Starting with polynomial:
P : 53098072606098965203605/274877906944*t^41 - 134384010916670220577025/68719476736*t^39 + 1260488001129780170222475/137438953472*t^37 - 1817067118511761024606425/68719476736*t^35 + 14415399140193304128544305/274877906944*t^33 - 1303310059250353523950581/17179869184*t^31 + 2845254354701476002990705/34359738368*t^29 - 1195831540381779769372905/17179869184*t^27 + 6264729413044846254475965/137438953472*t^25 - 803170437569852083907175/34359738368*t^23 + 645086097476738340407985/68719476736*t^21 - 100944918383096163551175/34359738368*t^19 + 97523056742991208854525/137438953472*t^17 - 2237371072376316532425/17179869184*t^15 + 610192110648086327025/34359738368*t^13 - 29933952597830650005/17179869184*t^11 + 32281713585895799025/274877906944*t^9 - 348782019535488825/68719476736*t^7 + 17315419409563275/137438953472*t^5 - 101259762629025/68719476736*t^3 + 1412926920405/274877906944*t
Extension levels are: 41
-------------------------------------------------
Ending with final polynomial:
P : 53098072606098965203605/274877906944*t^41 - 134384010916670220577025/68719476736*t^39 + 1260488001129780170222475/137438953472*t^37 - 1817067118511761024606425/68719476736*t^35 + 14415399140193304128544305/274877906944*t^33 - 1303310059250353523950581/17179869184*t^31 + 2845254354701476002990705/34359738368*t^29 - 1195831540381779769372905/17179869184*t^27 + 6264729413044846254475965/137438953472*t^25 - 803170437569852083907175/34359738368*t^23 + 645086097476738340407985/68719476736*t^21 - 100944918383096163551175/34359738368*t^19 + 97523056742991208854525/137438953472*t^17 - 2237371072376316532425/17179869184*t^15 + 610192110648086327025/34359738368*t^13 - 29933952597830650005/17179869184*t^11 + 32281713585895799025/274877906944*t^9 - 348782019535488825/68719476736*t^7 + 17315419409563275/137438953472*t^5 - 101259762629025/68719476736*t^3 + 1412926920405/274877906944*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:
| (0.97833867356108338447 - 4.6590472279422097482e-866j)  +/-  (1.53e-241, 1.53e-241j)
| (-0.99832158857477144152 - 1.8559275262709199975e-876j)  +/-  (4.49e-242, 4.49e-242j)
| (-0.9599068917303462261 + 1.8455487537985575321e-879j)  +/-  (1.41e-241, 1.41e-241j)
| (0.99832158857477144152 - 5.1116728452018591128e-899j)  +/-  (3.81e-242, 3.81e-242j)
| (0.93597698749785382568 + 8.7064436144473868993e-926j)  +/-  (1.01e-241, 1.01e-241j)
| (0.9599068917303462261 + 3.3969383305863830833e-936j)  +/-  (1.26e-241, 1.26e-241j)
| (-0.87220151169244140883 + 1.3601856455310250095e-944j)  +/-  (2.43e-242, 2.43e-242j)
| (-0.90668594475810117296 - 4.7821993189462703554e-944j)  +/-  (5.35e-242, 5.35e-242j)
| (-0.97833867356108338447 + 1.5315603825367486347e-942j)  +/-  (1.53e-241, 1.53e-241j)
| (0.78847114504740937274 - 1.1967144275664857692e-948j)  +/-  (2.08e-243, 2.08e-243j)
| (0.90668594475810117296 + 1.1048279064499375287e-944j)  +/-  (5.05e-242, 5.05e-242j)
| (-0.99116710969901630825 - 6.0491305830117483667e-952j)  +/-  (1.16e-241, 1.16e-241j)
| (-0.93597698749785382568 - 8.9030271359154472995e-955j)  +/-  (9.49e-242, 9.49e-242j)
