Starting with polynomial:
P : -1/8222838654177922817725562880000000*t^31 + 31/265252859812191058636308480000000*t^30 - 31/589450799582646796969574400000*t^29 + 899/60977668922342772100300800000*t^28 - 899/311110555726238633164800000*t^27 + 899/2133817254638125056000000*t^26 - 899/18939206402113536000000*t^25 + 899/212119111703671603200*t^24 - 899/2946098773662105600*t^23 + 20677/1152821259259084800*t^22 - 20677/23818621059072000*t^21 + 20677/594115264512000*t^20 - 20677/17823457935360*t^19 + 392863/12194997534720*t^18 - 392863/526944337920*t^17 + 6678671/464950886400*t^16 - 6678671/29059430400*t^15 + 392863/129153024*t^14 - 392863/11860992*t^13 + 268801/912384*t^12 - 268801/126720*t^11 + 2956811/241920*t^10 - 1344005/24192*t^9 + 175305/896*t^8 - 58435/112*t^7 + 81809/80*t^6 - 56637/40*t^5 + 31465/24*t^4 - 4495/6*t^3 + 465/2*t^2 - 31*t + 1
Extension levels are: 31
-------------------------------------------------
Ending with final polynomial:
P : -1/8222838654177922817725562880000000*t^31 + 31/265252859812191058636308480000000*t^30 - 31/589450799582646796969574400000*t^29 + 899/60977668922342772100300800000*t^28 - 899/311110555726238633164800000*t^27 + 899/2133817254638125056000000*t^26 - 899/18939206402113536000000*t^25 + 899/212119111703671603200*t^24 - 899/2946098773662105600*t^23 + 20677/1152821259259084800*t^22 - 20677/23818621059072000*t^21 + 20677/594115264512000*t^20 - 20677/17823457935360*t^19 + 392863/12194997534720*t^18 - 392863/526944337920*t^17 + 6678671/464950886400*t^16 - 6678671/29059430400*t^15 + 392863/129153024*t^14 - 392863/11860992*t^13 + 268801/912384*t^12 - 268801/126720*t^11 + 2956811/241920*t^10 - 1344005/24192*t^9 + 175305/896*t^8 - 58435/112*t^7 + 81809/80*t^6 - 56637/40*t^5 + 31465/24*t^4 - 4495/6*t^3 + 465/2*t^2 - 31*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: 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:   31 out of 31
Indefinite weights: 0 out of 31
Negative weights:   0 out of 31
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (107.95224382757871475 + 3.319002731210494119e-258j)  +/-  (8.66e-244, 8.66e-244j)
| (56.854992868715843621 - 7.7459170416076734592e-257j)  +/-  (1.39e-239, 1.39e-239j)
| (95.188939891525629981 - 4.212154429970702939e-266j)  +/-  (1.83e-242, 1.83e-242j)
| (85.230358607545669169 - 7.2595547388674823325e-265j)  +/-  (1.7e-241, 1.7e-241j)
| (76.807047763862732838 + 2.2690657710188766575e-262j)  +/-  (7.46e-241, 7.46e-241j)
| (29.953990872346445507 + 9.9150337665641163552e-266j)  +/-  (9.68e-240, 9.68e-240j)
| (20.563526336715822171 + 9.5053072271437397181e-272j)  +/-  (8.51e-241, 8.51e-241j)
| (69.425277191080345623 + 2.6071717973852857794e-277j)  +/-  (2.89e-240, 2.89e-240j)
| (2.6097034152566806504 + 2.894678614814356777e-304j)  +/-  (3.63e-248, 3.63e-248j)
| (17.898929826644757647 - 8.6883518712095162567e-287j)  +/-  (3.01e-241, 3.01e-241j)
| (1.7775956928747727212 + 2.5123575472968277501e-309j)  +/-  (2.44e-249, 2.44e-249j)
