Starting with polynomial:
P : 1/2658271574788448768043625811014615890319638528000000000*t^44 - 1/1373074160531223537212616637920772670619648000000000*t^43 + 43/63863914443312722661051936647477798633472000000000*t^42 - 43/108612099393388984117435266407275167744000000000*t^41 + 1763/10596302379842827718774172332417089536000000000*t^40 - 1763/33113444937008836621169288538803404800000000*t^39 + 1763/130625029337312964975026779245772800000000*t^38 - 1763/633223826427417420239049483878400000000*t^37 + 65231/136913259768090253024659347865600000000*t^36 - 65231/950786526167293423782356582400000000*t^35 + 65231/7761522662590150398223319040000000*t^34 - 65231/73855319453712503789322240000000*t^33 + 65231/813832721253030344785920000000*t^32 - 65231/10331860719032611799040000000*t^31 + 2022161/4666001615046985973760000000*t^30 - 2022161/77766693584116432896000000*t^29 + 58642669/42905761977443549184000000*t^28 - 58642669/930354532674158592000000*t^27 + 58642669/22971716856152064000000*t^26 - 58642669/645654763708416000000*t^25 + 58642669/20660952438669312000*t^24 - 58642669/753263890993152000*t^23 + 1348781387/720513287036928000*t^22 - 58642669/1488663816192000*t^21 + 58642669/81015717888000*t^20 - 58642669/5063482368000*t^19 + 1114210711/6928975872000*t^18 - 1114210711/577414656000*t^17 + 18941582087/951035904000*t^16 - 653158003/3714984000*t^15 + 653158003/495331200*t^14 - 21069613/2527200*t^13 + 273904969/6220800*t^12 - 273904969/1425600*t^11 + 177232627/259200*t^10 - 177232627/90720*t^9 + 177232627/40320*t^8 - 4790071/630*t^7 + 1764763/180*t^6 - 135751/15*t^5 + 135751/24*t^4 - 6622/3*t^3 + 473*t^2 - 44*t + 1
Extension levels are: 44
-------------------------------------------------
Ending with final polynomial:
P : 1/2658271574788448768043625811014615890319638528000000000*t^44 - 1/1373074160531223537212616637920772670619648000000000*t^43 + 43/63863914443312722661051936647477798633472000000000*t^42 - 43/108612099393388984117435266407275167744000000000*t^41 + 1763/10596302379842827718774172332417089536000000000*t^40 - 1763/33113444937008836621169288538803404800000000*t^39 + 1763/130625029337312964975026779245772800000000*t^38 - 1763/633223826427417420239049483878400000000*t^37 + 65231/136913259768090253024659347865600000000*t^36 - 65231/950786526167293423782356582400000000*t^35 + 65231/7761522662590150398223319040000000*t^34 - 65231/73855319453712503789322240000000*t^33 + 65231/813832721253030344785920000000*t^32 - 65231/10331860719032611799040000000*t^31 + 2022161/4666001615046985973760000000*t^30 - 2022161/77766693584116432896000000*t^29 + 58642669/42905761977443549184000000*t^28 - 58642669/930354532674158592000000*t^27 + 58642669/22971716856152064000000*t^26 - 58642669/645654763708416000000*t^25 + 58642669/20660952438669312000*t^24 - 58642669/753263890993152000*t^23 + 