Starting with polynomial:
P : 1/265252859812191058636308480000000*t^30 - 1/294725399791323398484787200000*t^29 + 29/20325889640780924033433600000*t^28 - 29/77777638931559658291200000*t^27 + 29/426763450927625011200000*t^26 - 29/3156534400352256000000*t^25 + 29/30302730243381657600*t^24 - 29/368262346707763200*t^23 + 667/128091251028787200*t^22 - 667/2381862105907200*t^21 + 667/54010478592000*t^20 - 667/1485288161280*t^19 + 12673/938076733440*t^18 - 12673/37638881280*t^17 + 215441/30996725760*t^16 - 215441/1816214400*t^15 + 215441/129153024*t^14 - 12673/658944*t^13 + 164749/912384*t^12 - 8671/6336*t^11 + 95381/11520*t^10 - 476905/12096*t^9 + 130065/896*t^8 - 5655/14*t^7 + 13195/16*t^6 - 23751/20*t^5 + 9135/8*t^4 - 2030/3*t^3 + 435/2*t^2 - 30*t + 1
Extension levels are: 30
-------------------------------------------------
Ending with final polynomial:
P : 1/265252859812191058636308480000000*t^30 - 1/294725399791323398484787200000*t^29 + 29/20325889640780924033433600000*t^28 - 29/77777638931559658291200000*t^27 + 29/426763450927625011200000*t^26 - 29/3156534400352256000000*t^25 + 29/30302730243381657600*t^24 - 29/368262346707763200*t^23 + 667/128091251028787200*t^22 - 667/2381862105907200*t^21 + 667/54010478592000*t^20 - 667/1485288161280*t^19 + 12673/938076733440*t^18 - 12673/37638881280*t^17 + 215441/30996725760*t^16 - 215441/1816214400*t^15 + 215441/129153024*t^14 - 12673/658944*t^13 + 164749/912384*t^12 - 8671/6336*t^11 + 95381/11520*t^10 - 476905/12096*t^9 + 130065/896*t^8 - 5655/14*t^7 + 13195/16*t^6 - 23751/20*t^5 + 9135/8*t^4 - 2030/3*t^3 + 435/2*t^2 - 30*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:   30 out of 30
Indefinite weights: 0 out of 30
Negative weights:   0 out of 30
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (104.15752443105889451 - 2.4724339598045209395e-536j)  +/-  (4.9e-244, 4.9e-244j)
| (53.841385406507505617 - 3.9624588766146062582e-536j)  +/-  (4.74e-240, 4.74e-240j)
| (81.736810506727685722 - 2.8601910306683015852e-541j)  +/-  (7.82e-242, 7.82e-242j)
| (91.556466522536838256 + 5.467739032384673962e-545j)  +/-  (9.19e-243, 9.19e-243j)
| (73.44123859555988224 + 2.9804798155708998465e-541j)  +/-  (3.52e-241, 3.52e-241j)
| (31.141586701111235818 + 2.8200057528378681444e-543j)  +/-  (3.68e-240, 3.68e-240j)
| (4.9272937658498824097 + 2.3594424078264343631e-559j)  +/-  (2.91e-246, 2.91e-246j)
| (66.180617794438489652 + 3.1664210406118871331e-551j)  +/-  (1.2e-240, 1.2e-240j)
| (39.116084949067889122 - 3.6922738880313123944e-561j)  +/-  (6.98e-240, 6.98e-240j)
| (9.6037759854792620798 - 4.2815153773441785672e-574j)  +/-  (7.7e-244, 7.7e-244j)
| (2.6965218745572151958 + 9.3694203193961203484e-578j)  +/-  (2.66e-248, 2.66e-248j)
| (24.340035764532693401 + 1.2043783072240545263e-569j)  +/-  (1.09e-240, 1.09e-240j)
