Starting with polynomial:
P : t^49 - 1176*t^47 + 635628*t^45 - 209757240*t^43 + 47352696930*t^41 - 7765842296520*t^39 + 959081523620220*t^37 - 91249756390152360*t^35 + 6786700631517581775*t^33 - 398153103715698130800*t^31 + 18514119322779963082200*t^29 - 683339313186242273761200*t^27 + 19987674910697586507515100*t^25 - 461254036400713534788810000*t^23 + 8335519372098608878683495000*t^21 - 116697271209380524301568930000*t^19 + 1247202086050254353473017939375*t^17 - 9977616688402034827784143515000*t^15 + 58202764015678536495407503837500*t^13 - 238937662801206623507462384175000*t^11 + 657078572703318214645521556481250*t^9 - 1126420410348545510820894096825000*t^7 + 1075219482605429805783580728787500*t^5 - 467486731567578176427643795125000*t^3 + 58435841445947272053455474390625*t
Extension levels are: 49
-------------------------------------------------
Ending with final polynomial:
P : t^49 - 1176*t^47 + 635628*t^45 - 209757240*t^43 + 47352696930*t^41 - 7765842296520*t^39 + 959081523620220*t^37 - 91249756390152360*t^35 + 6786700631517581775*t^33 - 398153103715698130800*t^31 + 18514119322779963082200*t^29 - 683339313186242273761200*t^27 + 19987674910697586507515100*t^25 - 461254036400713534788810000*t^23 + 8335519372098608878683495000*t^21 - 116697271209380524301568930000*t^19 + 1247202086050254353473017939375*t^17 - 9977616688402034827784143515000*t^15 + 58202764015678536495407503837500*t^13 - 238937662801206623507462384175000*t^11 + 657078572703318214645521556481250*t^9 - 1126420410348545510820894096825000*t^7 + 1075219482605429805783580728787500*t^5 - 467486731567578176427643795125000*t^3 + 58435841445947272053455474390625*t
-------------------------------------------------
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:   49 out of 49
Indefinite weights: 0 out of 49
Negative weights:   0 out of 49
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (-11.12712121198838918 - 6.7504567262345311621e-698j)  +/-  (8.36e-245, 8.36e-245j)
| (11.903912407887562255 + 4.5223895289909571154e-699j)  +/-  (1.63e-245, 1.63e-245j)
| (-8.055219008757501609 - 5.9171247022782315967e-709j)  +/-  (1.97e-243, 1.97e-243j)
| (-12.84021824817449052 - 2.0587372623773110066e-710j)  +/-  (9.53e-247, 9.53e-247j)
| (12.84021824817449052 + 5.7703149495907563403e-711j)  +/-  (9.06e-247, 9.06e-247j)
| (-5.5017254950349971529 - 5.8912623468051141485e-716j)  +/-  (1.48e-244, 1.48e-244j)
| (-4.0763795332421813896 - 1.4213550005574069493e-717j)  +/-  (3.26e-246, 3.26e-246j)
| (-5.9909092131181215654 + 1.1753839961138641104e-715j)  +/-  (3.22e-244, 3.22e-244j)
| (-9.7903923695131247826 + 1.0839747225358649774e-713j)  +/-  (7.87e-244, 7.87e-244j)
| (-6.9978729870212568821 + 3.2140309841570054196e-714j)  +/-  (1.5e-243, 1.5e-243j)
| (-11.903912407887562255 + 4.0057122991944240831e-717j)  +/-  (1.41e-245, 1.41e-245j)
| (-3.1521657049388672905 + 1.2801267767903896824e-719j)  +/-  (1.21e-247, 1.21e-247j)
| (-1.7909063487729003672 + 2.7000618934522601198e-722j)  +/-  (1.87e-250, 1.87e-250j)
| (-3.6121859695164179921 - 2.4595287474017030062e-718j)  +/-  (6.82e-247, 6.82e-247j)
| (-10.432454597950998523 + 1.6952923599492568249e-714j)  +/-  (3.01e-244, 3.01e-244j)
| (-6.4891092298320858964 + 1.6133244473513758395e-715j)  +/-  (8.06e-244, 8.06e-244j)
| (-2.6956674885649142853 - 4.9365334555597375967e-721j)  +/-  (1.75e-248, 1.75e-248j)
| (-4.545470293840825163 + 1.5130336177950861131e-717j)  +/-  (1.33e-245, 1.33e-245j)
| (1.3415802716789234046 + 2.0349599438241115829e-724j)  +/-  (1.9e-251, 1.9e-251j)
