Starting with polynomial:
P : 25674715590128696833261065/4398046511104*t^46 - 292014622371243969477200025/4398046511104*t^44 + 1551942880692116826547366425/4398046511104*t^42 - 5119627663892385393322921425/4398046511104*t^40 + 11745028170106060608211407975/4398046511104*t^38 - 19895794707432676162825589895/4398046511104*t^36 + 25790844991116432062922060975/4398046511104*t^34 - 26163949439450846993307913575/4398046511104*t^32 + 10533538086012678659643445725/2199023255552*t^30 - 6788280099874837358436887245/2199023255552*t^28 + 3515027229798203454094716957/2199023255552*t^26 - 1462719397803349708810221525/2199023255552*t^24 + 487573132601116569603407175/2199023255552*t^22 - 129310440448746185509055175/2199023255552*t^20 + 26998883170617335435956575/2199023255552*t^18 - 4371247751433282880107255/2199023255552*t^16 + 1074896988057364642649325/4398046511104*t^14 - 97523056742991208854525/4398046511104*t^12 + 6273413006859083610525/4398046511104*t^10 - 270146971587233265525/4398046511104*t^8 + 7135957740040123995/4398046511104*t^6 - 99943385714847675/4398046511104*t^4 + 556271163533475/4398046511104*t^2 - 514589420475/4398046511104
Extension levels are: 46
-------------------------------------------------
Ending with final polynomial:
P : 25674715590128696833261065/4398046511104*t^46 - 292014622371243969477200025/4398046511104*t^44 + 1551942880692116826547366425/4398046511104*t^42 - 5119627663892385393322921425/4398046511104*t^40 + 11745028170106060608211407975/4398046511104*t^38 - 19895794707432676162825589895/4398046511104*t^36 + 25790844991116432062922060975/4398046511104*t^34 - 26163949439450846993307913575/4398046511104*t^32 + 10533538086012678659643445725/2199023255552*t^30 - 6788280099874837358436887245/2199023255552*t^28 + 3515027229798203454094716957/2199023255552*t^26 - 1462719397803349708810221525/2199023255552*t^24 + 487573132601116569603407175/2199023255552*t^22 - 129310440448746185509055175/2199023255552*t^20 + 26998883170617335435956575/2199023255552*t^18 - 4371247751433282880107255/2199023255552*t^16 + 1074896988057364642649325/4398046511104*t^14 - 97523056742991208854525/4398046511104*t^12 + 6273413006859083610525/4398046511104*t^10 - 270146971587233265525/4398046511104*t^8 + 7135957740040123995/4398046511104*t^6 - 99943385714847675/4398046511104*t^4 + 556271163533475/4398046511104*t^2 - 514589420475/4398046511104
-------------------------------------------------
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 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:
| (0.96802139185399194274 + 7.3925869725456955398e-891j)  +/-  (9.44e-240, 9.44e-240j)
| (-0.96802139185399194274 + 3.1044153993594326172e-908j)  +/-  (1.13e-239, 1.13e-239j)
| (-0.92543379880675395098 + 6.1252998574754658436e-908j)  +/-  (4.75e-240, 4.75e-240j)
| (0.99866304213381798113 + 5.3129982931697564863e-906j)  +/-  (2.67e-240, 2.67e-240j)
| (0.92543379880675395098 + 4.7691652501239711969e-916j)  +/-  (4.27e-240, 4.27e-240j)
| (0.94889236344608979562 - 7.6959652010610747834e-937j)  +/-  (7.76e-240, 7.76e-240j)
| (-0.99866304213381798113 + 7.896392882661055571e-956j)  +/-  (3.09e-240, 3.09e-240j)
| (-0.8977527115339419657 + 5.0714605292643026405e-958j)  +/-  (2.17e-240, 2.17e-240j)
| (-0.98273366980416686348 - 2.9423313542882263149e-956j)  +/-  (1.12e-239, 1.12e-239j)
| (0.99296234890617436407 + 1.959295972319841837e-961j)  +/-  (7.51e-240, 7.51e-240j)
| (0.83024683706606605303 - 2.3572231059994417449e-981j)  +/-  (2.71e-241, 2.71e-241j)
| (-0.99296234890617436407 - 2.1660340479402654986e-988j)  +/-  (7.62e-240, 7.62e-240j)
