Starting with polynomial:
P : t
Extension levels are: 1 8 46
-------------------------------------------------
Trying to find an order 8 Kronrod extension for:
P1 : t
Solvable: 1
-------------------------------------------------
Trying to find an order 46 Kronrod extension for:
P2 : t^9 - 9/4*t^7 + 27/16*t^5 - 15/32*t^3 + 9/256*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^55 - 14*t^53 + 1483/16*t^51 - 6175/16*t^49 + 72569/64*t^47 - 39997/16*t^45 + 17586789/4096*t^43 - 24118743/4096*t^41 + 429651915/65536*t^39 - 196392911/32768*t^37 + 4753056815/1048576*t^35 - 2987475127/1048576*t^33 + 3127612553/2097152*t^31 - 42605315/65536*t^29 + 15804348979/67108864*t^27 - 4738081509/67108864*t^25 + 37380460455/2147483648*t^23 - 3756287205/1073741824*t^21 + 19463777025/34359738368*t^19 - 2500779765/34359738368*t^17 + 999629565/137438953472*t^15 - 18919455/34359738368*t^13 + 536257995/17592186044416*t^11 - 20669025/17592186044416*t^9 + 8261955/281474976710656*t^7 - 59787/140737488355328*t^5 + 13131/4503599627370496*t^3 - 27/4503599627370496*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
-------------------------------------------------
The nodes are:
| (-0.98480775301220805937 + 3.7273584562698046341e-863j)  +/-  (1.53e-235, 1.53e-235j)
| (0.97304487057982383883 + 2.5352863457905313129e-861j)  +/-  (9.48e-236, 9.48e-236j)
| (-0.97304487057982383883 + 2.8739133912343378095e-872j)  +/-  (9.77e-236, 9.77e-236j)
| (-1 + 6.8746425614991447256e-871j)  +/-  (1.45e-235, 1.45e-235j)
| (0.91821610688027401476 + 6.3097645534102779951e-871j)  +/-  (1.13e-236, 1.13e-236j)
| (0.93969262078590838405 + 5.706720733853342712e-874j)  +/-  (2.53e-236, 2.53e-236j)
| (0.99323835774194298855 + 2.4819678189045515226e-879j)  +/-  (2.12e-235, 2.12e-235j)
| (-0.91821610688027401476 + 2.0269310865403718736e-901j)  +/-  (1.13e-236, 1.13e-236j)
| (-0.17364817766693034885 - 2.4911567728590160392e-917j)  +/-  (5.94e-252, 5.94e-252j)
| (-0.99830815827126820805 - 8.8948092032281676924e-899j)  +/-  (2.69e-235, 2.69e-235j)
| (0.86602540378443864676 + 4.4336550752991894276e-899j)  +/-  (1.31e-237, 1.31e-237j)
| (0.98480775301220805937 + 3.187545938225855171e-901j)  +/-  (1.58e-235, 1.58e-235j)
| (-0.86602540378443864676 - 1.8954199766036482707e-921j)  +/-  (1.28e-237, 1.28e-237j)
| (-0.83548781141293641965 + 3.7133309386597516408e-921j)  +/-  (3.82e-238, 3.82e-238j)
| (-3.6524667379918952176e-950 - 3.3584247792059378361e-951j)  +/-  (2.02e-948, 2.02e-948j)
| (0.83548781141293641965 - 6.2665398905311650609e-918j)  +/-  (3.59e-238, 3.59e-238j)
| (0.89363264032341224819 + 3.861440073032781866e-917j)  +/-  (3.79e-237, 3.79e-237j)
