Starting with polynomial:
P : -1/10333147966386144929666651337523200000000*t^35 + 1/8435222829702975452789103132672000000*t^34 - 1/14593811124053590748770074624000000*t^33 + 1/40203336429899699032424448000000*t^32 - 1/157044282929295699345408000000*t^31 + 31/25329723053112209571840000000*t^30 - 31/168864820354081397145600000*t^29 + 899/40760473878571371724800000*t^28 - 899/415923202842565017600000*t^27 + 899/5134854356081049600000*t^26 - 899/75959383965696000000*t^25 + 899/1336885157796249600*t^24 - 899/27851774120755200*t^23 + 20677/15742307111731200*t^22 - 20677/455355990835200*t^21 + 20677/15488299008000*t^20 - 20677/619531960320*t^19 + 392863/554318069760*t^18 - 392863/30795448320*t^17 + 351509/1811496960*t^16 - 351509/141523200*t^15 + 351509/13208832*t^14 - 351509/1482624*t^13 + 198679/114048*t^12 - 198679/19008*t^11 + 2185469/43200*t^10 - 168113/864*t^9 + 168113/288*t^8 - 168113/126*t^7 + 40579/18*t^6 - 40579/15*t^5 + 6545/3*t^4 - 6545/6*t^3 + 595/2*t^2 - 35*t + 1
Extension levels are: 35
-------------------------------------------------
Ending with final polynomial:
P : -1/10333147966386144929666651337523200000000*t^35 + 1/8435222829702975452789103132672000000*t^34 - 1/14593811124053590748770074624000000*t^33 + 1/40203336429899699032424448000000*t^32 - 1/157044282929295699345408000000*t^31 + 31/25329723053112209571840000000*t^30 - 31/168864820354081397145600000*t^29 + 899/40760473878571371724800000*t^28 - 899/415923202842565017600000*t^27 + 899/5134854356081049600000*t^26 - 899/75959383965696000000*t^25 + 899/1336885157796249600*t^24 - 899/27851774120755200*t^23 + 20677/15742307111731200*t^22 - 20677/455355990835200*t^21 + 20677/15488299008000*t^20 - 20677/619531960320*t^19 + 392863/554318069760*t^18 - 392863/30795448320*t^17 + 351509/1811496960*t^16 - 351509/141523200*t^15 + 351509/13208832*t^14 - 351509/1482624*t^13 + 198679/114048*t^12 - 198679/19008*t^11 + 2185469/43200*t^10 - 168113/864*t^9 + 168113/288*t^8 - 168113/126*t^7 + 40579/18*t^6 - 40579/15*t^5 + 6545/3*t^4 - 6545/6*t^3 + 595/2*t^2 - 35*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:   35 out of 35
Indefinite weights: 0 out of 35
Negative weights:   0 out of 35
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (123.17325317537592765 + 2.5623595247917491495e-516j)  +/-  (1.54e-242, 1.54e-242j)
| (63.266373675384761537 + 4.5457320014337355021e-511j)  +/-  (1.02e-237, 1.02e-237j)
| (69.135413883648159662 - 3.8083431083468998826e-523j)  +/-  (6.39e-238, 6.39e-238j)
| (99.312973659441359472 - 3.9973375876148205898e-533j)  +/-  (3.77e-240, 3.77e-240j)
| (75.534435134729916579 - 1.664949923973770981e-533j)  +/-  (2.59e-238, 2.59e-238j)
| (82.57140552358264886 - 4.7219476200865373878e-547j)  +/-  (8.47e-239, 8.47e-239j)
| (6.714963279915739328 + 4.9748848171502628016e-567j)  +/-  (3.79e-244, 3.79e-244j)