| (21.327204321783128928 - 6.81635825129010325e-578j)  +/-  (5.12e-241, 5.12e-241j)
| (34.969652008249069544 - 6.223962416250050826e-591j)  +/-  (5.69e-240, 5.69e-240j)
| (13.666744693064236295 - 1.3800827247469926744e-603j)  +/-  (1.52e-242, 1.52e-242j)
| (1.8364545546225722915 + 1.4389079377461327017e-629j)  +/-  (2.07e-249, 2.07e-249j)
| (16.002221188981066255 + 8.6962427231411185916e-633j)  +/-  (5.33e-242, 5.33e-242j)
| (0.047407180540804851462 + 3.9027824351405259175e-660j)  +/-  (4.32e-255, 4.32e-255j)
| (59.699121859235495477 - 4.065105367213608636e-689j)  +/-  (2.64e-240, 2.64e-240j)
| (48.503986163804200427 + 9.1058666846679797011e-729j)  +/-  (6.35e-240, 6.35e-240j)
| (0.24992391675316022399 + 1.4832465461494514741e-759j)  +/-  (1.97e-253, 1.97e-253j)
| (0.61483345439276828461 - 3.0468511123513626653e-757j)  +/-  (6.91e-252, 6.91e-252j)
| (7.8616932933702604688 - 1.6903380336268052254e-746j)  +/-  (1.5e-244, 1.5e-244j)
| (43.613652908484827807 - 1.5687209071112695352e-752j)  +/-  (7.56e-240, 7.56e-240j)
| (1.1431958256661007983 + 7.7558700793262138224e-777j)  +/-  (1.29e-250, 1.29e-250j)
| (27.605554796780961028 - 1.1046222574434651849e-765j)  +/-  (2.65e-240, 2.65e-240j)
| (6.3045155909650745228 - 2.1160902195978762801e-779j)  +/-  (2.38e-245, 2.38e-245j)
| (3.7258145077795089493 + 4.351523342194313159e-782j)  +/-  (3.21e-247, 3.21e-247j)
| (11.536546597956139701 + 2.2937514678960637946e-774j)  +/-  (3.72e-243, 3.72e-243j)
| (18.552134840143150124 - 1.1971809967181065835e-774j)  +/-  (1.88e-241, 1.88e-241j)
-------------------------------------------------
The weights are:
| (8.7459804404651875591e-45 - 4.9466848556384693248e-571j)  +/-  (3.39e-98, 1.03e-215j)
| (2.3114097943886493589e-23 + 4.4917754872244489355e-559j)  +/-  (1.45e-90, 4.37e-208j)
| (2.8423235534027969144e-35 - 4.5019437276238633186e-566j)  +/-  (1.32e-95, 3.99e-213j)
| (1.8786080317495715678e-39 + 2.8664117922949233395e-568j)  +/-  (4.56e-97, 1.38e-214j)
| (9.8323750831056357108e-32 + 3.5701632331916218242e-564j)  +/-  (9.09e-95, 2.75e-212j)
| (1.0990180597534727279e-13 - 2.2658895609692260239e-555j)  +/-  (6.68e-88, 2.02e-205j)
| (0.0093380708816042351496 + 1.1522366903794086717e-550j)  +/-  (5.41e-71, 1.63e-188j)
| (1.2391497014482743994e-28 - 1.909721453241915491e-562j)  +/-  (3.61e-94, 1.09e-211j)
| (4.4378380598403008662e-17 - 7.2583623034624152474e-557j)  +/-  (3.77e-90, 1.14e-207j)
| (0.00012390745990688661704 - 2.0513571676810883456e-551j)  +/-  (2.49e-79, 7.52e-197j)
| (0.06367878036898826934 + 2.1279044229020558724e-550j)  +/-  (3.48e-69, 1.05e-186j)
| (8.4274791230570478545e-11 - 4.0973278032194690803e-554j)  +/-  (5.9e-87, 1.78e-204j)
| (1.5807455747783781037e-09 + 1.4974638105619009999e-553j)  +/-  (3.24e-86, 9.77e-204j)
| (2.5883126649592354134e-15 + 4.0072622619373494241e-556j)  +/-  (1.12e-89, 3.4e-207j)
