Starting with polynomial:
P : 549755813888*t^39 - 203684529045504*t^37 + 33913474086076416*t^35 - 3363086180202577920*t^33 + 221963687893370142720*t^31 - 10321311487041711636480*t^29 + 349204371978244577034240*t^27 - 8755052468883131895644160*t^25 + 164157233791558723043328000*t^23 - 2307321119403575384997888000*t^21 + 24226871753737541542477824000*t^19 - 188308866813141800171077632000*t^17 + 1067083578607803534302773248000*t^15 - 4309375990531514273145815040000*t^13 + 12004690259337789760906199040000*t^11 - 22008598808785947894994698240000*t^9 + 24759673659884191381869035520000*t^7 - 15292739613457882912330874880000*t^5 + 4247983225960523031203020800000*t^3 - 335367096786357081410764800000*t
Extension levels are: 39
-------------------------------------------------
Ending with final polynomial:
P : 549755813888*t^39 - 203684529045504*t^37 + 33913474086076416*t^35 - 3363086180202577920*t^33 + 221963687893370142720*t^31 - 10321311487041711636480*t^29 + 349204371978244577034240*t^27 - 8755052468883131895644160*t^25 + 164157233791558723043328000*t^23 - 2307321119403575384997888000*t^21 + 24226871753737541542477824000*t^19 - 188308866813141800171077632000*t^17 + 1067083578607803534302773248000*t^15 - 4309375990531514273145815040000*t^13 + 12004690259337789760906199040000*t^11 - 22008598808785947894994698240000*t^9 + 24759673659884191381869035520000*t^7 - 15292739613457882912330874880000*t^5 + 4247983225960523031203020800000*t^3 - 335367096786357081410764800000*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:
| (-4.0305528146024680372 - 7.2087514128115753185e-634j)  +/-  (1.97e-246, 1.97e-246j)
| (-7.9830347727197813822 - 2.0007280070178428806e-635j)  +/-  (1.87e-248, 1.87e-248j)
| (-7.2926336708657211684 + 3.9076492714518845332e-636j)  +/-  (2.21e-247, 2.21e-247j)
| (6.7184385064440925059 - 4.1818633877698232722e-633j)  +/-  (8.4e-247, 8.4e-247j)
| (7.9830347727197813822 + 9.1128775315912642432e-636j)  +/-  (1.86e-248, 1.86e-248j)
| (1.7791625828543134931 - 1.1330006574708305512e-636j)  +/-  (6.86e-250, 6.86e-250j)
| (-3.2552672359922294375 - 2.0346896446153962178e-634j)  +/-  (3.15e-247, 3.15e-247j)
| (6.2037579977281095498 + 2.4817389712704880391e-633j)  +/-  (2.27e-246, 2.27e-246j)
| (7.2926336708657211684 - 1.5064765238058166087e-635j)  +/-  (1.88e-247, 1.88e-247j)
| (-4.4324928825930372491 + 3.3731083529237667392e-638j)  +/-  (3.83e-246, 3.83e-246j)
| (-6.7184385064440925059 + 4.3086563604699108319e-640j)  +/-  (9.5e-247, 9.5e-247j)
| (3.6387464248745363955 - 4.4892290434064157172e-638j)  +/-  (1.07e-246, 1.07e-246j)
| (-5.2769133152304264787 + 9.2114476436981176524e-648j)  +/-  (6.36e-246, 6.36e-246j)
| (-5.726965451782105154 + 2.964070266137952652e-648j)  +/-  (4.57e-246, 4.57e-246j)
| (-1.7791625828543134931 + 4.7396027058978446724e-656j)  +/-  (5.66e-250, 5.66e-250j)