1348781387/720513287036928000*t^22 - 58642669/1488663816192000*t^21 + 58642669/81015717888000*t^20 - 58642669/5063482368000*t^19 + 1114210711/6928975872000*t^18 - 1114210711/577414656000*t^17 + 18941582087/951035904000*t^16 - 653158003/3714984000*t^15 + 653158003/495331200*t^14 - 21069613/2527200*t^13 + 273904969/6220800*t^12 - 273904969/1425600*t^11 + 177232627/259200*t^10 - 177232627/90720*t^9 + 177232627/40320*t^8 - 4790071/630*t^7 + 1764763/180*t^6 - 135751/15*t^5 + 135751/24*t^4 - 6622/3*t^3 + 473*t^2 - 44*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 roots: 848
 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
Sufficient bits for target precision reached
-------------------------------------------------
The nodes are:
| (143.02290852939820171 - 1.1076715457829007811e-265j)  +/-  (2.45e-238, 2.45e-238j)
| (84.914987385294541798 - 1.8951920462131335657e-273j)  +/-  (1.31e-233, 1.31e-233j)
| (157.61844630703226397 - 2.0459151250514555811e-291j)  +/-  (6.34e-240, 6.34e-240j)
| (131.50445027042242803 - 7.7525578244345019276e-284j)  +/-  (3.61e-237, 3.61e-237j)
| (105.03464200510522462 + 1.5946169362179914554e-286j)  +/-  (7.56e-235, 7.56e-235j)
| (121.65435750452927995 - 1.060705234027777813e-296j)  +/-  (2.94e-236, 2.94e-236j)
| (73.662946690570566177 + 3.7525780856352636308e-309j)  +/-  (3.46e-233, 3.46e-233j)
| (36.497284153138553232 + 1.5838595901331376524e-318j)  +/-  (5.1e-234, 5.1e-234j)
| (39.777239047486089557 + 1.2845831913039372794e-317j)  +/-  (9.6e-234, 9.6e-234j)
| (12.351411854387122415 - 8.3990833536253407637e-343j)  +/-  (2.5e-239, 2.5e-239j)
| (14.131475448155771762 - 1.0010528079183367615e-340j)  +/-  (1.25e-238, 1.25e-238j)
| (20.269630751903115872 - 3.2610133077759703577e-332j)  +/-  (1.09e-236, 1.09e-236j)
| (112.9261693284208068 + 2.1171950751673677514e-318j)  +/-  (1.77e-235, 1.77e-235j)
| (50.760722089977991275 - 3.4300636711605146805e-323j)  +/-  (3.89e-233, 3.89e-233j)
| (91.127398402554592499 - 4.0334016971191448006e-337j)  +/-  (6.15e-234, 6.15e-234j)
| (30.456535814027974506 + 3.0917341937222058506e-351j)  +/-  (9.82e-235, 9.82e-235j)
| (3.3527062878881513301 + 1.5016466988344259642e-381j)  +/-  (1.17e-245, 1.17e-245j)
| (46.898680026400839804 + 1.5910153538318168727e-380j)  +/-  (2.6e-233, 2.6e-233j)
| (68.540117989985371819 + 6.2911360224035207007e-418j)  +/-  (4.43e-233, 4.43e-233j)
| (1.2553546349398592816 + 7.1523231827909246963e-467j)  +/-  (4.51e-249, 4.51e-249j)
| (6.4879016571002008987 + 4.6234322067407889874e-461j)  +/-  (1.16e-242, 1.16e-242j)
| (2.539753180569348822 - 6.389794180397345837e-467j)  +/-  (8.81e-247, 8.81e-247j)
| (25.062304033571887877 - 4.5483136581527381084e-435j)  +/-  (1.27e-235, 1.27e-235j)
| (79.10900127131664053 - 2.5541357696095801248e-439j)  +/-  (2.28e-233, 2.28e-233j)