| (2.5893509291314845837e-06 - 3.9013632490311238585e-552j)  +/-  (3.55e-84, 1.07e-201j)
| (0.12372841596688099223 - 2.4069674078035367673e-550j)  +/-  (1.54e-73, 4.65e-191j)
| (2.7409428405360851638e-07 + 1.4601315411042442569e-552j)  +/-  (3.85e-85, 1.16e-202j)
| (0.11604408602039325562 - 3.6196478663328110773e-551j)  +/-  (1.42e-74, 4.3e-192j)
| (7.2745884982925408323e-26 + 9.2486410917532489207e-561j)  +/-  (2.26e-95, 6.84e-213j)
| (4.3939468922917157783e-21 - 2.241141252689304521e-558j)  +/-  (9.2e-94, 2.78e-211j)
| (0.22085112475069602168 + 1.1509005438980111766e-550j)  +/-  (2.8e-77, 8.46e-195j)
| (0.24139982758787346417 - 1.9003032502863304032e-550j)  +/-  (8.06e-78, 2.44e-195j)
| (0.0006351291219408776464 + 4.0408061398360690995e-551j)  +/-  (1.11e-84, 3.36e-202j)
| (5.3659183082123539536e-19 + 1.2215039135092189094e-557j)  +/-  (6.49e-93, 1.96e-210j)
| (0.19463676844641672701 + 2.3502679395490810998e-550j)  +/-  (1.75e-80, 5.29e-198j)
| (3.485161234907977146e-12 + 1.0171143390862962363e-554j)  +/-  (6.03e-90, 1.82e-207j)
| (0.0026806968913369005385 - 7.1877829542957302546e-551j)  +/-  (3.33e-85, 1.01e-202j)
| (0.026860475273380519411 - 1.6581834178866050809e-550j)  +/-  (2.62e-84, 7.91e-202j)
| (1.9828788438952961056e-05 + 9.4112308000211771027e-552j)  +/-  (4.44e-87, 1.34e-204j)
| (2.3328311650257961682e-08 - 4.9274961416082238773e-553j)  +/-  (1.21e-88, 3.64e-206j)
Starting with polynomial:
P : 1/265252859812191058636308480000000*t^30 - 1/294725399791323398484787200000*t^29 + 29/20325889640780924033433600000*t^28 - 29/77777638931559658291200000*t^27 + 29/426763450927625011200000*t^26 - 29/3156534400352256000000*t^25 + 29/30302730243381657600*t^24 - 29/368262346707763200*t^23 + 667/128091251028787200*t^22 - 667/2381862105907200*t^21 + 667/54010478592000*t^20 - 667/1485288161280*t^19 + 12673/938076733440*t^18 - 12673/37638881280*t^17 + 215441/30996725760*t^16 - 215441/1816214400*t^15 + 215441/129153024*t^14 - 12673/658944*t^13 + 164749/912384*t^12 - 8671/6336*t^11 + 95381/11520*t^10 - 476905/12096*t^9 + 130065/896*t^8 - 5655/14*t^7 + 13195/16*t^6 - 23751/20*t^5 + 9135/8*t^4 - 2030/3*t^3 + 435/2*t^2 - 30*t + 1
Extension levels are: 30
-------------------------------------------------
Ending with final polynomial:
P : 1/265252859812191058636308480000000*t^30 - 1/294725399791323398484787200000*t^29 + 29/20325889640780924033433600000*t^28 - 29/77777638931559658291200000*t^27 + 29/426763450927625011200000*t^26 - 29/3156534400352256000000*t^25 + 29/30302730243381657600*t^24 - 29/368262346707763200*t^23 + 667/128091251028787200*t^22 - 667/2381862105907200*t^21 + 667/54010478592000*t^20 - 667/1485288161280*t^19 + 12673/938076733440*t^18 - 12673/37638881280*t^17 + 215441/30996725760*t^16 - 215441/1816214400*t^15 + 215441/129153024*t^14 - 12673/658944*t^13 + 164749/912384*t^12 - 8671/6336*t^11 + 95381/11520*t^10 - 476905/12096*t^9 + 130065/896*t^8 - 5655/14*t^7 + 13195/16*t^6 - 23751/20*t^5 + 9135/8*t^4 - 2030/3*t^3 + 435/2*t^2 - 30*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:   30 out of 30