| (-0.86597539486685806292 - 3.7726467641044025239e-991j)  +/-  (9.1e-241, 9.1e-241j)
| (-0.747605359615666054 + 3.7649504955885701061e-993j)  +/-  (1.93e-242, 1.93e-242j)
| (0.98273366980416686348 + 9.5592180870966598083e-989j)  +/-  (1.03e-239, 1.03e-239j)
| (0.86597539486685806292 - 5.1449514319207839874e-997j)  +/-  (9.36e-241, 9.36e-241j)
| (0.65133484620199771511 - 8.0049800684006756579e-1005j)  +/-  (6.17e-244, 6.17e-244j)
| (-0.94889236344608979562 + 4.58674090785375769e-1003j)  +/-  (7.77e-240, 7.77e-240j)
| (-0.79073005707527425519 + 6.8500062341287732787e-1004j)  +/-  (9.48e-242, 9.48e-242j)
| (-0.83024683706606605303 + 5.1688870860597627975e-1004j)  +/-  (2.72e-241, 2.72e-241j)
| (0.79073005707527425519 - 1.4990890899272982258e-1002j)  +/-  (8.32e-242, 8.32e-242j)
| (0.747605359615666054 + 5.7462240522242803376e-1005j)  +/-  (2.07e-242, 2.07e-242j)
| (0.8977527115339419657 + 6.282390099252870976e-1009j)  +/-  (2.13e-240, 2.13e-240j)
| (-0.70106951202040569751 + 6.358010881558485837e-1019j)  +/-  (3.9e-243, 3.9e-243j)
| (-0.59862828971271515318 + 3.0051379583255686359e-1021j)  +/-  (8.11e-245, 8.11e-245j)
| (0.03377219001605204152 + 1.9072430337983942918e-1034j)  +/-  (2.4e-255, 2.4e-255j)
| (0.70106951202040569751 - 1.7060161243359593513e-1020j)  +/-  (3.59e-243, 3.59e-243j)
| (0.36307287702099571012 + 2.5283875246570065021e-1028j)  +/-  (6.04e-249, 6.04e-249j)
| (-0.16809117946710352861 - 7.6400968719071121161e-1032j)  +/-  (1.39e-252, 1.39e-252j)
| (-0.65133484620199771511 + 9.0106383183710050693e-1024j)  +/-  (6.24e-244, 6.24e-244j)
| (-0.23425292220626976863 + 6.7865111210579149976e-1031j)  +/-  (2.34e-251, 2.34e-251j)
| (0.42514331328282839732 + 2.3165724143050757978e-1025j)  +/-  (8.97e-248, 8.97e-248j)
| (0.59862828971271515318 - 6.3039624095299359278e-1025j)  +/-  (7.97e-245, 7.97e-245j)
| (0.10116247530558423952 + 3.2067767919477886368e-1036j)  +/-  (6.03e-254, 6.03e-254j)
| (-0.54319033026180263527 - 1.3889759495108218095e-1028j)  +/-  (8.38e-246, 8.38e-246j)
| (-0.36307287702099571012 - 8.1177296202614593812e-1034j)  +/-  (5.63e-249, 5.63e-249j)
| (0.16809117946710352861 - 8.6399188239850878628e-1035j)  +/-  (8.72e-253, 8.72e-253j)
| (0.54319033026180263527 - 7.6034798002150074207e-1031j)  +/-  (8.84e-246, 8.84e-246j)
| (0.23425292220626976863 - 5.7308600508204865893e-1037j)  +/-  (2.32e-251, 2.32e-251j)
| (-0.29934582270187001548 + 3.4086244547833039636e-1034j)  +/-  (3.76e-250, 3.76e-250j)
| (-0.48527391838816466277 - 1.1773047469877549876e-1030j)  +/-  (8.84e-247, 8.84e-247j)
| (-0.10116247530558423952 + 9.4710621673051155655e-1038j)  +/-  (5.31e-254, 5.31e-254j)
| (0.29934582270187001548 + 3.1391416169354708256e-1034j)  +/-  (3.65e-250, 3.65e-250j)
| (0.48527391838816466277 - 1.7735236977845958595e-1030j)  +/-  (1.04e-246, 1.04e-246j)
| (-0.03377219001605204152 - 5.7629955573310660311e-1039j)  +/-  (4.09e-255, 4.09e-255j)
| (-0.42514331328282839732 + 1.6017738071330785257e-1033j)  +/-  (8.7e-248, 8.7e-248j)
-------------------------------------------------
The weights are:
| (0.016933514007836238046 - 1.9254804636379096368e-891j)  +/-  (1.71e-65, 4.93e-181j)
| (0.016933514007836238046 + 6.4658940446551339611e-893j)  +/-  (5.56e-66, 1.6e-181j)
| (0.025589286397130010635 + 1.2275372014198565709e-892j)  +/-  (5.43e-66, 1.57e-181j)
| (0.003430300868107048286 - 3.7888543330355749398e-892j)  +/-  (1.42e-66, 4.09e-182j)
| (0.025589286397130010635 - 5.4576615381374197286e-891j)  +/-  (1.49e-66, 4.29e-182j)