| (54.839922879698535962 + 1.3260909754626908332e-450j)  +/-  (5.23e-233, 5.23e-233j)
| (22.593210746149934807 - 1.8471204467801658883e-466j)  +/-  (3.79e-236, 3.79e-236j)
| (4.2808623390397896541 - 9.9975750770742096231e-478j)  +/-  (1.39e-244, 1.39e-244j)
| (5.3254562311950980118 + 1.2254544048811463256e-475j)  +/-  (1.27e-243, 1.27e-243j)
| (18.087305655181373049 + 9.3552154707842751628e-470j)  +/-  (2.75e-237, 2.75e-237j)
| (63.71089252666221735 + 2.4517021071551614951e-464j)  +/-  (5.37e-233, 5.37e-233j)
| (43.241174058322882201 + 5.9698623114972979623e-472j)  +/-  (1.78e-233, 1.78e-233j)
| (9.1729648155123339985 + 8.5742689237375040921e-482j)  +/-  (7.01e-241, 7.01e-241j)
| (0.032491102009891548652 - 3.743148911131534305e-495j)  +/-  (5.37e-255, 5.37e-255j)
| (7.7698022801391393551 + 1.0982733226345414273e-482j)  +/-  (9.23e-242, 9.23e-242j)
| (59.15092890953106033 + 1.9304507824837911962e-472j)  +/-  (5.59e-233, 5.59e-233j)
| (27.681650371089359721 + 6.7818837108698895927e-484j)  +/-  (3.75e-235, 3.75e-235j)
| (16.042404007748893278 + 1.4315894747313387476e-487j)  +/-  (6.39e-238, 6.39e-238j)
| (0.42103666620350700365 - 1.8234628867570995602e-500j)  +/-  (1.18e-251, 1.18e-251j)
| (10.699414295322846003 + 3.3493585566021043164e-489j)  +/-  (4.43e-240, 4.43e-240j)
| (33.392870721505014606 + 4.4096339209944763514e-482j)  +/-  (2.35e-234, 2.35e-234j)
| (97.80675721268905111 + 3.72852016845331225e-490j)  +/-  (2.35e-234, 2.35e-234j)
| (0.17123817581147099157 + 2.7663266618012483017e-523j)  +/-  (2.7e-253, 2.7e-253j)
| (0.78225492892140341678 + 2.3592463048352538931e-520j)  +/-  (2.44e-250, 2.44e-250j)
| (1.8409374130893730666 - 1.3128243793017934873e-518j)  +/-  (7.42e-248, 7.42e-248j)
-------------------------------------------------
The weights are:
| (9.7491969325256837961e-62 + 1.1785485284552162327e-323j)  +/-  (2.41e-73, 4.73e-187j)
| (7.9446326470626281771e-37 + 7.4396412811706784687e-310j)  +/-  (1.75e-64, 3.45e-178j)
| (6.0968766605970140908e-68 - 7.8156658551431204542e-327j)  +/-  (1.49e-75, 2.92e-189j)
| (8.1635880779569829958e-57 - 4.0770753215981469771e-321j)  +/-  (3.12e-72, 6.13e-186j)
| (1.8248279941640302342e-45 + 3.9889474522747391973e-315j)  +/-  (2.49e-69, 4.9e-183j)
| (1.3529229150132986873e-52 + 6.401450550556717943e-319j)  +/-  (2.39e-71, 4.7e-185j)
| (5.3844240906606391781e-32 + 3.2445892740030666378e-308j)  +/-  (1.33e-64, 2.62e-178j)
| (4.5013130617747169943e-16 - 4.8527793639141683343e-301j)  +/-  (1.94e-55, 3.81e-169j)
| (1.7891730269504985841e-17 + 1.0834242778915294747e-301j)  +/-  (1.15e-56, 2.27e-170j)
| (7.4175943906737162437e-06 - 2.4180502635765840104e-296j)  +/-  (3.24e-41, 6.36e-155j)
| (1.3451654398253108206e-06 + 1.1291293494963287466e-296j)  +/-  (3.44e-43, 6.75e-157j)
| (3.5451417463090716692e-09 - 7.6014551536869583002e-298j)  +/-  (1.11e-48, 2.18e-162j)