| (11.146649755619291359 + 5.8749178365439548423e-295j)  +/-  (5.67e-243, 5.67e-243j)
| (41.795830870182219981 + 2.1534486082726114296e-297j)  +/-  (2.41e-239, 2.41e-239j)
| (23.451973482011858591 + 8.1430744511828002176e-313j)  +/-  (2.48e-240, 2.48e-240j)
| (0.2419801638247720489 - 3.0641412388365200877e-339j)  +/-  (2.23e-253, 2.23e-253j)
| (3.6051968023400442699 + 4.7569595211177341533e-336j)  +/-  (3.38e-247, 3.38e-247j)
| (7.6014009492331374229 - 5.5588807509151178168e-331j)  +/-  (1.91e-244, 1.91e-244j)
| (15.447268315549310076 + 1.2406292822670310976e-327j)  +/-  (9.51e-242, 9.51e-242j)
| (62.826855908786321454 + 2.8544685085754468929e-359j)  +/-  (7e-240, 7e-240j)
| (51.405314476797755162 + 7.5258355456495739339e-404j)  +/-  (1.9e-239, 1.9e-239j)
| (6.097554567181740927 - 4.2586800992181601404e-429j)  +/-  (2.91e-245, 2.91e-245j)
| (0.59525389422235073707 + 5.2105073335020944779e-444j)  +/-  (7.63e-252, 7.63e-252j)
| (37.539164407330440883 + 3.3787455047311026998e-438j)  +/-  (2.3e-239, 2.3e-239j)
| (46.403866806411123136 + 4.5876030542185154633e-463j)  +/-  (2.32e-239, 2.32e-239j)
| (33.600759532902202735 - 3.7265120350484580529e-479j)  +/-  (1.8e-239, 1.8e-239j)
| (9.2827143134708894183 - 7.5406949635855473624e-494j)  +/-  (1.08e-243, 1.08e-243j)
| (1.1066894995329987162 + 6.0672510824919499039e-501j)  +/-  (1.76e-250, 1.76e-250j)
| (4.7667470844717611314 - 5.8302520010581101829e-496j)  +/-  (3.48e-246, 3.48e-246j)
| (26.57708135211826046 - 1.5953334141358384654e-488j)  +/-  (5.23e-240, 5.23e-240j)
| (0.045901947621108290743 - 1.6734944826573432673e-515j)  +/-  (4.23e-255, 4.23e-255j)
| (13.199189576244998522 + 9.4288140822965855231e-500j)  +/-  (2.5e-242, 2.5e-242j)
-------------------------------------------------
The weights are:
| (1.9909984582531456482e-46 - 3.1700379271383158947e-293j)  +/-  (2.3e-96, 1.94e-213j)
| (1.1582201904525643635e-24 + 4.4071612598223985407e-281j)  +/-  (9.42e-89, 7.95e-206j)
| (5.0363643921161490411e-41 + 1.9957546222443105434e-290j)  +/-  (5.2e-95, 4.39e-212j)
| (8.7663710117162041473e-37 - 3.3661656986367683531e-288j)  +/-  (6.02e-94, 5.09e-211j)
| (3.4500071104808394132e-33 + 2.8512105938581803724e-286j)  +/-  (4.44e-93, 3.75e-210j)
| (3.437754181941162052e-13 + 1.3023302740189335371e-276j)  +/-  (7.44e-85, 6.28e-202j)
| (3.2551249938271570855e-09 - 7.8523101540256982976e-275j)  +/-  (1.9e-81, 1.61e-198j)
| (4.9143017308057432741e-30 - 1.6240366681324265045e-284j)  +/-  (1.44e-92, 1.22e-209j)
| (0.067186168923899300671 - 8.5178343181929334007e-272j)  +/-  (1.15e-63, 9.75e-181j)
| (4.307554518773110093e-08 + 2.4842093086765999569e-274j)  +/-  (1.35e-80, 1.14e-197j)
| (0.12698283289306190144 + 9.5188270720612453973e-272j)  +/-  (1.13e-61, 9.55e-179j)
| (2.8229237864310816394e-05 - 4.2805082640563820084e-273j)  +/-  (1.81e-77, 1.52e-194j)
| (3.1212687280713526832e-18 - 8.3954818139501282561e-279j)  +/-  (4.63e-89, 3.91e-206j)
| (1.9620246675410594996e-10 + 2.2340395656579085814e-275j)  +/-  (2.6e-83, 2.2e-200j)