| (-6.2037579977281095498 - 4.1953784065777296615e-650j)  +/-  (2.4e-246, 2.4e-246j)
| (-2.8786703113749548192 - 1.0371509730373687102e-651j)  +/-  (8.79e-248, 8.79e-248j)
| (5.726965451782105154 - 8.8712440223822116643e-657j)  +/-  (4.1e-246, 4.1e-246j)
| (-1.0628655672811787022 - 7.4129027771958602896e-676j)  +/-  (1.07e-251, 1.07e-251j)
| (2.8786703113749548192 + 2.0310595005467182215e-683j)  +/-  (9.85e-248, 9.85e-248j)
| (5.2769133152304264787 - 6.278030458760431247e-711j)  +/-  (7.2e-246, 7.2e-246j)
| (2.1415530119868800425 + 4.688455742488902203e-728j)  +/-  (4.38e-249, 4.38e-249j)
| (4.0305528146024680372 - 6.3539341356581680632e-740j)  +/-  (2.59e-246, 2.59e-246j)
| (4.8469005687435258414 + 2.4381120178310038561e-764j)  +/-  (5.04e-246, 5.04e-246j)
| (-3.6387464248745363955 + 1.0316816553062003128e-776j)  +/-  (1.01e-246, 1.01e-246j)
| (1.8005775536745200812e-788 - 1.5951333264564393865e-788j)  +/-  (9.38e-787, 9.38e-787j)
| (0.3535358469963293291 + 6.1340989831708954519e-786j)  +/-  (5.8e-254, 5.8e-254j)
| (-4.8469005687435258414 - 5.0979090028080558814e-779j)  +/-  (5.88e-246, 5.88e-246j)
| (0.70763327334857228424 + 4.8949468776101686519e-786j)  +/-  (6.32e-253, 6.32e-253j)
| (-0.70763327334857228424 + 1.9339869649727708781e-787j)  +/-  (7.22e-253, 7.22e-253j)
| (-0.3535358469963293291 - 1.2189411588324603252e-787j)  +/-  (5.8e-254, 5.8e-254j)
| (3.2552672359922294375 - 9.8123989676785680358e-780j)  +/-  (3.84e-247, 3.84e-247j)
| (1.0628655672811787022 - 2.5553968716234954367e-793j)  +/-  (1.17e-251, 1.17e-251j)
| (2.5077666938913194404 - 8.1977632900370657119e-791j)  +/-  (2.11e-248, 2.11e-248j)
| (-2.1415530119868800425 + 9.2949099995560461647e-796j)  +/-  (3.77e-249, 3.77e-249j)
| (-2.5077666938913194404 - 1.2914445207227948177e-798j)  +/-  (2.17e-248, 2.17e-248j)
| (4.4324928825930372491 - 3.5990330434221200354e-805j)  +/-  (3.82e-246, 3.82e-246j)
| (-1.4198301576857357027 + 8.1111195747954994296e-815j)  +/-  (9.96e-251, 9.96e-251j)
| (1.4198301576857357027 + 1.2341780371360595117e-816j)  +/-  (8.88e-251, 8.88e-251j)
-------------------------------------------------
The weights are:
| (1.9698729205993583361e-08 + 3.0551671109179354808e-641j)  +/-  (7.92e-79, 5.08e-201j)
| (9.4433445750631279265e-29 + 1.3211981959800566854e-651j)  +/-  (2.01e-90, 1.29e-212j)
| (2.7847875052254917614e-24 - 2.6571329826912839616e-649j)  +/-  (6.63e-89, 4.25e-211j)
| (7.5924505422064005531e-21 - 6.7865367801079686148e-648j)  +/-  (8.85e-90, 5.67e-212j)
| (9.4433445750631279265e-29 - 6.5347669200532835066e-652j)  +/-  (5.67e-93, 3.63e-215j)
| (0.0085880830293622383457 + 7.0282068390724245495e-639j)  +/-  (7.45e-72, 4.77e-194j)
| (5.3565849013735357365e-06 - 3.8016899152849174007e-639j)  +/-  (5.2e-80, 3.33e-202j)
