Starting with polynomial:
P : t^39 - 741*t^37 + 246753*t^35 - 48939345*t^33 + 6459993540*t^31 - 600779399220*t^29 + 40652739347220*t^27 - 2038444501553460*t^25 + 76441668808254750*t^23 - 2148860245387605750*t^21 + 45126065153139720750*t^19 - 701505194653353840750*t^17 + 7950392206071343528500*t^15 - 64214706279807005422500*t^13 + 357767649273210458782500*t^11 - 1311814714001771682202500*t^9 + 2951583106503986284955625*t^7 - 3646073249210806587298125*t^5 + 2025596249561559215165625*t^3 - 319830986772877770815625*t
Extension levels are: 39
-------------------------------------------------
Ending with final polynomial:
P : t^39 - 741*t^37 + 246753*t^35 - 48939345*t^33 + 6459993540*t^31 - 600779399220*t^29 + 40652739347220*t^27 - 2038444501553460*t^25 + 76441668808254750*t^23 - 2148860245387605750*t^21 + 45126065153139720750*t^19 - 701505194653353840750*t^17 + 7950392206071343528500*t^15 - 64214706279807005422500*t^13 + 357767649273210458782500*t^11 - 1311814714001771682202500*t^9 + 2951583106503986284955625*t^7 - 3646073249210806587298125*t^5 + 2025596249561559215165625*t^3 - 319830986772877770815625*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
Positive weights:   39 out of 39
Indefinite weights: 0 out of 39
Negative weights:   0 out of 39
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (-6.2684915496852881528 + 1.3660114466370892548e-542j)  +/-  (5.89e-246, 5.89e-246j)
| (8.0991522131524126325 + 1.5629815284786918115e-552j)  +/-  (6.3e-246, 6.3e-246j)
| (11.289716044476333204 - 2.2753338581138549544e-564j)  +/-  (3.04e-248, 3.04e-248j)
| (2.5161158543393155629 + 9.0004837613867903619e-574j)  +/-  (1.19e-249, 1.19e-249j)
| (-0.49997518960726837551 + 3.3382818235030822051e-591j)  +/-  (6.32e-254, 6.32e-254j)
| (9.501306853782876159 + 4.0013016073271526359e-583j)  +/-  (1.32e-246, 1.32e-246j)
| (7.4626823778660405121 - 1.3409051539111854229e-608j)  +/-  (8.68e-246, 8.68e-246j)
| (-10.313341442756992673 - 3.4588815425531923205e-626j)  +/-  (3.01e-247, 3.01e-247j)
| (-3.0286133140927971477 + 8.7756898259738166068e-633j)  +/-  (6.7e-249, 6.7e-249j)
| (10.313341442756992673 - 4.3422885066584300436e-635j)  +/-  (3.27e-247, 3.27e-247j)
| (-11.289716044476333204 - 1.2508156619684760463e-650j)  +/-  (2.74e-248, 2.74e-248j)
| (5.145964544094181794 - 2.4785265036197812034e-664j)  +/-  (1.28e-246, 1.28e-246j)
| (-7.4626823778660405121 - 1.9914813262411812105e-677j)  +/-  (8.98e-246, 8.98e-246j)
| (-8.7734386980676491068 + 3.6890712982452446026e-684j)  +/-  (3.9e-246, 3.9e-246j)
| (-5.145964544094181794 + 6.9055145678735417346e-687j)  +/-  (1.24e-246, 1.24e-246j)
| (-9.501306853782876159 + 3.9971699721656475713e-696j)  +/-  (1.32e-246, 1.32e-246j)