| (-0.93969262078590838405 + 4.9702848721088980659e-920j)  +/-  (2.58e-236, 2.58e-236j)
| (-0.80212319275504378508 - 6.2333885576328536215e-932j)  +/-  (9.42e-239, 9.42e-239j)
| (-0.89363264032341224819 + 3.0235803039019795624e-928j)  +/-  (3.82e-237, 3.82e-237j)
| (0.99830815827126820805 + 5.7191159697732206256e-932j)  +/-  (2.58e-235, 2.58e-235j)
| (0.80212319275504378508 + 4.050896710284311881e-955j)  +/-  (8.85e-239, 8.85e-239j)
| (-0.95798951231548887444 - 5.7878950263014134639e-952j)  +/-  (5.42e-236, 5.42e-236j)
| (-0.72737364157304869599 + 2.2489501468674050149e-957j)  +/-  (4.01e-240, 4.01e-240j)
| (-0.7660444431189780352 - 4.4616877022039164299e-957j)  +/-  (1.81e-239, 1.81e-239j)
| (0.95798951231548887444 + 1.9421893715529699984e-953j)  +/-  (6.08e-236, 6.08e-236j)
| (0.68624163786873358573 - 4.6319498068861014165e-972j)  +/-  (7.13e-241, 7.13e-241j)
| (0.72737364157304869599 + 8.35115222616185328e-971j)  +/-  (3.64e-240, 3.64e-240j)
| (1 + 8.6836852175411085074e-971j)  +/-  (1.63e-235, 1.63e-235j)
| (-0.68624163786873358573 - 5.2187980391578417598e-984j)  +/-  (6.74e-241, 6.74e-241j)
| (-0.23061587074244017845 + 8.8168470269366156263e-995j)  +/-  (1.36e-250, 1.36e-250j)
| (0.7660444431189780352 - 3.074085215699706396e-984j)  +/-  (1.84e-239, 1.84e-239j)
| (0.64278760968653932632 - 1.0582339033000164069e-986j)  +/-  (9.48e-242, 9.48e-242j)
| (-0.058144828910475828539 - 8.313550846871869333e-999j)  +/-  (1e-254, 1e-254j)
| (-0.64278760968653932632 + 1.1599375045836800625e-984j)  +/-  (9.39e-242, 9.39e-242j)
| (-0.59715859170278616485 - 7.7845429922334880766e-986j)  +/-  (1.02e-242, 1.02e-242j)
| (0.11609291412523022968 - 6.6731290029013570284e-997j)  +/-  (2.26e-253, 2.26e-253j)
| (0.59715859170278616485 + 7.2570302618212189509e-988j)  +/-  (1.09e-242, 1.09e-242j)
| (0.2868032327110902531 + 1.8386413299269738584e-994j)  +/-  (1.82e-249, 1.82e-249j)
| (-0.3960797660391568237 + 3.8960063751224208643e-990j)  +/-  (5.22e-247, 5.22e-247j)
| (-0.54950897807080603526 - 5.2590604183182553523e-987j)  +/-  (1.02e-243, 1.02e-243j)
| (-0.99323835774194298855 - 4.9315735953227296427e-991j)  +/-  (2.32e-235, 2.32e-235j)
| (0.54950897807080603526 + 2.3760499589071273909e-1000j)  +/-  (1.08e-243, 1.08e-243j)
| (0.5 + 4.1243621915388977907e-1002j)  +/-  (1.14e-244, 1.14e-244j)
| (0.058144828910475828539 + 3.5365847105793231309e-1013j)  +/-  (1e-254, 1e-254j)
| (-0.5 - 5.6021417163393297146e-1003j)  +/-  (1.03e-244, 1.03e-244j)
| (-0.34202014332566873304 + 2.2736343829057229778e-1006j)  +/-  (3.26e-248, 3.26e-248j)
| (0.23061587074244017845 + 2.3559155291733601482e-1009j)  +/-  (1.22e-250, 1.22e-250j)
| (0.44879918020046217279 - 1.2638012065856201662e-1005j)  +/-  (8.07e-246, 8.07e-246j)