| (-0.78847114504740937274 + 1.5176442475990298374e-955j)  +/-  (2.19e-243, 2.19e-243j)
| (0.99116710969901630825 - 9.608974055851938271e-952j)  +/-  (1.05e-241, 1.05e-241j)
| (0.87220151169244140883 + 9.7421949116215805998e-963j)  +/-  (2.16e-242, 2.16e-242j)
| (0.83272120040136133124 - 6.3835769924259082733e-974j)  +/-  (7.25e-243, 7.25e-243j)
| (-0.83272120040136133124 - 9.4912754577994328151e-978j)  +/-  (7.12e-243, 7.12e-243j)
| (-0.73970480306992618106 - 8.1016873800903798629e-982j)  +/-  (4.61e-244, 4.61e-244j)
| (-0.22513960563342277561 + 1.0350618018386055474e-989j)  +/-  (5.02e-252, 5.02e-252j)
| (0.50541659919940603271 - 1.0300781913890045937e-983j)  +/-  (2.01e-247, 2.01e-247j)
| (0.73970480306992618106 - 7.2682868375363330619e-982j)  +/-  (4.75e-244, 4.75e-244j)
| (0.15081335486399216357 + 8.5097063866293568602e-992j)  +/-  (2.8e-253, 2.8e-253j)
| (-0.56922094161021586965 + 4.1710702510087435811e-987j)  +/-  (1.79e-246, 1.79e-246j)
| (-0.62976483907219632049 + 7.2067481643924514155e-986j)  +/-  (1.52e-245, 1.52e-245j)
| (0.075623258989162996924 - 9.2798039919385875619e-993j)  +/-  (1.09e-254, 1.09e-254j)
| (0.68670150203495128958 + 4.6142357777395781083e-985j)  +/-  (8.85e-245, 8.85e-245j)
| (0.43871727705140708852 + 4.5115197375215301823e-991j)  +/-  (1.79e-248, 1.79e-248j)
| (-0.15081335486399216357 - 5.9251349915770403036e-995j)  +/-  (2.8e-253, 2.8e-253j)
| (-0.68670150203495128958 - 8.4686764738487658673e-990j)  +/-  (9.33e-245, 9.33e-245j)
| (-0.075623258989162996924 - 1.9173992768949894465e-995j)  +/-  (1.26e-254, 1.26e-254j)
| (0.36950502264048144143 - 1.3861210815711375134e-992j)  +/-  (1.51e-249, 1.51e-249j)
| (0.62976483907219632049 + 2.3356811170750908472e-991j)  +/-  (1.56e-245, 1.56e-245j)
| (1.3086252794241481923e-998 + 7.4261501358593166029e-999j)  +/-  (6.17e-997, 6.17e-997j)
| (-0.43871727705140708852 + 6.1478352202853840667e-1000j)  +/-  (2.24e-248, 2.24e-248j)
| (-0.36950502264048144143 + 5.0856881139187741887e-1000j)  +/-  (1.28e-249, 1.28e-249j)
| (0.22513960563342277561 + 1.4900310121943210826e-997j)  +/-  (4.3e-252, 4.3e-252j)
| (0.56922094161021586965 + 1.1293831559639291695e-996j)  +/-  (1.65e-246, 1.65e-246j)
| (0.29817627734182486592 - 3.5947775814476306996e-1000j)  +/-  (9.02e-251, 9.02e-251j)
| (-0.29817627734182486592 + 7.9680021105541017719e-1004j)  +/-  (9.82e-251, 9.82e-251j)
| (-0.50541659919940603271 + 1.2989125745025703069e-1004j)  +/-  (1.93e-247, 1.93e-247j)
-------------------------------------------------
The weights are:
| (0.015644938407818588531 + 1.6640811604329860911e-866j)  +/-  (1.35e-74, 2.43e-191j)
| (0.004306140358164887684 + 5.4123408796063910349e-869j)  +/-  (3.77e-75, 6.81e-192j)
| (0.021201063368779553076 - 5.9280765414613964567e-868j)  +/-  (3.35e-75, 6.04e-192j)
| (0.004306140358164887684 - 5.3537532460694905181e-867j)  +/-  (2.01e-75, 3.63e-192j)
| (0.026635899207110445468 + 3.8182977328400761952e-866j)  +/-  (1.42e-75, 2.56e-192j)
| (0.021201063368779553076 - 6.2338346970576874565e-866j)  +/-  (2.46e-75, 4.44e-192j)
