Starting with polynomial:
P : 414847067813984717066925/549755813888*t^43 - 4407140026306214111899215/549755813888*t^41 + 10885104884250287866739025/274877906944*t^39 - 33192850696417544482525175/274877906944*t^37 + 139914168125405598894694725/549755813888*t^35 - 216230987102899561928164575/549755813888*t^33 + 31713878108425269082797471/68719476736*t^31 - 28859008454829256601762865/68719476736*t^29 + 82512376286342804086730445/274877906944*t^27 - 46637430074889411005543295/274877906944*t^25 + 10441215688408077090793275/137438953472*t^23 - 3694584012821319585973005/137438953472*t^21 + 2052546673789621992207225/274877906944*t^19 - 442604642141267794032075/274877906944*t^17 + 18218593017921434621175/68719476736*t^15 - 2237371072376316532425/68719476736*t^13 + 1586499487685024450265/549755813888*t^11 - 96845140757687397075/549755813888*t^9 + 1898924328582105825/274877906944*t^7 - 42832879592077575/274877906944*t^5 + 911337863661225/549755813888*t^3 - 2893136075115/549755813888*t
Extension levels are: 43
-------------------------------------------------
Ending with final polynomial:
P : 414847067813984717066925/549755813888*t^43 - 4407140026306214111899215/549755813888*t^41 + 10885104884250287866739025/274877906944*t^39 - 33192850696417544482525175/274877906944*t^37 + 139914168125405598894694725/549755813888*t^35 - 216230987102899561928164575/549755813888*t^33 + 31713878108425269082797471/68719476736*t^31 - 28859008454829256601762865/68719476736*t^29 + 82512376286342804086730445/274877906944*t^27 - 46637430074889411005543295/274877906944*t^25 + 10441215688408077090793275/137438953472*t^23 - 3694584012821319585973005/137438953472*t^21 + 2052546673789621992207225/274877906944*t^19 - 442604642141267794032075/274877906944*t^17 + 18218593017921434621175/68719476736*t^15 - 2237371072376316532425/68719476736*t^13 + 1586499487685024450265/549755813888*t^11 - 96845140757687397075/549755813888*t^9 + 1898924328582105825/274877906944*t^7 - 42832879592077575/274877906944*t^5 + 911337863661225/549755813888*t^3 - 2893136075115/549755813888*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:
| (-0.99847233224250771352 - 3.2872507066833181105e-844j)  +/-  (2.03e-241, 2.03e-241j)
| (0.96348661301407999341 + 2.2958469903877178815e-842j)  +/-  (7.01e-241, 7.01e-241j)
| (-0.88345376521861686334 + 1.1402874753456021822e-867j)  +/-  (1.19e-241, 1.19e-241j)
| (0.99195955759324414642 - 2.4853159148899972172e-864j)  +/-  (5.5e-241, 5.5e-241j)
| (0.91494790720613872946 + 1.7787258079344620004e-880j)  +/-  (2.88e-241, 2.88e-241j)
| (0.80683596413693863528 + 2.0063189050177382424e-889j)  +/-  (1.59e-242, 1.59e-242j)
| (-0.35328261286430380665 + 9.0248194887237463004e-903j)  +/-  (1.25e-249, 1.25e-249j)
| (-0.91494790720613872946 + 2.7000662147649515137e-892j)  +/-  (2.86e-241, 2.86e-241j)
| (-0.94167195684763786182 - 1.3005803945072250031e-892j)  +/-  (5e-241, 5e-241j)
| (-0.99195955759324414642 - 2.0972117054883428074e-892j)  +/-  (5.52e-241, 5.52e-241j)
| (0.88345376521861686334 + 2.018646825849681951e-894j)  +/-  (1.46e-241, 1.46e-241j)
| (-0.96348661301407999341 + 1.1655933949038236156e-908j)  +/-  (7.56e-241, 7.56e-241j)
| (-0.072152990874586235422 + 6.302566947635932502e-914j)  +/-  (1.01e-254, 1.01e-254j)