| (0.021309998754136501054 + 9.235510960602119418e-891j)  +/-  (3.01e-66, 8.68e-182j)
| (0.003430300868107048286 - 5.9031712168825202136e-894j)  +/-  (4.31e-68, 1.24e-183j)
| (0.029751829552202755799 - 1.5615963677122126141e-892j)  +/-  (3.07e-68, 8.85e-184j)
| (0.012479883770988684207 - 4.0631236762871565539e-893j)  +/-  (5.36e-68, 1.54e-183j)
| (0.0079698982297246224516 + 1.6255561991648061452e-891j)  +/-  (1.72e-68, 4.95e-184j)
| (0.037651305357386071328 + 3.0103020529403308156e-891j)  +/-  (2.85e-70, 8.2e-186j)
| (0.0079698982297246224516 + 2.0674790160963641212e-893j)  +/-  (3.79e-68, 1.09e-183j)
| (0.033778627999106896521 + 1.9217326075050220109e-892j)  +/-  (7.79e-70, 2.25e-185j)
| (0.044864395277318126767 - 3.1442361029070627688e-892j)  +/-  (1.41e-71, 4.07e-187j)
| (0.012479883770988684207 - 5.3874451696081974512e-891j)  +/-  (3.83e-69, 1.11e-184j)
| (0.033778627999106896521 - 3.4537870481536472127e-891j)  +/-  (5.28e-71, 1.52e-186j)
| (0.051259598007143021335 + 2.0802001950753075718e-891j)  +/-  (2.05e-73, 5.9e-189j)
| (0.021309998754136501054 - 9.2161867501020309036e-893j)  +/-  (1.32e-69, 3.81e-185j)
| (0.041352190109678729704 + 2.7141795965676718007e-892j)  +/-  (3.85e-72, 1.11e-187j)
| (0.037651305357386071328 - 2.3063468422066570173e-892j)  +/-  (1.55e-71, 4.48e-187j)
| (0.041352190109678729704 - 2.6924989335071949391e-891j)  +/-  (6.61e-74, 1.9e-189j)
| (0.044864395277318126767 + 2.4473426530296174733e-891j)  +/-  (1.15e-74, 3.3e-190j)
| (0.029751829552202755799 + 4.1463509056263934092e-891j)  +/-  (7.5e-73, 2.16e-188j)
| (0.04817189510171220053 + 3.595740269237643676e-892j)  +/-  (1.3e-75, 3.74e-191j)
| (0.054113415385856754492 + 4.5609257981781580307e-892j)  +/-  (2.56e-77, 7.39e-193j)
| (0.06751868584903645882 + 1.0659252404772502219e-891j)  +/-  (2.86e-80, 8.24e-196j)
| (0.04817189510171220053 - 2.2482019530339124221e-891j)  +/-  (1.62e-76, 4.68e-192j)
| (0.062946621064394508179 - 1.4818270157469675249e-891j)  +/-  (4.65e-80, 1.34e-195j)
| (0.066595874768454887376 - 8.5862560926911808703e-892j)  +/-  (6.57e-81, 1.89e-196j)
| (0.051259598007143021335 - 4.0681068103572307685e-892j)  +/-  (5.44e-78, 1.57e-193j)
| (0.065677274267781207379 + 7.9464663715356291613e-892j)  +/-  (3.95e-81, 1.14e-196j)
| (0.061147027724650481015 + 1.5809558291252693056e-891j)  +/-  (1.69e-80, 4.86e-196j)
| (0.054113415385856754492 - 1.9343547315705956834e-891j)  +/-  (2.06e-79, 5.95e-195j)
| (0.067210613600678175862 - 1.1409381732414117066e-891j)  +/-  (1.27e-81, 3.65e-197j)
| (0.056720325843991235817 - 5.0739564815832543179e-892j)  +/-  (8.4e-81, 2.42e-196j)
| (0.062946621064394508179 + 6.7345271734449095764e-892j)  +/-  (4.73e-82, 1.36e-197j)
| (0.066595874768454887376 + 1.2194755662973747213e-891j)  +/-  (2.7e-82, 7.79e-198j)
| (0.056720325843991235817 + 1.8049109883200226e-891j)  +/-  (9.59e-82, 2.76e-197j)
| (0.065677274267781207379 - 1.3020227498501908771e-891j)  +/-  (1.38e-82, 3.99e-198j)
| (0.064459003467139069588 - 7.3295761732770241028e-892j)  +/-  (4.19e-83, 1.21e-198j)
| (0.059068434595546314808 + 5.6071287159567588289e-892j)  +/-  (3.85e-83, 1.11e-198j)
| (0.067210613600678175862 + 9.2503493466681357353e-892j)  +/-  (9.52e-84, 2.76e-199j)
| (0.064459003467139069588 + 1.3892035191864222026e-891j)  +/-  (9.61e-84, 2.78e-199j)
| (0.059068434595546314808 - 1.6880075639382753537e-891j)  +/-  (9.98e-84, 2.88e-199j)
| (0.06751868584903645882 - 9.9405688273212439035e-892j)  +/-  (3.96e-84, 1.16e-199j)
| (0.061147027724650481015 - 6.1605512948816634334e-892j)  +/-  (2.74e-84, 7.37e-200j)