Indefinite weights: 0 out of 30
Negative weights:   0 out of 30
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (104.15752443105889451 - 2.4724339598045209395e-536j)  +/-  (4.9e-244, 4.9e-244j)
| (53.841385406507505617 - 3.9624588766146062582e-536j)  +/-  (4.74e-240, 4.74e-240j)
| (81.736810506727685722 - 2.8601910306683015852e-541j)  +/-  (7.82e-242, 7.82e-242j)
| (91.556466522536838256 + 5.467739032384673962e-545j)  +/-  (9.19e-243, 9.19e-243j)
| (73.44123859555988224 + 2.9804798155708998465e-541j)  +/-  (3.52e-241, 3.52e-241j)
| (31.141586701111235818 + 2.8200057528378681444e-543j)  +/-  (3.68e-240, 3.68e-240j)
| (4.9272937658498824097 + 2.3594424078264343631e-559j)  +/-  (2.91e-246, 2.91e-246j)
| (66.180617794438489652 + 3.1664210406118871331e-551j)  +/-  (1.2e-240, 1.2e-240j)
| (39.116084949067889122 - 3.6922738880313123944e-561j)  +/-  (6.98e-240, 6.98e-240j)
| (9.6037759854792620798 - 4.2815153773441785672e-574j)  +/-  (7.7e-244, 7.7e-244j)
| (2.6965218745572151958 + 9.3694203193961203484e-578j)  +/-  (2.66e-248, 2.66e-248j)
| (24.340035764532693401 + 1.2043783072240545263e-569j)  +/-  (1.09e-240, 1.09e-240j)
| (21.327204321783128928 - 6.81635825129010325e-578j)  +/-  (5.12e-241, 5.12e-241j)
| (34.969652008249069544 - 6.223962416250050826e-591j)  +/-  (5.69e-240, 5.69e-240j)
| (13.666744693064236295 - 1.3800827247469926744e-603j)  +/-  (1.52e-242, 1.52e-242j)
| (1.8364545546225722915 + 1.4389079377461327017e-629j)  +/-  (2.07e-249, 2.07e-249j)
| (16.002221188981066255 + 8.6962427231411185916e-633j)  +/-  (5.33e-242, 5.33e-242j)
| (0.047407180540804851462 + 3.9027824351405259175e-660j)  +/-  (4.32e-255, 4.32e-255j)
| (59.699121859235495477 - 4.065105367213608636e-689j)  +/-  (2.64e-240, 2.64e-240j)
| (48.503986163804200427 + 9.1058666846679797011e-729j)  +/-  (6.35e-240, 6.35e-240j)
| (0.24992391675316022399 + 1.4832465461494514741e-759j)  +/-  (1.97e-253, 1.97e-253j)
| (0.61483345439276828461 - 3.0468511123513626653e-757j)  +/-  (6.91e-252, 6.91e-252j)
| (7.8616932933702604688 - 1.6903380336268052254e-746j)  +/-  (1.5e-244, 1.5e-244j)
| (43.613652908484827807 - 1.5687209071112695352e-752j)  +/-  (7.56e-240, 7.56e-240j)
| (1.1431958256661007983 + 7.7558700793262138224e-777j)  +/-  (1.29e-250, 1.29e-250j)
| (27.605554796780961028 - 1.1046222574434651849e-765j)  +/-  (2.65e-240, 2.65e-240j)
| (6.3045155909650745228 - 2.1160902195978762801e-779j)  +/-  (2.38e-245, 2.38e-245j)
| (3.7258145077795089493 + 4.351523342194313159e-782j)  +/-  (3.21e-247, 3.21e-247j)
| (11.536546597956139701 + 2.2937514678960637946e-774j)  +/-  (3.72e-243, 3.72e-243j)
