Starting with polynomial:
P : 128*t^8 - 256*t^6 + 160*t^4 - 32*t^2 + 1
Extension levels are: 8 48
-------------------------------------------------
Trying to find an order 48 Kronrod extension for:
P1 : 128*t^8 - 256*t^6 + 160*t^4 - 32*t^2 + 1
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 128*t^56 - 1792*t^54 + 11872*t^52 - 49504*t^50 + 145775*t^48 - 322420*t^46 + 1112349/2*t^44 - 1533939/2*t^42 + 440240493/512*t^40 - 202947745/256*t^38 + 1240628389/2048*t^36 - 789490793/2048*t^34 + 13421343481/65536*t^32 - 744296329/8192*t^30 + 2202509545/65536*t^28 - 676868787/65536*t^26 + 43996471155/16777216*t^24 - 4578818265/8388608*t^22 + 6185421165/67108864*t^20 - 835867725/67108864*t^18 + 2841950265/2147483648*t^16 - 57998985/536870912*t^14 + 28224105/4294967296*t^12 - 1227135/4294967296*t^10 + 18407025/2199023255552*t^8 - 166257/1099511627776*t^6 + 12789/8796093022208*t^4 - 49/8796093022208*t^2 + 1/281474976710656
-------------------------------------------------
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:   56 out of 56
Indefinite weights: 0 out of 56
Negative weights:   0 out of 56
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (-0.83146961230254523708 + 3.3169071110997318148e-894j)  +/-  (5.93e-238, 5.93e-238j)
| (0.99646149411761914653 + 3.6973167780698894894e-889j)  +/-  (8.3e-236, 8.3e-236j)
| (-0.861312628232408941 + 2.4195812661486964919e-904j)  +/-  (2.22e-237, 2.22e-237j)
| (0.99960662638305288551 + 3.0208599662542861468e-900j)  +/-  (2.94e-236, 2.94e-236j)
| (0.91278326506131890892 - 6.0182290886970011966e-910j)  +/-  (1.22e-236, 1.22e-236j)
| (0.93424894029459985508 - 1.2888085012783157832e-910j)  +/-  (2.91e-236, 2.91e-236j)
| (-0.99018112533644559044 - 3.9209173914928154648e-913j)  +/-  (1.13e-235, 1.13e-235j)
| (-0.91278326506131890892 + 2.2277182491579790379e-918j)  +/-  (1.43e-236, 1.43e-236j)
| (-0.98078528040323044913 + 3.0443526160946470952e-916j)  +/-  (9.89e-236, 9.89e-236j)
| (0.68699692603490163354 - 1.2648242467863049366e-927j)  +/-  (1.43e-240, 1.43e-240j)
| (0.88844563597887230031 + 3.4559293190895160153e-923j)  +/-  (4.96e-237, 4.96e-237j)
| (-0.99960662638305288551 - 8.2476719335575197946e-921j)  +/-  (3.03e-236, 3.03e-236j)
| (-0.68699692603490163354 - 1.4346197629431563985e-936j)  +/-  (1.25e-240, 1.25e-240j)
| (-0.88844563597887230031 + 1.5342901649073647009e-930j)  +/-  (5.12e-237, 5.12e-237j)
| (0.99018112533644559044 - 2.3139449112254292836e-930j)  +/-  (1.08e-235, 1.08e-235j)
| (0.861312628232408941 - 5.3272339873244798191e-945j)  +/-  (1.87e-237, 1.87e-237j)
| (0.83146961230254523708 - 6.1327602989624298474e-951j)  +/-  (5.88e-238, 5.88e-238j)
| (0.98078528040323044913 - 3.2779322888496068092e-957j)  +/-  (9.87e-236, 9.87e-236j)