| (2.6956674885649142853 + 8.3724861687856641293e-721j)  +/-  (1.87e-248, 1.87e-248j)
| (-5.020274351287228556 + 6.2969814459648568798e-717j)  +/-  (5.75e-245, 5.75e-245j)
| (-8.6093464848963215723 + 7.5546499442160364744e-715j)  +/-  (1.87e-243, 1.87e-243j)
| (2.242097365824567205 - 1.4325115154327071714e-723j)  +/-  (2.05e-249, 2.05e-249j)
| (-2.242097365824567205 - 2.4882915146020769165e-722j)  +/-  (1.92e-249, 1.92e-249j)
| (-1.3415802716789234046 + 1.2483992731594785766e-724j)  +/-  (2.06e-251, 2.06e-251j)
| (0.89363122561294883361 + 3.0741454607036014505e-726j)  +/-  (1.16e-252, 1.16e-252j)
| (-7.51910675394986206 + 1.8410248888110989554e-716j)  +/-  (1.99e-243, 1.99e-243j)
| (-0.44659011754045766484 + 1.4670976858707738421e-736j)  +/-  (6.76e-254, 6.76e-254j)
| (-9.1857308370149604373 - 1.2590073549242996111e-715j)  +/-  (1.38e-243, 1.38e-243j)
| (1.7909063487729003672 + 1.4988526401723660836e-723j)  +/-  (2.16e-250, 2.16e-250j)
| (-2.7783709232251517334e-744 - 2.5315830183547356074e-744j)  +/-  (1.84e-742, 1.84e-742j)
| (-0.89363122561294883361 - 6.3828819228076170579e-726j)  +/-  (1.61e-252, 1.61e-252j)
| (0.44659011754045766484 - 5.574828044897612355e-727j)  +/-  (6.76e-254, 6.76e-254j)
| (6.9978729870212568821 - 7.6970145184151776411e-716j)  +/-  (1.3e-243, 1.3e-243j)
| (5.9909092131181215654 - 6.0170663767881781409e-721j)  +/-  (3.25e-244, 3.25e-244j)
| (10.432454597950998523 + 2.1520451475505536809e-725j)  +/-  (2.84e-244, 2.84e-244j)
| (9.1857308370149604373 + 4.3262818251439497987e-734j)  +/-  (1.45e-243, 1.45e-243j)
| (11.12712121198838918 + 8.7104234938097974414e-740j)  +/-  (8.25e-245, 8.25e-245j)
| (4.545470293840825163 + 1.3632499355429711754e-745j)  +/-  (1.17e-245, 1.17e-245j)
| (3.1521657049388672905 - 3.904401672950283405e-752j)  +/-  (1.25e-247, 1.25e-247j)
| (9.7903923695131247826 - 9.4879621174592758041e-746j)  +/-  (8.55e-244, 8.55e-244j)
| (5.020274351287228556 - 1.6711636485795018664e-755j)  +/-  (5.18e-245, 5.18e-245j)
| (4.0763795332421813896 + 3.2069410480716730468e-764j)  +/-  (2.89e-246, 2.89e-246j)
| (8.055219008757501609 - 1.3567363995091651435e-775j)  +/-  (2.32e-243, 2.32e-243j)
| (3.6121859695164179921 - 1.9205032672622332841e-795j)  +/-  (6.92e-247, 6.92e-247j)
| (8.6093464848963215723 + 4.6600499598525082301e-801j)  +/-  (2.37e-243, 2.37e-243j)
| (5.5017254950349971529 + 5.7030953790928356163e-843j)  +/-  (1.42e-244, 1.42e-244j)
| (6.4891092298320858964 + 9.0718839159161110388e-896j)  +/-  (7.3e-244, 7.3e-244j)
| (7.51910675394986206 - 9.8798758086548863019e-930j)  +/-  (2.05e-243, 2.05e-243j)
-------------------------------------------------
The weights are:
| (3.7836563879618741236e-28 - 1.4210042439793657919e-724j)  +/-  (2.67e-63, 6.71e-184j)
| (5.655218285268774114e-32 + 1.203562978196799714e-728j)  +/-  (1.62e-65, 4.07e-186j)
| (1.7659919001699999965e-15 + 1.7956406477678935818e-719j)  +/-  (3.13e-57, 7.85e-178j)
| (6.8113891231162985079e-37 + 6.3262531603455387765e-730j)  +/-  (1.23e-66, 3.09e-187j)
| (6.8113891231162985079e-37 - 4.6162451776884135574e-731j)  +/-  (1.91e-67, 4.8e-188j)
| (5.1752892276907664847e-08 - 5.3084805676223538711e-716j)  +/-  (9.74e-51, 2.44e-171j)
| (4.5863561644566030383e-05 + 1.2607137758031012276e-714j)  +/-  (4.78e-46, 1.2e-166j)
| (3.1661432936719304414e-09 + 1.4380989278529380012e-716j)  +/-  (2.2e-52, 5.51e-173j)
| (3.8052750102425209274e-22 - 1.9161218503291108686e-722j)  +/-  (4.2e-62, 1.05e-182j)
