Starting with polynomial:
P : 1024*t^11 - 2816*t^9 + 2816*t^7 - 1232*t^5 + 220*t^3 - 11*t
Extension levels are: 11 44
-------------------------------------------------
Trying to find an order 44 Kronrod extension for:
P1 : 1024*t^11 - 2816*t^9 + 2816*t^7 - 1232*t^5 + 220*t^3 - 11*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 1024*t^55 - 14080*t^53 + 91520*t^51 - 374000*t^49 + 1078000*t^47 - 2330636*t^45 + 3924030*t^43 - 84366645/16*t^41 + 367982175/64*t^39 - 1317269525/256*t^37 + 1949558897/512*t^35 - 9586673915/4096*t^33 + 2452404955/2048*t^31 - 4177173275/8192*t^29 + 2954585975/16384*t^27 - 13827462363/262144*t^25 + 26591273775/2097152*t^23 - 20828459025/8388608*t^21 + 6567532125/16777216*t^19 - 6567532125/134217728*t^17 + 637988835/134217728*t^15 - 187643775/536870912*t^13 + 20160075/1073741824*t^11 - 48208875/68719476736*t^9 + 4665375/274877906944*t^7 - 261261/1099511627776*t^5 + 3465/2199023255552*t^3 - 55/17592186044416*t
-------------------------------------------------
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:   55 out of 55
Indefinite weights: 0 out of 55
Negative weights:   0 out of 55
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (-0.99959219282818922963 + 7.7234117256182138035e-914j)  +/-  (1.49e-236, 1.49e-236j)
| (0.98008256109239340856 + 1.8031305415218748567e-911j)  +/-  (4.66e-236, 4.66e-236j)
| (-0.88443293099781432224 + 1.654977041218787782e-937j)  +/-  (2.23e-237, 2.23e-237j)
| (0.98982144188093273238 - 1.4406427627568203522e-934j)  +/-  (5.49e-236, 5.49e-236j)
| (0.93186402921145231619 - 6.6931100313889376752e-946j)  +/-  (1.42e-236, 1.42e-236j)
| (0.95105651629515357212 - 4.5492794936774204436e-961j)  +/-  (2.86e-236, 2.86e-236j)
| (-0.98982144188093273238 - 6.3105147614762691706e-985j)  +/-  (6.06e-236, 6.06e-236j)
| (-0.90963199535451837141 + 9.1007679697800408888e-986j)  +/-  (5.72e-237, 5.72e-237j)
| (-0.98008256109239340856 - 7.4567210064103881419e-984j)  +/-  (4.41e-236, 4.41e-236j)
| (0.99959219282818922963 + 6.4304478804016903672e-983j)  +/-  (1.51e-236, 1.51e-236j)
| (0.85634903025158897463 + 2.3146348875840650668e-1005j)  +/-  (8.16e-238, 8.16e-238j)
| (-0.93186402921145231619 - 9.7568237628713571029e-1002j)  +/-  (1.36e-236, 1.36e-236j)
| (-0.85634903025158897463 - 8.1003948994849782334e-1006j)  +/-  (7.18e-238, 7.18e-238j)
| (-0.82547189696277395698 - 6.8280826355111546484e-1007j)  +/-  (2.42e-238, 2.42e-238j)
| (0.67617490027401943528 - 9.4188364762795313727e-1010j)  +/-  (4.72e-241, 4.72e-241j)
| (0.82547189696277395698 - 3.1931349229092923102e-1007j)  +/-  (2.27e-238, 2.27e-238j)
| (0.90963199535451837141 + 7.5578376749855391124e-1004j)  +/-  (6.12e-237, 6.12e-237j)
