Starting with polynomial:
P : 1/295232799039604140847618609643520000000*t^34 - 1/255391694670937838103476305920000000*t^33 + 1/469038925015496488711618560000000*t^32 - 1/1374137475631337369272320000000*t^31 + 31/177308061371785467002880000000*t^30 - 31/985044785398808150016000000*t^29 + 899/203802369392856858624000000*t^28 - 899/1819664012436221952000000*t^27 + 899/19968878051426304000000*t^26 - 899/265857843879936000000*t^25 + 899/4253725502078976000*t^24 - 899/81234341185536000*t^23 + 20677/42383134531584000*t^22 - 20677/1138389977088000*t^21 + 20677/36139364352000*t^20 - 20677/1355226163200*t^19 + 392863/1141243084800*t^18 - 392863/59880038400*t^17 + 6678671/63402393600*t^16 - 351509/247665600*t^15 + 351509/22014720*t^14 - 351509/2358720*t^13 + 4569617/3991680*t^12 - 198679/27720*t^11 + 2185469/60480*t^10 - 2185469/15120*t^9 + 504339/1120*t^8 - 336226/315*t^7 + 168113/90*t^6 - 11594/5*t^5 + 5797/3*t^4 - 2992/3*t^3 + 561/2*t^2 - 34*t + 1
Extension levels are: 34
-------------------------------------------------
Ending with final polynomial:
P : 1/295232799039604140847618609643520000000*t^34 - 1/255391694670937838103476305920000000*t^33 + 1/469038925015496488711618560000000*t^32 - 1/1374137475631337369272320000000*t^31 + 31/177308061371785467002880000000*t^30 - 31/985044785398808150016000000*t^29 + 899/203802369392856858624000000*t^28 - 899/1819664012436221952000000*t^27 + 899/19968878051426304000000*t^26 - 899/265857843879936000000*t^25 + 899/4253725502078976000*t^24 - 899/81234341185536000*t^23 + 20677/42383134531584000*t^22 - 20677/1138389977088000*t^21 + 20677/36139364352000*t^20 - 20677/1355226163200*t^19 + 392863/1141243084800*t^18 - 392863/59880038400*t^17 + 6678671/63402393600*t^16 - 351509/247665600*t^15 + 351509/22014720*t^14 - 351509/2358720*t^13 + 4569617/3991680*t^12 - 198679/27720*t^11 + 2185469/60480*t^10 - 2185469/15120*t^9 + 504339/1120*t^8 - 336226/315*t^7 + 168113/90*t^6 - 11594/5*t^5 + 5797/3*t^4 - 2992/3*t^3 + 561/2*t^2 - 34*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:   34 out of 34
Indefinite weights: 0 out of 34
Negative weights:   0 out of 34
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (119.36210667770356736 + 1.5518582854389692147e-624j)  +/-  (7.74e-243, 7.74e-243j)
| (79.26155448779584694 - 1.0418227140548004282e-619j)  +/-  (3.58e-239, 3.58e-239j)
| (95.777190422188147563 + 6.145787556837560685e-628j)  +/-  (1.73e-240, 1.73e-240j)
| (106.13344848238270913 + 2.4798367169703117917e-630j)  +/-  (1.91e-241, 1.91e-241j)
| (66.033914923530762855 - 1.5386072992018326753e-640j)  +/-  (2.53e-238, 2.53e-238j)
| (86.988886814947418934 - 3.2976630076276745295e-668j)  +/-  (1.07e-239, 1.07e-239j)
| (41.211903857730832085 + 6.1908133230668674587e-700j)  +/-  (7.02e-238, 7.02e-238j)
| (13.999555947016372232 + 1.7956307645289632432e-719j)  +/-  (2.81e-241, 2.81e-241j)
| (11.976170700835034769 - 2.4315404721305113395e-723j)  +/-  (6.61e-242, 6.61e-242j)
| (45.461183306440897319 - 2.2878315257583046884e-721j)  +/-  (7.45e-238, 7.45e-238j)
| (21.159797649874966938 - 3.3495019460536248794e-727j)  +/-  (1.21e-239, 1.21e-239j)
| (23.934791306586670858 - 3.1711223619831769969e-726j)  +/-  (3.52e-239, 3.52e-239j)
| (33.564194916500607828 - 8.7547229591371245786e-735j)  +/-  (3.18e-238, 3.18e-238j)