| (-0.80683596413693863528 - 5.1995983895922647078e-911j)  +/-  (1.7e-242, 1.7e-242j)
| (0.99847233224250771352 - 1.2694809052801696841e-906j)  +/-  (1.94e-241, 1.94e-241j)
| (0.847353716209315049 - 1.9701492797586736426e-922j)  +/-  (4.94e-242, 4.94e-242j)
| (0.66099731375149813317 - 2.2496010138519975154e-931j)  +/-  (1.28e-244, 1.28e-244j)
| (-0.847353716209315049 + 2.4738570199778161171e-929j)  +/-  (5.17e-242, 5.17e-242j)
| (-0.76211174719495512146 - 2.3244487524306894079e-931j)  +/-  (3.95e-243, 3.95e-243j)
| (-0.98027822098025533151 + 7.668938633061273743e-928j)  +/-  (8.19e-241, 8.19e-241j)
| (0.98027822098025533151 - 1.8702017875652574129e-930j)  +/-  (7.98e-241, 7.98e-241j)
| (0.71341423526895705485 + 1.2652320810848143488e-945j)  +/-  (7.88e-244, 7.88e-244j)
| (-0.41986137602926925249 + 6.7822758735661242199e-952j)  +/-  (2.19e-248, 2.19e-248j)
| (-0.66099731375149813317 - 1.4023828348398811414e-948j)  +/-  (1.22e-244, 1.22e-244j)
| (-0.71341423526895705485 + 1.0000866948803823097e-947j)  +/-  (7.33e-244, 7.33e-244j)
| (0.28486199803291362711 + 1.7006059928636623062e-952j)  +/-  (9.75e-251, 9.75e-251j)
| (0.76211174719495512146 + 5.4422089691869103284e-947j)  +/-  (4.12e-243, 4.12e-243j)
| (0.35328261286430380665 + 4.086441808539820604e-955j)  +/-  (1.61e-249, 1.61e-249j)
| (0.94167195684763786182 - 5.7184443031569346547e-954j)  +/-  (4.82e-241, 4.82e-241j)
| (-0.60513425963960093573 + 6.8703175334094373767e-976j)  +/-  (1.91e-245, 1.91e-245j)
| (7.6687018615601102335e-985 + 1.6621396463261723652e-984j)  +/-  (7.87e-983, 7.87e-983j)
| (0.48425117678573472407 - 2.9730244586114198191e-974j)  +/-  (2.28e-247, 2.28e-247j)
| (0.54611631666008471914 + 2.2263844147397088958e-974j)  +/-  (2.46e-246, 2.46e-246j)
| (0.072152990874586235422 + 3.1229548054309238647e-984j)  +/-  (1.37e-254, 1.37e-254j)
| (-0.48425117678573472407 - 3.6776868609755229443e-979j)  +/-  (2.33e-247, 2.33e-247j)
| (-0.28486199803291362711 + 3.9867126593835217696e-981j)  +/-  (8.68e-251, 8.68e-251j)
| (0.14392980951071331077 - 2.4197596451806841881e-983j)  +/-  (2.69e-253, 2.69e-253j)
| (0.60513425963960093573 - 2.7084157957747620613e-978j)  +/-  (1.88e-245, 1.88e-245j)
| (0.21495624486051820901 + 5.3352597563060681014e-986j)  +/-  (5.01e-252, 5.01e-252j)
| (-0.21495624486051820901 + 3.3838368462301339175e-985j)  +/-  (4.78e-252, 4.78e-252j)
| (-0.54611631666008471914 + 2.4189199594083852601e-981j)  +/-  (2.15e-246, 2.15e-246j)
| (-0.14392980951071331077 + 2.835212456855086043e-987j)  +/-  (3.29e-253, 3.29e-253j)
| (0.41986137602926925249 - 1.6919077936455872329e-982j)  +/-  (1.93e-248, 1.93e-248j)
-------------------------------------------------
The weights are:
| (0.003919490253844127283 - 4.0036427867108933948e-844j)  +/-  (3.5e-76, 2.24e-192j)
| (0.019319901423683900396 - 5.9538569845472192946e-843j)  +/-  (1.36e-76, 8.65e-193j)
| (0.033826492086860292345 + 2.7699890589628348002e-844j)  +/-  (6.52e-77, 4.16e-193j)
| (0.0091039966374014033189 + 5.0566554813179472217e-843j)  +/-  (4.12e-77, 2.63e-193j)
| (0.029134413261498494916 - 1.6900394863442363303e-842j)  +/-  (6.5e-77, 4.15e-193j)
| (0.042658057197982083764 + 9.2579935350745313446e-843j)  +/-  (2.71e-77, 1.73e-193j)
