Starting with polynomial:
P : 2*t^2 - 1
Extension levels are: 2 12 28
-------------------------------------------------
Trying to find an order 12 Kronrod extension for:
P1 : 2*t^2 - 1
Solvable: 1
-------------------------------------------------
Trying to find an order 28 Kronrod extension for:
P2 : 2*t^14 - 7*t^12 + 77/8*t^10 - 105/16*t^8 + 147/64*t^6 - 49/128*t^4 + 49/2048*t^2 - 1/4096
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 2*t^42 - 21*t^40 + 819/8*t^38 - 4921/16*t^36 + 81585/128*t^34 - 247401/256*t^32 + 284053/256*t^30 - 504339/512*t^28 + 5607063/8192*t^26 - 6135675/16384*t^24 + 84672315/524288*t^22 - 57358665/1048576*t^20 + 121090515/8388608*t^18 - 49142835/16777216*t^16 + 15043725/33554432*t^14 - 3380195/67108864*t^12 + 8580495/2147483648*t^10 - 908523/4294967296*t^8 + 235543/34359738368*t^6 - 8085/68719476736*t^4 + 441/549755813888*t^2 - 1/1099511627776
-------------------------------------------------
Computing nodes and weights
  current precision for roots: 53
  current precision for roots: 106
 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:
| (0.96592582628906828675 - 6.3862005042114513004e-839j)  +/-  (5.53e-241, 5.53e-241j)
| (-0.9993007047883985527 - 5.7603697796061440034e-849j)  +/-  (2.3e-241, 2.3e-241j)
| (-0.91656225586997618582 + 3.6929049678255814782e-857j)  +/-  (1.76e-241, 1.76e-241j)
| (0.99371220989324258353 - 2.5486773832931827855e-867j)  +/-  (5.22e-241, 5.22e-241j)
| (0.91656225586997618582 - 2.1289764195877352797e-900j)  +/-  (1.84e-241, 1.84e-241j)
| (0.9438833303083675629 + 3.0154449876379055798e-916j)  +/-  (3.22e-241, 3.22e-241j)
| (-0.33027906195516708177 + 2.0383545909170327039e-934j)  +/-  (3.13e-250, 3.13e-250j)
| (-0.88411539350460978945 + 9.3967513477904278664e-925j)  +/-  (7.69e-242, 7.69e-242j)
| (-0.99371220989324258353 + 3.828126444781466875e-922j)  +/-  (6.21e-241, 6.21e-241j)
| (0.9993007047883985527 + 2.1795333840784205553e-922j)  +/-  (2.14e-241, 2.14e-241j)
| (0.84672419922828416835 - 1.7212968222462199876e-930j)  +/-  (3.02e-242, 3.02e-242j)
| (-0.98256647323328823615 + 6.8608284096038732856e-927j)  +/-  (6.31e-241, 6.31e-241j)
| (-0.9438833303083675629 + 2.0231719125638841215e-930j)  +/-  (3.8e-241, 3.8e-241j)
| (-0.84672419922828416835 + 1.086136194305547212e-931j)  +/-  (3.42e-242, 3.42e-242j)
| (0.98256647323328823615 - 3.7908612726718057965e-930j)  +/-  (6.22e-241, 6.22e-241j)
| (0.88411539350460978945 + 1.123722353319140347e-939j)  +/-  (7.71e-242, 7.71e-242j)
| (0.80459777976666832735 + 5.9884958453727456126e-946j)  +/-  (8.07e-243, 8.07e-243j)
| (-0.46726862827306198914 + 7.1971992438301581446e-954j)  +/-  (6.33e-248, 6.33e-248j)
| (-0.75797172314545298179 + 7.5924309848450396397e-948j)  +/-  (1.99e-243, 1.99e-243j)
| (-0.96592582628906828675 + 4.5303938005693550944e-950j)  +/-  (6.02e-241, 6.02e-241j)
