Starting with polynomial:
P : t^41 - 820*t^39 + 303810*t^37 - 67445820*t^35 + 10032565725*t^33 - 1059438940560*t^31 + 82106517893400*t^29 - 4762178037817200*t^27 + 208940561409229650*t^25 - 6964685380307655000*t^23 + 176206540121783671500*t^21 - 3363943038688597365000*t^19 + 47936188301312512451250*t^17 - 501486277613730899490000*t^15 + 3761147082102981746175000*t^13 - 19557964826935505080110000*t^11 + 67230504092590798712878125*t^9 - 142370479254898161980212500*t^7 + 166098892464047855643581250*t^5 - 87420469717919924022937500*t^3 + 13113070457687988603440625*t
Extension levels are: 41
-------------------------------------------------
Ending with final polynomial:
P : t^41 - 820*t^39 + 303810*t^37 - 67445820*t^35 + 10032565725*t^33 - 1059438940560*t^31 + 82106517893400*t^29 - 4762178037817200*t^27 + 208940561409229650*t^25 - 6964685380307655000*t^23 + 176206540121783671500*t^21 - 3363943038688597365000*t^19 + 47936188301312512451250*t^17 - 501486277613730899490000*t^15 + 3761147082102981746175000*t^13 - 19557964826935505080110000*t^11 + 67230504092590798712878125*t^9 - 142370479254898161980212500*t^7 + 166098892464047855643581250*t^5 - 87420469717919924022937500*t^3 + 13113070457687988603440625*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:
| (8.45609908326939009 - 1.8613912405639560765e-710j)  +/-  (1.66e-245, 1.66e-245j)
| (10.647536786319334291 - 4.7943984439781603777e-723j)  +/-  (7.15e-247, 7.15e-247j)
| (-10.647536786319334291 - 1.21674194570727169e-733j)  +/-  (6.06e-247, 6.06e-247j)
| (6.0863491648784754603 - 8.5996584221950500969e-743j)  +/-  (1.11e-245, 1.11e-245j)
| (-9.8434332491579956481 + 1.3676847332322936895e-747j)  +/-  (3.4e-246, 3.4e-246j)
| (-11.614937254337464376 + 8.4586845017957231768e-752j)  +/-  (5.35e-248, 5.35e-248j)
| (-3.4554322177809930379 + 5.8545651912399791723e-753j)  +/-  (4.89e-248, 4.89e-248j)
| (-7.2260226637327884096 - 4.0904830536023801798e-750j)  +/-  (2.62e-245, 2.62e-245j)
| (-2.4531593459070483465 - 2.2015007599055825208e-767j)  +/-  (1.25e-249, 1.25e-249j)
| (9.1230699079844733565 - 1.7366998818729736938e-762j)  +/-  (9.07e-246, 9.07e-246j)
| (2.951937016381190549 + 2.3351104562881488463e-776j)  +/-  (7.76e-249, 7.76e-249j)
| (6.6473084707471885927 - 3.8760852001038255643e-780j)  +/-  (1.84e-245, 1.84e-245j)
| (4.4808783315940069013 - 1.1074763369394465713e-789j)  +/-  (8.15e-247, 8.15e-247j)
| (-1.9581707119772914057 + 1.6033006824274559699e-793j)  +/-  (1.43e-250, 1.43e-250j)
| (-9.1230699079844733565 + 8.7616140193621093062e-788j)  +/-  (1.06e-245, 1.06e-245j)
| (-6.6473084707471885927 + 1.2372647157970633497e-788j)  +/-  (1.81e-245, 1.81e-245j)
| (11.614937254337464376 + 2.6884720382401984959e-788j)  +/-  (7.11e-248, 7.11e-248j)
| (9.8434332491579956481 - 8.7093672440471057983e-793j)  +/-  (3.23e-246, 3.23e-246j)