| (-0.95277512272289628966 - 2.3527847802798663428e-965j)  +/-  (5.24e-236, 5.24e-236j)
| (-0.50807534524652945854 + 1.14481403887191732e-983j)  +/-  (3.1e-244, 3.1e-244j)
| (0.95277512272289628966 + 7.5813589699364367647e-973j)  +/-  (5.03e-236, 5.03e-236j)
| (0.79901048535824903392 + 2.1867285742426813062e-986j)  +/-  (1.51e-238, 1.51e-238j)
| (-0.93424894029459985508 + 9.0817461226730475836e-982j)  +/-  (2.71e-236, 2.71e-236j)
| (-0.76403737582160743666 + 2.2754827659733257934e-994j)  +/-  (4.25e-239, 4.25e-239j)
| (-0.79901048535824903392 + 1.0088703482558803625e-993j)  +/-  (1.48e-238, 1.48e-238j)
| (0.24977647816722684996 - 1.4364109636721027384e-1006j)  +/-  (4.63e-250, 4.63e-250j)
| (0.72666032203402704716 + 1.0415385742266080574e-994j)  +/-  (7.26e-240, 7.26e-240j)
| (0.96830352212226143939 + 6.7999678642070365023e-992j)  +/-  (7.78e-236, 7.78e-236j)
| (-0.96830352212226143939 + 1.0812969836493198599e-1001j)  +/-  (8.96e-236, 8.96e-236j)
| (-0.64517198354208763329 + 1.8768351752985906189e-1014j)  +/-  (2.19e-241, 2.19e-241j)
| (-0.99646149411761914653 - 9.5795153106327815645e-1013j)  +/-  (7.32e-236, 7.32e-236j)
| (0.76403737582160743666 - 1.9333983976406572065e-1020j)  +/-  (3.59e-239, 3.59e-239j)
| (0.60131709129840580824 - 2.6312092961834452352e-1020j)  +/-  (2.7e-242, 2.7e-242j)
| (0.084050524929247545051 - 2.1438071823498335264e-1032j)  +/-  (5.35e-254, 5.35e-254j)
| (-0.60131709129840580824 + 6.4865326158120777106e-1019j)  +/-  (2.84e-242, 2.84e-242j)
| (-0.72666032203402704716 + 3.7477552007897844891e-1021j)  +/-  (7.81e-240, 7.81e-240j)
| (0.028046256275868958377 - 4.3982759742887062351e-1036j)  +/-  (4.04e-255, 4.04e-255j)
| (0.64517198354208763329 - 4.4480029835962206877e-1024j)  +/-  (1.93e-241, 1.93e-241j)
| (0.40844425693599613546 - 3.7296287138037889052e-1029j)  +/-  (1.76e-246, 1.76e-246j)
| (-0.35662153266231302436 - 7.4835616265940538864e-1031j)  +/-  (1.18e-247, 1.18e-247j)
| (-0.55557023301960222474 + 1.6205908744407632968e-1027j)  +/-  (3.26e-243, 3.26e-243j)
| (-0.19509032201612826785 + 9.8777467471863840245e-1036j)  +/-  (2.05e-251, 2.05e-251j)
| (0.55557023301960222474 - 1.5208124537928020433e-1027j)  +/-  (3.57e-243, 3.57e-243j)
| (0.50807534524652945854 + 1.7940824030071281532e-1030j)  +/-  (2.79e-244, 2.79e-244j)
| (-0.028046256275868958377 + 1.9426540647747007843e-1042j)  +/-  (3.34e-255, 3.34e-255j)
| (-0.45898186446753768136 - 8.9577081062336538275e-1033j)  +/-  (2.85e-245, 2.85e-245j)
| (-0.30367674510961473081 + 3.4503884005037317319e-1036j)  +/-  (7.12e-249, 7.12e-249j)
| (0.13979033953549947793 - 7.0116285451180546031e-1041j)  +/-  (1.27e-252, 1.27e-252j)
| (0.45898186446753768136 - 4.6101871438664970381e-1032j)  +/-  (2.58e-245, 2.58e-245j)
