Starting with polynomial:
P : 8*t^4 - 8*t^2 + 1
Extension levels are: 4 48
-------------------------------------------------
Trying to find an order 48 Kronrod extension for:
P1 : 8*t^4 - 8*t^2 + 1
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 8*t^52 - 104*t^50 + 637*t^48 - 2444*t^46 + 210795/32*t^44 - 424281/32*t^42 + 5294289/256*t^40 - 3277417/128*t^38 + 209456741/8192*t^36 - 170488045/8192*t^34 + 910893269/65536*t^32 - 62611289/8192*t^30 + 1815727381/524288*t^28 - 676868787/524288*t^26 + 1654002675/4194304*t^24 - 205632765/2097152*t^22 + 5277907635/268435456*t^20 - 842691135/268435456*t^18 + 842691135/2147483648*t^16 - 20160075/536870912*t^14 + 366913365/137438953472*t^12 - 18599295/137438953472*t^10 + 5072535/1099511627776*t^8 - 53235/549755813888*t^6 + 38025/35184372088832*t^4 - 169/35184372088832*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:   52 out of 52
Indefinite weights: 0 out of 52
Negative weights:   0 out of 52
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (0.99589655761709097004 - 1.4278149173442701014e-915j)  +/-  (2.74e-237, 2.74e-237j)
| (0.99954378448953337255 + 2.4400708609860331674e-939j)  +/-  (1.1e-237, 1.1e-237j)
| (-0.92387953251128675613 - 2.2849056937500108276e-952j)  +/-  (8.17e-238, 8.17e-238j)
| (-0.97772691637084689527 + 1.087833483649113514e-950j)  +/-  (3.25e-237, 3.25e-237j)
| (0.92387953251128675613 - 3.2831571826242589413e-950j)  +/-  (7.89e-238, 7.89e-238j)
| (0.89908811376542595756 - 1.8147420963756488217e-954j)  +/-  (3.28e-238, 3.28e-238j)
| (-0.99954378448953337255 + 1.9502843694499631246e-956j)  +/-  (1.09e-237, 1.09e-237j)
| (-0.89908811376542595756 - 1.670393504453171102e-958j)  +/-  (3.65e-238, 3.65e-238j)
| (-0.491254611083877374 + 3.0439659903571759806e-966j)  +/-  (1.99e-245, 1.99e-245j)
| (0.94529981503464026167 - 4.6260842753732978561e-956j)  +/-  (1.45e-237, 1.45e-237j)
| (0.87101601999551557359 - 1.1032279838534543288e-967j)  +/-  (1.26e-238, 1.26e-238j)
| (-0.99589655761709097004 + 3.2599677034587664464e-971j)  +/-  (2.9e-237, 2.9e-237j)
| (-0.94529981503464026167 - 8.5070954378686699229e-974j)  +/-  (1.65e-237, 1.65e-237j)
| (-0.83976568322739790211 + 1.2055401368759554703e-976j)  +/-  (4.17e-239, 4.17e-239j)
| (0.98861541220753422615 - 2.6485418882297921962e-972j)  +/-  (3.55e-237, 3.55e-237j)
| (0.83976568322739790211 - 8.697500883710878918e-995j)  +/-  (4.47e-239, 4.47e-239j)
| (0.8054511325509459412 - 3.6421091256690183713e-995j)  +/-  (1.17e-239, 1.17e-239j)
| (-0.98861541220753422615 - 2.554287250145833522e-993j)  +/-  (3.73e-237, 3.73e-237j)
| (-0.8054511325509459412 - 5.5559150263143751522e-997j)  +/-  (1.19e-239, 1.19e-239j)
| (-0.9632708010475163164 - 6.5964570245269771925e-994j)  +/-  (2.79e-237, 2.79e-237j)
| (0.9632708010475163164 - 5.6845321779563050008e-994j)  +/-  (2.54e-237, 2.54e-237j)
| (0.72814095387578841136 + 3.4373568124814561094e-1015j)  +/-  (5.09e-241, 5.09e-241j)
| (0.97772691637084689527 - 1.7501874917876703931e-1016j)  +/-  (3.78e-237, 3.78e-237j)
| (-0.87101601999551557359 - 3.9369026133706092716e-1039j)  +/-  (1.34e-238, 1.34e-238j)
| (-0.76819757804028051367 - 3.9814202636717760622e-1041j)  +/-  (2.82e-240, 2.82e-240j)
| (0.26853186747437675144 + 4.4478421866416896311e-1052j)  +/-  (4.83e-250, 4.83e-250j)
| (0.76819757804028051367 - 1.5749754979936345619e-1045j)  +/-  (3.1e-240, 3.1e-240j)