| (6.2684915496852881528 - 7.7974612741891173967e-716j)  +/-  (5.54e-246, 5.54e-246j)
| (-4.6036430742889894854 + 1.2760872152660518118e-733j)  +/-  (6.56e-247, 6.56e-247j)
| (4.6036430742889894854 - 1.2560249537643341172e-736j)  +/-  (5.86e-247, 5.86e-247j)
| (-5.7000624542718612359 - 2.6856962147778483479e-746j)  +/-  (3.4e-246, 3.4e-246j)
| (6.8545525197909621489 - 4.0820652113625700241e-746j)  +/-  (8.37e-246, 8.37e-246j)
| (2.0079430652654975667 + 1.8107033100726841805e-766j)  +/-  (1.26e-250, 1.26e-250j)
| (-4.0710545959472416128 + 1.2181914494458392906e-761j)  +/-  (1.72e-247, 1.72e-247j)
| (-2.0079430652654975667 - 8.7871005130235010884e-766j)  +/-  (1.32e-250, 1.32e-250j)
| (-3.5465176697686418438 + 3.5947044083170868864e-762j)  +/-  (3.81e-248, 3.81e-248j)
| (-8.0991522131524126325 - 6.5386232196895482168e-762j)  +/-  (5.9e-246, 5.9e-246j)
| (0.49997518960726837551 - 3.0577792108184510666e-773j)  +/-  (7.24e-254, 7.24e-254j)
| (5.7000624542718612359 + 1.7710186401642859789e-759j)  +/-  (3.59e-246, 3.59e-246j)
| (-2.5161158543393155629 + 5.4271816194585656507e-777j)  +/-  (1.03e-249, 1.03e-249j)
| (-1.0007445723560185484 + 3.3743302300743856367e-780j)  +/-  (7.97e-253, 7.97e-253j)
| (-1.5031189002284162687 + 2.7217755758997760283e-777j)  +/-  (1.47e-251, 1.47e-251j)
| (3.0286133140927971477 + 1.2980835751664838231e-771j)  +/-  (7.67e-249, 7.67e-249j)
| (8.7734386980676491068 - 8.0987066792799228882e-774j)  +/-  (3.62e-246, 3.62e-246j)
| (4.0710545959472416128 + 5.4158431060483458529e-780j)  +/-  (1.63e-247, 1.63e-247j)
| (-6.8545525197909621489 + 3.7730071070410656242e-784j)  +/-  (8.42e-246, 8.42e-246j)
| (-2.9910876504589326801e-800 - 1.4425452191133590633e-800j)  +/-  (1.3e-798, 1.3e-798j)
| (1.5031189002284162687 + 8.5194374197000204766e-792j)  +/-  (1.19e-251, 1.19e-251j)
| (1.0007445723560185484 + 7.9750595308752634063e-793j)  +/-  (7.97e-253, 7.97e-253j)
| (3.5465176697686418438 - 3.543512501673707893e-788j)  +/-  (3.92e-248, 3.92e-248j)
-------------------------------------------------
The weights are:
| (6.7486463647877897353e-10 + 2.8893759858889710763e-551j)  +/-  (5.71e-84, 7.47e-206j)
| (1.486129587733259219e-15 - 9.5215020056089366892e-556j)  +/-  (1.62e-88, 2.13e-210j)
| (9.4433445750631279265e-29 - 1.9640177713354605595e-562j)  +/-  (2.12e-94, 2.77e-216j)
| (0.0085880830293622383457 - 3.7435913441692920998e-549j)  +/-  (4.35e-72, 5.7e-194j)
| (0.17611902770144990074 - 2.5816756891497420874e-548j)  +/-  (4.35e-72, 5.7e-194j)
| (7.5924505422064005531e-21 - 1.9607739053765608935e-558j)  +/-  (1.48e-91, 1.94e-213j)
| (1.9987266806237302738e-13 + 1.1553982646561564921e-554j)  +/-  (6.38e-88, 8.35e-210j)
| (2.7847875052254917614e-24 - 1.4640513040815570289e-559j)  +/-  (5.71e-96, 7.47e-218j)