| (52.831925058015623889 + 3.3163784394759046811e-566j)  +/-  (1.97e-237, 1.97e-237j)
| (109.79599094490647516 - 6.2081562814111724908e-588j)  +/-  (3.39e-241, 3.39e-241j)
| (57.850795022134440333 + 2.0320913743418076171e-589j)  +/-  (1.67e-237, 1.67e-237j)
| (90.408523864400746415 - 4.5572522543709293445e-608j)  +/-  (2.09e-239, 2.09e-239j)
| (5.3914027346738231891 + 2.5528676089849267502e-623j)  +/-  (4.27e-245, 4.27e-245j)
| (26.049948710370233228 - 2.1935682643248433786e-635j)  +/-  (1.49e-238, 1.49e-238j)
| (43.819260118606670766 - 2.4479843735285115337e-668j)  +/-  (1.98e-237, 1.98e-237j)
| (23.174507997799254137 + 1.0082465288981508985e-684j)  +/-  (5.6e-239, 5.6e-239j)
| (0.98138617345907802054 + 1.9024371484603027835e-709j)  +/-  (2.04e-250, 2.04e-250j)
| (18.010773287835124877 - 9.3632129922340810359e-697j)  +/-  (5.86e-240, 5.86e-240j)
| (48.166197974018779925 + 4.281053286886530472e-709j)  +/-  (2.14e-237, 2.14e-237j)
| (35.97602876989402268 - 2.2047239431043424885e-720j)  +/-  (1.08e-237, 1.08e-237j)
| (2.3122282965132124406 - 4.0450010776993337321e-734j)  +/-  (4.77e-248, 4.77e-248j)
| (1.5757259475774519583 + 2.259668775539306952e-734j)  +/-  (3.75e-249, 3.75e-249j)
| (0.2146874527351445693 + 3.9732657585029202319e-738j)  +/-  (3.02e-253, 3.02e-253j)
| (4.2180641250297159632 + 6.3508336930331007308e-732j)  +/-  (5.04e-246, 5.04e-246j)
| (15.706263395762777371 - 1.395186703521033268e-726j)  +/-  (1.59e-240, 1.59e-240j)
| (29.133979209544429426 + 1.5350104945253198959e-722j)  +/-  (3.18e-238, 3.18e-238j)
| (13.577539357307804534 - 2.6149291459731428426e-731j)  +/-  (3.59e-241, 3.59e-241j)
| (32.438171837677936939 + 4.0510816239412706672e-727j)  +/-  (6.22e-238, 6.22e-238j)
| (11.618816388907337457 + 8.413172160094513295e-741j)  +/-  (7.86e-242, 7.86e-242j)
| (39.763434104800269334 + 2.1035358741250897953e-739j)  +/-  (1.54e-237, 1.54e-237j)
| (20.497671107146630511 - 1.3475700069370207198e-747j)  +/-  (1.9e-239, 1.9e-239j)
| (9.8250204970927057888 + 2.0501334389514637357e-756j)  +/-  (1.5e-242, 1.5e-242j)
| (3.1923979394931200889 + 1.7389845796839690328e-761j)  +/-  (5.63e-247, 5.63e-247j)
| (0.52801038431934377708 - 2.9589948620719708614e-766j)  +/-  (9.51e-252, 9.51e-252j)
| (8.1917017588376206933 + 1.1991602011215070679e-757j)  +/-  (2.36e-243, 2.36e-243j)
| (0.040729209061713438974 + 1.9669094585367080836e-768j)  +/-  (3.49e-255, 3.49e-255j)
-------------------------------------------------
The weights are:
| (5.1067238137005542892e-53 - 3.2814284462692843097e-552j)  +/-  (8.7e-86, 2.21e-201j)
| (1.8809869282202612865e-27 - 4.2076561415413020285e-538j)  +/-  (2.43e-76, 6.17e-192j)
| (5.7751551043945367004e-30 - 8.4386946134566526059e-540j)  +/-  (1.04e-77, 2.65e-193j)