| (7.4906320001857964083e-49 - 6.0190705218526653677e-317j)  +/-  (5.48e-72, 1.08e-185j)
| (3.5769253394433421061e-22 - 7.2321813915906493992e-304j)  +/-  (5.9e-62, 1.16e-175j)
| (1.7075673006534858597e-39 + 1.163997373378239771e-311j)  +/-  (2.27e-69, 4.46e-183j)
| (1.6921351798562200845e-13 - 7.6416498991975251279e-300j)  +/-  (3.4e-56, 6.67e-170j)
| (0.030453601526712088402 + 7.1816077550824256822e-295j)  +/-  (2.62e-33, 5.14e-147j)
| (1.6110088076301566982e-20 + 4.1913563666519632907e-303j)  +/-  (4.33e-61, 8.51e-175j)
| (8.5094074042832241773e-30 - 2.7035891314353832555e-307j)  +/-  (1.93e-66, 3.78e-180j)
| (0.1508168593611155573 - 9.5342409944449958166e-295j)  +/-  (2.14e-27, 4.2e-141j)
| (0.0018593963396704135829 - 2.5672375875186078489e-295j)  +/-  (2.8e-43, 5.51e-157j)
| (0.059615669160148300685 - 8.6591098424901003666e-295j)  +/-  (2.39e-34, 4.69e-148j)
| (3.3188838105772107803e-11 - 8.8331860912251540755e-299j)  +/-  (9.23e-56, 1.81e-169j)
| (2.472131270708897879e-34 - 4.4154000720097529479e-309j)  +/-  (3.66e-68, 7.19e-182j)
| (6.3943184936733352431e-24 + 1.1413914270208291881e-304j)  +/-  (3.92e-64, 7.71e-178j)
| (3.6923725415892435609e-10 + 2.6865586286530580026e-298j)  +/-  (1.09e-55, 2.14e-169j)
| (0.013639238157495726824 - 5.4933312565924243318e-295j)  +/-  (5.25e-44, 1.03e-157j)
| (0.0053686489776001399437 + 3.8944754324067210936e-295j)  +/-  (1.01e-45, 1.99e-159j)
| (2.9490632955423945225e-08 + 2.0033963862938716278e-297j)  +/-  (1.44e-54, 2.83e-168j)
| (1.0045415380509179408e-27 + 2.1870926692625565968e-306j)  +/-  (1.65e-66, 3.24e-180j)
| (5.9146170302014354312e-19 - 2.2245589066695804574e-302j)  +/-  (3.79e-62, 7.44e-176j)
| (0.00015202198109067774847 - 9.0378523756245043043e-296j)  +/-  (8.5e-53, 1.67e-166j)
| (0.080721916657043033687 - 1.105996375732021287e-295j)  +/-  (4.88e-46, 9.58e-160j)
| (0.0005668121163648623812 + 1.5769204077706403888e-295j)  +/-  (9.35e-52, 1.84e-165j)
| (9.0722659997989230908e-26 - 1.6482392506398216912e-305j)  +/-  (8.14e-66, 1.6e-179j)
| (2.5630778362084552023e-12 + 2.6978784533594265797e-299j)  +/-  (2.27e-59, 4.46e-173j)
| (2.1328501793815213921e-07 - 4.9233733511807314034e-297j)  +/-  (1.59e-56, 3.13e-170j)
| (0.20048200417187739244 - 6.3032704388576971912e-295j)  +/-  (8.28e-52, 1.63e-165j)
| (3.5840969733131475047e-05 + 4.8369205128547674477e-296j)  +/-  (3.78e-55, 7.42e-169j)
| (9.4962683637369700813e-15 + 2.0035694994049691706e-300j)  +/-  (6.37e-61, 1.25e-174j)
| (2.313584762386537184e-42 - 2.1390183430370331299e-313j)  +/-  (6.2e-75, 1.22e-188j)
| (0.16364683768650249774 + 3.621098405664736494e-295j)  +/-  (2.78e-54, 5.48e-168j)
| (0.19075711214018403659 + 8.4167308143380364143e-295j)  +/-  (9.57e-55, 1.9e-168j)
| (0.10187503126867065378 + 9.5561274919335446938e-295j)  +/-  (6.83e-55, 1.33e-168j)
