Starting with polynomial:
P : -1/10888869450418352160768000000*t^27 + 1/14936720782466875392000000*t^26 - 1/44191481604931584000000*t^25 + 1/212119111703671603200*t^24 - 1/1473049386831052800*t^23 + 23/320228127571968000*t^22 - 23/3969770176512000*t^21 + 23/63012225024000*t^20 - 23/1260244500480*t^19 + 437/596957921280*t^18 - 437/18424627200*t^17 + 7429/11921817600*t^16 - 7429/558835200*t^15 + 7429/32288256*t^14 - 7429/2306304*t^13 + 96577/2661120*t^12 - 96577/295680*t^11 + 62491/26880*t^10 - 312455/24192*t^9 + 49335/896*t^8 - 9867/56*t^7 + 3289/8*t^6 - 2691/4*t^5 + 2925/4*t^4 - 975/2*t^3 + 351/2*t^2 - 27*t + 1
Extension levels are: 27
-------------------------------------------------
Ending with final polynomial:
P : -1/10888869450418352160768000000*t^27 + 1/14936720782466875392000000*t^26 - 1/44191481604931584000000*t^25 + 1/212119111703671603200*t^24 - 1/1473049386831052800*t^23 + 23/320228127571968000*t^22 - 23/3969770176512000*t^21 + 23/63012225024000*t^20 - 23/1260244500480*t^19 + 437/596957921280*t^18 - 437/18424627200*t^17 + 7429/11921817600*t^16 - 7429/558835200*t^15 + 7429/32288256*t^14 - 7429/2306304*t^13 + 96577/2661120*t^12 - 96577/295680*t^11 + 62491/26880*t^10 - 312455/24192*t^9 + 49335/896*t^8 - 9867/56*t^7 + 3289/8*t^6 - 2691/4*t^5 + 2925/4*t^4 - 975/2*t^3 + 351/2*t^2 - 27*t + 1
-------------------------------------------------
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
Positive weights:   27 out of 27
Indefinite weights: 0 out of 27
Negative weights:   0 out of 27
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (92.802613525557044106 + 5.4558460093893373882e-632j)  +/-  (5.65e-245, 5.65e-245j)
| (35.445670666132857125 + 5.3875224707799384281e-641j)  +/-  (2.48e-241, 2.48e-241j)
| (71.331848055160100582 + 1.7453621761621946572e-662j)  +/-  (6.61e-243, 6.61e-243j)
| (80.712763847096054384 + 1.7649894160190338089e-683j)  +/-  (9.45e-244, 9.45e-244j)
| (31.302070792021055544 - 2.631656385052186037e-712j)  +/-  (1.97e-241, 1.97e-241j)
| (2.9958355818751640334 - 3.7122387356188959722e-743j)  +/-  (1.74e-248, 1.74e-248j)
| (63.440546684688830166 + 3.3081179053454448625e-736j)  +/-  (2.57e-242, 2.57e-242j)
| (56.564130901518344418 - 2.4851618268664120031e-763j)  +/-  (6.8e-242, 6.8e-242j)
| (39.980722621126703659 + 4.7993593544661437835e-791j)  +/-  (2.63e-241, 2.63e-241j)
| (10.720979045996847232 + 1.4478786678714798846e-804j)  +/-  (3.29e-244, 3.29e-244j)
| (2.0391592782504855136 + 2.9394863941846229551e-810j)  +/-  (1.58e-249, 1.58e-249j)
| (12.897150901909760499 + 8.6830743817344886847e-803j)  +/-  (1.45e-243, 1.45e-243j)
| (17.952580164010659706 - 1.0157096757363655035e-812j)  +/-  (1.37e-242, 1.37e-242j)
| (44.959864785337983666 + 5.8572716905629002179e-832j)  +/-  (2.16e-241, 2.16e-241j)
| (15.30372419706892525 + 4.7413179444480540916e-845j)  +/-  (4.42e-243, 4.42e-243j)
| (5.4823717160490678277 + 1.8187990577316452163e-848j)  +/-  (1.77e-246, 1.77e-246j)
| (4.1421944825632467621 - 1.338653878952521831e-849j)  +/-  (1.91e-247, 1.91e-247j)
| (0.27722910598770463964 + 6.1067282583726532788e-856j)  +/-  (1.88e-253, 1.88e-253j)
| (50.454196152727714413 + 2.1353426121347084721e-842j)  +/-  (1.31e-241, 1.31e-241j)