| (0.037017716703507988435 + 1.4316492977803248623e-867j)  +/-  (1.25e-76, 2.25e-193j)
| (0.031918211731699281787 - 1.1253990920814342576e-867j)  +/-  (1.47e-76, 2.65e-193j)
| (0.015644938407818588531 + 3.7252184932061370964e-868j)  +/-  (8.73e-77, 1.58e-193j)
| (0.046552648369014342061 + 1.9676075253471645934e-866j)  +/-  (7.23e-79, 1.31e-195j)
| (0.031918211731699281787 - 2.9606757937958581001e-866j)  +/-  (1.32e-77, 2.39e-194j)
| (0.0099999387739059453385 - 1.895561468583414642e-868j)  +/-  (4.6e-77, 8.3e-194j)
| (0.026635899207110445468 + 8.4494701043112445706e-868j)  +/-  (2.73e-77, 4.92e-194j)
| (0.046552648369014342061 + 2.114459483730245521e-867j)  +/-  (6.03e-80, 1.09e-196j)
| (0.0099999387739059453385 + 2.910190541953321295e-866j)  +/-  (4.8e-78, 8.67e-195j)
| (0.037017716703507988435 + 2.496132846387883531e-866j)  +/-  (2.69e-79, 4.86e-196j)
| (0.041905195195909689429 - 2.1911912976073097547e-866j)  +/-  (7.12e-80, 1.29e-196j)
| (0.041905195195909689429 - 1.7618177305762202585e-867j)  +/-  (3e-80, 5.42e-197j)
| (0.050933454294617494781 - 2.4884531657808541749e-867j)  +/-  (7.88e-82, 1.42e-198j)
| (0.073751882027223469939 - 6.1893353796383852878e-867j)  +/-  (2.56e-85, 4.63e-202j)
| (0.065314196453527410436 - 1.3126638472827355946e-866j)  +/-  (9.43e-85, 1.7e-201j)
| (0.050933454294617494781 - 1.7915607376484792631e-866j)  +/-  (9.95e-83, 1.8e-199j)
| (0.074829623176221551891 + 9.1992137658752951393e-867j)  +/-  (8.66e-86, 1.56e-202j)
| (0.062233542580966316472 + 3.7310013848846436599e-867j)  +/-  (5.63e-85, 1.02e-201j)
| (0.058796420949871944991 - 3.2972656985831548966e-867j)  +/-  (1.81e-84, 3.26e-201j)
| (0.075478747092715824027 - 8.5429384506493263549e-867j)  +/-  (1.56e-86, 2.81e-203j)
| (0.05502251924257874188 + 1.6459507183025520777e-866j)  +/-  (3.48e-85, 6.29e-202j)
| (0.068020736760876766736 + 1.2226475121143066478e-866j)  +/-  (1.41e-86, 2.55e-203j)
| (0.074829623176221551891 + 6.7418577050587533971e-867j)  +/-  (1.91e-87, 3.46e-204j)
| (0.05502251924257874188 + 2.8829359123412156944e-867j)  +/-  (7.93e-86, 1.43e-202j)
| (0.075478747092715824027 - 7.3170026229564628701e-867j)  +/-  (1.2e-87, 2.16e-204j)
| (0.070337660620817497482 - 1.1394863825144002663e-866j)  +/-  (5.34e-88, 9.64e-205j)
| (0.058796420949871944991 - 1.5211539217784112977e-866j)  +/-  (2.43e-87, 4.4e-204j)
| (0.075695535647298372319 + 7.9165709690191756505e-867j)  +/-  (3.84e-88, 6.94e-205j)
| (0.068020736760876766736 + 4.6558977260896800811e-867j)  +/-  (4.48e-89, 8.09e-206j)
| (0.070337660620817497482 - 5.1471669623681858789e-867j)  +/-  (3.54e-89, 6.39e-206j)
| (0.073751882027223469939 - 9.8894581920593650833e-867j)  +/-  (3.51e-89, 6.34e-206j)
| (0.062233542580966316472 + 1.411316747701567349e-866j)  +/-  (4.16e-89, 7.51e-206j)
| (0.072251696861023073396 + 1.0618996112069828188e-866j)  +/-  (2.3e-89, 4.14e-206j)
| (0.072251696861023073396 + 5.6580942003214842369e-867j)  +/-  (4.17e-90, 7.63e-207j)
| (0.065314196453527410436 - 4.1838955579008482875e-867j)  +/-  (2.84e-90, 5e-207j)