| (7.0802327339258537996e-43 - 5.7659742441336680097e-547j)  +/-  (1.07e-83, 2.71e-199j)
| (1.0511407467805984576e-32 + 1.8002682871400776039e-541j)  +/-  (1.29e-79, 3.28e-195j)
| (1.0212770131874045815e-35 - 3.7284329736386896607e-543j)  +/-  (3.37e-81, 8.54e-197j)
| (0.0016972232991259838798 - 4.6790546576059493246e-528j)  +/-  (1.68e-54, 4.28e-170j)
| (5.4936947240754559482e-23 - 1.2797384536159182613e-536j)  +/-  (3.74e-77, 9.51e-193j)
| (2.3974946333650172388e-47 + 2.7330830481285837097e-549j)  +/-  (1.86e-86, 4.71e-202j)
| (3.9126925656364653134e-25 + 2.1774987091674405193e-537j)  +/-  (6.65e-78, 1.69e-193j)
| (4.5273473120817516735e-39 + 5.8424175416075401631e-545j)  +/-  (4.61e-83, 1.17e-198j)
| (0.0056853255717743371717 + 7.4980445539598432162e-528j)  +/-  (6.11e-58, 1.55e-173j)
| (1.4473323990388579873e-11 + 1.2931924833949822254e-531j)  +/-  (1.31e-73, 3.33e-189j)
| (3.9129108119233423665e-19 - 5.2776135973382422897e-535j)  +/-  (2.02e-77, 5.13e-193j)
| (2.3913229815921465354e-10 - 4.602336394843776818e-531j)  +/-  (4.22e-73, 1.07e-188j)
| (0.1962716678964444167 - 1.7465283432667679216e-527j)  +/-  (6.25e-58, 1.59e-173j)
| (3.6077854386915525045e-08 - 4.4149363331990285102e-530j)  +/-  (8.46e-72, 2.15e-187j)
| (5.4327194067067156311e-21 + 8.3966889529019512948e-536j)  +/-  (4.96e-78, 1.26e-193j)
| (8.6948402143307648797e-16 - 1.6063442928868877508e-533j)  +/-  (5.14e-77, 1.31e-192j)
| (0.08003040046414025277 - 1.7492418126061797422e-527j)  +/-  (1.74e-60, 4.42e-176j)
| (0.13760074201312757452 + 1.8708615375327723833e-527j)  +/-  (1.54e-58, 3.92e-174j)
| (0.19648238336171276626 - 8.0738128859426293832e-528j)  +/-  (4.68e-58, 1.19e-173j)
| (0.016186726526125783826 - 1.0968288875052321563e-527j)  +/-  (5.8e-64, 1.47e-179j)
| (3.3446109572663336308e-07 + 1.1944738181567797111e-529j)  +/-  (1.54e-72, 3.92e-188j)
| (7.1013552778116401459e-13 - 3.3030413668644530278e-532j)  +/-  (5.4e-76, 1.37e-191j)
| (2.5916721474280000449e-06 - 2.9590479510888156818e-529j)  +/-  (1.05e-72, 2.67e-188j)
| (2.7933695093215839594e-14 + 7.6534003342265504352e-533j)  +/-  (6.52e-77, 1.66e-192j)
| (1.6870264869314439671e-05 + 6.7189646227999938351e-529j)  +/-  (6.34e-73, 1.61e-188j)
| (2.1088459367771633669e-17 + 3.0538832531924746628e-534j)  +/-  (1.57e-78, 4e-194j)
| (3.2335690322102271572e-09 + 1.4920298041831113892e-530j)  +/-  (9.37e-75, 2.38e-190j)
| (9.2634053063653426884e-05 - 1.3992163295718768377e-528j)  +/-  (2.87e-73, 7.3e-189j)
| (0.039125771428883304215 + 1.4581890691402488483e-527j)  +/-  (8.86e-72, 2.24e-187j)
| (0.22601456693434385115 + 1.3647921258541841482e-527j)  +/-  (1.92e-71, 4.86e-187j)
| (0.0004304850681416781334 + 2.6725413841235293263e-528j)  +/-  (4.64e-73, 1.18e-188j)
| (0.1003622374192359274 + 2.5064274382980434258e-528j)  +/-  (5.11e-72, 1.29e-187j)
