Starting with polynomial:
P : t^4 - 6*t^2 + 3
Extension levels are: 4 38
-------------------------------------------------
Trying to find an order 38 Kronrod extension for:
P1 : t^4 - 6*t^2 + 3
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^42 - 4045882219562673470908898221/5151895684408414257614025*t^40 + 24376810132734679059613141558852/87582226634943042379438425*t^38 - 5171049819931180062755435552502016/87582226634943042379438425*t^36 + 6993083893890325790949689527087983/834116444142314689327985*t^34 - 41434643274003584747363943829412943/49065673184842040548705*t^32 + 133108651611516588090384987301063008/2133290138471393067335*t^30 - 169285345822931147272588378160755918224/49065673184842040548705*t^28 + 7085649529991605108769941281571063313082/49065673184842040548705*t^26 - 3472265122413101989649699098094001359730/754856510536031393057*t^24 + 3661343774126288084285568102060089692920/32819848284175277959*t^22 - 67360507935408110415252716555874034241520/32819848284175277959*t^20 + 932867496083740574519879794738583700316770/32819848284175277959*t^18 - 9608107725469082448430251652865175961401810/32819848284175277959*t^16 + 72336824877615454460508589802200082636937600/32819848284175277959*t^14 - 388580315202673640832303510933087278607445200/32819848284175277959*t^12 + 1438933380059224246865362547936364112519732275/32819848284175277959*t^10 - 18270911670714842390722255008176392046555025/171831666409294649*t^8 + 5110564143810981789083466260932546938403262700/32819848284175277959*t^6 - 3924662865141826628081179641294639559636914000/32819848284175277959*t^4 + 1186701471380143445471422752077936261452171125/32819848284175277959*t^2 - 58966886019780348627966223500001232220043125/32819848284175277959
-------------------------------------------------
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:
| (9.6727388993798062126 + 1.6395290249432178086e-567j)  +/-  (4.37e-246, 4.37e-246j)
| (-10.480813143022532671 - 1.5132949974340590837e-584j)  +/-  (8.74e-247, 8.74e-247j)
| (10.480813143022532671 + 1.0919830376064947996e-583j)  +/-  (8.94e-247, 8.94e-247j)
| (-5.8933019196306996468 - 1.0533822089924223857e-593j)  +/-  (1.81e-245, 1.81e-245j)
| (-9.6727388993798062126 - 2.9244115141420959149e-596j)  +/-  (3.95e-246, 3.95e-246j)
| (8.2779626884639782703 - 2.0124976223112861186e-602j)  +/-  (2.15e-245, 2.15e-245j)
| (-2.7251535435204744547 - 2.8367368255863826853e-614j)  +/-  (3.38e-248, 3.38e-248j)
| (11.452699789356969031 - 7.1430967178896020814e-612j)  +/-  (8.75e-248, 8.75e-248j)
| (-7.0405481186183066431 - 2.7344548154262793449e-615j)  +/-  (3.21e-245, 3.21e-245j)
| (6.4580938434079702776 - 4.4004145490148466147e-619j)  +/-  (2.56e-245, 2.56e-245j)
| (-8.2779626884639782703 - 3.003566796576900963e-635j)  +/-  (2.1e-245, 2.1e-245j)
| (5.3428747567822306683 + 1.5876538255676115404e-641j)  +/-  (9.32e-246, 9.32e-246j)
| (8.9486113584431791814 + 9.7265217974106815843e-662j)  +/-  (1.01e-245, 1.01e-245j)
| (-4.2753200819883107203 + 2.135365823511657667e-675j)  +/-  (1.04e-246, 1.04e-246j)