| (5.3707014584627634225e-18 + 1.9317067294422917471e-646j)  +/-  (2.64e-89, 1.69e-211j)
| (2.7847875052254917614e-24 + 1.2119059483479370993e-649j)  +/-  (2.12e-91, 1.36e-213j)
| (6.7486463647877897353e-10 - 1.7369963843542967616e-641j)  +/-  (4.25e-85, 2.72e-207j)
| (7.5924505422064005531e-21 + 1.6204761450372291761e-647j)  +/-  (2.46e-91, 1.57e-213j)
| (3.8841182837132748212e-07 + 8.6044279481764130435e-641j)  +/-  (1.51e-85, 9.65e-208j)
| (1.9987266806237302738e-13 - 1.4708309333892467658e-643j)  +/-  (1.56e-88, 1e-210j)
| (1.486129587733259219e-15 + 1.0183094283912565506e-644j)  +/-  (8.68e-90, 5.56e-212j)
| (0.0085880830293622383457 - 3.0995228285174569889e-638j)  +/-  (7.54e-80, 4.83e-202j)
| (5.3707014584627634225e-18 - 5.08503140310280947e-646j)  +/-  (6.36e-91, 4.08e-213j)
| (5.3077421124172060332e-05 + 9.585762521119825141e-639j)  +/-  (6.58e-84, 4.21e-206j)
| (1.486129587733259219e-15 - 3.4451319805103190375e-645j)  +/-  (2.07e-93, 1.33e-215j)
| (0.064901574583169076128 - 5.399529079692862203e-638j)  +/-  (1.37e-79, 8.79e-202j)
| (5.3077421124172060332e-05 + 1.3619784012858115205e-639j)  +/-  (9.71e-88, 6.22e-210j)
| (1.9987266806237302738e-13 + 4.2944900708474214879e-644j)  +/-  (3.99e-93, 2.56e-215j)
| (0.0020938374388806516975 + 1.8001520548197781551e-638j)  +/-  (4.33e-86, 2.78e-208j)
| (1.9698729205993583361e-08 - 1.7368321877745803866e-641j)  +/-  (2.6e-91, 1.67e-213j)
| (1.4917200104489123594e-11 - 4.005873475399502396e-643j)  +/-  (6.78e-93, 4.34e-215j)
| (3.8841182837132748212e-07 - 6.1646521903037765019e-640j)  +/-  (3.71e-90, 2.37e-212j)
| (0.19940865344744050552 + 4.9458570517504447902e-638j)  +/-  (2.5e-84, 1.6e-206j)
| (0.17611902770144990074 - 3.3542311616077131412e-638j)  +/-  (1.63e-84, 1.04e-206j)
| (1.4917200104489123594e-11 + 1.6826100628833507829e-642j)  +/-  (2.4e-92, 1.54e-214j)
| (0.12124212806312441272 + 1.4695540710162984526e-638j)  +/-  (2.94e-85, 1.88e-207j)
| (0.12124212806312441272 + 6.0264717879501261306e-638j)  +/-  (1.91e-85, 1.22e-207j)
| (0.17611902770144990074 - 5.8995504546687071882e-638j)  +/-  (3.25e-85, 2.08e-207j)
| (5.3565849013735357365e-06 - 3.6433824090370104565e-640j)  +/-  (3.08e-90, 1.97e-212j)
| (0.064901574583169076128 + 4.4975944254499390755e-639j)  +/-  (7.24e-87, 4.63e-209j)
| (0.00038593816976903694594 - 4.7407684400689729391e-639j)  +/-  (5.12e-89, 3.28e-211j)
| (0.0020938374388806516975 + 2.0573817924032375578e-638j)  +/-  (1.52e-89, 9.74e-212j)
| (0.00038593816976903694594 - 1.32004523133544556e-638j)  +/-  (5.42e-90, 3.47e-212j)
| (6.7486463647877897353e-10 + 2.9288694387923971904e-642j)  +/-  (2.73e-93, 1.77e-215j)
| (0.026906241483958106987 + 4.3059064720196337411e-638j)  +/-  (5.22e-89, 3.35e-211j)
| (0.026906241483958106987 - 2.8360695963748734497e-638j)  +/-  (4.31e-89, 2.62e-211j)