| (0.54294898220147867019 - 4.0300381971150573824e-1048j)  +/-  (2.14e-244, 2.14e-244j)
| (-0.72814095387578841136 + 3.1691037136260738266e-1043j)  +/-  (5.58e-241, 5.58e-241j)
| (-0.64021284046248801391 + 2.0501207130942491751e-1045j)  +/-  (1.72e-242, 1.72e-242j)
| (-0.20988110206484756643 + 3.3982609491838300671e-1056j)  +/-  (2.34e-251, 2.34e-251j)
| (0.6854274223350397682 - 5.8985980360050625644e-1047j)  +/-  (1e-241, 1e-241j)
| (0.64021284046248801391 - 9.0165712277497210252e-1051j)  +/-  (1.58e-242, 1.58e-242j)
| (0.090498875829637827548 - 1.5481104051089511597e-1059j)  +/-  (5.86e-254, 5.86e-254j)
| (-0.59266219136401683547 - 3.002169413925500555e-1047j)  +/-  (1.93e-243, 1.93e-243j)
| (-0.6854274223350397682 + 1.3898071883436098779e-1050j)  +/-  (1.11e-241, 1.11e-241j)
| (0.030203027800888846965 + 1.7385135320984817662e-1064j)  +/-  (3.5e-255, 3.5e-255j)
| (0.59266219136401683547 - 7.326529323486655905e-1056j)  +/-  (1.95e-243, 1.95e-243j)
| (0.3262027892208693379 - 3.4763299569347402187e-1061j)  +/-  (7.37e-249, 7.37e-249j)
| (-0.15046450327478300943 - 3.0473467380322938666e-1064j)  +/-  (1.18e-252, 1.18e-252j)
| (-0.54294898220147867019 - 5.055358636262619108e-1057j)  +/-  (2.15e-244, 2.15e-244j)
| (-0.090498875829637827548 - 1.4940828907587755317e-1066j)  +/-  (5.86e-254, 5.86e-254j)
| (0.38268343236508977173 + 4.5646647173179533224e-1061j)  +/-  (1.14e-247, 1.14e-247j)
| (0.43776770516534048091 - 3.6701738134400052938e-1058j)  +/-  (1.53e-246, 1.53e-246j)
| (-0.030203027800888846965 - 1.0645302820556636721e-1067j)  +/-  (3.73e-255, 3.73e-255j)
| (-0.43776770516534048091 + 8.739076579747870384e-1059j)  +/-  (1.6e-246, 1.6e-246j)
| (-0.3262027892208693379 - 1.0268201320745706677e-1061j)  +/-  (7.71e-249, 7.71e-249j)
| (0.15046450327478300943 + 6.4038989985102242723e-1065j)  +/-  (9.13e-253, 9.13e-253j)
| (0.491254611083877374 + 2.1133688942336081794e-1058j)  +/-  (2.01e-245, 2.01e-245j)
| (0.20988110206484756643 - 3.175331510492211355e-1064j)  +/-  (2.53e-251, 2.53e-251j)
| (-0.26853186747437675144 + 2.5244940448913342038e-1063j)  +/-  (4.97e-250, 4.97e-250j)
| (-0.38268343236508977173 + 5.3879411189299475973e-1060j)  +/-  (1.14e-247, 1.14e-247j)
-------------------------------------------------
The weights are:
| (0.019230769230769230769 + 1.6694231745779940985e-915j)  +/-  (7.33e-57, 1.25e-170j)
| (0.019230769230769230769 + 2.5125406118279277223e-915j)  +/-  (6.18e-57, 1.06e-170j)
| (0.019230769230769230769 + 6.0480374131962857612e-917j)  +/-  (3.23e-58, 5.51e-172j)
| (0.019230769230769230769 - 3.2265204417061727336e-917j)  +/-  (2.64e-58, 4.51e-172j)
| (0.019230769230769230769 - 1.6122406612877896015e-915j)  +/-  (2.86e-58, 4.88e-172j)
| (0.019230769230769230769 + 1.372005548227440444e-915j)  +/-  (1.96e-58, 3.35e-172j)
| (0.019230769230769230769 + 4.5923726428660299139e-918j)  +/-  (8.64e-60, 1.48e-173j)
| (0.019230769230769230769 - 7.009118547795259537e-917j)  +/-  (1.05e-59, 1.8e-173j)
| (0.019230769230769230769 - 1.7770367647833952981e-916j)  +/-  (3.79e-61, 6.47e-175j)
| (0.019230769230769230769 + 1.9560975054355484107e-915j)  +/-  (3.18e-59, 5.44e-173j)
| (0.019230769230769230769 - 1.1935407931282451348e-915j)  +/-  (9.93e-60, 1.7e-173j)
| (0.019230769230769230769 - 1.3785557832129153269e-917j)  +/-  (8.44e-60, 1.44e-173j)
| (0.019230769230769230769 - 5.0985136456595341534e-917j)  +/-  (4.5e-60, 7.69e-174j)
