Starting with polynomial:
P : 1/815915283247897734345611269596115894272000000000*t^40 - 1/509947052029936083966007043497572433920000000*t^39 + 1/670541817264873220205137466794967040000000*t^38 - 1/1393092418140318324525908864532480000000*t^37 + 37/150604585744899278327125282652160000000*t^36 - 37/581036210435568203422551244800000000*t^35 + 37/2845891642949721812681883648000000*t^34 - 37/17232907872532917550841856000000*t^33 + 37/126596201083804720300032000000*t^32 - 37/1112661923588127424512000000*t^31 + 1147/358923201157460459520000000*t^30 - 1147/4386839125257850060800000*t^29 + 33263/1815243775968765542400000*t^28 - 33263/30099705468869836800000*t^27 + 33263/578046469909708800000*t^26 - 33263/12826474924032000000*t^25 + 33263/328357758055219200*t^24 - 33263/9691114387046400*t^23 + 765049/7584350389862400*t^22 - 765049/297732763238400*t^21 + 765049/13502619648000*t^20 - 765049/708887531520*t^19 + 14535931/820817141760*t^18 - 631997/2533386240*t^17 + 10743949/3576545280*t^16 - 10743949/349272000*t^15 + 10743949/40360320*t^14 - 10743949/5559840*t^13 + 139671337/11975040*t^12 - 4816253/83160*t^11 + 52978783/226800*t^10 - 1708993/2268*t^9 + 1708993/896*t^8 - 155363/42*t^7 + 63973/12*t^6 - 27417/5*t^5 + 45695/12*t^4 - 4940/3*t^3 + 390*t^2 - 40*t + 1
Extension levels are: 40
-------------------------------------------------
Ending with final polynomial:
P : 1/815915283247897734345611269596115894272000000000*t^40 - 1/509947052029936083966007043497572433920000000*t^39 + 1/670541817264873220205137466794967040000000*t^38 - 1/1393092418140318324525908864532480000000*t^37 + 37/150604585744899278327125282652160000000*t^36 - 37/581036210435568203422551244800000000*t^35 + 37/2845891642949721812681883648000000*t^34 - 37/17232907872532917550841856000000*t^33 + 37/126596201083804720300032000000*t^32 - 37/1112661923588127424512000000*t^31 + 1147/358923201157460459520000000*t^30 - 1147/4386839125257850060800000*t^29 + 33263/1815243775968765542400000*t^28 - 33263/30099705468869836800000*t^27 + 33263/578046469909708800000*t^26 - 33263/12826474924032000000*t^25 + 33263/328357758055219200*t^24 - 33263/9691114387046400*t^23 + 765049/7584350389862400*t^22 - 765049/297732763238400*t^21 + 765049/13502619648000*t^20 - 765049/708887531520*t^19 + 14535931/820817141760*t^18 - 631997/2533386240*t^17 + 10743949/3576545280*t^16 - 10743949/349272000*t^15 + 10743949/40360320*t^14 - 10743949/5559840*t^13 + 139671337/11975040*t^12 - 4816253/83160*t^11 + 52978783/226800*t^10 - 1708993/2268*t^9 + 1708993/896*t^8 - 155363/42*t^7 + 63973/12*t^6 - 27417/5*t^5 + 45695/12*t^4 - 4940/3*t^3 + 390*t^2 - 40*t + 1
-------------------------------------------------
Computing nodes and weights
  current precision for roots: 53
  current precision for roots: 106
  current precision for roots: 212
 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: 0
  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:
| (142.28004446915999789 - 3.2104047675827836533e-510j)  +/-  (4.55e-241, 4.55e-241j)
| (91.789874671236376992 + 2.0986305907955561817e-503j)  +/-  (2.27e-236, 2.27e-236j)
| (107.67244063938827252 - 9.6569580949478723985e-506j)  +/-  (1.25e-237, 1.25e-237j)
| (40.811492823886920466 + 1.4153823511173106177e-507j)  +/-  (2.66e-235, 2.66e-235j)
| (25.072560772426203794 - 5.057704288548169173e-514j)  +/-  (5.58e-237, 5.58e-237j)