| (0.53203207651533656356 - 1.0040402140762883957e-955j)  +/-  (6.11e-247, 6.11e-247j)
| (0.7071067811865475244 + 1.3615740436177913976e-952j)  +/-  (4.4e-244, 4.4e-244j)
| (0.33027906195516708177 + 1.8466003008479202712e-961j)  +/-  (3.39e-250, 3.39e-250j)
| (-0.80459777976666832735 - 1.8046201914639865599e-954j)  +/-  (6.72e-243, 6.72e-243j)
| (-0.7071067811865475244 + 3.5993274604003898813e-957j)  +/-  (3.39e-244, 3.39e-244j)
| (0.25881904510252076235 + 3.6780416755553699923e-963j)  +/-  (2.52e-251, 2.52e-251j)
| (0.75797172314545298179 + 2.5153770220127066938e-956j)  +/-  (2.33e-243, 2.33e-243j)
| (0.59382018557350161165 - 4.8577023762360950406e-960j)  +/-  (7.29e-246, 7.29e-246j)
| (-0.11196447610330785847 + 5.572048828403007934e-971j)  +/-  (4.48e-254, 4.48e-254j)
| (-0.65228741127812115437 - 2.8414837366123097549e-963j)  +/-  (5.25e-245, 5.25e-245j)
| (-0.25881904510252076235 + 3.2887018897343584995e-969j)  +/-  (2.19e-251, 2.19e-251j)
| (0.39989202431974097188 - 9.7619863371398527868e-966j)  +/-  (6.22e-249, 6.22e-249j)
| (0.65228741127812115437 - 1.0266531991761099325e-965j)  +/-  (6.15e-245, 6.15e-245j)
| (0.037391194276325621096 - 9.6182199263933137631e-978j)  +/-  (3.07e-255, 3.07e-255j)
| (-0.59382018557350161165 - 4.7732873286786221621e-971j)  +/-  (8.02e-246, 8.02e-246j)
| (-0.39989202431974097188 - 3.9654613199866526184e-974j)  +/-  (5.52e-249, 5.52e-249j)
| (0.11196447610330785847 + 2.3500743361024167876e-981j)  +/-  (5.57e-254, 5.57e-254j)
| (0.46726862827306198914 + 1.5330677562691846564e-974j)  +/-  (6.33e-248, 6.33e-248j)
| (0.18591160716291458111 + 4.5772042861777265463e-979j)  +/-  (1.08e-252, 1.08e-252j)
| (-0.18591160716291458111 + 1.2762705154800948868e-981j)  +/-  (1.14e-252, 1.14e-252j)
| (-0.53203207651533656356 + 2.6254665071243653307e-976j)  +/-  (6.64e-247, 6.64e-247j)
| (-0.037391194276325621096 - 3.7146136505320656882e-984j)  +/-  (2.84e-255, 2.84e-255j)
-------------------------------------------------
The weights are:
| (0.023809523809523809524 + 1.096262556103082794e-839j)  +/-  (2.11e-77, 1.83e-193j)
| (0.023809523809523809524 + 1.1177728495539428023e-841j)  +/-  (4.29e-78, 3.72e-194j)
| (0.023809523809523809524 - 1.2479797245532707548e-840j)  +/-  (4e-78, 3.47e-194j)
| (0.023809523809523809524 - 2.3672561528939582633e-839j)  +/-  (3.1e-78, 2.68e-194j)
| (0.023809523809523809524 + 4.7591917919181762177e-839j)  +/-  (2.99e-78, 2.59e-194j)
| (0.023809523809523809524 - 8.8027283724572227366e-839j)  +/-  (6.32e-78, 5.48e-194j)
| (0.023809523809523809524 + 4.2780089566971910694e-840j)  +/-  (8.31e-80, 7.2e-196j)
| (0.023809523809523809524 + 1.4838234959167394312e-840j)  +/-  (1.1e-79, 9.51e-196j)
| (0.023809523809523809524 - 3.3566134121490426165e-841j)  +/-  (6.64e-80, 5.75e-196j)