| (4.7716470401248638296e-12 + 6.9445218275827424741e-718j)  +/-  (6.37e-56, 1.6e-176j)
| (5.655218285268774114e-32 - 4.0199378669034764505e-727j)  +/-  (3.98e-66, 9.98e-187j)
| (0.0012714992687608799387 + 5.868363113266917302e-714j)  +/-  (3.42e-45, 8.59e-166j)
| (0.036126467371490124764 - 2.671628697652549802e-713j)  +/-  (3.96e-38, 9.93e-159j)
| (0.00027054068897748627963 - 2.8727234373999768098e-714j)  +/-  (6.67e-47, 1.67e-167j)
| (6.1704339611101352037e-25 + 1.4847788377340852571e-723j)  +/-  (1.09e-63, 2.75e-184j)
| (1.441769692730351445e-10 - 3.398529059451153561e-717j)  +/-  (3.35e-55, 8.4e-176j)
| (0.0047966312683466149577 - 1.078043561862647356e-713j)  +/-  (4.93e-45, 1.24e-165j)
| (6.1394013052101912198e-06 - 4.9415077297340683786e-715j)  +/-  (5.56e-51, 1.39e-171j)
| (0.072761047201653365219 + 2.8378290272486360854e-713j)  +/-  (1.11e-41, 2.79e-162j)
| (0.0047966312683466149577 - 6.5707756287034214918e-714j)  +/-  (2.79e-52, 7.01e-173j)
| (6.4195815258947118211e-07 + 1.7221879213666305708e-715j)  +/-  (2.59e-52, 6.5e-173j)
| (1.8087686462259733884e-17 - 2.2179785659925395548e-720j)  +/-  (1.53e-61, 3.85e-182j)
| (0.014612681974828686505 + 1.1858910579121301325e-713j)  +/-  (2.13e-51, 5.34e-172j)
| (0.014612681974828686505 + 1.7854978718375466535e-713j)  +/-  (8.35e-47, 2.1e-167j)
| (0.072761047201653365219 + 3.6172521734886094952e-713j)  +/-  (1.19e-43, 2.99e-164j)
| (0.11973328340805418324 - 3.7762890353607555687e-713j)  +/-  (1.22e-43, 3.06e-164j)
| (1.1139838337988044584e-13 - 1.214335550712429249e-718j)  +/-  (3.34e-59, 8.38e-180j)
| (0.16130826286314713598 + 4.9340688378020260061e-713j)  +/-  (2.83e-45, 7.09e-166j)
| (1.1191499622209997681e-19 + 2.2625680304036524521e-721j)  +/-  (6.58e-63, 1.65e-183j)
| (0.036126467371490124764 - 1.9299237536485205311e-713j)  +/-  (4.95e-51, 1.24e-171j)
| (0.17813377193108357593 - 4.9766298347115816071e-713j)  +/-  (1.64e-45, 4.13e-166j)
| (0.11973328340805418324 - 4.4368669247157010821e-713j)  +/-  (4.14e-46, 1.04e-166j)
| (0.16130826286314713598 + 4.5527521121896946774e-713j)  +/-  (4.06e-46, 1.02e-166j)
| (4.7716470401248638296e-12 + 1.5776811992847565867e-718j)  +/-  (1.77e-71, 4.44e-192j)
| (3.1661432936719304414e-09 + 4.3058557643427537807e-717j)  +/-  (2.89e-69, 7.25e-190j)
| (6.1704339611101352037e-25 + 4.7266528952591074532e-725j)  +/-  (4.54e-78, 1.14e-198j)
| (1.1191499622209997681e-19 + 2.1492462342567251023e-722j)  +/-  (1.34e-76, 3.36e-197j)
| (3.7836563879618741236e-28 - 1.120753967848971939e-726j)  +/-  (2.55e-79, 6.41e-200j)
| (6.1394013052101912198e-06 - 2.0722526103248340083e-715j)  +/-  (1.04e-68, 2.61e-189j)
| (0.0012714992687608799387 + 3.2745325041070526004e-714j)  +/-  (9.27e-65, 2.33e-185j)
| (3.8052750102425209274e-22 - 1.2145838830863650706e-723j)  +/-  (1.2e-77, 3.01e-198j)
| (6.4195815258947118211e-07 + 6.5027118860827279086e-716j)  +/-  (3.86e-70, 9.7e-191j)
| (4.5863561644566030383e-05 + 5.8395252645098174302e-715j)  +/-  (2.99e-68, 7.51e-189j)
| (1.7659919001699999965e-15 + 2.8648075076478496374e-720j)  +/-  (3.01e-76, 7.56e-197j)
| (0.00027054068897748627963 - 1.4631372834899701943e-714j)  +/-  (3.93e-68, 9.86e-189j)
| (1.8087686462259733884e-17 - 2.8155625432536669439e-721j)  +/-  (4.93e-77, 1.24e-197j)
| (5.1752892276907664847e-08 - 1.7925001840242027628e-716j)  +/-  (2.42e-72, 6.07e-193j)
| (1.441769692730351445e-10 - 8.9259657904911298816e-718j)  +/-  (3.02e-74, 7.58e-195j)
| (1.1139838337988044584e-13 - 2.3421371740135051604e-719j)  +/-  (7.13e-76, 1.79e-196j)