| (16.200152028494295725 + 4.114640506824714374e-745j)  +/-  (1.14e-240, 1.14e-240j)
| (6.9162567116922616751 - 1.0972080982616804714e-760j)  +/-  (3.44e-244, 3.44e-244j)
| (5.5519292890365679174 + 2.5324524530212222487e-763j)  +/-  (4.65e-245, 4.65e-245j)
| (72.330193077791065383 - 2.7041135313084191119e-755j)  +/-  (1.02e-238, 1.02e-238j)
| (3.2864001540017709208 - 1.0039440205804805908e-781j)  +/-  (5.07e-247, 5.07e-247j)
| (54.949412893952780329 - 6.310648787796730822e-771j)  +/-  (6.02e-238, 6.02e-238j)
| (8.4391447956883803209 + 1.1997609927892191284e-788j)  +/-  (2.31e-243, 2.31e-243j)
| (18.584427107409875677 + 9.2722234001317435477e-783j)  +/-  (3.87e-240, 3.87e-240j)
| (1.0099677654843248194 - 2.4790501246279605037e-795j)  +/-  (1.96e-250, 1.96e-250j)
| (26.919252581223641739 - 7.1850751567079009584e-783j)  +/-  (8.25e-239, 8.25e-239j)
| (0.22091640195235958414 - 1.1704135857237913361e-813j)  +/-  (2.53e-253, 2.53e-253j)
| (37.25373335110333273 - 4.0700096886851722766e-797j)  +/-  (4.75e-238, 4.75e-238j)
| (60.265621684680180788 - 9.1572121519522725837e-815j)  +/-  (4.32e-238, 4.32e-238j)
| (1.6217519534739487791 - 7.439986547775562646e-846j)  +/-  (3.26e-249, 3.26e-249j)
| (30.124605652368005541 - 6.4636086687825948644e-834j)  +/-  (1.84e-238, 1.84e-238j)
| (50.029000541299324397 - 2.1550138053550489695e-851j)  +/-  (6.98e-238, 6.98e-238j)
| (4.3429101670516818998 + 8.9886511877215187816e-870j)  +/-  (5.05e-246, 5.05e-246j)
| (0.041909920020069111635 - 3.8608591120873721559e-888j)  +/-  (3.52e-255, 3.52e-255j)
| (10.124346108943487757 - 2.4621646907298144278e-866j)  +/-  (1.46e-242, 1.46e-242j)
| (0.54335369455654153227 - 1.2449888139742830201e-875j)  +/-  (7.3e-252, 7.3e-252j)
| (2.3800146262422685601 - 1.3337085731868349797e-872j)  +/-  (4.38e-248, 4.38e-248j)
-------------------------------------------------
The weights are:
| (2.2838380513187915366e-51 - 2.5293037926279379898e-663j)  +/-  (1.05e-90, 3.81e-209j)
| (2.7557883418055028208e-34 + 1.4174102501192889412e-653j)  +/-  (2.44e-85, 8.83e-204j)
| (2.399497948459266321e-41 - 5.6387312432507309873e-658j)  +/-  (4.52e-88, 1.64e-206j)
| (9.2320704761907659737e-46 + 2.2628870341619557313e-660j)  +/-  (1.22e-89, 4.42e-208j)
| (1.2625667474662367948e-28 + 1.340953759759004699e-651j)  +/-  (1.06e-84, 3.84e-203j)
| (1.364760308970172189e-37 + 8.6619554644647256653e-656j)  +/-  (5.05e-87, 1.83e-205j)
| (5.1837051891587659509e-18 - 7.4621894532244002039e-647j)  +/-  (1.24e-80, 4.52e-199j)
| (1.7561240277004808819e-06 + 1.4759097843801618504e-641j)  +/-  (9.53e-70, 3.46e-188j)
| (1.2186620326459149982e-05 - 3.4879106705768400369e-641j)  +/-  (3.19e-68, 1.16e-186j)
| (7.9479678599438775344e-20 + 1.0924772647674039661e-647j)  +/-  (6.59e-82, 2.39e-200j)
| (1.7279159840337805171e-09 - 6.393125942805208176e-643j)  +/-  (4.92e-75, 1.78e-193j)
| (1.1596787831018540088e-10 + 1.8498387534704865078e-643j)  +/-  (2.04e-76, 7.39e-195j)
| (9.4387659042618731585e-15 - 2.3927100632751791954e-645j)  +/-  (5.3e-80, 1.92e-198j)
| (2.1107760990325595093e-07 - 5.6964260296807097964e-642j)  +/-  (4.35e-73, 1.58e-191j)
| (0.0014308099465646645906 + 2.6711709156413595469e-640j)  +/-  (3.88e-68, 1.41e-186j)