| (0.067558402229365169192 + 2.0604576456248390688e-843j)  +/-  (2.8e-78, 1.79e-194j)
| (0.029134413261498494916 - 1.298710490224085601e-844j)  +/-  (8.89e-78, 5.67e-194j)
| (0.024290456613838815902 - 1.5826358334598215019e-845j)  +/-  (2.91e-78, 1.85e-194j)
| (0.0091039966374014033189 + 6.1698424933982650406e-844j)  +/-  (7.2e-79, 4.59e-195j)
| (0.033826492086860292345 + 1.2814881376664607089e-842j)  +/-  (6.03e-80, 3.84e-196j)
| (0.019319901423683900396 + 1.6603700732616575058e-844j)  +/-  (8.76e-79, 5.59e-195j)
| (0.072027501971421974345 + 2.9728064471945541272e-843j)  +/-  (4.01e-82, 2.56e-198j)
| (0.042658057197982083764 + 5.8428695233510378988e-844j)  +/-  (1.91e-80, 1.22e-196j)
| (0.003919490253844127283 - 1.1790455878844702946e-843j)  +/-  (3.7e-81, 2.36e-197j)
| (0.038342222194132657572 - 1.0650061316327199497e-842j)  +/-  (1.58e-80, 1.01e-196j)
| (0.054187080318881786863 - 6.8430255125541027312e-843j)  +/-  (1.83e-82, 1.17e-198j)
| (0.038342222194132657572 - 4.2807102109762596111e-844j)  +/-  (1.75e-80, 1.12e-196j)
| (0.046751494754346580011 - 7.4626443719356527237e-844j)  +/-  (7.21e-82, 4.6e-198j)
| (0.014248756431576486109 - 3.3828370258498114434e-844j)  +/-  (2.36e-80, 1.51e-196j)
| (0.014248756431576486109 - 1.6747611101942040337e-842j)  +/-  (3.37e-82, 2.15e-198j)
| (0.050601192784390156524 + 7.4781002453162027669e-843j)  +/-  (1.78e-83, 1.13e-199j)
| (0.065541242126322797491 - 1.8522276678156998581e-843j)  +/-  (2.02e-84, 1.29e-200j)
| (0.054187080318881786863 - 1.088729077611045805e-843j)  +/-  (9.61e-84, 6.13e-200j)
| (0.050601192784390156524 + 9.1434329876797916819e-844j)  +/-  (4.68e-83, 2.98e-199j)
| (0.069223344193656684282 - 4.3560021121844778834e-843j)  +/-  (3.9e-87, 2.49e-203j)
| (0.046751494754346580011 - 8.2555471039893281495e-843j)  +/-  (1.39e-84, 8.89e-201j)
| (0.067558402229365169192 + 4.6822111624151673585e-843j)  +/-  (2.72e-87, 1.73e-203j)
| (0.024290456613838815902 + 2.8644999966317877669e-842j)  +/-  (3.35e-84, 2.14e-200j)
| (0.057490461956910519428 + 1.2695686212416487532e-843j)  +/-  (4.9e-86, 3.13e-202j)
| (0.072215751693798987977 - 3.2238666712484444223e-843j)  +/-  (7.52e-88, 4.8e-204j)
| (0.063182380449396112326 + 5.4139982040118484425e-843j)  +/-  (1.11e-87, 7.1e-204j)
| (0.06049411524999129452 - 5.8337883421441527558e-843j)  +/-  (1.69e-87, 1.08e-203j)
| (0.072027501971421974345 + 3.4860333973593236609e-843j)  +/-  (9.9e-89, 6.32e-205j)
| (0.063182380449396112326 + 1.6511528429145259378e-843j)  +/-  (2.41e-88, 1.54e-204j)
| (0.069223344193656684282 - 2.276156519569237734e-843j)  +/-  (4.36e-89, 2.78e-205j)
| (0.071463734252514141298 - 3.7607612683818932546e-843j)  +/-  (2e-89, 1.28e-205j)
| (0.057490461956910519428 + 6.3041965828139711204e-843j)  +/-  (4.39e-89, 2.79e-205j)
| (0.070527387765085028126 + 4.0499323518862507022e-843j)  +/-  (1.35e-89, 8.63e-206j)
| (0.070527387765085028126 + 2.4997342279349628723e-843j)  +/-  (1.82e-90, 1.17e-206j)
| (0.06049411524999129452 - 1.4569942586160075501e-843j)  +/-  (2.26e-90, 1.43e-206j)
| (0.071463734252514141298 - 2.7317224253738271799e-843j)  +/-  (1.54e-90, 9.9e-207j)
| (0.065541242126322797491 - 5.032900841217838285e-843j)  +/-  (9.62e-91, 5.5e-207j)