| (0.21552760818089123795 - 4.451573378540893702e-272j)  +/-  (1.68e-65, 1.41e-182j)
| (0.029303224993879487405 + 6.7351057599487433708e-272j)  +/-  (1.09e-70, 9.24e-188j)
| (0.00079549548307940382922 - 1.7417734131656787268e-272j)  +/-  (2.57e-76, 2.17e-193j)
| (4.5931839841801061674e-07 - 7.0924002237826525912e-274j)  +/-  (1.78e-80, 1.5e-197j)
| (3.2472922591425422435e-27 + 8.3604915838858255887e-283j)  +/-  (8.4e-93, 7.09e-210j)
| (2.4672796386616696011e-22 - 2.2852431138732605333e-280j)  +/-  (2.33e-91, 1.97e-208j)
| (0.0031851272582386980321 + 3.0292641109863391808e-272j)  +/-  (1.38e-78, 1.16e-195j)
| (0.23830825164569654732 + 7.3876593699291400113e-272j)  +/-  (1.94e-73, 1.64e-190j)
| (2.0368066110115247398e-16 + 5.0170585258039915135e-278j)  +/-  (2.73e-89, 2.31e-206j)
| (3.3729581704161052453e-20 + 1.3242457165500443658e-279j)  +/-  (6.39e-91, 5.4e-208j)
| (9.6795247130446716997e-15 - 2.7279484186974189742e-277j)  +/-  (1.07e-88, 9.07e-206j)
| (0.00016480052126636687318 + 9.0695513172031558753e-273j)  +/-  (2.1e-83, 1.78e-200j)
| (0.1953883092979022925 - 9.2046578874921986033e-272j)  +/-  (3.88e-80, 3.28e-197j)
| (0.01059756991529573609 - 4.7609647013176599771e-272j)  +/-  (5.72e-82, 4.84e-199j)
| (9.319049908661758713e-12 - 5.6969184474132495323e-276j)  +/-  (1.24e-87, 1.04e-204j)
| (0.11252789550372583821 + 1.3961071821328158241e-272j)  +/-  (1.77e-82, 1.44e-199j)
| (3.9802902551008580387e-06 + 1.8309852480570271918e-273j)  +/-  (9.85e-85, 8.33e-202j)
Starting with polynomial:
P : -1/8222838654177922817725562880000000*t^31 + 31/265252859812191058636308480000000*t^30 - 31/589450799582646796969574400000*t^29 + 899/60977668922342772100300800000*t^28 - 899/311110555726238633164800000*t^27 + 899/2133817254638125056000000*t^26 - 899/18939206402113536000000*t^25 + 899/212119111703671603200*t^24 - 899/2946098773662105600*t^23 + 20677/1152821259259084800*t^22 - 20677/23818621059072000*t^21 + 20677/594115264512000*t^20 - 20677/17823457935360*t^19 + 392863/12194997534720*t^18 - 392863/526944337920*t^17 + 6678671/464950886400*t^16 - 6678671/29059430400*t^15 + 392863/129153024*t^14 - 392863/11860992*t^13 + 268801/912384*t^12 - 268801/126720*t^11 + 2956811/241920*t^10 - 1344005/24192*t^9 + 175305/896*t^8 - 58435/112*t^7 + 81809/80*t^6 - 56637/40*t^5 + 31465/24*t^4 - 4495/6*t^3 + 465/2*t^2 - 31*t + 1
Extension levels are: 31
-------------------------------------------------
Ending with final polynomial:
P : -1/8222838654177922817725562880000000*t^31 + 31/265252859812191058636308480000000*t^30 - 31/589450799582646796969574400000*t^29 + 899/60977668922342772100300800000*t^28 - 899/311110555726238633164800000*t^27 + 899/2133817254638125056000000*t^26 - 899/18939206402113536000000*t^25 + 899/212119111703671603200*t^24 - 899/2946098773662105600*t^23 + 20677/1152821259259084800*t^22 - 20677/23818621059072000*t^21 + 20677/594115264512000*t^20 - 20677/17823457935360*t^19 + 392863/12194997534720*t^18 - 392863/526944337920*t^17 + 6678671/464950886400*t^16 - 6678671/29059430400*t^15 + 392863/129153024*t^14 - 392863/11860992*t^13 + 268801/912384*t^12 - 268801/126720*t^11 + 2956811/241920*t^10 - 1344005/24192*t^9 + 175305/896*t^8 - 58435/112*t^7 + 81809/80*t^6 - 56637/40*t^5 + 31465/24*t^4 - 4495/6*t^3 + 465/2*t^2 - 31*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: 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:   31 out of 31