| (0.019230769230769230769 - 8.9741151040195061863e-917j)  +/-  (8.6e-62, 1.47e-175j)
| (0.019230769230769230769 - 6.2698873550324006895e-915j)  +/-  (3.07e-60, 5.24e-174j)
| (0.019230769230769230769 + 1.0551048475091554007e-915j)  +/-  (2.04e-61, 3.48e-175j)
| (0.019230769230769230769 - 9.4419580166733620551e-916j)  +/-  (3.1e-62, 5.3e-176j)
| (0.019230769230769230769 + 2.3004125058296515424e-917j)  +/-  (1.18e-60, 2.01e-174j)
| (0.019230769230769230769 + 9.9824021634286099725e-917j)  +/-  (7.28e-64, 1.24e-177j)
| (0.019230769230769230769 + 4.1586242579405157655e-917j)  +/-  (6.28e-61, 1.07e-174j)
| (0.019230769230769230769 - 2.4972419829509265711e-915j)  +/-  (4.29e-62, 7.32e-176j)
| (0.019230769230769230769 - 7.7669103746439760456e-916j)  +/-  (3.71e-66, 6.34e-180j)
| (0.019230769230769230769 + 3.5047122817406073578e-915j)  +/-  (4.76e-62, 8.14e-176j)
| (0.019230769230769230769 + 7.9837705153682540836e-917j)  +/-  (9.21e-64, 1.57e-177j)
| (0.019230769230769230769 - 1.1011031650905824736e-916j)  +/-  (6.45e-66, 1.1e-179j)
| (0.019230769230769230769 + 4.0181076559889597346e-916j)  +/-  (2.89e-70, 4.94e-184j)
| (0.019230769230769230769 + 8.53077883748185218e-916j)  +/-  (6.67e-66, 1.14e-179j)
| (0.019230769230769230769 - 5.6251689517768664538e-916j)  +/-  (1.61e-69, 2.75e-183j)
| (0.019230769230769230769 + 1.2062578468879060421e-916j)  +/-  (1.1e-67, 1.88e-181j)
| (0.019230769230769230769 + 1.4245771734694011499e-916j)  +/-  (3.34e-69, 5.71e-183j)
| (0.019230769230769230769 + 2.4602300855466875095e-916j)  +/-  (3.23e-72, 5.51e-186j)
| (0.019230769230769230769 + 7.1157783742859918929e-916j)  +/-  (1.12e-68, 1.91e-182j)
| (0.019230769230769230769 - 6.5529120097162905067e-916j)  +/-  (1.53e-69, 2.62e-183j)
| (0.019230769230769230769 - 3.3373383568861560327e-916j)  +/-  (1.73e-73, 2.96e-187j)
| (0.019230769230769230769 - 1.5383717731598202318e-916j)  +/-  (2.72e-71, 4.64e-185j)
| (0.019230769230769230769 - 1.3139820671481717281e-916j)  +/-  (5.17e-70, 8.83e-184j)
| (0.019230769230769230769 + 3.1404211111817155332e-916j)  +/-  (2.87e-74, 4.9e-188j)
| (0.019230769230769230769 + 6.0604803160672614267e-916j)  +/-  (8.52e-72, 1.46e-185j)
| (0.019230769230769230769 - 4.2827103405557932146e-916j)  +/-  (3.99e-74, 6.82e-188j)
| (0.019230769230769230769 - 2.6165638556584383618e-916j)  +/-  (3.42e-75, 5.85e-189j)
| (0.019230769230769230769 + 1.6557260440257779077e-916j)  +/-  (9.84e-74, 1.68e-187j)
| (0.019230769230769230769 + 2.781324661940635945e-916j)  +/-  (2.27e-75, 3.88e-189j)
| (0.019230769230769230769 + 4.5711901885736433636e-916j)  +/-  (2.61e-75, 4.46e-189j)
| (0.019230769230769230769 - 4.887572011492887012e-916j)  +/-  (2.43e-75, 4.15e-189j)
| (0.019230769230769230769 - 2.955545827192817847e-916j)  +/-  (4.37e-76, 7.46e-190j)
| (0.019230769230769230769 + 1.9027432215932943032e-916j)  +/-  (6.47e-77, 1.11e-190j)
| (0.019230769230769230769 + 2.1693562089534839361e-916j)  +/-  (1.21e-77, 2.07e-191j)
| (0.019230769230769230769 + 3.547921919990814188e-916j)  +/-  (2.35e-77, 4.01e-191j)
| (0.019230769230769230769 + 5.2368264662245635662e-916j)  +/-  (4.29e-77, 7.34e-191j)
| (0.019230769230769230769 - 3.7740866975005800885e-916j)  +/-  (1.77e-77, 3.02e-191j)
| (0.019230769230769230769 - 2.3114235429712494721e-916j)  +/-  (1.97e-78, 3.41e-192j)
| (0.019230769230769230769 - 2.0333341859203694461e-916j)  +/-  (1.69e-78, 2.83e-192j)