| (0.17364817766693034885 + 6.2701156132937621165e-1010j)  +/-  (5.17e-252, 5.17e-252j)
| (-0.2868032327110902531 - 1.4767010532331018721e-1007j)  +/-  (2.18e-249, 2.18e-249j)
| (-0.44879918020046217279 - 3.0268945284213887075e-1004j)  +/-  (9.26e-246, 9.26e-246j)
| (-0.11609291412523022968 - 2.3958953744568908184e-1011j)  +/-  (2.3e-253, 2.3e-253j)
| (0.34202014332566873304 + 9.6936066902284388151e-1006j)  +/-  (3.92e-248, 3.92e-248j)
| (0.3960797660391568237 - 1.0340691175615218673e-1004j)  +/-  (5.4e-247, 5.4e-247j)
-------------------------------------------------
The weights are:
| (0.018518518518518518519 + 1.2708550973462998174e-863j)  +/-  (4.99e-53, 3.05e-165j)
| (0.018518518518518518519 + 4.2914208231553497384e-862j)  +/-  (4.5e-54, 2.75e-166j)
| (0.018518518518518518519 - 8.2805648382042776315e-863j)  +/-  (3.04e-53, 1.86e-165j)
| (0.0092592592592592592593 + 1.0819447078624548969e-863j)  +/-  (7.7e-54, 4.7e-166j)
| (0.018518518518518518519 + 8.5666046585761610576e-862j)  +/-  (1.83e-54, 1.12e-166j)
| (0.018518518518518518519 - 1.408052222807060491e-861j)  +/-  (2.09e-54, 1.28e-166j)
| (0.018518518518518518519 + 2.3246455711540666415e-861j)  +/-  (1.37e-55, 8.39e-168j)
| (0.018518518518518518519 + 3.5190011129069144164e-863j)  +/-  (5.18e-56, 3.16e-168j)
| (0.018518518518518518519 - 4.1794549141060199081e-863j)  +/-  (6.72e-58, 4.1e-170j)
| (0.018518518518518518519 - 2.7312216580895591946e-863j)  +/-  (2.89e-54, 1.76e-166j)
| (0.018518518518518518519 + 4.3907580997609266779e-862j)  +/-  (2.59e-56, 1.58e-168j)
| (0.018518518518518518519 - 3.990996689044189015e-861j)  +/-  (2.32e-55, 1.42e-167j)
| (0.018518518518518518519 + 3.1340128039496738228e-863j)  +/-  (4.58e-57, 2.8e-169j)
| (0.018518518518518518519 - 3.0582766759383935807e-863j)  +/-  (1.62e-57, 9.91e-170j)
| (0.018518518518518518519 + 4.895124112264267388e-863j)  +/-  (4.31e-59, 2.63e-171j)
| (0.018518518518518518519 - 3.4169026805598224173e-862j)  +/-  (9.44e-58, 5.76e-170j)
| (0.018518518518518518519 - 5.9158303156160658122e-862j)  +/-  (9.1e-57, 5.55e-169j)
| (0.018518518518518518519 - 3.9845618393127414226e-863j)  +/-  (2.58e-57, 1.57e-169j)
| (0.018518518518518518519 + 3.0226436828455741416e-863j)  +/-  (4.07e-59, 2.49e-171j)
| (0.018518518518518518519 - 3.2722117803589346239e-863j)  +/-  (7.86e-58, 4.8e-170j)
| (0.018518518518518518519 - 1.8580698786778946582e-861j)  +/-  (3.81e-59, 2.33e-171j)
| (0.018518518518518518519 + 2.750720151815380806e-862j)  +/-  (2.39e-60, 1.46e-172j)
| (0.018518518518518518519 + 5.0051400304953998685e-863j)  +/-  (1.44e-57, 8.76e-170j)
| (0.018518518518518518519 + 3.0291975646575515232e-863j)  +/-  (2.18e-61, 1.33e-173j)