| (-5.5398844404581244029 + 1.0042310697465896441e-796j)  +/-  (5.41e-246, 5.41e-246j)
| (-8.45609908326939009 + 7.9165162906646881087e-799j)  +/-  (1.6e-245, 1.6e-245j)
| (-5.0053966834041254145 - 2.8066420135298532019e-804j)  +/-  (2.31e-246, 2.31e-246j)
| (2.4531593459070483465 + 1.1396011194349447615e-815j)  +/-  (1.22e-249, 1.22e-249j)
| (5.5398844404581244029 - 2.1979033760227465309e-811j)  +/-  (6.49e-246, 6.49e-246j)
| (1.9581707119772914057 - 6.7530928002309090848e-830j)  +/-  (1.72e-250, 1.72e-250j)
| (-3.9646840280332662892 - 2.6321320413226893023e-824j)  +/-  (2.27e-247, 2.27e-247j)
| (5.0053966834041254145 - 1.7567821787333012191e-830j)  +/-  (2.42e-246, 2.42e-246j)
| (-0.97623876718004938104 - 4.337331939616050087e-851j)  +/-  (1.39e-252, 1.39e-252j)
| (3.9646840280332662892 - 5.1113353570201641873e-845j)  +/-  (2.14e-247, 2.14e-247j)
| (7.2260226637327884096 + 2.5268115557772164224e-858j)  +/-  (2.24e-245, 2.24e-245j)
| (-6.0863491648784754603 - 1.8863546079059408325e-870j)  +/-  (1.03e-245, 1.03e-245j)
| (-4.4808783315940069013 + 1.3818004473502143051e-879j)  +/-  (7.51e-247, 7.51e-247j)
| (3.4554322177809930379 - 4.3786085064072552643e-888j)  +/-  (4.24e-248, 4.24e-248j)
| (0.97623876718004938104 - 4.554136215355213673e-899j)  +/-  (9.51e-253, 9.51e-253j)
| (3.8399019850675975489e-897 + 2.0554132553787184356e-897j)  +/-  (1.79e-895, 1.79e-895j)
| (-2.951937016381190549 + 2.5562917633770663022e-891j)  +/-  (8.01e-249, 8.01e-249j)
| (-7.8268820040538693475 - 3.0115073462082546703e-905j)  +/-  (2.21e-245, 2.21e-245j)
| (7.8268820040538693475 - 9.8438426725087341475e-935j)  +/-  (2.19e-245, 2.19e-245j)
| (0.48776856931943457461 + 5.6950075068566143713e-964j)  +/-  (7.76e-254, 7.76e-254j)
| (1.4661254572959666344 - 5.3738998899094226463e-961j)  +/-  (1.51e-251, 1.51e-251j)
| (-1.4661254572959666344 - 6.0427786684827855872e-962j)  +/-  (1.73e-251, 1.73e-251j)
| (-0.48776856931943457461 + 2.800271071136656204e-961j)  +/-  (5.54e-254, 5.54e-254j)
-------------------------------------------------
The weights are:
| (7.6559822919668644893e-17 + 6.0252996981344972378e-726j)  +/-  (3.12e-85, 2.53e-208j)
| (8.3085589387825795953e-26 + 2.1422583742258037516e-731j)  +/-  (2.73e-89, 2.22e-212j)
| (8.3085589387825795953e-26 - 2.4574514521742565261e-732j)  +/-  (1.53e-90, 1.24e-213j)
| (1.9947947567573446943e-09 + 3.0696207222372613442e-723j)  +/-  (3.1e-81, 2.52e-204j)
| (2.7468912285222892516e-22 + 1.4750911803017640082e-730j)  +/-  (1.73e-89, 1.41e-212j)
| (2.2578639565830996743e-30 + 1.2193186432388899538e-734j)  +/-  (2.14e-92, 1.74e-215j)
| (0.00051580144434318631277 - 3.1053589421026728024e-721j)  +/-  (3.01e-75, 2.44e-198j)
| (1.0778183949358886362e-12 + 1.0782168151544908465e-725j)  +/-  (8.61e-86, 6.99e-209j)
| (0.0097779027382082639586 - 1.4762698581593043476e-720j)  +/-  (1.05e-70, 8.51e-194j)
