633288 - 1.084520974634763784e-978j)  +/-  (1.22e-245, 1.22e-245j)
| (4.0798099079253934537 - 8.3777967115107487489e-977j)  +/-  (2.63e-245, 2.63e-245j)
| (-6.4633149436642537851 + 6.5717006479603938623e-987j)  +/-  (7.93e-245, 7.93e-245j)
| (-4.0798099079253934537 - 1.0020358499992974351e-988j)  +/-  (3.22e-245, 3.22e-245j)
| (-2.3285579714531896165 + 6.8315109856600046626e-994j)  +/-  (4.52e-248, 4.52e-248j)
| (4.4479690736019315509 + 3.2436495032710123273e-987j)  +/-  (5.84e-245, 5.84e-245j)
| (-3.0148178197492258368 - 9.4397590098508058589e-995j)  +/-  (1.16e-246, 1.16e-246j)
| (-1.6549291191547923421 + 1.9658121928528024658e-997j)  +/-  (1.33e-249, 1.33e-249j)
| (-0.32938389969666915384 - 4.5151313196912285306e-1002j)  +/-  (3.62e-254, 3.62e-254j)
| (-2.6698124652513463097 - 5.1226987454075898553e-995j)  +/-  (2.62e-247, 2.62e-247j)
| (1.6549291191547923421 - 1.1792088824626522185e-996j)  +/-  (1.08e-249, 1.08e-249j)
| (1.3215117856392311609 - 3.8828214845503082649e-999j)  +/-  (1.27e-250, 1.27e-250j)
| (3.3642645958565403212 + 1.5085409395991209771e-991j)  +/-  (4.28e-246, 4.28e-246j)
| (-1.9904454586466384434 + 8.272085559119910254e-999j)  +/-  (7.96e-249, 7.96e-249j)
| (-0.65916168887413517201 - 1.6155388279453306004e-1002j)  +/-  (7.94e-253, 7.94e-253j)
| (1.9904454586466384434 + 4.028343172468634109e-998j)  +/-  (7.1e-249, 7.1e-249j)
| (0.98973342486571132626 - 3.6598750780737993067e-1001j)  +/-  (1.05e-251, 1.05e-251j)
| (0.65916168887413517201 + 9.8910200727590600848e-1003j)  +/-  (7.94e-253, 7.94e-253j)
| (-4.4479690736019315509 + 1.4966565447849227133e-994j)  +/-  (5.53e-245, 5.53e-245j)
| (-0.98973342486571132626 - 8.6419722187818543956e-1005j)  +/-  (1.46e-251, 1.46e-251j)
| (6.4633149436642537851 - 1.4503383986411058546e-1003j)  +/-  (7.74e-245, 7.74e-245j)
| (2.5799173214755496494e-1028 - 5.3521458605653893526e-1028j)  +/-  (2.67e-1026, 2.67e-1026j)
| (5.2120588631620083271 - 4.7794143595441034125e-1027j)  +/-  (1.44e-244, 1.44e-244j)
| (0.32938389969666915384 - 1.3228886647074438367e-1037j)  +/-  (4.64e-254, 4.64e-254j)
-------------------------------------------------
The weights are:
| (3.9909217645671260268e-22 + 2.6884841151607590877e-920j)  +/-  (1.42e-86, 3.83e-208j)
| (7.0494524380290660924e-29 - 1.5419073635237015664e-924j)  +/-  (1.81e-89, 4.89e-211j)
| (3.3558982158459878593e-25 - 7.844035364607002095e-924j)  +/-  (1.2e-89, 3.25e-211j)
| (4.8238702869483447161e-15 - 1.0764638544155575047e-918j)  +/-  (9.8e-85, 2.65e-206j)
| (4.8238702869483447161e-15 - 1.0274245429630034465e-917j)  +/-  (1.88e-84, 5.08e-206j)
| (3.3558982158459878593e-25 + 2.2525316837815888699e-922j)  +/-  (1.91e-88, 5.16e-210j)
| (3.9873883949890406994e-17 + 9.4728632878987952747e-920j)  +/-  (2.4e-86, 6.48e-208j)
| (1.2586012667617326391e-33 - 4.424282512048530832e-928j)  +/-  (7.69e-94, 2.08e-215j)
| (7.0494524380290660924e-29 + 1.0942978034695829064e-925j)  +/-  (5.49e-92, 1.48e-213j)
| (1.2586012667617326391e-33 + 3.9835423151537453309e-927j)  +/-  (1.17e-94, 3.18e-216j)