| (0.0049902953926279236717 - 4.3867849554530005241e-640j)  +/-  (7.63e-67, 2.77e-185j)
| (2.5494564787226176001e-31 - 1.2035122848717557798e-652j)  +/-  (4.34e-88, 1.57e-206j)
| (0.036680933967009896719 - 8.8775735896283756505e-640j)  +/-  (1.04e-65, 3.78e-184j)
| (6.9856955463833589865e-24 + 1.5654838700597313806e-649j)  +/-  (9.81e-86, 3.56e-204j)
| (0.00034670576855407069327 - 1.483694586184056721e-640j)  +/-  (2.59e-71, 9.41e-190j)
| (2.1041408830914042987e-08 + 2.0020385819860837717e-642j)  +/-  (8.41e-76, 3.05e-194j)
| (0.19632330935126626945 + 1.1054319055598521336e-639j)  +/-  (1.3e-65, 4.72e-184j)
| (6.3019775165523611326e-12 - 4.833954559778705971e-644j)  +/-  (2.56e-79, 9.28e-198j)
| (0.20093362433727521991 + 5.1781581485210515954e-640j)  +/-  (1.51e-67, 5.48e-186j)
| (2.5294403274624066009e-16 + 4.4890291154581368382e-646j)  +/-  (3.23e-82, 1.17e-200j)
| (3.7137865397764482586e-26 - 1.5299178901229052658e-650j)  +/-  (2.03e-87, 7.36e-206j)
| (0.13527946838507060964 - 1.1719503011790069236e-639j)  +/-  (7.8e-73, 2.83e-191j)
| (2.7428169246147321086e-13 + 1.1364134585465500589e-644j)  +/-  (3.79e-81, 1.38e-199j)
| (8.876789005200357708e-22 - 1.4004176008504764464e-648j)  +/-  (2.03e-85, 7.36e-204j)
| (0.014718804216281606215 + 6.5557477646377595666e-640j)  +/-  (4.31e-76, 1.56e-194j)
| (0.1031503857573014814 - 1.612302075378966705e-640j)  +/-  (2.61e-75, 9.62e-194j)
| (7.087155216351781433e-05 + 7.526500288098881725e-641j)  +/-  (2.71e-77, 9.88e-196j)
| (0.22905771330341420328 - 8.7061084295498507224e-640j)  +/-  (1.27e-75, 4.9e-194j)
| (0.077002901308627824299 + 1.0816997826793882798e-639j)  +/-  (7.48e-76, 2.67e-194j)
Starting with polynomial:
P : 1/295232799039604140847618609643520000000*t^34 - 1/255391694670937838103476305920000000*t^33 + 1/469038925015496488711618560000000*t^32 - 1/1374137475631337369272320000000*t^31 + 31/177308061371785467002880000000*t^30 - 31/985044785398808150016000000*t^29 + 899/203802369392856858624000000*t^28 - 899/1819664012436221952000000*t^27 + 899/19968878051426304000000*t^26 - 899/265857843879936000000*t^25 + 899/4253725502078976000*t^24 - 899/81234341185536000*t^23 + 20677/42383134531584000*t^22 - 20677/1138389977088000*t^21 + 20677/36139364352000*t^20 - 20677/1355226163200*t^19 + 392863/1141243084800*t^18 - 392863/59880038400*t^17 + 6678671/63402393600*t^16 - 351509/247665600*t^15 + 351509/22014720*t^14 - 351509/2358720*t^13 + 4569617/3991680*t^12 - 198679/27720*t^11 + 2185469/60480*t^10 - 2185469/15120*t^9 + 504339/1120*t^8 - 336226/315*t^7 + 168113/90*t^6 - 11594/5*t^5 + 5797/3*t^4 - 2992/3*t^3 + 561/2*t^2 - 34*t + 1
Extension levels are: 34
-------------------------------------------------
Ending with final polynomial:
P : 1/295232799039604140847618609643520000000*t^34 - 1/255391694670937838103476305920000000*t^33 + 1/469038925015496488711618560000000*t^32 - 1/1374137475631337369272320000000*t^31 + 31/177308061371785467002880000000*t^30 - 31/985044785398808150016000000*t^29 + 899/203802369392856858624000000*t^28 - 899/1819664012436221952000000*t^27 + 899/19968878051426304000000*t^26 - 899/265857843879936000000*t^25 + 899/4253725502078976000*t^24 - 899/81234341185536000*t^23 + 20677/42383134531584000*t^22 - 20677/1138389977088000*t^21 + 20677/36139364352000*t^20 - 20677/1355226163200*t^19 + 392863/1141243084800*t^18 - 392863/59880038400*t^17 + 6678671/63402393600*t^16 - 351509/247665600*t^15 + 351509/22014720*t^14 - 351509/2358720*t^13 + 4569617/3991680*t^12 - 198679/27720*t^11 + 2185469/60480*t^10 - 2185469/15120*t^9 + 504339/1120*t^8 - 336226/315*t^7 + 168113/90*t^6 - 11594/5*t^5 + 5797/3*t^4 - 2992/3*t^3 + 561/2*t^2 - 34*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:   34 out of 34