| (0.99633173086269138762 - 9.1394399366418101194e-1003j)  +/-  (4.13e-236, 4.13e-236j)
| (-0.79190224592227509676 - 4.2993744237263052817e-1013j)  +/-  (6.63e-239, 6.63e-239j)
| (-0.95105651629515357212 - 1.5128057716094209212e-1009j)  +/-  (2.36e-236, 2.36e-236j)
| (-0.99633173086269138762 + 1.0542393770520515859e-1009j)  +/-  (3.85e-236, 3.85e-236j)
| (0.79190224592227509676 + 1.3030589425506242015e-1015j)  +/-  (5.98e-239, 5.98e-239j)
| (-0.96714685470195713906 - 2.4929797679362151049e-1014j)  +/-  (3.54e-236, 3.54e-236j)
| (-0.7171318047589634878 - 2.651657228798946021e-1018j)  +/-  (2.54e-240, 2.54e-240j)
| (-0.75574957435425828377 + 1.2281601814553257355e-1017j)  +/-  (1.3e-239, 1.3e-239j)
| (0.88443293099781432224 - 1.652968092808499425e-1016j)  +/-  (2.23e-237, 2.23e-237j)
| (0.75574957435425828377 - 1.1655895714411063534e-1020j)  +/-  (1.28e-239, 1.28e-239j)
| (0.7171318047589634878 - 3.6522337724650684296e-1023j)  +/-  (2.62e-240, 2.62e-240j)
| (0.96714685470195713906 - 7.4789439691565458448e-1028j)  +/-  (4.25e-236, 4.25e-236j)
| (-0.63301245380887038873 - 1.8007191497137588621e-1040j)  +/-  (5.84e-242, 5.84e-242j)
| (-0.38927010631739149039 + 2.4191157033319068874e-1047j)  +/-  (5.06e-247, 5.06e-247j)
| (0.54064081745559758211 + 3.4412717171211058522e-1045j)  +/-  (8.82e-244, 8.82e-244j)
| (0.63301245380887038873 + 8.1828080954260050839e-1046j)  +/-  (5.86e-242, 5.86e-242j)
| (-0.22649676742576438039 + 1.9359515885274794756e-1051j)  +/-  (9.66e-251, 9.66e-251j)
| (-0.58778525229247312917 - 2.3937363752782390727e-1042j)  +/-  (7.35e-243, 7.35e-243j)
| (-0.67617490027401943528 + 3.2226601257395965218e-1046j)  +/-  (4.46e-241, 4.46e-241j)
| (0.057088810862767983749 - 2.6917793124490426298e-1060j)  +/-  (1.51e-254, 1.51e-254j)
| (0.58778525229247312917 - 8.3662320513684670159e-1050j)  +/-  (7.38e-243, 7.38e-243j)
| (0.22649676742576438039 + 7.5061569869263905679e-1057j)  +/-  (9.84e-251, 9.84e-251j)
| (-0.1139914098905406253 + 2.1347370625257184691e-1059j)  +/-  (2.42e-253, 2.42e-253j)
| (-0.54064081745559758211 - 3.6104416936552016904e-1050j)  +/-  (7.3e-244, 7.3e-244j)
| (-0.1705221926326237844 + 3.9412323248868713741e-1060j)  +/-  (5.48e-252, 5.48e-252j)
| (0.28173255684142969771 + 1.276077739179067252e-1056j)  +/-  (1.87e-249, 1.87e-249j)
| (0.49173292464560377284 + 3.7225661535848816739e-1052j)  +/-  (7.03e-245, 7.03e-245j)
| (7.9141998256726830263e-1089 - 4.7180103618211090806e-1089j)  +/-  (5.07e-1087, 5.07e-1087j)
| (-0.49173292464560377284 + 2.8368289248354525487e-1053j)  +/-  (7.91e-245, 7.91e-245j)
| (-0.28173255684142969771 - 6.4725769208436925122e-1059j)  +/-  (2.22e-249, 2.22e-249j)
| (0.1705221926326237844 + 6.2195785194540085792e-1061j)  +/-  (5.02e-252, 5.02e-252j)