| (0.023809523809523809524 + 6.5818301720059593352e-840j)  +/-  (8.66e-80, 7.5e-196j)
| (0.023809523809523809524 + 2.622120598964707322e-839j)  +/-  (1.64e-81, 1.42e-197j)
| (0.023809523809523809524 + 5.6053767608604569398e-841j)  +/-  (3.04e-80, 2.63e-196j)
| (0.023809523809523809524 + 1.0159868588186880745e-840j)  +/-  (1.1e-80, 9.5e-197j)
| (0.023809523809523809524 - 1.7243319727488128816e-840j)  +/-  (1.33e-81, 1.15e-197j)
| (0.023809523809523809524 + 6.563467325006034053e-839j)  +/-  (2.29e-80, 1.99e-196j)
| (0.023809523809523809524 - 3.3554823808729133733e-839j)  +/-  (1.12e-81, 9.68e-198j)
| (0.023809523809523809524 - 2.1624302599507682647e-839j)  +/-  (2.91e-83, 2.52e-199j)
| (0.023809523809523809524 + 3.6241057452934400319e-840j)  +/-  (2.02e-85, 1.75e-201j)
| (0.023809523809523809524 - 2.2229237786825001637e-840j)  +/-  (1.85e-84, 1.61e-200j)
| (0.023809523809523809524 - 7.8708107457067774708e-841j)  +/-  (4.87e-82, 4.21e-198j)
| (0.023809523809523809524 + 1.1464512879154475793e-839j)  +/-  (1.61e-86, 1.4e-202j)
| (0.023809523809523809524 - 1.6050397789242973966e-839j)  +/-  (1.96e-85, 1.7e-201j)
| (0.023809523809523809524 - 8.7236755346139446331e-840j)  +/-  (1.01e-87, 8.76e-204j)
| (0.023809523809523809524 + 1.9703812274762358822e-840j)  +/-  (1.21e-84, 1.05e-200j)
| (0.023809523809523809524 + 2.4830051705555985205e-840j)  +/-  (5.53e-86, 4.79e-202j)
| (0.023809523809523809524 + 8.025198892565334771e-840j)  +/-  (3.4e-88, 2.95e-204j)
| (0.023809523809523809524 + 1.8427589614868389879e-839j)  +/-  (1.03e-85, 8.93e-202j)
| (0.023809523809523809524 - 1.2703096727627888357e-839j)  +/-  (2.66e-87, 2.31e-203j)
| (0.023809523809523809524 - 5.4160552982234412138e-840j)  +/-  (1.13e-89, 9.76e-206j)
| (0.023809523809523809524 - 2.7517836260029121293e-840j)  +/-  (5.68e-88, 4.92e-204j)
| (0.023809523809523809524 - 4.633350737764007585e-840j)  +/-  (2.11e-89, 1.83e-205j)
| (0.023809523809523809524 + 9.5129810322841120662e-840j)  +/-  (6.21e-89, 5.38e-205j)
| (0.023809523809523809524 + 1.4197791118158179435e-839j)  +/-  (1.34e-87, 1.16e-203j)
| (0.023809523809523809524 - 6.3225913926893205684e-840j)  +/-  (7.48e-91, 6.48e-207j)
| (0.023809523809523809524 + 3.030553628791094163e-840j)  +/-  (4.72e-90, 4.09e-206j)
| (0.023809523809523809524 - 3.942450168640804772e-840j)  +/-  (3.04e-90, 2.63e-206j)
| (0.023809523809523809524 + 6.8362736598473616989e-840j)  +/-  (3.08e-91, 2.67e-207j)
| (0.023809523809523809524 - 1.0416069967905771874e-839j)  +/-  (1.82e-90, 1.57e-206j)
| (0.023809523809523809524 - 7.4004213968576530194e-840j)  +/-  (2.94e-91, 2.55e-207j)
| (0.023809523809523809524 + 5.0115005353168560172e-840j)  +/-  (7.53e-92, 6.54e-208j)
| (0.023809523809523809524 - 3.3207745451833395749e-840j)  +/-  (6.85e-92, 5.98e-208j)
| (0.023809523809523809524 + 5.8513360695597498707e-840j)  +/-  (6.92e-92, 5.98e-208j)