| (0.052579898206364311724 - 1.1681275418590909012e-862j)  +/-  (3.07e-255, 3.07e-255j)
| (7.0213760246055511674 + 4.7548210241088073823e-854j)  +/-  (1.31e-245, 1.31e-245j)
| (0.68216391137800683477 + 2.2469469545521385433e-860j)  +/-  (3.88e-252, 3.88e-252j)
| (8.7652027168507095569 + 4.2210597448003144499e-853j)  +/-  (7.58e-245, 7.58e-245j)
| (24.036690385983112967 + 5.7364398867791468957e-850j)  +/-  (7.03e-242, 7.03e-242j)
| (27.509627633675776867 + 2.1605544770682445141e-857j)  +/-  (1.31e-241, 1.31e-241j)
| (20.857892743471171967 + 1.7747657337609642313e-869j)  +/-  (3.42e-242, 3.42e-242j)
| (1.2688141807507568016 + 2.7646503317966956017e-886j)  +/-  (6.84e-251, 6.84e-251j)
-------------------------------------------------
The weights are:
| (7.1797423782947117356e-40 + 1.6837927751778919821e-669j)  +/-  (8.22e-100, 3.66e-218j)
| (1.7490517511153701591e-15 - 4.5786711645318717229e-656j)  +/-  (8.31e-90, 3.7e-208j)
| (8.9474191153692017126e-31 + 8.4193989827435276166e-665j)  +/-  (2.77e-97, 1.23e-215j)
| (9.2093109169179076818e-35 - 7.1971137439528946562e-667j)  +/-  (1.26e-98, 5.62e-217j)
| (1.0083497673165065622e-13 + 1.6226874709062229006e-655j)  +/-  (3.62e-90, 1.61e-208j)
| (0.052539385475132147555 + 4.627652424780407893e-651j)  +/-  (1.37e-70, 6.11e-189j)
| (2.0570430367975796844e-27 - 4.8816805441936159848e-663j)  +/-  (1.19e-96, 5.31e-215j)
| (1.7574720104286018628e-24 + 1.7863224058608311026e-661j)  +/-  (5.74e-96, 2.55e-214j)
| (2.0559670832614961682e-17 - 2.3924617614350714393e-657j)  +/-  (3.49e-93, 1.55e-211j)
| (4.557654440373496251e-05 - 3.3839061947991624178e-652j)  +/-  (2.88e-85, 1.28e-203j)
| (0.11231094931185077493 - 5.4222359952436986557e-651j)  +/-  (2.69e-74, 1.2e-192j)
| (5.7357561191908691764e-06 + 1.4437172869282025176e-652j)  +/-  (1.05e-86, 4.66e-205j)
| (4.4307691576321170409e-08 + 1.929683036270709175e-653j)  +/-  (1.75e-89, 7.79e-208j)
| (1.5562957367237999155e-19 + 1.0521090267559068513e-658j)  +/-  (2.62e-95, 1.17e-213j)
| (5.702097017139381355e-07 - 5.5509652960563773948e-653j)  +/-  (1.62e-88, 7.22e-207j)
| (0.0059841135557009914541 + 2.2880373142165152358e-651j)  +/-  (1.62e-84, 7.22e-203j)
| (0.019740923275744470301 - 3.4576156265856393375e-651j)  +/-  (2.85e-83, 1.27e-201j)
| (0.23841884939414312646 + 2.7670155170277093512e-651j)  +/-  (4.21e-81, 1.87e-199j)
| (7.0812651779011907449e-22 - 4.7655513163217830611e-660j)  +/-  (1.48e-96, 6.59e-215j)
| (0.12804572690683746145 - 8.7750419055054814594e-652j)  +/-  (1.22e-81, 5.44e-200j)
| (0.0014641503609227878196 - 1.3501461584844363621e-651j)  +/-  (3.26e-86, 1.45e-204j)
| (0.25049340652300296789 - 4.5008389985587565998e-651j)  +/-  (1.24e-82, 5.52e-201j)
| (0.000288498003965843353 + 7.1338349366089545874e-652j)  +/-  (4.01e-87, 1.78e-205j)
| (1.2089475247687209827e-10 + 1.7882652913164614892e-654j)  +/-  (6.7e-93, 2.98e-211j)
| (4.0962644275901271899e-12 - 5.062468398685605785e-655j)  +/-  (1.19e-93, 5.28e-212j)
| (2.6561653164937994334e-09 - 6.1068570875107296001e-654j)  +/-  (3.26e-92, 1.45e-210j)
| (0.19066206759352427455 + 5.4471945815656973995e-651j)  +/-  (8.51e-88, 3.78e-206j)
