Starting with polynomial:
P : -1/608281864034267560872252163321295376887552831379210240000000000*t^49 + 1/253345216174205564711475286681089286500438497034240000000000*t^48 - 1/219917722373442330478711186355112227864963973120000000000*t^47 + 47/14037301428092063647577309767347589012657274880000000000*t^46 - 47/26535541451969874570089432452452909286686720000000000*t^45 + 47/65519855436962653259480080129513356263424000000000*t^44 - 47/203057403213727231176074628500557922304000000000*t^43 + 2021/33055856337118386470523776732648964096000000000*t^42 - 2021/149913180667203566759745019195686912000000000*t^41 + 82861/32907771365971514654578174945394688000000000*t^40 - 82861/205673571037321966591113593408716800000000*t^39 + 82861/1487448574234412644643162082508800000000*t^38 - 82861/12361068483942487351605225062400000000*t^37 + 3065857/4343078115979792853266700697600000000*t^36 - 3065857/46915967302250848723560038400000000*t^35 + 3065857/574481232272459372125224960000000*t^34 - 3065857/7951297332490787157442560000000*t^33 + 3065857/124124935401600901447680000000*t^32 - 3065857/2181883630106265845760000000*t^31 + 95041567/1337283515226421002240000000*t^30 - 95041567/29717411449476022272000000*t^29 + 2756205443/21519504842724016128000000*t^28 - 2756205443/603863656300929024000000*t^27 + 2756205443/19051939773554688000000*t^26 - 2756205443/676400228646912000000*t^25 + 2756205443/27056009145876480000*t^24 - 2756205443/1221278190612480000*t^23 + 63392725189/1433674397675520000*t^22 - 63392725189/82939841187840000*t^21 + 2185956041/188072202240000*t^20 - 2185956041/14105415168000*t^19 + 1339779509/742390272000*t^18 - 1339779509/73322496000*t^17 + 22776251653/142331904000*t^16 - 1339779509/1111968000*t^15 + 1339779509/172972800*t^14 - 9378456563/222393600*t^13 + 3295133387/17107200*t^12 - 173428073/237600*t^11 + 146746831/64800*t^10 - 146746831/25920*t^9 + 3579191/320*t^8 - 511313/30*t^7 + 582659/30*t^6 - 158907/10*t^5 + 52969/6*t^4 - 9212/3*t^3 + 588*t^2 - 49*t + 1
Extension levels are: 49
-------------------------------------------------
Ending with final polynomial:
P : -1/608281864034267560872252163321295376887552831379210240000000000*t^49 + 1/253345216174205564711475286681089286500438497034240000000000*t^48 - 1/219917722373442330478711186355112227864963973120000000000*t^47 + 47/14037301428092063647577309767347589012657274880000000000*t^46 - 47/26535541451969874570089432452452909286686720000000000*t^45 + 47/65519855436962653259480080129513356263424000000000*t^44 - 47/203057403213727231176074628500557922304000000000*t^43 + 2021/33055856337118386470523776732648964096000000000*t^42 - 2021/149913180667203566759745019195686912000000000*t^41 + 82861/32907771365971514654578174945394688000000000*t^40 - 82861/205673571037321966591113593408716800000000*t^39 + 82861/1487448574234412644643162082508800000000*t^38 - 82861/12361068483942487351605225062400000000*t^37 + 3065857/4343078115979792853266700697600000000*t^36 - 3065857/46915967302250848723560038400000000*t^35 + 3065857/574481232272459372125224960000000*t^34 - 3065857/7951297332490787157442560000000*t^33 + 3065857/124124935401600901447680000000*t^32 - 3065857/2181883630106265845760000000*t^31 + 95041567/1337283515226421002240000000*t^30 - 95041567/29717411449476022272000000*t^29 + 2756205443/21519504842724016128000000*t^28 - 2756205443/603863656300929024000000*t^27 + 2756205443/19051939773554688000000*t^26 - 2756205443/676400228646912000000*t^25 + 2756205443/27056009145876480000*t^24 - 2756205443/1221278190612480000*t^23 + 63392725189/1433674397675520000*t^22 - 63392725189/82939841187840000*t^21 + 2185956041/188072202240000*t^20 - 2185956041/14105415168000*t^19 + 1339779509/742390272000*t^18 - 1339779509/73322496000*t^17 + 22776251653/142331904000*t^16 - 1339779509/1111968000*t^15 + 1339779509/172972800*t^14 - 9378456563/222393600*t^13 + 3295133387/17107200*t^12 - 173428073/237600*t^11 + 146746831/64800*t^10 - 146746831/25920*t^9 + 3579191/320*t^8 - 511313/30*t^7 + 582659/30*t^6 - 158907/10*t^5 + 52969/6*t^4 - 9212/3*t^3 + 588*t^2 - 49*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: 0
  current precision for roots: 424
  current precision for roots: 848
 current precision for weights: 424
Linear system for weights solvable: 1
  current precision for roots: 848
  current precision for roots: 1696
 current precision for weights: 848
Linear system for weights solvable: 1
Sufficient bits for target precision reached
-------------------------------------------------
The nodes are:
| (161.64877015704720903 - 1.5495964614923014872e-1313j)  +/-  (4.44e-492, 4.44e-492j)
| (149.62081975792771442 + 2.8267609687066562446e-1311j)  +/-  (8.18e-491, 8.18e-491j)
| (176.84630940701588372 + 5.2396299638359093311e-1320j)  +/-  (9.84e-494, 9.84e-494j)
| (139.30719756334274304 + 1.0319743659022597474e-1318j)  +/-  (7.69e-490, 7.69e-490j)
| (18.078810942749133439 - 1.0048065353099372522e-1326j)  +/-  (3.06e-491, 3.06e-491j)
| (32.313099151279634562 + 2.1253027846494774197e-1321j)  +/-  (6.05e-488, 6.05e-488j)
| (35.159750653922479026 + 1.2504446749109670096e-1326j)  +/-  (1.42e-487, 1.42e-487j)
| (29.608849498801545395 - 6.1375955990897715062e-1350j)  +/-  (2.1e-488, 2.1e-488j)
| (72.92171766800947992 - 7.306524518523086259e-1417j)  +/-  (7.27e-486, 7.27e-486j)
| (59.577158088622115924 + 3.5036354061114054957e-1471j)  +/-  (6.09e-486, 6.09e-486j)
| (94.35557619641319289 - 2.6479118548433705802e-1526j)  +/-  (1.64e-486, 1.64e-486j)
| (11.052216938021527933 + 7.348502246849562918e-1564j)  +/-  (3.68e-494, 3.68e-494j)
| (107.13554136224855814 - 1.5581414422353727295e-1556j)  +/-  (2.98e-487, 2.98e-487j)
| (8.2183116110416122313 - 1.6065686673183692611e-1578j)  +/-  (8.12e-496, 8.12e-496j)
| (130.14381522449526056 + 1.2589459613390465008e-1568j)  +/-  (5.39e-489, 5.39e-489j)
| (55.55527556274067845 - 7.2484942806071587642e-1579j)  +/-  (4.76e-486, 4.76e-486j)
| (6.964931933467086902 + 1.4144161885764909657e-1607j)  +/-  (1.01e-496, 1.01e-496j)
| (14.333661328574403395 + 8.9872633747694021128e-1604j)  +/-  (1.28e-492, 1.28e-492j)
| (27.042461866105614232 - 9.5556551950346680891e-1598j)  +/-  (6.5e-489, 6.5e-489j)
| (48.07968507536735705 - 2.1616311701676309587e-1597j)  +/-  (2.14e-486, 2.14e-486j)
| (38.153829667484568178 + 8.482567062340954372e-1626j)  +/-  (3.24e-487, 3.24e-487j)
| (5.8186559764242346173 + 3.3764319240131785326e-1659j)  +/-  (1.04e-497, 1.04e-497j)
| (88.53630611197943572 + 2.4816825014387185211e-1653j)  +/-  (2.71e-486, 2.71e-486j)
| (20.131234622737801578 + 7.2835038839527758265e-1681j)  +/-  (1.39e-490, 1.39e-490j)