| (0.44122110124322129326 + 9.9972939800515030494e-1054j)  +/-  (6.2e-246, 6.2e-246j)
| (0.1139914098905406253 - 2.0856936271761521524e-1061j)  +/-  (3.19e-253, 3.19e-253j)
| (-0.3360493932154301264 - 1.708464334380902152e-1056j)  +/-  (3.83e-248, 3.83e-248j)
| (-0.44122110124322129326 - 2.7297586937273037099e-1055j)  +/-  (6.17e-246, 6.17e-246j)
| (-0.057088810862767983749 - 1.0795358591688303596e-1062j)  +/-  (1.12e-254, 1.12e-254j)
| (0.3360493932154301264 + 1.7272169379771512337e-1057j)  +/-  (3.45e-248, 3.45e-248j)
| (0.38927010631739149039 + 1.7171368407121237526e-1055j)  +/-  (4.69e-247, 4.69e-247j)
-------------------------------------------------
The weights are:
| (0.018181818181818181818 + 8.8449548040922890641e-913j)  +/-  (9.82e-47, 4.46e-160j)
| (0.018181818181818181818 - 4.078551512836315845e-912j)  +/-  (4.28e-47, 1.94e-160j)
| (0.018181818181818181818 + 6.1246465018160986214e-913j)  +/-  (1.26e-47, 5.73e-161j)
| (0.018181818181818181818 - 2.4120365408215676567e-911j)  +/-  (2.45e-47, 1.11e-160j)
| (0.018181818181818181818 + 1.2430581570147191788e-911j)  +/-  (6.76e-48, 3.07e-161j)
| (0.018181818181818181818 - 1.7583002831537569862e-911j)  +/-  (1.1e-47, 4.98e-161j)
| (0.018181818181818181818 + 8.355243281749988895e-913j)  +/-  (2.37e-49, 1.08e-162j)
| (0.018181818181818181818 - 5.8998491303740366504e-913j)  +/-  (1.32e-49, 6.01e-163j)
| (0.018181818181818181818 - 6.6781396231824687344e-913j)  +/-  (1.1e-49, 4.97e-163j)
| (0.018181818181818181818 - 2.4156215311272057917e-912j)  +/-  (4.38e-50, 1.99e-163j)
| (0.018181818181818181818 - 6.9034216890093414166e-912j)  +/-  (3.49e-51, 1.58e-164j)
| (0.018181818181818181818 + 5.7668548995749456445e-913j)  +/-  (3.76e-50, 1.71e-163j)
| (0.018181818181818181818 - 6.4149051297555983265e-913j)  +/-  (5.57e-51, 2.53e-164j)
| (0.018181818181818181818 + 6.754898233598475128e-913j)  +/-  (7.67e-52, 3.48e-165j)
| (0.018181818181818181818 + 4.0236406353973745904e-912j)  +/-  (7.3e-54, 3.31e-167j)
| (0.018181818181818181818 + 6.0420102858726682821e-912j)  +/-  (1.18e-52, 5.37e-166j)
| (0.018181818181818181818 - 9.744978679997219369e-912j)  +/-  (6.62e-52, 3.01e-165j)
| (0.018181818181818181818 + 8.6919361006511435949e-912j)  +/-  (3.95e-51, 1.79e-164j)
| (0.018181818181818181818 - 7.1348648570555478468e-913j)  +/-  (1.59e-53, 7.21e-167j)
| (0.018181818181818181818 - 5.7725507991622429958e-913j)  +/-  (3.39e-52, 1.54e-165j)
| (0.018181818181818181818 - 1.3621512570173083167e-912j)  +/-  (1.89e-52, 8.6e-166j)
| (0.018181818181818181818 - 5.3737754780725129423e-912j)  +/-  (2.48e-56, 1.12e-169j)
| (0.018181818181818181818 + 6.0082756155698354085e-913j)  +/-  (2.12e-52, 9.63e-166j)
| (0.018181818181818181818 - 7.9923089917464991699e-913j)  +/-  (3.33e-57, 1.51e-170j)
