Starting with polynomial:
P : -1/8841761993739701954543616000000*t^29 + 29/304888344611713860501504000000*t^28 - 29/777776389315596582912000000*t^27 + 29/3200725881957187584000000*t^26 - 29/18939206402113536000000*t^25 + 29/151513651216908288000*t^24 - 29/1578267200176128000*t^23 + 667/480342191357952000*t^22 - 667/7939540353024000*t^21 + 667/162031435776000*t^20 - 667/4050785894400*t^19 + 12673/2345191833600*t^18 - 12673/86858956800*t^17 + 215441/66421555200*t^16 - 215441/3632428800*t^15 + 215441/242161920*t^14 - 215441/19768320*t^13 + 164749/1520640*t^12 - 164749/190080*t^11 + 95381/17280*t^10 - 95381/3456*t^9 + 95381/896*t^8 - 8671/28*t^7 + 2639/4*t^6 - 7917/8*t^5 + 7917/8*t^4 - 609*t^3 + 203*t^2 - 29*t + 1
Extension levels are: 29
-------------------------------------------------
Ending with final polynomial:
P : -1/8841761993739701954543616000000*t^29 + 29/304888344611713860501504000000*t^28 - 29/777776389315596582912000000*t^27 + 29/3200725881957187584000000*t^26 - 29/18939206402113536000000*t^25 + 29/151513651216908288000*t^24 - 29/1578267200176128000*t^23 + 667/480342191357952000*t^22 - 667/7939540353024000*t^21 + 667/162031435776000*t^20 - 667/4050785894400*t^19 + 12673/2345191833600*t^18 - 12673/86858956800*t^17 + 215441/66421555200*t^16 - 215441/3632428800*t^15 + 215441/242161920*t^14 - 215441/19768320*t^13 + 164749/1520640*t^12 - 164749/190080*t^11 + 95381/17280*t^10 - 95381/3456*t^9 + 95381/896*t^8 - 8671/28*t^7 + 2639/4*t^6 - 7917/8*t^5 + 7917/8*t^4 - 609*t^3 + 203*t^2 - 29*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
-------------------------------------------------
The nodes are:
| (100.3674916027665953 + 7.7131061775496519179e-507j)  +/-  (2.15e-244, 2.15e-244j)
| (45.631467701277814616 + 1.2481314658808686546e-501j)  +/-  (2.3e-240, 2.3e-240j)
| (87.9325936429861272 + 3.8024116931826054612e-513j)  +/-  (4.19e-243, 4.19e-243j)
| (14.170205843320575453 + 2.2304531120606116118e-511j)  +/-  (9.9e-243, 9.9e-243j)
| (11.955771944042638355 + 7.0479371667660025317e-512j)  +/-  (2.77e-243, 2.77e-243j)
| (78.255370419410440893 - 3.9637344709532790573e-510j)  +/-  (3.4e-242, 3.4e-242j)
| (56.593462896661908285 + 4.6468271808892303029e-508j)  +/-  (9.83e-241, 9.83e-241j)
| (70.090894596424175386 - 6.3543390789785943583e-513j)  +/-  (1.42e-241, 1.42e-241j)
| (6.5263028851929060403 + 4.0720752186936425663e-523j)  +/-  (1.95e-245, 1.95e-245j)
| (9.9485488936348848047 + 2.9404461236760102471e-521j)  +/-  (6.31e-244, 6.31e-244j)
| (62.954728501149267077 + 1.7907228302944344539e-515j)  +/-  (4.74e-241, 4.74e-241j)
| (50.853191515990184193 + 1.4783217802741523378e-530j)  +/-  (1.79e-240, 1.79e-240j)
| (19.258047913130726766 - 2.3665581822172468862e-558j)  +/-  (1.08e-241, 1.08e-241j)
| (40.85572233672914434 + 2.2598019089764457008e-603j)  +/-  (2.58e-240, 2.58e-240j)
| (28.72574102526642285 - 2.8606003898640546691e-645j)  +/-  (1.22e-240, 1.22e-240j)
| (36.472189713639477741 - 1.3803462650211033303e-671j)  +/-  (2.4e-240, 2.4e-240j)
| (1.899366498002682385 - 5.0098390239230490908e-710j)  +/-  (1.75e-249, 1.75e-249j)
| (22.154345434871591218 + 3.6422919739151126585e-700j)  +/-  (2.75e-241, 2.75e-241j)
| (25.304383763050153815 + 5.7025329138304252816e-724j)  +/-  (6.04e-241, 6.04e-241j)
| (0.049014489994713646422 - 9.2098378768260876094e-754j)  +/-  (5.4e-255, 5.4e-255j)