| (0.018518518518518518519 - 3.0151986620506682546e-863j)  +/-  (2.01e-60, 1.22e-172j)
| (0.018518518518518518519 + 3.1188295425874263913e-861j)  +/-  (4.03e-60, 2.46e-172j)
| (0.018518518518518518519 - 1.6411326672514349902e-862j)  +/-  (8.92e-65, 5.44e-177j)
| (0.018518518518518518519 + 1.9151118188579958722e-862j)  +/-  (2.92e-64, 1.78e-176j)
| (0.0092592592592592592593 + 8.7071318211457742955e-862j)  +/-  (5.25e-61, 3.2e-173j)
| (0.018518518518518518519 - 3.0607030304015882978e-863j)  +/-  (2.8e-65, 1.71e-177j)
| (0.018518518518518518519 + 3.992101757529455587e-863j)  +/-  (5.62e-68, 3.43e-180j)
| (0.018518518518518518519 - 2.272041417092827418e-862j)  +/-  (7.37e-64, 4.5e-176j)
| (0.018518518518518518519 + 1.4258522808933748488e-862j)  +/-  (2.63e-66, 1.6e-178j)
| (0.018518518518518518519 - 4.6274568574411647416e-863j)  +/-  (9.21e-69, 5.62e-181j)
| (0.018518518518518518519 + 3.1074233918333470489e-863j)  +/-  (6.24e-67, 3.81e-179j)
| (0.018518518518518518519 - 3.1681031543402912699e-863j)  +/-  (6.98e-68, 4.26e-180j)
| (0.018518518518518518519 + 5.5413895029622799576e-863j)  +/-  (1.34e-70, 8.17e-183j)
| (0.018518518518518518519 - 1.2534045103420138924e-862j)  +/-  (5.98e-69, 3.65e-181j)
| (0.018518518518518518519 - 6.8958582332268737782e-863j)  +/-  (2.55e-71, 1.55e-183j)
| (0.018518518518518518519 - 3.5464244835431426495e-863j)  +/-  (5.29e-71, 3.23e-183j)
| (0.018518518518518518519 + 3.2421877766477128178e-863j)  +/-  (8.23e-70, 5.02e-182j)
| (0.018518518518518518519 + 5.7997095988698204929e-863j)  +/-  (7.47e-67, 4.56e-179j)
| (0.018518518518518518519 + 1.1130174891621491497e-862j)  +/-  (9.88e-71, 6.03e-183j)
| (0.018518518518518518519 - 9.9714968478241385056e-863j)  +/-  (1.36e-71, 8.31e-184j)
| (0.018518518518518518519 - 5.1978629590805325991e-863j)  +/-  (3.51e-72, 2.14e-184j)
| (0.018518518518518518519 - 3.3296347952906777515e-863j)  +/-  (1.31e-71, 8.02e-184j)
| (0.018518518518518518519 + 3.6775305457058391721e-863j)  +/-  (1.62e-72, 9.9e-185j)
| (0.018518518518518518519 + 6.3805939951772042179e-863j)  +/-  (9.19e-74, 5.61e-186j)
| (0.018518518518518518519 + 9.00382421048938589e-863j)  +/-  (7.87e-74, 4.8e-186j)
| (0.018518518518518518519 - 5.9327312866855173054e-863j)  +/-  (1.09e-73, 6.65e-186j)
| (0.018518518518518518519 - 3.8255089291656195634e-863j)  +/-  (8.75e-74, 5.34e-186j)
| (0.018518518518518518519 + 3.4308083266632546903e-863j)  +/-  (1.37e-73, 8.37e-186j)
| (0.018518518518518518519 + 4.3901827670791182648e-863j)  +/-  (3.89e-74, 2.37e-186j)
| (0.018518518518518518519 + 7.4922615742653788335e-863j)  +/-  (1.99e-75, 1.22e-187j)
| (0.018518518518518518519 - 8.1873494607751577863e-863j)  +/-  (1.9e-75, 1.16e-187j)