| (0.0020938374388806516975 + 5.0119354190921689066e-549j)  +/-  (7.93e-79, 1.04e-200j)
| (2.7847875052254917614e-24 + 3.5712986395759465166e-560j)  +/-  (1.87e-93, 2.44e-215j)
| (9.4433445750631279265e-29 + 6.8677733456321848039e-562j)  +/-  (1.18e-97, 1.54e-219j)
| (3.8841182837132748212e-07 + 1.9375533783080614084e-551j)  +/-  (5.1e-86, 6.67e-208j)
| (1.9987266806237302738e-13 - 1.3285125084820217982e-553j)  +/-  (5.82e-92, 7.61e-214j)
| (5.3707014584627634225e-18 - 3.2830659962472568283e-556j)  +/-  (2.59e-94, 3.39e-216j)
| (3.8841182837132748212e-07 + 1.9702080979683182696e-550j)  +/-  (1.33e-88, 1.74e-210j)
| (7.5924505422064005531e-21 + 9.5647311380378221052e-558j)  +/-  (1.94e-95, 2.53e-217j)
| (6.7486463647877897353e-10 + 7.3532269370925859175e-553j)  +/-  (2.7e-91, 3.53e-213j)
| (5.3565849013735357365e-06 - 4.9332367477658619716e-550j)  +/-  (3.98e-88, 5.21e-210j)
| (5.3565849013735357365e-06 - 7.5542586275379219306e-551j)  +/-  (5e-89, 6.54e-211j)
| (1.9698729205993583361e-08 - 8.7620450103963204436e-551j)  +/-  (5.86e-90, 7.67e-212j)
| (1.4917200104489123594e-11 - 1.0444117394035750944e-553j)  +/-  (3.15e-92, 4.12e-214j)
| (0.026906241483958106987 + 7.0330856064093990392e-549j)  +/-  (1.73e-83, 2.27e-205j)
| (5.3077421124172060332e-05 + 1.1765249930581254479e-549j)  +/-  (6.15e-88, 8.04e-210j)
| (0.026906241483958106987 + 1.3662295682269795251e-548j)  +/-  (7.09e-85, 9.28e-207j)
| (0.00038593816976903694594 - 2.5611651713024280366e-549j)  +/-  (2.05e-87, 2.68e-209j)
| (1.486129587733259219e-15 + 7.4727966592830286155e-555j)  +/-  (8.48e-95, 1.11e-216j)
| (0.17611902770144990074 - 2.2002676563101652197e-548j)  +/-  (5.72e-85, 7.47e-207j)
| (1.9698729205993583361e-08 - 4.1614060625776219646e-552j)  +/-  (2.8e-92, 3.66e-214j)
| (0.0085880830293622383457 - 8.7640425452102954637e-549j)  +/-  (1.18e-86, 1.54e-208j)
| (0.12124212806312441272 + 2.3456571966191106038e-548j)  +/-  (5.7e-85, 7.45e-207j)
| (0.064901574583169076128 - 1.8971139740449835189e-548j)  +/-  (1.66e-85, 2.17e-207j)
| (0.0020938374388806516975 + 1.7465717253314279341e-549j)  +/-  (7.59e-90, 9.91e-212j)
| (5.3707014584627634225e-18 + 5.4673214605873204152e-557j)  +/-  (1.81e-97, 2.36e-219j)
| (5.3077421124172060332e-05 + 2.5004380853171489986e-550j)  +/-  (1.72e-91, 2.26e-213j)
| (1.4917200104489123594e-11 + 2.338640855127325263e-552j)  +/-  (2.92e-94, 3.92e-216j)
| (0.19940865344744050552 + 2.5279683360239403573e-548j)  +/-  (4.19e-88, 5.68e-210j)
| (0.064901574583169076128 - 1.1632666231897701401e-548j)  +/-  (1.25e-89, 1.69e-211j)
| (0.12124212806312441272 + 1.6998111493277599351e-548j)  +/-  (2.11e-89, 2.9e-211j)
| (0.00038593816976903694594 - 7.1028203260593484194e-550j)  +/-  (3.74e-91, 4.85e-213j)