Indefinite weights: 0 out of 31
Negative weights:   0 out of 31
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (107.95224382757871475 + 3.319002731210494119e-258j)  +/-  (8.66e-244, 8.66e-244j)
| (56.854992868715843621 - 7.7459170416076734592e-257j)  +/-  (1.39e-239, 1.39e-239j)
| (95.188939891525629981 - 4.212154429970702939e-266j)  +/-  (1.83e-242, 1.83e-242j)
| (85.230358607545669169 - 7.2595547388674823325e-265j)  +/-  (1.7e-241, 1.7e-241j)
| (76.807047763862732838 + 2.2690657710188766575e-262j)  +/-  (7.46e-241, 7.46e-241j)
| (29.953990872346445507 + 9.9150337665641163552e-266j)  +/-  (9.68e-240, 9.68e-240j)
| (20.563526336715822171 + 9.5053072271437397181e-272j)  +/-  (8.51e-241, 8.51e-241j)
| (69.425277191080345623 + 2.6071717973852857794e-277j)  +/-  (2.89e-240, 2.89e-240j)
| (2.6097034152566806504 + 2.894678614814356777e-304j)  +/-  (3.63e-248, 3.63e-248j)
| (17.898929826644757647 - 8.6883518712095162567e-287j)  +/-  (3.01e-241, 3.01e-241j)
| (1.7775956928747727212 + 2.5123575472968277501e-309j)  +/-  (2.44e-249, 2.44e-249j)
| (11.146649755619291359 + 5.8749178365439548423e-295j)  +/-  (5.67e-243, 5.67e-243j)
| (41.795830870182219981 + 2.1534486082726114296e-297j)  +/-  (2.41e-239, 2.41e-239j)
| (23.451973482011858591 + 8.1430744511828002176e-313j)  +/-  (2.48e-240, 2.48e-240j)
| (0.2419801638247720489 - 3.0641412388365200877e-339j)  +/-  (2.23e-253, 2.23e-253j)
| (3.6051968023400442699 + 4.7569595211177341533e-336j)  +/-  (3.38e-247, 3.38e-247j)
| (7.6014009492331374229 - 5.5588807509151178168e-331j)  +/-  (1.91e-244, 1.91e-244j)
| (15.447268315549310076 + 1.2406292822670310976e-327j)  +/-  (9.51e-242, 9.51e-242j)
| (62.826855908786321454 + 2.8544685085754468929e-359j)  +/-  (7e-240, 7e-240j)
| (51.405314476797755162 + 7.5258355456495739339e-404j)  +/-  (1.9e-239, 1.9e-239j)
| (6.097554567181740927 - 4.2586800992181601404e-429j)  +/-  (2.91e-245, 2.91e-245j)
| (0.59525389422235073707 + 5.2105073335020944779e-444j)  +/-  (7.63e-252, 7.63e-252j)
| (37.539164407330440883 + 3.3787455047311026998e-438j)  +/-  (2.3e-239, 2.3e-239j)
| (46.403866806411123136 + 4.5876030542185154633e-463j)  +/-  (2.32e-239, 2.32e-239j)
| (33.600759532902202735 - 3.7265120350484580529e-479j)  +/-  (1.8e-239, 1.8e-239j)
| (9.2827143134708894183 - 7.5406949635855473624e-494j)  +/-  (1.08e-243, 1.08e-243j)
| (1.1066894995329987162 + 6.0672510824919499039e-501j)  +/-  (1.76e-250, 1.76e-250j)
| (4.7667470844717611314 - 5.8302520010581101829e-496j)  +/-  (3.48e-246, 3.48e-246j)
| (26.57708135211826046 - 1.5953334141358384654e-488j)  +/-  (5.23e-240, 5.23e-240j)