Starting with polynomial:
P : -1/10333147966386144929666651337523200000000*t^35 + 1/8435222829702975452789103132672000000*t^34 - 1/14593811124053590748770074624000000*t^33 + 1/40203336429899699032424448000000*t^32 - 1/157044282929295699345408000000*t^31 + 31/25329723053112209571840000000*t^30 - 31/168864820354081397145600000*t^29 + 899/40760473878571371724800000*t^28 - 899/415923202842565017600000*t^27 + 899/5134854356081049600000*t^26 - 899/75959383965696000000*t^25 + 899/1336885157796249600*t^24 - 899/27851774120755200*t^23 + 20677/15742307111731200*t^22 - 20677/455355990835200*t^21 + 20677/15488299008000*t^20 - 20677/619531960320*t^19 + 392863/554318069760*t^18 - 392863/30795448320*t^17 + 351509/1811496960*t^16 - 351509/141523200*t^15 + 351509/13208832*t^14 - 351509/1482624*t^13 + 198679/114048*t^12 - 198679/19008*t^11 + 2185469/43200*t^10 - 168113/864*t^9 + 168113/288*t^8 - 168113/126*t^7 + 40579/18*t^6 - 40579/15*t^5 + 6545/3*t^4 - 6545/6*t^3 + 595/2*t^2 - 35*t + 1
Extension levels are: 35
-------------------------------------------------
Ending with final polynomial:
P : -1/10333147966386144929666651337523200000000*t^35 + 1/8435222829702975452789103132672000000*t^34 - 1/14593811124053590748770074624000000*t^33 + 1/40203336429899699032424448000000*t^32 - 1/157044282929295699345408000000*t^31 + 31/25329723053112209571840000000*t^30 - 31/168864820354081397145600000*t^29 + 899/40760473878571371724800000*t^28 - 899/415923202842565017600000*t^27 + 899/5134854356081049600000*t^26 - 899/75959383965696000000*t^25 + 899/1336885157796249600*t^24 - 899/27851774120755200*t^23 + 20677/15742307111731200*t^22 - 20677/455355990835200*t^21 + 20677/15488299008000*t^20 - 20677/619531960320*t^19 + 392863/554318069760*t^18 - 392863/30795448320*t^17 + 351509/1811496960*t^16 - 351509/141523200*t^15 + 351509/13208832*t^14 - 351509/1482624*t^13 + 198679/114048*t^12 - 198679/19008*t^11 + 2185469/43200*t^10 - 168113/864*t^9 + 168113/288*t^8 - 168113/126*t^7 + 40579/18*t^6 - 40579/15*t^5 + 6545/3*t^4 - 6545/6*t^3 + 595/2*t^2 - 35*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:   35 out of 35
Indefinite weights: 0 out of 35
Negative weights:   0 out of 35
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (123.17325317537592765 + 2.5623595247917491495e-516j)  +/-  (1.54e-242, 1.54e-242j)
| (63.266373675384761537 + 4.5457320014337355021e-511j)  +/-  (1.02e-237, 1.02e-237j)
| (69.135413883648159662 - 3.8083431083468998826e-523j)  +/-  (6.39e-238, 6.39e-238j)
| (99.312973659441359472 - 3.9973375876148205898e-533j)  +/-  (3.77e-240, 3.77e-240j)
| (75.534435134729916579 - 1.664949923973770981e-533j)  +/-  (2.59e-238, 2.59e-238j)
| (82.57140552358264886 - 4.7219476200865373878e-547j)  +/-  (8.47e-239, 8.47e-239j)
| (6.714963279915739328 + 4.9748848171502628016e-567j)  +/-  (3.79e-244, 3.79e-244j)