| (3.8548761581952923541 + 3.8752177120689194744e-745j)  +/-  (2.65e-247, 2.65e-247j)
| (1.1822010556248429509 - 1.6176709244119786409e-750j)  +/-  (7.65e-251, 7.65e-251j)
| (2.7893635383562917989 + 1.6807505713028699287e-746j)  +/-  (2.2e-248, 2.2e-248j)
| (5.0992000886986005335 + 6.2149922939032840863e-746j)  +/-  (2.1e-246, 2.1e-246j)
| (32.439666742324382897 - 1.5659922221515941945e-737j)  +/-  (1.87e-240, 1.87e-240j)
| (8.140899733223032023 + 1.0421177588712457609e-750j)  +/-  (1.05e-244, 1.05e-244j)
| (0.25840729791877858038 + 6.8872042298676087018e-759j)  +/-  (1.51e-253, 1.51e-253j)
| (0.63574721580068027188 - 1.1789425575941011422e-756j)  +/-  (4.63e-252, 4.63e-252j)
| (16.60079655231566823 - 5.122758909104814197e-745j)  +/-  (3.59e-242, 3.59e-242j)
-------------------------------------------------
The weights are:
| (3.8222471284651841026e-43 - 5.7614782838527929702e-534j)  +/-  (3e-96, 6.55e-215j)
| (7.5940399307102119821e-20 - 4.6353549720946221027e-521j)  +/-  (1.69e-87, 3.68e-206j)
| (6.9437307100088383887e-38 + 2.9742022104660126281e-531j)  +/-  (7.38e-95, 1.61e-213j)
| (1.6278500050223849868e-06 + 7.4414651224657115072e-516j)  +/-  (8.52e-76, 1.86e-194j)
| (1.3547034631790887642e-05 - 1.9245377970244450674e-515j)  +/-  (4.28e-74, 9.33e-193j)
| (9.0992518504373094716e-34 - 4.1646180731341000312e-529j)  +/-  (6.12e-94, 1.33e-212j)
| (1.5926368145878628336e-24 + 4.4096790311307294358e-524j)  +/-  (3.51e-91, 7.66e-210j)
| (2.7572669535983463902e-30 + 2.8938477449456804972e-527j)  +/-  (2.16e-93, 4.7e-212j)
| (0.0022258990960670322465 + 1.5740730715809721571e-514j)  +/-  (6.11e-74, 1.33e-192j)
| (9.1113489992727080196e-05 + 4.3547267816534394281e-515j)  +/-  (6.61e-77, 1.44e-195j)
| (3.0640076404632419341e-27 - 1.2908696805502414408e-525j)  +/-  (1.68e-92, 3.67e-211j)
| (4.4924215049305739335e-22 - 1.4738189117175583684e-522j)  +/-  (6.6e-91, 1.44e-209j)
| (1.2009533101199117513e-08 + 9.3067361079216076719e-517j)  +/-  (5.12e-85, 1.12e-203j)
| (8.2542983474716321863e-18 + 1.9579408584653714337e-520j)  +/-  (3.01e-90, 6.56e-209j)
| (1.1925479056622079597e-12 - 1.7632263718632369993e-518j)  +/-  (5.91e-89, 1.29e-207j)
| (6.0783312942285316944e-16 - 8.277556731821001192e-520j)  +/-  (3.16e-90, 6.89e-209j)
| (0.12020699960179554665 + 5.5695216982106395308e-514j)  +/-  (7.55e-78, 1.65e-196j)
| (7.2205280676333159579e-10 - 2.7457210361953007007e-517j)  +/-  (8.72e-88, 1.9e-206j)
| (3.3624013158479019449e-11 + 7.3099572778777153176e-518j)  +/-  (1.53e-88, 3.34e-207j)
| (0.11978686722479543442 + 8.5664694646526887522e-515j)  +/-  (3.96e-80, 8.64e-199j)
| (0.024444040022708565224 + 3.7472379223354265132e-514j)  +/-  (9.88e-83, 2.15e-201j)
| (0.19362026449763877698 - 5.4859791726453256337e-514j)  +/-  (1.29e-80, 2.81e-199j)
| (0.060062606051822768879 - 4.870925728259170971e-514j)  +/-  (5.62e-82, 1.23e-200j)
| (0.0081456248702861073504 - 2.5655322633219637125e-514j)  +/-  (1.07e-83, 2.33e-202j)
| (3.1562047238627133475e-14 + 3.9060223736786620235e-519j)  +/-  (1.45e-90, 3.16e-209j)
| (0.00049828632134452034355 - 8.6954374687908120021e-515j)  +/-  (2.15e-85, 4.66e-204j)
| (0.22642938894472312828 - 2.716840828385615143e-514j)  +/-  (6.54e-84, 1.4e-202j)
| (0.24447356535568403026 + 4.4653056822059054575e-514j)  +/-  (6.69e-84, 1.42e-202j)
| (1.5687206990177648663e-07 - 2.8545081919461739807e-516j)  +/-  (1.92e-87, 4.21e-206j)