Indefinite weights: 0 out of 34
Negative weights:   0 out of 34
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (119.36210667770356736 + 1.5518582854389692147e-624j)  +/-  (7.74e-243, 7.74e-243j)
| (79.26155448779584694 - 1.0418227140548004282e-619j)  +/-  (3.58e-239, 3.58e-239j)
| (95.777190422188147563 + 6.145787556837560685e-628j)  +/-  (1.73e-240, 1.73e-240j)
| (106.13344848238270913 + 2.4798367169703117917e-630j)  +/-  (1.91e-241, 1.91e-241j)
| (66.033914923530762855 - 1.5386072992018326753e-640j)  +/-  (2.53e-238, 2.53e-238j)
| (86.988886814947418934 - 3.2976630076276745295e-668j)  +/-  (1.07e-239, 1.07e-239j)
| (41.211903857730832085 + 6.1908133230668674587e-700j)  +/-  (7.02e-238, 7.02e-238j)
| (13.999555947016372232 + 1.7956307645289632432e-719j)  +/-  (2.81e-241, 2.81e-241j)
| (11.976170700835034769 - 2.4315404721305113395e-723j)  +/-  (6.61e-242, 6.61e-242j)
| (45.461183306440897319 - 2.2878315257583046884e-721j)  +/-  (7.45e-238, 7.45e-238j)
| (21.159797649874966938 - 3.3495019460536248794e-727j)  +/-  (1.21e-239, 1.21e-239j)
| (23.934791306586670858 - 3.1711223619831769969e-726j)  +/-  (3.52e-239, 3.52e-239j)
| (33.564194916500607828 - 8.7547229591371245786e-735j)  +/-  (3.18e-238, 3.18e-238j)
| (16.200152028494295725 + 4.114640506824714374e-745j)  +/-  (1.14e-240, 1.14e-240j)
| (6.9162567116922616751 - 1.0972080982616804714e-760j)  +/-  (3.44e-244, 3.44e-244j)
| (5.5519292890365679174 + 2.5324524530212222487e-763j)  +/-  (4.65e-245, 4.65e-245j)
| (72.330193077791065383 - 2.7041135313084191119e-755j)  +/-  (1.02e-238, 1.02e-238j)
| (3.2864001540017709208 - 1.0039440205804805908e-781j)  +/-  (5.07e-247, 5.07e-247j)
| (54.949412893952780329 - 6.310648787796730822e-771j)  +/-  (6.02e-238, 6.02e-238j)
| (8.4391447956883803209 + 1.1997609927892191284e-788j)  +/-  (2.31e-243, 2.31e-243j)
| (18.584427107409875677 + 9.2722234001317435477e-783j)  +/-  (3.87e-240, 3.87e-240j)
| (1.0099677654843248194 - 2.4790501246279605037e-795j)  +/-  (1.96e-250, 1.96e-250j)
| (26.919252581223641739 - 7.1850751567079009584e-783j)  +/-  (8.25e-239, 8.25e-239j)
| (0.22091640195235958414 - 1.1704135857237913361e-813j)  +/-  (2.53e-253, 2.53e-253j)
| (37.25373335110333273 - 4.0700096886851722766e-797j)  +/-  (4.75e-238, 4.75e-238j)
| (60.265621684680180788 - 9.1572121519522725837e-815j)  +/-  (4.32e-238, 4.32e-238j)
| (1.6217519534739487791 - 7.439986547775562646e-846j)  +/-  (3.26e-249, 3.26e-249j)
| (30.124605652368005541 - 6.4636086687825948644e-834j)  +/-  (1.84e-238, 1.84e-238j)
| (50.029000541299324397 - 2.1550138053550489695e-851j)  +/-  (6.98e-238, 6.98e-238j)
| (4.3429101670516818998 + 8.9886511877215187816e-870j)  +/-  (5.05e-246, 5.05e-246j)
| (0.041909920020069111635 - 3.8608591120873721559e-888j)  +/-  (3.52e-255, 3.52e-255j)
| (10.124346108943487757 - 2.4621646907298144278e-866j)  +/-  (1.46e-242, 1.46e-242j)