| (52.831925058015623889 + 3.3163784394759046811e-566j)  +/-  (1.97e-237, 1.97e-237j)
| (109.79599094490647516 - 6.2081562814111724908e-588j)  +/-  (3.39e-241, 3.39e-241j)
| (57.850795022134440333 + 2.0320913743418076171e-589j)  +/-  (1.67e-237, 1.67e-237j)
| (90.408523864400746415 - 4.5572522543709293445e-608j)  +/-  (2.09e-239, 2.09e-239j)
| (5.3914027346738231891 + 2.5528676089849267502e-623j)  +/-  (4.27e-245, 4.27e-245j)
| (26.049948710370233228 - 2.1935682643248433786e-635j)  +/-  (1.49e-238, 1.49e-238j)
| (43.819260118606670766 - 2.4479843735285115337e-668j)  +/-  (1.98e-237, 1.98e-237j)
| (23.174507997799254137 + 1.0082465288981508985e-684j)  +/-  (5.6e-239, 5.6e-239j)
| (0.98138617345907802054 + 1.9024371484603027835e-709j)  +/-  (2.04e-250, 2.04e-250j)
| (18.010773287835124877 - 9.3632129922340810359e-697j)  +/-  (5.86e-240, 5.86e-240j)
| (48.166197974018779925 + 4.281053286886530472e-709j)  +/-  (2.14e-237, 2.14e-237j)
| (35.97602876989402268 - 2.2047239431043424885e-720j)  +/-  (1.08e-237, 1.08e-237j)
| (2.3122282965132124406 - 4.0450010776993337321e-734j)  +/-  (4.77e-248, 4.77e-248j)
| (1.5757259475774519583 + 2.259668775539306952e-734j)  +/-  (3.75e-249, 3.75e-249j)
| (0.2146874527351445693 + 3.9732657585029202319e-738j)  +/-  (3.02e-253, 3.02e-253j)
| (4.2180641250297159632 + 6.3508336930331007308e-732j)  +/-  (5.04e-246, 5.04e-246j)
| (15.706263395762777371 - 1.395186703521033268e-726j)  +/-  (1.59e-240, 1.59e-240j)
| (29.133979209544429426 + 1.5350104945253198959e-722j)  +/-  (3.18e-238, 3.18e-238j)
| (13.577539357307804534 - 2.6149291459731428426e-731j)  +/-  (3.59e-241, 3.59e-241j)
| (32.438171837677936939 + 4.0510816239412706672e-727j)  +/-  (6.22e-238, 6.22e-238j)
| (11.618816388907337457 + 8.413172160094513295e-741j)  +/-  (7.86e-242, 7.86e-242j)
| (39.763434104800269334 + 2.1035358741250897953e-739j)  +/-  (1.54e-237, 1.54e-237j)
| (20.497671107146630511 - 1.3475700069370207198e-747j)  +/-  (1.9e-239, 1.9e-239j)
| (9.8250204970927057888 + 2.0501334389514637357e-756j)  +/-  (1.5e-242, 1.5e-242j)
| (3.1923979394931200889 + 1.7389845796839690328e-761j)  +/-  (5.63e-247, 5.63e-247j)
| (0.52801038431934377708 - 2.9589948620719708614e-766j)  +/-  (9.51e-252, 9.51e-252j)
| (8.1917017588376206933 + 1.1991602011215070679e-757j)  +/-  (2.36e-243, 2.36e-243j)
| (0.040729209061713438974 + 1.9669094585367080836e-768j)  +/-  (3.49e-255, 3.49e-255j)
-------------------------------------------------
The weights are:
| (5.1067238137005542892e-53 - 3.2814284462692843097e-552j)  +/-  (8.7e-86, 2.21e-201j)
| (1.8809869282202612865e-27 - 4.2076561415413020285e-538j)  +/-  (2.43e-76, 6.17e-192j)
| (5.7751551043945367004e-30 - 8.4386946134566526059e-540j)  +/-  (1.04e-77, 2.65e-193j)