| (0.19509032201612826785 + 9.1306712605059772623e-1039j)  +/-  (1.96e-251, 1.96e-251j)
| (-0.24977647816722684996 - 1.7737248476053014782e-1037j)  +/-  (4.23e-250, 4.23e-250j)
| (-0.40844425693599613546 - 1.4739334730077381642e-1034j)  +/-  (1.97e-246, 1.97e-246j)
| (-0.084050524929247545051 + 1.3743558673337097221e-1041j)  +/-  (6.36e-254, 6.36e-254j)
| (0.35662153266231302436 + 1.3060859525362477498e-1034j)  +/-  (1.19e-247, 1.19e-247j)
| (0.30367674510961473081 + 5.4333046545071396651e-1036j)  +/-  (8.44e-249, 8.44e-249j)
| (-0.13979033953549947793 - 3.0565519587889030475e-1040j)  +/-  (1.31e-252, 1.31e-252j)
-------------------------------------------------
The weights are:
| (0.017857142857142857143 - 2.3874588692068775015e-890j)  +/-  (7.86e-52, 8.14e-165j)
| (0.017857142857142857143 - 4.6563787125662085618e-889j)  +/-  (2.77e-52, 2.86e-165j)
| (0.017857142857142857143 + 2.1484740259927891408e-890j)  +/-  (2.32e-52, 2.4e-165j)
| (0.017857142857142857143 - 7.0047749954911303106e-889j)  +/-  (2.27e-52, 2.35e-165j)
| (0.017857142857142857143 - 3.8342329030937523914e-889j)  +/-  (2.04e-53, 2.11e-166j)
| (0.017857142857142857143 + 4.5028524515941641844e-889j)  +/-  (2.61e-53, 2.7e-166j)
| (0.017857142857142857143 - 5.5274267253295156273e-891j)  +/-  (4.52e-55, 4.68e-168j)
| (0.017857142857142857143 + 1.6805182408060406988e-890j)  +/-  (1.88e-54, 1.95e-167j)
| (0.017857142857142857143 + 7.7506987886068980317e-891j)  +/-  (3.1e-55, 3.21e-168j)
| (0.017857142857142857143 + 1.8444997440918731391e-889j)  +/-  (1.25e-56, 1.29e-169j)
| (0.017857142857142857143 + 3.3378450578981321091e-889j)  +/-  (2.96e-55, 3.06e-168j)
| (0.017857142857142857143 - 1.103734814582394218e-891j)  +/-  (8.74e-56, 9.05e-169j)
| (0.017857142857142857143 - 3.3906299107778563481e-890j)  +/-  (4.59e-57, 4.75e-170j)
| (0.017857142857142857143 - 1.9128603817032695788e-890j)  +/-  (5.96e-55, 6.18e-168j)
| (0.017857142857142857143 + 1.7484379166193560419e-888j)  +/-  (4.93e-56, 5.11e-169j)
| (0.017857142857142857143 - 2.9530708909091051007e-889j)  +/-  (7.77e-57, 8.04e-170j)
| (0.017857142857142857143 + 2.6450539744957803245e-889j)  +/-  (1.51e-57, 1.56e-170j)
| (0.017857142857142857143 - 9.7758099360638726395e-889j)  +/-  (7.49e-57, 7.76e-170j)
| (0.017857142857142857143 + 1.2238118400376300705e-890j)  +/-  (5.02e-59, 5.2e-172j)
| (0.017857142857142857143 - 4.4969022857887559477e-890j)  +/-  (2.54e-62, 2.63e-175j)
| (0.017857142857142857143 - 5.4603911277670899332e-889j)  +/-  (3.43e-57, 3.55e-170j)
| (0.017857142857142857143 - 2.3922266499909791304e-889j)  +/-  (6.32e-59, 6.54e-172j)
| (0.017857142857142857143 - 1.4509742165015113239e-890j)  +/-  (6.64e-59, 6.88e-172j)
| (0.017857142857142857143 - 2.878608244159156627e-890j)  +/-  (3.24e-61, 3.36e-174j)