| (-6.4580938434079702776 - 9.6165361754818021398e-673j)  +/-  (2.48e-245, 2.48e-245j)
| (3.7542758603045681561 + 1.6549178252373780051e-681j)  +/-  (3.58e-247, 3.58e-247j)
| (-3.239171317646847415 - 2.2183690159781667611e-697j)  +/-  (9.78e-248, 9.78e-248j)
| (7.0405481186183066431 - 9.3145890977748585386e-719j)  +/-  (3.01e-245, 3.01e-245j)
| (-2.2703046359125909249 + 1.7745047069748524934e-740j)  +/-  (3.63e-248, 3.63e-248j)
| (-4.8042445341543277909 - 2.1753243841134748265e-739j)  +/-  (3.16e-246, 3.16e-246j)
| (5.8933019196306996468 + 5.1525142024128821782e-750j)  +/-  (1.48e-245, 1.48e-245j)
| (2.2703046359125909249 - 2.5427670558962462603e-765j)  +/-  (3.35e-248, 3.35e-248j)
| (-1.7381055518605618029 + 2.6029355470242686986e-775j)  +/-  (3.18e-250, 3.18e-250j)
| (4.2753200819883107203 - 5.7234366758702222927e-776j)  +/-  (1.16e-246, 1.16e-246j)
| (-8.9486113584431791814 - 1.1571841071478458708e-789j)  +/-  (1.14e-245, 1.14e-245j)
| (7.6450883864123484039 + 7.3477969796739099605e-798j)  +/-  (2.85e-245, 2.85e-245j)
| (1.2382974062605601015 - 1.3649427342147764096e-813j)  +/-  (1.26e-251, 1.26e-251j)
| (0.74196378430272585765 - 7.1178908971879159959e-814j)  +/-  (6.55e-253, 6.55e-253j)
| (-5.3428747567822306683 + 5.0462223057447871196e-807j)  +/-  (8.61e-246, 8.61e-246j)
| (-1.2382974062605601015 - 1.9352998122518596352e-814j)  +/-  (1.31e-251, 1.31e-251j)
| (-7.6450883864123484039 + 3.1444225552441247583e-807j)  +/-  (2.83e-245, 2.83e-245j)
| (3.239171317646847415 - 5.3928704294555726818e-809j)  +/-  (1.01e-247, 1.01e-247j)
| (2.7251535435204744547 + 1.2236131827982231042e-810j)  +/-  (3.42e-248, 3.42e-248j)
| (2.3344142183389772393 - 6.5393826934312089294e-809j)  +/-  (4.77e-248, 4.77e-248j)
| (-3.7542758603045681561 + 8.7209926072105977429e-809j)  +/-  (3.34e-247, 3.34e-247j)
| (-0.74196378430272585765 + 3.8400223598207771291e-815j)  +/-  (5.9e-253, 5.9e-253j)
| (1.7381055518605618029 + 3.0989000189387092767e-811j)  +/-  (3e-250, 3e-250j)
| (0.24716483038267304362 - 6.061703410789527798e-826j)  +/-  (2.82e-254, 2.82e-254j)
| (4.8042445341543277909 - 8.1086896706303826708e-808j)  +/-  (3.56e-246, 3.56e-246j)
| (-11.452699789356969031 + 2.4112200601958120286e-818j)  +/-  (8.4e-248, 8.4e-248j)
| (-0.24716483038267304362 - 3.4832894429161484302e-830j)  +/-  (3.77e-254, 3.77e-254j)
| (-2.3344142183389772393 - 1.6516216026275250431e-818j)  +/-  (4.49e-248, 4.49e-248j)
-------------------------------------------------
The weights are:
| (1.4602488077300143253e-21 - 1.2105391009232930918e-587j)  +/-  (3.23e-96, 4.5e-218j)
| (4.858761290988438263e-25 - 1.8284062011653398374e-591j)  +/-  (1.97e-98, 2.74e-220j)
| (4.858761290988438263e-25 - 4.5600858856390943465e-590j)  +/-  (6.77e-98, 9.44e-220j)
| (6.3844690469024448017e-09 + 9.7110447011732411374e-583j)  +/-  (2.09e-89, 2.92e-211j)
| (1.4602488077300143253e-21 + 1.2375606996202452143e-589j)  +/-  (3.4e-97, 4.74e-219j)
| (3.4178839620079310029e-16 - 1.1608629695500750533e-585j)  +/-  (6.55e-95, 9.13e-217j)
| (0.0050656371475360588678 + 1.7503312813539988234e-578j)  +/-  (5.74e-79, 8.01e-201j)