| (8.5640170175861637627 + 5.3296160794035022587e-523j)  +/-  (4.95e-242, 4.95e-242j)
| (78.572802911571309281 - 1.8328267473689589124e-516j)  +/-  (1.61e-235, 1.61e-235j)
| (72.695158847612462118 + 6.2796453223756033349e-515j)  +/-  (2.74e-235, 2.74e-235j)
| (62.100179072775111612 - 3.2349422920001099481e-515j)  +/-  (6.03e-235, 6.03e-235j)
| (84.911231135704984543 + 1.5955950106334490596e-521j)  +/-  (6.37e-236, 6.37e-236j)
| (128.20184198825565119 + 6.7300879015461161976e-528j)  +/-  (1.45e-239, 1.45e-239j)
| (99.32080871744680825 - 3.8233468495212425441e-523j)  +/-  (6.51e-237, 6.51e-237j)
| (22.468249983498418351 - 4.3100380317811451686e-521j)  +/-  (1.83e-237, 1.83e-237j)
| (30.800145739445462701 + 5.7093280999770249502e-534j)  +/-  (3.46e-236, 3.46e-236j)
| (33.938657084913719609 - 2.0759910728816318313e-553j)  +/-  (7.76e-236, 7.76e-236j)
| (117.12230951269068881 + 3.3443529611775195285e-569j)  +/-  (1.8e-238, 1.8e-238j)
| (27.847480009168862721 + 1.0502254964449532991e-572j)  +/-  (1.48e-236, 1.48e-236j)
| (13.640933712537087228 + 2.3845830029858473935e-584j)  +/-  (9.72e-240, 9.72e-240j)
| (4.7116411465549726936 - 2.8936153088826857285e-599j)  +/-  (8.5e-245, 8.5e-245j)
| (57.301863323393627495 + 1.4981704042445179187e-598j)  +/-  (6.14e-235, 6.14e-235j)
| (37.272245880476004328 - 1.4144168061898306021e-625j)  +/-  (1.51e-235, 1.51e-235j)
| (67.219370927126998799 + 1.1653561523764741549e-652j)  +/-  (4.01e-235, 4.01e-235j)
| (44.568603175334462707 + 2.6951109469078737054e-682j)  +/-  (4.07e-235, 4.07e-235j)
| (17.746905950095663043 + 2.6365451681577996562e-696j)  +/-  (1.82e-238, 1.82e-238j)
| (10.116634048451939407 - 1.21252460290568286e-703j)  +/-  (3.07e-241, 3.07e-241j)
| (0.188162283158698516 - 8.695682010003216386e-722j)  +/-  (3.14e-253, 3.14e-253j)
| (0.85977296397293492226 + 3.2796845446451790938e-720j)  +/-  (1.97e-250, 1.97e-250j)
| (2.7933693535068164577 + 1.4213834555196321073e-715j)  +/-  (8.01e-247, 8.01e-247j)
| (20.02823283457489053 - 5.236603291375725347e-704j)  +/-  (6.17e-238, 6.17e-238j)
| (48.557763533059992281 + 6.0909374700160708003e-713j)  +/-  (5.59e-235, 5.59e-235j)
| (3.6887026779082702096 - 2.7178917397694251114e-741j)  +/-  (7.48e-246, 7.48e-246j)
| (7.1472479081022882507 - 7.7080950236227218118e-737j)  +/-  (6.63e-243, 6.63e-243j)
| (15.619285893339073837 - 2.2513473177358825021e-729j)  +/-  (4.2e-239, 4.2e-239j)
| (2.0242091359228267334 + 8.5146729314834617841e-746j)  +/-  (5.25e-248, 5.25e-248j)
| (52.795611187216932969 - 5.1616951754978600048e-732j)  +/-  (6.44e-235, 6.44e-235j)
| (11.807892294004584843 + 5.2658619043844735683e-749j)  +/-  (1.91e-240, 1.91e-240j)
| (1.3800108205273371865 - 1.1477746568723567512e-756j)  +/-  (3.54e-249, 3.54e-249j)
| (0.46269428131457645356 - 5.1280333189986551007e-759j)  +/-  (8.59e-252, 8.59e-252j)
| (5.8638508783437181143 - 6.6303141977737076099e-752j)  +/-  (8.01e-244, 8.01e-244j)
| (0.035700394308888385122 + 1.0210888524900152718e-767j)  +/-  (4.21e-255, 4.21e-255j)
-------------------------------------------------
The weights are:
| (2.7003609402170336406e-61 - 3.5532341131342742552e-548j)  +/-  (1.23e-80, 2.9e-196j)
| (9.8274157251479333061e-40 + 3.4265480506405527325e-537j)  +/-  (1.4e-73, 3.3e-189j)