| (3.9909217645671260268e-22 + 2.802624243874968891e-922j)  +/-  (1.51e-89, 4.09e-211j)
| (3.5329767895712444802e-13 + 9.5159208251050595609e-918j)  +/-  (6.28e-86, 1.7e-207j)
| (1.6723735784722372867e-11 - 3.782696854850608271e-916j)  +/-  (1.06e-86, 2.86e-208j)
| (2.2106807141298168192e-05 + 2.3362319746478143443e-913j)  +/-  (2.02e-81, 5.46e-203j)
| (2.4121676760232760059e-06 - 2.9329823516399534325e-914j)  +/-  (3.02e-83, 8.16e-205j)
| (1.987368663904519585e-07 + 2.7014978943585091198e-914j)  +/-  (4.09e-84, 1.11e-205j)
| (0.00084635652553851746335 + 1.2297433492929433948e-912j)  +/-  (3.46e-79, 9.37e-201j)
| (3.9873883949890406994e-17 + 1.3664868134067690519e-918j)  +/-  (5.19e-90, 1.4e-211j)
| (0.03271890357088915539 - 4.2619959133029065408e-912j)  +/-  (5.75e-75, 1.56e-196j)
| (0.00015528891031995773364 - 5.68992709566246999e-913j)  +/-  (1.4e-80, 3.78e-202j)
| (1.6723735784722372867e-11 - 6.7628394400062075396e-917j)  +/-  (4.49e-88, 1.21e-209j)
| (1.987368663904519585e-07 + 8.1381795503163581206e-915j)  +/-  (3.37e-86, 9.12e-208j)
| (1.2137319718199660403e-08 - 7.5227366282343380534e-915j)  +/-  (6.38e-87, 1.73e-208j)
| (1.8194154217810188513e-19 - 6.1906415251027454926e-921j)  +/-  (9.42e-92, 2.55e-213j)
| (1.2137319718199660403e-08 - 1.9452279349445992283e-915j)  +/-  (2.89e-87, 7.83e-209j)
| (0.00084635652553851746335 + 6.1087901303866550185e-913j)  +/-  (1.89e-84, 5.1e-206j)
| (5.3701070616709938353e-10 + 1.8174923407871433262e-915j)  +/-  (2.46e-89, 6.67e-211j)
| (2.2106807141298168192e-05 + 9.1912326345575049093e-914j)  +/-  (5.85e-86, 1.58e-207j)
| (0.012196449810369717932 + 2.5010256779715383729e-912j)  +/-  (1.59e-83, 4.32e-205j)
| (0.16679455536492150609 + 1.0938811741244580414e-911j)  +/-  (1.06e-82, 2.87e-204j)
| (0.00015528891031995773364 - 2.523608523416686576e-913j)  +/-  (1.84e-85, 4.98e-207j)
| (0.012196449810369717932 + 4.0716166881971639851e-912j)  +/-  (4.27e-85, 1.15e-206j)
| (0.03271890357088915539 - 6.2720626516341391667e-912j)  +/-  (2.47e-84, 6.68e-206j)
| (2.4121676760232760059e-06 - 8.4743743471590105953e-914j)  +/-  (1.89e-88, 5.12e-210j)
| (0.0036148025252847930448 - 1.3103444849541915233e-912j)  +/-  (1.48e-85, 3.98e-207j)
| (0.12060955967502577057 - 8.8974293087516369287e-912j)  +/-  (3.4e-84, 9.06e-206j)
| (0.0036148025252847930448 - 2.3673239899014815781e-912j)  +/-  (2.99e-86, 8.08e-208j)
| (0.070140332209734467647 + 8.6699318050858150767e-912j)  +/-  (4.59e-85, 1.22e-206j)
| (0.12060955967502577057 - 1.0769261710027774981e-911j)  +/-  (4.18e-85, 1.11e-206j)
| (5.3701070616709938353e-10 + 3.9592234677564548482e-916j)  +/-  (2.79e-90, 7.45e-212j)
| (0.070140332209734467647 + 6.5017501071304256503e-912j)  +/-  (1.42e-85, 3.78e-207j)
| (1.8194154217810188513e-19 - 1.7930298102113081215e-919j)  +/-  (1.39e-96, 3.81e-218j)
| (0.18579804200964016094 - 1.209424824280834139e-911j)  +/-  (2.09e-86, 4.96e-208j)
| (3.5329767895712444802e-13 + 6.7405446313622194403e-917j)  +/-  (2.1e-93, 5.83e-215j)
| (0.16679455536492150609 + 1.2031279940205726156e-911j)  +/-  (1.55e-86, 3.55e-208j)