| (7.0802327339258537996e-43 - 5.7659742441336680097e-547j)  +/-  (1.07e-83, 2.71e-199j)
| (1.0511407467805984576e-32 + 1.8002682871400776039e-541j)  +/-  (1.29e-79, 3.28e-195j)
| (1.0212770131874045815e-35 - 3.7284329736386896607e-543j)  +/-  (3.37e-81, 8.54e-197j)
| (0.0016972232991259838798 - 4.6790546576059493246e-528j)  +/-  (1.68e-54, 4.28e-170j)
| (5.4936947240754559482e-23 - 1.2797384536159182613e-536j)  +/-  (3.74e-77, 9.51e-193j)
| (2.3974946333650172388e-47 + 2.7330830481285837097e-549j)  +/-  (1.86e-86, 4.71e-202j)
| (3.9126925656364653134e-25 + 2.1774987091674405193e-537j)  +/-  (6.65e-78, 1.69e-193j)
| (4.5273473120817516735e-39 + 5.8424175416075401631e-545j)  +/-  (4.61e-83, 1.17e-198j)
| (0.0056853255717743371717 + 7.4980445539598432162e-528j)  +/-  (6.11e-58, 1.55e-173j)
| (1.4473323990388579873e-11 + 1.2931924833949822254e-531j)  +/-  (1.31e-73, 3.33e-189j)
| (3.9129108119233423665e-19 - 5.2776135973382422897e-535j)  +/-  (2.02e-77, 5.13e-193j)
| (2.3913229815921465354e-10 - 4.602336394843776818e-531j)  +/-  (4.22e-73, 1.07e-188j)
| (0.1962716678964444167 - 1.7465283432667679216e-527j)  +/-  (6.25e-58, 1.59e-173j)
| (3.6077854386915525045e-08 - 4.4149363331990285102e-530j)  +/-  (8.46e-72, 2.15e-187j)
| (5.4327194067067156311e-21 + 8.3966889529019512948e-536j)  +/-  (4.96e-78, 1.26e-193j)
| (8.6948402143307648797e-16 - 1.6063442928868877508e-533j)  +/-  (5.14e-77, 1.31e-192j)
| (0.08003040046414025277 - 1.7492418126061797422e-527j)  +/-  (1.74e-60, 4.42e-176j)
| (0.13760074201312757452 + 1.8708615375327723833e-527j)  +/-  (1.54e-58, 3.92e-174j)
| (0.19648238336171276626 - 8.0738128859426293832e-528j)  +/-  (4.68e-58, 1.19e-173j)
| (0.016186726526125783826 - 1.0968288875052321563e-527j)  +/-  (5.8e-64, 1.47e-179j)
| (3.3446109572663336308e-07 + 1.1944738181567797111e-529j)  +/-  (1.54e-72, 3.92e-188j)
| (7.1013552778116401459e-13 - 3.3030413668644530278e-532j)  +/-  (5.4e-76, 1.37e-191j)
| (2.5916721474280000449e-06 - 2.9590479510888156818e-529j)  +/-  (1.05e-72, 2.67e-188j)
| (2.7933695093215839594e-14 + 7.6534003342265504352e-533j)  +/-  (6.52e-77, 1.66e-192j)
| (1.6870264869314439671e-05 + 6.7189646227999938351e-529j)  +/-  (6.34e-73, 1.61e-188j)
| (2.1088459367771633669e-17 + 3.0538832531924746628e-534j)  +/-  (1.57e-78, 4e-194j)
| (3.2335690322102271572e-09 + 1.4920298041831113892e-530j)  +/-  (9.37e-75, 2.38e-190j)
| (9.2634053063653426884e-05 - 1.3992163295718768377e-528j)  +/-  (2.87e-73, 7.3e-189j)
| (0.039125771428883304215 + 1.4581890691402488483e-527j)  +/-  (8.86e-72, 2.24e-187j)
| (0.22601456693434385115 + 1.3647921258541841482e-527j)  +/-  (1.92e-71, 4.86e-187j)
| (0.0004304850681416781334 + 2.6725413841235293263e-528j)  +/-  (4.64e-73, 1.18e-188j)
| (0.1003622374192359274 + 2.5064274382980434258e-528j)  +/-  (5.11e-72, 1.29e-187j)