| (1.4733313651753866001e-29 + 9.464558739255013533e-593j)  +/-  (2.53e-100, 3.52e-222j)
| (4.0724839116636452148e-12 + 1.5133805181741421789e-584j)  +/-  (3.41e-93, 4.75e-215j)
| (2.006814101096888414e-10 + 6.7260801485950918424e-583j)  +/-  (1.49e-92, 2.07e-214j)
| (3.4178839620079310029e-16 + 9.0199485860654840602e-587j)  +/-  (5.91e-96, 8.24e-218j)
| (1.3736436333597067853e-07 + 2.0558709224728329791e-581j)  +/-  (1.16e-90, 1.62e-212j)
| (1.1314115866943745641e-18 + 1.0869175222053762349e-586j)  +/-  (3.05e-96, 4.25e-218j)
| (2.2475903785468445024e-05 - 1.4776961564410833753e-580j)  +/-  (1.8e-88, 2.51e-210j)
| (2.006814101096888414e-10 - 1.3404119080844647571e-583j)  +/-  (1.03e-92, 1.44e-214j)
| (0.00017963449082399562618 - 1.4697889652176696647e-579j)  +/-  (2.12e-88, 2.95e-210j)
| (0.0010782211916278024152 - 2.8686473848003995103e-579j)  +/-  (6.71e-86, 9.36e-208j)
| (4.0724839116636452148e-12 - 9.609319792683741059e-584j)  +/-  (2.08e-94, 2.91e-216j)
| (0.024767606194947539392 + 2.0377674286273458202e-577j)  +/-  (2.79e-83, 3.9e-205j)
| (2.0705512504297230204e-06 + 3.1337767894232344874e-581j)  +/-  (2.4e-90, 3.34e-212j)
| (6.3844690469024448017e-09 - 3.9996041480160649689e-582j)  +/-  (1.07e-92, 1.5e-214j)
| (0.024767606194947539392 - 3.2877218829226041933e-577j)  +/-  (2.59e-86, 3.61e-208j)
| (0.044318410385160739313 - 3.9645145997369616725e-578j)  +/-  (2.71e-83, 3.77e-205j)
| (2.2475903785468445024e-05 + 3.8186758974806094877e-580j)  +/-  (1.03e-90, 1.44e-212j)
| (1.1314115866943745641e-18 - 4.226690877181999147e-588j)  +/-  (2.26e-99, 3.16e-221j)
| (5.0099581765195337028e-14 + 1.1511425475759526736e-584j)  +/-  (5.22e-96, 7.28e-218j)
| (0.092214587118267086783 - 4.890334056294523384e-578j)  +/-  (6.45e-85, 8.99e-207j)
| (0.15006897271640559887 + 4.7412774596398225651e-578j)  +/-  (7.98e-85, 1.11e-206j)
| (1.3736436333597067853e-07 - 5.9282570748422964384e-582j)  +/-  (7.94e-93, 1.11e-214j)
| (0.092214587118267086783 + 3.7803225398766453805e-578j)  +/-  (9.71e-86, 1.35e-207j)
| (5.0099581765195337028e-14 - 1.3478104028708005578e-585j)  +/-  (7.65e-97, 1.07e-218j)
| (0.0010782211916278024152 + 5.7572594064324689128e-579j)  +/-  (4.71e-91, 6.57e-213j)
| (0.0050656371475360588678 - 3.1234476230463856192e-578j)  +/-  (1.9e-90, 2.65e-212j)
| (-0.0090236930289538090475 + 3.2341307857395613478e-577j)  +/-  (2.23e-89, 3.11e-211j)
| (0.00017963449082399562618 + 6.4786490679972272091e-580j)  +/-  (1.4e-92, 1.96e-214j)
| (0.15006897271640559887 - 4.0657217048134736585e-578j)  +/-  (2.03e-89, 2.82e-211j)
| (0.044318410385160739313 + 5.7013925459345514804e-578j)  +/-  (5.64e-90, 7.86e-212j)
| (0.19130593337551237022 - 4.6228681302555128673e-578j)  +/-  (9.82e-90, 1.35e-211j)
| (2.0705512504297230204e-06 - 9.3186170634035035927e-581j)  +/-  (5.69e-94, 7.95e-216j)
| (1.4733313651753866001e-29 + 7.9745299707065398189e-594j)  +/-  (2.88e-107, 3.98e-229j)
| (0.19130593337551237022 + 4.3925008911324317382e-578j)  +/-  (7.81e-91, 9.06e-213j)
| (-0.0090236930289538090475 - 1.9765802546220547993e-577j)  +/-  (1.23e-90, 1.79e-212j)