Starting with polynomial:
P : -1/10888869450418352160768000000*t^27 + 1/14936720782466875392000000*t^26 - 1/44191481604931584000000*t^25 + 1/212119111703671603200*t^24 - 1/1473049386831052800*t^23 + 23/320228127571968000*t^22 - 23/3969770176512000*t^21 + 23/63012225024000*t^20 - 23/1260244500480*t^19 + 437/596957921280*t^18 - 437/18424627200*t^17 + 7429/11921817600*t^16 - 7429/558835200*t^15 + 7429/32288256*t^14 - 7429/2306304*t^13 + 96577/2661120*t^12 - 96577/295680*t^11 + 62491/26880*t^10 - 312455/24192*t^9 + 49335/896*t^8 - 9867/56*t^7 + 3289/8*t^6 - 2691/4*t^5 + 2925/4*t^4 - 975/2*t^3 + 351/2*t^2 - 27*t + 1
Extension levels are: 27
-------------------------------------------------
Ending with final polynomial:
P : -1/10888869450418352160768000000*t^27 + 1/14936720782466875392000000*t^26 - 1/44191481604931584000000*t^25 + 1/212119111703671603200*t^24 - 1/1473049386831052800*t^23 + 23/320228127571968000*t^22 - 23/3969770176512000*t^21 + 23/63012225024000*t^20 - 23/1260244500480*t^19 + 437/596957921280*t^18 - 437/18424627200*t^17 + 7429/11921817600*t^16 - 7429/558835200*t^15 + 7429/32288256*t^14 - 7429/2306304*t^13 + 96577/2661120*t^12 - 96577/295680*t^11 + 62491/26880*t^10 - 312455/24192*t^9 + 49335/896*t^8 - 9867/56*t^7 + 3289/8*t^6 - 2691/4*t^5 + 2925/4*t^4 - 975/2*t^3 + 351/2*t^2 - 27*t + 1
-------------------------------------------------
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
Positive weights:   27 out of 27
Indefinite weights: 0 out of 27
Negative weights:   0 out of 27
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (92.802613525557044106 + 5.4558460093893373882e-632j)  +/-  (5.65e-245, 5.65e-245j)
| (35.445670666132857125 + 5.3875224707799384281e-641j)  +/-  (2.48e-241, 2.48e-241j)
| (71.331848055160100582 + 1.7453621761621946572e-662j)  +/-  (6.61e-243, 6.61e-243j)
| (80.712763847096054384 + 1.7649894160190338089e-683j)  +/-  (9.45e-244, 9.45e-244j)
| (31.302070792021055544 - 2.631656385052186037e-712j)  +/-  (1.97e-241, 1.97e-241j)
| (2.9958355818751640334 - 3.7122387356188959722e-743j)  +/-  (1.74e-248, 1.74e-248j)
| (63.440546684688830166 + 3.3081179053454448625e-736j)  +/-  (2.57e-242, 2.57e-242j)
| (56.564130901518344418 - 2.4851618268664120031e-763j)  +/-  (6.8e-242, 6.8e-242j)
| (39.980722621126703659 + 4.7993593544661437835e-791j)  +/-  (2.63e-241, 2.63e-241j)
| (10.720979045996847232 + 1.4478786678714798846e-804j)  +/-  (3.29e-244, 3.29e-244j)
| (2.0391592782504855136 + 2.9394863941846229551e-810j)  +/-  (1.58e-249, 1.58e-249j)
| (12.897150901909760499 + 8.6830743817344886847e-803j)  +/-  (1.45e-243, 1.45e-243j)
| (17.952580164010659706 - 1.0157096757363655035e-812j)  +/-  (1.37e-242, 1.37e-242j)
| (44.959864785337983666 + 5.8572716905629002179e-832j)  +/-  (2.16e-241, 2.16e-241j)
| (15.30372419706892525 + 4.7413179444480540916e-845j)  +/-  (4.42e-243, 4.42e-243j)
| (5.4823717160490678277 + 1.8187990577316452163e-848j)  +/-  (1.77e-246, 1.77e-246j)
| (4.1421944825632467621 - 1.338653878952521831e-849j)  +/-  (1.91e-247, 1.91e-247j)
| (0.27722910598770463964 + 6.1067282583726532788e-856j)  +/-  (1.88e-253, 1.88e-253j)
| (50.454196152727714413 + 2.1353426121347084721e-842j)  +/-  (1.31e-241, 1.31e-241j)