| (0.017857142857142857143 + 2.6305739504674031862e-890j)  +/-  (1.42e-60, 1.47e-173j)
| (0.017857142857142857143 - 1.0186661448329255554e-889j)  +/-  (4.54e-66, 4.7e-179j)
| (0.017857142857142857143 - 2.0001799251585689309e-889j)  +/-  (2.53e-62, 2.62e-175j)
| (0.017857142857142857143 + 6.968003503014599758e-889j)  +/-  (4.05e-59, 4.19e-172j)
| (0.017857142857142857143 - 9.9863685308658708349e-891j)  +/-  (2.91e-60, 3.01e-173j)
| (0.017857142857142857143 + 3.6558756441679545542e-890j)  +/-  (2.53e-64, 2.62e-177j)
| (0.017857142857142857143 + 3.312952715664687115e-891j)  +/-  (1.6e-60, 1.66e-173j)
| (0.017857142857142857143 + 2.180481600924317705e-889j)  +/-  (9.11e-63, 9.44e-176j)
| (0.017857142857142857143 + 1.5883810088108454622e-889j)  +/-  (4.67e-66, 4.84e-179j)
| (0.017857142857142857143 + 8.5788216727054188668e-890j)  +/-  (4.13e-69, 4.28e-182j)
| (0.017857142857142857143 - 3.9281674703041984488e-890j)  +/-  (4.56e-66, 4.72e-179j)
| (0.017857142857142857143 + 3.1317517342207758639e-890j)  +/-  (3.41e-64, 3.54e-177j)
| (0.017857142857142857143 - 8.1082111966620341554e-890j)  +/-  (1.29e-69, 1.34e-182j)
| (0.017857142857142857143 - 1.7084705084782549196e-889j)  +/-  (1.43e-66, 1.49e-179j)
| (0.017857142857142857143 + 1.2193700867871512745e-889j)  +/-  (1.11e-69, 1.15e-182j)
| (0.017857142857142857143 + 5.4236879239497033916e-890j)  +/-  (2.02e-70, 2.1e-183j)
| (0.017857142857142857143 + 4.2082416983633134755e-890j)  +/-  (8.81e-68, 9.13e-181j)
| (0.017857142857142857143 - 6.4657380704235212413e-890j)  +/-  (2.28e-71, 2.37e-184j)
| (0.017857142857142857143 - 1.4814019364156907847e-889j)  +/-  (2.35e-69, 2.44e-182j)
| (0.017857142857142857143 + 1.3853371026908825397e-889j)  +/-  (4.69e-70, 4.86e-183j)
| (0.017857142857142857143 + 7.664279444565926027e-890j)  +/-  (3.46e-72, 3.58e-185j)
| (0.017857142857142857143 + 4.7950313515430641963e-890j)  +/-  (7.12e-71, 7.38e-184j)
| (0.017857142857142857143 - 5.7564883451173087853e-890j)  +/-  (3.99e-72, 4.13e-185j)
| (0.017857142857142857143 - 9.0794216310536872691e-890j)  +/-  (7.46e-73, 7.73e-186j)
| (0.017857142857142857143 - 1.2984547162055998936e-889j)  +/-  (2.14e-72, 2.22e-185j)
| (0.017857142857142857143 + 9.6138638678895171004e-890j)  +/-  (3.91e-73, 4.05e-186j)
| (0.017857142857142857143 + 6.1033387260578057615e-890j)  +/-  (1.64e-73, 1.7e-186j)
| (0.017857142857142857143 - 5.1036011392291345146e-890j)  +/-  (5.25e-73, 5.45e-186j)
| (0.017857142857142857143 - 7.2441639596751987688e-890j)  +/-  (3.19e-74, 3.33e-187j)
| (0.017857142857142857143 - 1.1469622924852995157e-889j)  +/-  (1.06e-74, 1.11e-187j)
| (0.017857142857142857143 + 1.0803138283000319252e-889j)  +/-  (9.02e-75, 9.55e-188j)
| (0.017857142857142857143 + 6.8453756030571760014e-890j)  +/-  (8.28e-75, 8.21e-188j)