| (100.53934816696116679 - 2.475337813187453602e-1674j)  +/-  (7.01e-487, 7.01e-487j)
| (68.246266539083530447 + 6.4545886523096319446e-1685j)  +/-  (7.81e-486, 7.81e-486j)
| (0.70304396884142983204 - 1.9140697155931160248e-1721j)  +/-  (1.23e-505, 1.23e-505j)
| (1.128044490309591159 - 1.6793178593397753253e-1719j)  +/-  (2.85e-504, 2.85e-504j)
| (4.7782094313820545368 + 6.6028095252048008582e-1714j)  +/-  (1.13e-498, 1.13e-498j)
| (83.043699098598646675 - 2.819659280875468641e-1700j)  +/-  (4.34e-486, 4.34e-486j)
| (12.636059013857258321 + 1.6759137427597373664e-1724j)  +/-  (2.29e-493, 2.29e-493j)
| (77.847207598448202152 + 1.2272463953951301792e-1715j)  +/-  (6.17e-486, 6.17e-486j)
| (0.15393253808220807687 - 3.131400446913749752e-1754j)  +/-  (1.65e-508, 1.65e-508j)
| (63.803130293042612384 - 6.1370297209578936922e-1731j)  +/-  (6.71e-486, 6.71e-486j)
| (121.8363987866031854 + 4.8980114262968790632e-1748j)  +/-  (2.61e-488, 2.61e-488j)
| (51.726107311014212165 + 5.6797581505695355318e-1756j)  +/-  (3.49e-486, 3.49e-486j)
| (9.5802149118588324906 - 4.9769054755215271558e-1771j)  +/-  (5.74e-495, 5.74e-495j)
| (22.307212582338767813 - 3.5692957356511260068e-1765j)  +/-  (5.38e-490, 5.38e-490j)
| (2.2811192334764465321 + 2.1485635221100251949e-1777j)  +/-  (6.58e-502, 6.58e-502j)
| (41.300914917174047198 - 3.7581254197008476857e-1761j)  +/-  (6.62e-487, 6.62e-487j)
| (16.147137441534024491 + 8.162562504107064769e-1778j)  +/-  (6.87e-492, 6.87e-492j)
| (3.8424552273966829212 - 4.4733296830687926661e-1786j)  +/-  (9.91e-500, 9.91e-500j)
| (44.607218840628768181 - 2.7210712315064500748e-1771j)  +/-  (1.23e-486, 1.23e-486j)
| (1.6538890653988436359 - 4.5776209884608362633e-1801j)  +/-  (4.36e-503, 4.36e-503j)
| (24.609825808892310949 + 8.9096205819937295502e-1784j)  +/-  (2.08e-489, 2.08e-489j)
| (3.0103862812012883053 + 4.5985223516091559139e-1804j)  +/-  (8.33e-501, 8.33e-501j)
| (0.029208949494039041802 - 1.4039275816804630684e-1813j)  +/-  (3.28e-510, 3.28e-510j)
| (114.20653122712858724 - 5.0023246857216451302e-1789j)  +/-  (9.94e-488, 9.94e-488j)
| (0.37845191143399290465 + 1.999494484955227551e-1822j)  +/-  (5.41e-507, 5.41e-507j)
-------------------------------------------------
The weights are:
| (8.2809007208632384331e-70 - 1.6851981148200875965e-1364j)  +/-  (1.06e-190, 2.52e-433j)
| (1.1572992654957395408e-64 + 6.682865172923462519e-1362j)  +/-  (2.64e-189, 6.26e-432j)
| (2.8279750003325821749e-76 + 9.2169037783320565835e-1368j)  +/-  (2.72e-193, 6.45e-436j)
| (3.057061976162802177e-60 - 1.1491482744135333114e-1359j)  +/-  (2.7e-188, 6.41e-431j)
| (2.8033345801065296398e-08 - 2.8641921998152132258e-1333j)  +/-  (2.04e-151, 4.83e-394j)
| (2.569262121318159861e-14 - 2.6482670713951702033e-1335j)  +/-  (1.27e-162, 3.02e-405j)
| (1.5689908316032601676e-15 - 4.9392068478578767025e-1336j)  +/-  (1.83e-164, 4.34e-407j)
| (3.6454794443904144377e-13 + 7.2920345713901560499e-1335j)  +/-  (2.35e-161, 5.58e-404j)
| (1.0268210726661318796e-31 - 4.0185031548426691124e-1345j)  +/-  (1.16e-179, 2.75e-422j)
| (5.5089208818042342812e-26 + 3.9648772416078032705e-1342j)  +/-  (4.88e-176, 1.16e-418j)
| (6.3044324836145438074e-41 - 7.4099310353867585073e-1350j)  +/-  (7.61e-185, 1.81e-427j)
| (2.4215740862756427231e-05 - 4.5192214573078452939e-1332j)  +/-  (8.62e-151, 2.05e-393j)