| (2.3263841455871582916e-19 + 1.177801230500952872e-727j)  +/-  (2.05e-89, 1.67e-212j)
| (0.0025616424286497854431 + 1.4976356410872432345e-720j)  +/-  (3.14e-75, 2.55e-198j)
| (5.769853428092129242e-11 - 6.8396238972288270218e-724j)  +/-  (3.84e-85, 3.12e-208j)
| (9.0586086224329800688e-06 - 1.2331264784436553631e-721j)  +/-  (1.09e-80, 8.84e-204j)
| (0.028937211747934410842 + 2.6603430521177214496e-720j)  +/-  (4.19e-71, 3.4e-194j)
| (2.3263841455871582916e-19 - 4.468692794571224534e-729j)  +/-  (3.09e-90, 2.51e-213j)
| (5.769853428092129242e-11 - 8.1911631227881232735e-725j)  +/-  (1.65e-86, 1.34e-209j)
| (2.2578639565830996743e-30 - 7.7474651977167857726e-734j)  +/-  (1.67e-95, 1.36e-218j)
| (2.7468912285222892516e-22 - 1.9457084969806774468e-729j)  +/-  (7.73e-92, 6.28e-215j)
| (4.6673477081073025676e-08 - 2.5140260965416576341e-723j)  +/-  (8.23e-86, 6.68e-209j)
| (7.6559822919668644893e-17 + 8.4263312408291275533e-728j)  +/-  (2.61e-90, 2.12e-213j)
| (7.6581860779823375197e-07 + 1.0587849619118550827e-722j)  +/-  (4.84e-85, 3.93e-208j)
| (0.0097779027382082639586 - 2.6828537514087968318e-720j)  +/-  (2.82e-80, 2.29e-203j)
| (4.6673477081073025676e-08 - 1.2065733197024913198e-722j)  +/-  (8.02e-87, 6.51e-210j)
| (0.028937211747934410842 + 4.2637481839700198604e-720j)  +/-  (1.09e-79, 8.86e-203j)
| (7.8947193195046351929e-05 + 1.1650846883764833801e-721j)  +/-  (1.57e-84, 1.27e-207j)
| (7.6581860779823375197e-07 + 4.130413936348300926e-722j)  +/-  (3.24e-86, 2.63e-209j)
| (0.12114891701151043663 + 6.0100563787146649845e-720j)  +/-  (5.38e-81, 4.37e-204j)
| (7.8947193195046351929e-05 + 3.2219832820289542743e-721j)  +/-  (4.82e-85, 3.92e-208j)
| (1.0778183949358886362e-12 + 1.3746078777193029068e-724j)  +/-  (2.82e-90, 2.29e-213j)
| (1.9947947567573446943e-09 + 5.0020693434059570873e-724j)  +/-  (4.2e-89, 3.42e-212j)
| (9.0586086224329800688e-06 - 3.789099887364506242e-722j)  +/-  (4.72e-87, 3.83e-210j)
| (0.00051580144434318631277 - 7.3969294965702645391e-721j)  +/-  (9.38e-86, 7.61e-209j)
| (0.12114891701151043663 + 7.5788691056631656919e-720j)  +/-  (3.37e-84, 2.69e-207j)
| (0.19454502775360049319 + 8.4952884704479119434e-720j)  +/-  (1.77e-84, 1.4e-207j)
| (0.0025616424286497854431 + 7.2258092573398135141e-721j)  +/-  (1.02e-85, 8.3e-209j)
| (1.2203348742027845996e-14 - 1.1049527797506983635e-726j)  +/-  (4.62e-92, 3.76e-215j)
| (1.2203348742027845996e-14 - 2.8594146296056361345e-725j)  +/-  (3.62e-92, 2.93e-215j)
| (0.17284953105060153903 - 8.4977683723305914031e-720j)  +/-  (6.92e-85, 5.41e-208j)
| (0.066847659354466382969 - 6.0242875243147807775e-720j)  +/-  (2.68e-85, 2.19e-208j)
| (0.066847659354466382969 - 4.2439687529830573979e-720j)  +/-  (9.77e-86, 8.65e-209j)
| (0.17284953105060153903 - 7.570888753270068211e-720j)  +/-  (2.7e-85, 1.84e-208j)