| (18.552134840143150124 - 1.1971809967181065835e-774j)  +/-  (1.88e-241, 1.88e-241j)
-------------------------------------------------
The weights are:
| (8.7459804404651875591e-45 - 4.9466848556384693248e-571j)  +/-  (3.39e-98, 1.03e-215j)
| (2.3114097943886493589e-23 + 4.4917754872244489355e-559j)  +/-  (1.45e-90, 4.37e-208j)
| (2.8423235534027969144e-35 - 4.5019437276238633186e-566j)  +/-  (1.32e-95, 3.99e-213j)
| (1.8786080317495715678e-39 + 2.8664117922949233395e-568j)  +/-  (4.56e-97, 1.38e-214j)
| (9.8323750831056357108e-32 + 3.5701632331916218242e-564j)  +/-  (9.09e-95, 2.75e-212j)
| (1.0990180597534727279e-13 - 2.2658895609692260239e-555j)  +/-  (6.68e-88, 2.02e-205j)
| (0.0093380708816042351496 + 1.1522366903794086717e-550j)  +/-  (5.41e-71, 1.63e-188j)
| (1.2391497014482743994e-28 - 1.909721453241915491e-562j)  +/-  (3.61e-94, 1.09e-211j)
| (4.4378380598403008662e-17 - 7.2583623034624152474e-557j)  +/-  (3.77e-90, 1.14e-207j)
| (0.00012390745990688661704 - 2.0513571676810883456e-551j)  +/-  (2.49e-79, 7.52e-197j)
| (0.06367878036898826934 + 2.1279044229020558724e-550j)  +/-  (3.48e-69, 1.05e-186j)
| (8.4274791230570478545e-11 - 4.0973278032194690803e-554j)  +/-  (5.9e-87, 1.78e-204j)
| (1.5807455747783781037e-09 + 1.4974638105619009999e-553j)  +/-  (3.24e-86, 9.77e-204j)
| (2.5883126649592354134e-15 + 4.0072622619373494241e-556j)  +/-  (1.12e-89, 3.4e-207j)
| (2.5893509291314845837e-06 - 3.9013632490311238585e-552j)  +/-  (3.55e-84, 1.07e-201j)
| (0.12372841596688099223 - 2.4069674078035367673e-550j)  +/-  (1.54e-73, 4.65e-191j)
| (2.7409428405360851638e-07 + 1.4601315411042442569e-552j)  +/-  (3.85e-85, 1.16e-202j)
| (0.11604408602039325562 - 3.6196478663328110773e-551j)  +/-  (1.42e-74, 4.3e-192j)
| (7.2745884982925408323e-26 + 9.2486410917532489207e-561j)  +/-  (2.26e-95, 6.84e-213j)
| (4.3939468922917157783e-21 - 2.241141252689304521e-558j)  +/-  (9.2e-94, 2.78e-211j)
| (0.22085112475069602168 + 1.1509005438980111766e-550j)  +/-  (2.8e-77, 8.46e-195j)
| (0.24139982758787346417 - 1.9003032502863304032e-550j)  +/-  (8.06e-78, 2.44e-195j)
| (0.0006351291219408776464 + 4.0408061398360690995e-551j)  +/-  (1.11e-84, 3.36e-202j)
| (5.3659183082123539536e-19 + 1.2215039135092189094e-557j)  +/-  (6.49e-93, 1.96e-210j)
| (0.19463676844641672701 + 2.3502679395490810998e-550j)  +/-  (1.75e-80, 5.29e-198j)
| (3.485161234907977146e-12 + 1.0171143390862962363e-554j)  +/-  (6.03e-90, 1.82e-207j)
| (0.0026806968913369005385 - 7.1877829542957302546e-551j)  +/-  (3.33e-85, 1.01e-202j)
| (0.026860475273380519411 - 1.6581834178866050809e-550j)  +/-  (2.62e-84, 7.91e-202j)
| (1.9828788438952961056e-05 + 9.4112308000211771027e-552j)  +/-  (4.44e-87, 1.34e-204j)
| (2.3328311650257961682e-08 - 4.9274961416082238773e-553j)  +/-  (1.21e-88, 3.64e-206j)