| (2.0207744806281245399e-46 - 1.1719609346555537944e-1352j)  +/-  (2.46e-187, 5.84e-430j)
| (0.00035256445257952796174 - 1.317221712898342669e-1331j)  +/-  (6.26e-148, 1.49e-390j)
| (2.6224925529738896529e-56 + 1.125170528887879705e-1357j)  +/-  (1.44e-190, 3.42e-433j)
| (2.9265253963677376616e-24 - 3.274274532570823857e-1341j)  +/-  (3.38e-176, 8.01e-419j)
| (0.0011329382879219968064 + 2.0685242717055550305e-1331j)  +/-  (1.39e-147, 3.3e-390j)
| (1.0454160851747352603e-06 - 1.2493781050012647123e-1332j)  +/-  (3.97e-157, 9.42e-400j)
| (4.5014244602601205006e-12 - 1.259369115403765977e-1334j)  +/-  (2.05e-165, 4.87e-408j)
| (4.6824406636607998388e-21 - 1.7972344160081623626e-1339j)  +/-  (9.8e-175, 2.33e-417j)
| (8.2619858798203741282e-17 + 5.7496790461791770316e-1337j)  +/-  (9.2e-171, 2.18e-413j)
| (0.0032484319441125322549 - 3.0654025534386551455e-1331j)  +/-  (4.4e-150, 1.04e-392j)
| (2.0009829067406554334e-38 + 1.4112622100891687179e-1348j)  +/-  (2.73e-185, 6.48e-428j)
| (3.8208638360505177995e-09 + 1.417853357679587552e-1333j)  +/-  (1.25e-164, 2.97e-407j)
| (1.3842124699661131278e-43 + 3.2589228832926450912e-1351j)  +/-  (1.43e-187, 3.4e-430j)
| (1.0463123946586174978e-29 + 4.4355861470368416856e-1344j)  +/-  (1.57e-181, 3.73e-424j)
| (0.18552097769024816373 + 6.7647187302322119992e-1331j)  +/-  (3.6e-144, 8.55e-387j)
| (0.15385159705647258027 - 7.9085203622391607387e-1331j)  +/-  (3.6e-144, 8.55e-387j)
| (0.0083094567553004113222 + 4.2775368127838436247e-1331j)  +/-  (2.92e-155, 6.93e-398j)
| (4.5932261896037041049e-36 - 2.2952628565428534606e-1347j)  +/-  (7.27e-185, 1.72e-427j)
| (5.33550463386921158e-06 + 2.4410513965987196815e-1332j)  +/-  (2.29e-164, 5.42e-407j)
| (7.8577150515906496817e-34 + 3.238753432824968284e-1346j)  +/-  (6.47e-184, 1.53e-426j)
| (0.14966713739885059577 + 2.795012301985019607e-1331j)  +/-  (6.25e-153, 1.48e-395j)
| (8.4598512802784300454e-28 - 4.4013415279430540308e-1343j)  +/-  (2.91e-181, 6.91e-424j)
| (9.710017173667550737e-53 - 7.2396313772158034292e-1356j)  +/-  (5.89e-194, 1.4e-436j)
| (1.2825421635777321523e-22 + 2.5048134228151844751e-1340j)  +/-  (2.3e-179, 5.46e-422j)
| (9.7866999979974351997e-05 + 7.9295388161733845169e-1332j)  +/-  (3.27e-167, 7.76e-410j)
| (4.5931194973068088536e-10 - 6.1572805656572855078e-1334j)  +/-  (5e-173, 1.19e-415j)
| (0.069284474263013599865 - 7.8335329399383028557e-1331j)  +/-  (1.49e-164, 3.55e-407j)
| (3.7312238847194706308e-18 - 8.2561001786695208985e-1338j)  +/-  (5.52e-178, 1.31e-420j)
| (1.8185799128085156792e-07 + 6.0015364947759216957e-1333j)  +/-  (1.16e-171, 2.74e-414j)
| (0.01894848115229705683 - 5.6047592025631503534e-1331j)  +/-  (2.11e-168, 5e-411j)
| (1.4364651261491782747e-19 + 1.2301462106008340266e-1338j)  +/-  (8.57e-179, 2.03e-421j)
| (0.11027518085855621793 + 8.2448109573429693265e-1331j)  +/-  (1.62e-168, 3.83e-411j)
| (4.8561572077355317223e-11 + 2.7103759713471706702e-1334j)  +/-  (2.28e-174, 5.39e-417j)
| (0.038458814563586367564 + 6.8694863927262030203e-1331j)  +/-  (2.44e-169, 5.74e-412j)
| (0.072805353155079524163 - 8.4592089838076168574e-1332j)  +/-  (8.43e-170, 1.98e-412j)
| (1.8453568247360652068e-49 + 3.3405808171260637271e-1354j)  +/-  (4.96e-194, 1.18e-436j)
| (0.18801591453545189051 - 4.9461965811862835877e-1331j)  +/-  (2.9e-169, 6.78e-412j)