| (1.5309086846066868536e-46 + 1.1168680871115078516e-540j)  +/-  (2.92e-76, 6.87e-192j)
| (6.8803364842843023409e-18 - 4.749211338638880775e-525j)  +/-  (3.63e-62, 8.55e-178j)
| (3.4724414848038224856e-11 + 1.0979353432414624436e-522j)  +/-  (3.92e-55, 9.23e-171j)
| (0.00028327168532432471583 + 8.8940585306526556565e-520j)  +/-  (6.16e-40, 1.45e-155j)
| (4.5852916145026869176e-34 + 2.9233015238701133522e-534j)  +/-  (6.8e-72, 1.6e-187j)
| (1.5217354931814569975e-31 - 6.066512036733158133e-533j)  +/-  (4.24e-71, 9.99e-187j)
| (5.3105847773213307528e-27 - 1.5685982828417060498e-530j)  +/-  (1.19e-69, 2.8e-185j)
| (8.762158657486248561e-37 - 1.137540437141170088e-535j)  +/-  (2.53e-73, 5.95e-189j)
| (2.5666336050123721838e-55 + 3.8179465935807127191e-545j)  +/-  (5.43e-82, 1.28e-197j)
| (5.8011520191697791085e-43 - 7.545540802956370804e-539j)  +/-  (2.13e-76, 5.02e-192j)
| (4.4031741042328488129e-10 - 3.1739531982392891509e-522j)  +/-  (2.46e-60, 5.79e-176j)
| (1.2797725976766356072e-13 + 1.1504280914516622671e-523j)  +/-  (4.63e-64, 1.09e-179j)
| (5.8941771723511529447e-15 - 3.7788999711509574856e-524j)  +/-  (2.56e-65, 6.02e-181j)
| (1.3819863056493280997e-50 - 9.6970961727481364255e-543j)  +/-  (4.1e-81, 9.67e-197j)
| (2.3053815449168221616e-12 - 3.5746147780296851654e-523j)  +/-  (2.1e-63, 4.96e-179j)
| (2.2684528787793650545e-06 - 1.1927012626019858859e-520j)  +/-  (1.8e-59, 4.25e-175j)
| (0.0097746252467144596189 - 3.461035372988624638e-519j)  +/-  (1.9e-51, 4.48e-167j)
| (6.044762511587663289e-25 + 2.0751928247883203134e-529j)  +/-  (5.59e-72, 1.32e-187j)
| (2.2322175799045774184e-16 + 1.4972988625852746264e-524j)  +/-  (3.96e-67, 9.34e-183j)
| (3.3925280532805218961e-29 + 1.0515777008063194759e-531j)  +/-  (1.56e-73, 3.68e-189j)
| (1.7056037368180867485e-19 - 4.2655271478317022025e-526j)  +/-  (8.79e-70, 2.07e-185j)
| (4.3228213222820885689e-08 - 2.2140370236965980018e-521j)  +/-  (2.07e-64, 4.87e-180j)
| (6.5509405003246292798e-05 - 4.8843140861910382939e-520j)  +/-  (2.87e-62, 6.77e-178j)
| (0.1768147390957222956 + 2.613743142758827145e-519j)  +/-  (4.07e-56, 9.59e-172j)
| (0.19408119531860179966 + 5.9520811630105452621e-519j)  +/-  (3.73e-56, 8.8e-172j)
| (0.050932204361044237026 - 5.7758444897801492679e-519j)  +/-  (3.37e-57, 7.95e-173j)
| (4.7284937709907793279e-09 + 8.6414225007586691339e-522j)  +/-  (8.77e-65, 2.07e-180j)
| (3.3537119406661829355e-21 + 3.0285419851191019999e-527j)  +/-  (1.66e-71, 3.92e-187j)
| (0.02397619301568484184 + 4.6638568179635238852e-519j)  +/-  (4.22e-60, 9.94e-176j)
| (0.001062246893896871935 - 1.5070760641000507359e-519j)  +/-  (2.07e-62, 4.87e-178j)
| (3.3796264822006792108e-07 + 5.314591328808225355e-521j)  +/-  (9.3e-65, 2.19e-180j)
| (0.093326798435770880507 + 6.523441785360133005e-519j)  +/-  (3.7e-61, 8.72e-177j)
| (5.1461995601366791408e-23 - 2.5288072508276423793e-528j)  +/-  (1.18e-72, 2.78e-188j)
| (1.3116069073267784125e-05 + 2.4991655573234289137e-520j)  +/-  (4.03e-64, 9.48e-180j)
| (0.14643428242412511441 - 6.6366141354753387244e-519j)  +/-  (8.45e-62, 1.96e-177j)
| (0.21136311701596243103 - 4.5117716127077276655e-519j)  +/-  (5.6e-62, 1.3e-177j)
| (0.0034579399930184868613 + 2.3723468196619868925e-519j)  +/-  (4.33e-63, 1.03e-178j)
| (0.08841210619034244094 - 8.0204949282395105752e-520j)  +/-  (1.44e-62, 3.31e-178j)