| (0.54335369455654153227 - 1.2449888139742830201e-875j)  +/-  (7.3e-252, 7.3e-252j)
| (2.3800146262422685601 - 1.3337085731868349797e-872j)  +/-  (4.38e-248, 4.38e-248j)
-------------------------------------------------
The weights are:
| (2.2838380513187915366e-51 - 2.5293037926279379898e-663j)  +/-  (1.05e-90, 3.81e-209j)
| (2.7557883418055028208e-34 + 1.4174102501192889412e-653j)  +/-  (2.44e-85, 8.83e-204j)
| (2.399497948459266321e-41 - 5.6387312432507309873e-658j)  +/-  (4.52e-88, 1.64e-206j)
| (9.2320704761907659737e-46 + 2.2628870341619557313e-660j)  +/-  (1.22e-89, 4.42e-208j)
| (1.2625667474662367948e-28 + 1.340953759759004699e-651j)  +/-  (1.06e-84, 3.84e-203j)
| (1.364760308970172189e-37 + 8.6619554644647256653e-656j)  +/-  (5.05e-87, 1.83e-205j)
| (5.1837051891587659509e-18 - 7.4621894532244002039e-647j)  +/-  (1.24e-80, 4.52e-199j)
| (1.7561240277004808819e-06 + 1.4759097843801618504e-641j)  +/-  (9.53e-70, 3.46e-188j)
| (1.2186620326459149982e-05 - 3.4879106705768400369e-641j)  +/-  (3.19e-68, 1.16e-186j)
| (7.9479678599438775344e-20 + 1.0924772647674039661e-647j)  +/-  (6.59e-82, 2.39e-200j)
| (1.7279159840337805171e-09 - 6.393125942805208176e-643j)  +/-  (4.92e-75, 1.78e-193j)
| (1.1596787831018540088e-10 + 1.8498387534704865078e-643j)  +/-  (2.04e-76, 7.39e-195j)
| (9.4387659042618731585e-15 - 2.3927100632751791954e-645j)  +/-  (5.3e-80, 1.92e-198j)
| (2.1107760990325595093e-07 - 5.6964260296807097964e-642j)  +/-  (4.35e-73, 1.58e-191j)
| (0.0014308099465646645906 + 2.6711709156413595469e-640j)  +/-  (3.88e-68, 1.41e-186j)
| (0.0049902953926279236717 - 4.3867849554530005241e-640j)  +/-  (7.63e-67, 2.77e-185j)
| (2.5494564787226176001e-31 - 1.2035122848717557798e-652j)  +/-  (4.34e-88, 1.57e-206j)
| (0.036680933967009896719 - 8.8775735896283756505e-640j)  +/-  (1.04e-65, 3.78e-184j)
| (6.9856955463833589865e-24 + 1.5654838700597313806e-649j)  +/-  (9.81e-86, 3.56e-204j)
| (0.00034670576855407069327 - 1.483694586184056721e-640j)  +/-  (2.59e-71, 9.41e-190j)
| (2.1041408830914042987e-08 + 2.0020385819860837717e-642j)  +/-  (8.41e-76, 3.05e-194j)
| (0.19632330935126626945 + 1.1054319055598521336e-639j)  +/-  (1.3e-65, 4.72e-184j)
| (6.3019775165523611326e-12 - 4.833954559778705971e-644j)  +/-  (2.56e-79, 9.28e-198j)
| (0.20093362433727521991 + 5.1781581485210515954e-640j)  +/-  (1.51e-67, 5.48e-186j)
| (2.5294403274624066009e-16 + 4.4890291154581368382e-646j)  +/-  (3.23e-82, 1.17e-200j)
| (3.7137865397764482586e-26 - 1.5299178901229052658e-650j)  +/-  (2.03e-87, 7.36e-206j)
| (0.13527946838507060964 - 1.1719503011790069236e-639j)  +/-  (7.8e-73, 2.83e-191j)
| (2.7428169246147321086e-13 + 1.1364134585465500589e-644j)  +/-  (3.79e-81, 1.38e-199j)
| (8.876789005200357708e-22 - 1.4004176008504764464e-648j)  +/-  (2.03e-85, 7.36e-204j)
| (0.014718804216281606215 + 6.5557477646377595666e-640j)  +/-  (4.31e-76, 1.56e-194j)
| (0.1031503857573014814 - 1.612302075378966705e-640j)  +/-  (2.61e-75, 9.62e-194j)
| (7.087155216351781433e-05 + 7.526500288098881725e-641j)  +/-  (2.71e-77, 9.88e-196j)
| (0.22905771330341420328 - 8.7061084295498507224e-640j)  +/-  (1.27e-75, 4.9e-194j)
| (0.077002901308627824299 + 1.0816997826793882798e-639j)  +/-  (7.48e-76, 2.67e-194j)