| (0.018181818181818181818 + 7.5486313039641529363e-913j)  +/-  (3.18e-56, 1.44e-169j)
| (0.018181818181818181818 + 8.0665247321312901501e-912j)  +/-  (2.24e-56, 1.02e-169j)
| (0.018181818181818181818 + 4.8374008980163023057e-912j)  +/-  (1.59e-58, 7.21e-172j)
| (0.018181818181818181818 - 4.3954420433132754633e-912j)  +/-  (2.76e-59, 1.25e-172j)
| (0.018181818181818181818 + 3.2449490543804585981e-911j)  +/-  (1.35e-56, 6.11e-170j)
| (0.018181818181818181818 - 8.9610636015995698292e-913j)  +/-  (6.45e-62, 2.93e-175j)
| (0.018181818181818181818 + 1.184692446497984354e-912j)  +/-  (1.47e-64, 6.66e-178j)
| (0.018181818181818181818 - 3.1871834197580153782e-912j)  +/-  (1.5e-63, 6.8e-177j)
| (0.018181818181818181818 - 3.7055340176062427941e-912j)  +/-  (8.89e-62, 4.03e-175j)
| (0.018181818181818181818 - 1.3946004487120814255e-912j)  +/-  (2.39e-66, 1.08e-179j)
| (0.018181818181818181818 + 9.4844048466017454699e-913j)  +/-  (1.07e-63, 4.85e-177j)
| (0.018181818181818181818 + 8.4635434018417871925e-913j)  +/-  (3.24e-62, 1.47e-175j)
| (0.018181818181818181818 + 1.8321204603056855967e-912j)  +/-  (4.47e-68, 2.03e-181j)
| (0.018181818181818181818 + 3.4295238633387835336e-912j)  +/-  (1.79e-64, 8.13e-178j)
| (0.018181818181818181818 - 2.1727863509824511209e-912j)  +/-  (2.56e-68, 1.16e-181j)
| (0.018181818181818181818 - 1.5542267707526453875e-912j)  +/-  (2.17e-68, 9.85e-182j)
| (0.018181818181818181818 - 1.0033735882737903482e-912j)  +/-  (2.17e-66, 9.83e-180j)
| (0.018181818181818181818 + 1.4721936851275103408e-912j)  +/-  (2.82e-68, 1.28e-181j)
| (0.018181818181818181818 + 2.3049895084507496855e-912j)  +/-  (4.35e-69, 1.97e-182j)
| (0.018181818181818181818 + 2.9722305803402242966e-912j)  +/-  (5.55e-68, 2.52e-181j)
| (0.018181818181818181818 - 1.7335884904241491263e-912j)  +/-  (3.68e-69, 1.67e-182j)
| (0.018181818181818181818 + 1.0609752706973623599e-912j)  +/-  (3.64e-68, 1.65e-181j)
| (0.018181818181818181818 + 1.3210414048269761378e-912j)  +/-  (5.19e-69, 2.36e-182j)
| (0.018181818181818181818 + 2.0507304322101267299e-912j)  +/-  (4.9e-70, 2.22e-183j)
| (0.018181818181818181818 - 2.7798787146567964039e-912j)  +/-  (3e-70, 1.36e-183j)
| (0.018181818181818181818 - 1.9375333824999400633e-912j)  +/-  (4.39e-70, 1.99e-183j)
| (0.018181818181818181818 - 1.2511701097672980873e-912j)  +/-  (4.06e-70, 1.84e-183j)
| (0.018181818181818181818 - 1.1213616736399897101e-912j)  +/-  (5.08e-70, 2.3e-183j)
| (0.018181818181818181818 + 1.6411736818942955856e-912j)  +/-  (9.78e-71, 4.44e-184j)
| (0.018181818181818181818 - 2.4488975138225730865e-912j)  +/-  (5.53e-72, 2.52e-185j)
| (0.018181818181818181818 + 2.6064117367188077125e-912j)  +/-  (5.21e-72, 2.35e-185j)