| (0.045901947621108290743 - 1.6734944826573432673e-515j)  +/-  (4.23e-255, 4.23e-255j)
| (13.199189576244998522 + 9.4288140822965855231e-500j)  +/-  (2.5e-242, 2.5e-242j)
-------------------------------------------------
The weights are:
| (1.9909984582531456482e-46 - 3.1700379271383158947e-293j)  +/-  (2.3e-96, 1.94e-213j)
| (1.1582201904525643635e-24 + 4.4071612598223985407e-281j)  +/-  (9.42e-89, 7.95e-206j)
| (5.0363643921161490411e-41 + 1.9957546222443105434e-290j)  +/-  (5.2e-95, 4.39e-212j)
| (8.7663710117162041473e-37 - 3.3661656986367683531e-288j)  +/-  (6.02e-94, 5.09e-211j)
| (3.4500071104808394132e-33 + 2.8512105938581803724e-286j)  +/-  (4.44e-93, 3.75e-210j)
| (3.437754181941162052e-13 + 1.3023302740189335371e-276j)  +/-  (7.44e-85, 6.28e-202j)
| (3.2551249938271570855e-09 - 7.8523101540256982976e-275j)  +/-  (1.9e-81, 1.61e-198j)
| (4.9143017308057432741e-30 - 1.6240366681324265045e-284j)  +/-  (1.44e-92, 1.22e-209j)
| (0.067186168923899300671 - 8.5178343181929334007e-272j)  +/-  (1.15e-63, 9.75e-181j)
| (4.307554518773110093e-08 + 2.4842093086765999569e-274j)  +/-  (1.35e-80, 1.14e-197j)
| (0.12698283289306190144 + 9.5188270720612453973e-272j)  +/-  (1.13e-61, 9.55e-179j)
| (2.8229237864310816394e-05 - 4.2805082640563820084e-273j)  +/-  (1.81e-77, 1.52e-194j)
| (3.1212687280713526832e-18 - 8.3954818139501282561e-279j)  +/-  (4.63e-89, 3.91e-206j)
| (1.9620246675410594996e-10 + 2.2340395656579085814e-275j)  +/-  (2.6e-83, 2.2e-200j)
| (0.21552760818089123795 - 4.451573378540893702e-272j)  +/-  (1.68e-65, 1.41e-182j)
| (0.029303224993879487405 + 6.7351057599487433708e-272j)  +/-  (1.09e-70, 9.24e-188j)
| (0.00079549548307940382922 - 1.7417734131656787268e-272j)  +/-  (2.57e-76, 2.17e-193j)
| (4.5931839841801061674e-07 - 7.0924002237826525912e-274j)  +/-  (1.78e-80, 1.5e-197j)
| (3.2472922591425422435e-27 + 8.3604915838858255887e-283j)  +/-  (8.4e-93, 7.09e-210j)
| (2.4672796386616696011e-22 - 2.2852431138732605333e-280j)  +/-  (2.33e-91, 1.97e-208j)
| (0.0031851272582386980321 + 3.0292641109863391808e-272j)  +/-  (1.38e-78, 1.16e-195j)
| (0.23830825164569654732 + 7.3876593699291400113e-272j)  +/-  (1.94e-73, 1.64e-190j)
| (2.0368066110115247398e-16 + 5.0170585258039915135e-278j)  +/-  (2.73e-89, 2.31e-206j)
| (3.3729581704161052453e-20 + 1.3242457165500443658e-279j)  +/-  (6.39e-91, 5.4e-208j)
| (9.6795247130446716997e-15 - 2.7279484186974189742e-277j)  +/-  (1.07e-88, 9.07e-206j)
| (0.00016480052126636687318 + 9.0695513172031558753e-273j)  +/-  (2.1e-83, 1.78e-200j)
| (0.1953883092979022925 - 9.2046578874921986033e-272j)  +/-  (3.88e-80, 3.28e-197j)
| (0.01059756991529573609 - 4.7609647013176599771e-272j)  +/-  (5.72e-82, 4.84e-199j)
| (9.319049908661758713e-12 - 5.6969184474132495323e-276j)  +/-  (1.24e-87, 1.04e-204j)
| (0.11252789550372583821 + 1.3961071821328158241e-272j)  +/-  (1.77e-82, 1.44e-199j)
| (3.9802902551008580387e-06 + 1.8309852480570271918e-273j)  +/-  (9.85e-85, 8.33e-202j)