| (0.052579898206364311724 - 1.1681275418590909012e-862j)  +/-  (3.07e-255, 3.07e-255j)
| (7.0213760246055511674 + 4.7548210241088073823e-854j)  +/-  (1.31e-245, 1.31e-245j)
| (0.68216391137800683477 + 2.2469469545521385433e-860j)  +/-  (3.88e-252, 3.88e-252j)
| (8.7652027168507095569 + 4.2210597448003144499e-853j)  +/-  (7.58e-245, 7.58e-245j)
| (24.036690385983112967 + 5.7364398867791468957e-850j)  +/-  (7.03e-242, 7.03e-242j)
| (27.509627633675776867 + 2.1605544770682445141e-857j)  +/-  (1.31e-241, 1.31e-241j)
| (20.857892743471171967 + 1.7747657337609642313e-869j)  +/-  (3.42e-242, 3.42e-242j)
| (1.2688141807507568016 + 2.7646503317966956017e-886j)  +/-  (6.84e-251, 6.84e-251j)
-------------------------------------------------
The weights are:
| (7.1797423782947117356e-40 + 1.6837927751778919821e-669j)  +/-  (8.22e-100, 3.66e-218j)
| (1.7490517511153701591e-15 - 4.5786711645318717229e-656j)  +/-  (8.31e-90, 3.7e-208j)
| (8.9474191153692017126e-31 + 8.4193989827435276166e-665j)  +/-  (2.77e-97, 1.23e-215j)
| (9.2093109169179076818e-35 - 7.1971137439528946562e-667j)  +/-  (1.26e-98, 5.62e-217j)
| (1.0083497673165065622e-13 + 1.6226874709062229006e-655j)  +/-  (3.62e-90, 1.61e-208j)
| (0.052539385475132147555 + 4.627652424780407893e-651j)  +/-  (1.37e-70, 6.11e-189j)
| (2.0570430367975796844e-27 - 4.8816805441936159848e-663j)  +/-  (1.19e-96, 5.31e-215j)
| (1.7574720104286018628e-24 + 1.7863224058608311026e-661j)  +/-  (5.74e-96, 2.55e-214j)
| (2.0559670832614961682e-17 - 2.3924617614350714393e-657j)  +/-  (3.49e-93, 1.55e-211j)
| (4.557654440373496251e-05 - 3.3839061947991624178e-652j)  +/-  (2.88e-85, 1.28e-203j)
| (0.11231094931185077493 - 5.4222359952436986557e-651j)  +/-  (2.69e-74, 1.2e-192j)
| (5.7357561191908691764e-06 + 1.4437172869282025176e-652j)  +/-  (1.05e-86, 4.66e-205j)
| (4.4307691576321170409e-08 + 1.929683036270709175e-653j)  +/-  (1.75e-89, 7.79e-208j)
| (1.5562957367237999155e-19 + 1.0521090267559068513e-658j)  +/-  (2.62e-95, 1.17e-213j)
| (5.702097017139381355e-07 - 5.5509652960563773948e-653j)  +/-  (1.62e-88, 7.22e-207j)
| (0.0059841135557009914541 + 2.2880373142165152358e-651j)  +/-  (1.62e-84, 7.22e-203j)
| (0.019740923275744470301 - 3.4576156265856393375e-651j)  +/-  (2.85e-83, 1.27e-201j)
| (0.23841884939414312646 + 2.7670155170277093512e-651j)  +/-  (4.21e-81, 1.87e-199j)
| (7.0812651779011907449e-22 - 4.7655513163217830611e-660j)  +/-  (1.48e-96, 6.59e-215j)
| (0.12804572690683746145 - 8.7750419055054814594e-652j)  +/-  (1.22e-81, 5.44e-200j)
| (0.0014641503609227878196 - 1.3501461584844363621e-651j)  +/-  (3.26e-86, 1.45e-204j)
| (0.25049340652300296789 - 4.5008389985587565998e-651j)  +/-  (1.24e-82, 5.52e-201j)
| (0.000288498003965843353 + 7.1338349366089545874e-652j)  +/-  (4.01e-87, 1.78e-205j)
| (1.2089475247687209827e-10 + 1.7882652913164614892e-654j)  +/-  (6.7e-93, 2.98e-211j)
| (4.0962644275901271899e-12 - 5.062468398685605785e-655j)  +/-  (1.19e-93, 5.28e-212j)
| (2.6561653164937994334e-09 - 6.1068570875107296001e-654j)  +/-  (3.26e-92, 1.45e-210j)
| (0.19066206759352427455 + 5.4471945815656973995e-651j)  +/-  (8.51e-88, 3.78e-206j)
