Starting with polynomial:
P : t
Extension levels are: 1 2 8 20
-------------------------------------------------
Trying to find an order 2 Kronrod extension for:
P1 : t
Solvable: 1
-------------------------------------------------
Trying to find an order 8 Kronrod extension for:
P2 : t^3 - 3*t
Solvable: 1
-------------------------------------------------
Trying to find an order 20 Kronrod extension for:
P3 : t^11 - 149/3*t^9 + 798*t^7 - 4914*t^5 + 10605*t^3 - 5355*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^31 - 839960958043992074604091/2365356289365091915347*t^29 + 2698037903741261798437846981/49672482076666930222287*t^27 - 338615629034213939422960946901/71749140777407788098859*t^25 + 18567379275860563346158780812975/71749140777407788098859*t^23 - 96492572023781136168310663908825/10249877253915398299837*t^21 + 183450007534697194219496911709775/788452096455030638449*t^19 - 40363279205729767325022504147850575/10249877253915398299837*t^17 + 465959432528072010082336333496199975/10249877253915398299837*t^15 - 278069518359491907958617208562638875/788452096455030638449*t^13 + 1411180472218607278042279672274126625/788452096455030638449*t^11 - 4488675124281877372533298302559870125/788452096455030638449*t^9 + 1196634927084926705618126933082461625/112636013779290091207*t^7 - 1180710553849397652456998867946623625/112636013779290091207*t^5 + 516885121451999669467183496495431875/112636013779290091207*t^3 - 68540125432790089255610669508669375/112636013779290091207*t
-------------------------------------------------
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: 1
  current precision for roots: 212
  current precision for roots: 424
 current precision for weights: 212
Linear system for weights solvable: 1
Sufficient bits for target precision reached
Positive weights:   31 out of 31
Indefinite weights: 0 out of 31
Negative weights:   0 out of 31
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (4.3394221426603944777 + 1.0206514861483695106e-370j)  +/-  (7.32e-121, 7.32e-121j)
| (-8.0130130598043254019 + 2.8833225811544255266e-376j)  +/-  (2.79e-121, 2.79e-121j)
| (8.0130130598043254019 + 1.1601065870845955137e-373j)  +/-  (2.9e-121, 2.9e-121j)
| (1.7320508075688772935 + 7.2069339612390368435e-379j)  +/-  (2.25e-123, 2.25e-123j)
| (-9.0508037980317400421 - 7.2689751033144076625e-382j)  +/-  (4.05e-122, 4.05e-122j)
| (7.1482776511870860001 + 3.2992682271319540861e-379j)  +/-  (8.7e-121, 8.7e-121j)
| (-4.3394221426603944777 + 8.6879489886310393721e-387j)  +/-  (6.82e-121, 6.82e-121j)
| (9.0508037980317400421 - 5.6231232443291177036e-387j)  +/-  (4.39e-122, 4.39e-122j)
| (-2.6840395601585691766 - 1.6114589432283773462e-391j)  +/-  (5.78e-122, 5.78e-122j)
| (1.243545700652809326 + 1.4501452701580666772e-389j)  +/-  (3.26e-124, 3.26e-124j)
| (3.7355715460409572598 + 6.9784640986031831496e-402j)  +/-  (3.7e-121, 3.7e-121j)
| (6.3725842092196922567 + 4.9678006460454487479e-422j)  +/-  (1.26e-120, 1.26e-120j)
| (-7.1482776511870860001 + 3.6887372179834094602e-431j)  +/-  (8.04e-121, 8.04e-121j)
| (-1.7320508075688772935 + 2.1959096650227342737e-437j)  +/-  (2.22e-123, 2.22e-123j)
| (-4.9791465117195582423 + 5.7486379781270790515e-437j)  +/-  (1.24e-120, 1.24e-120j)
| (0.84628809835102169611 + 3.6117151207656316804e-451j)  +/-  (4.9e-125, 4.9e-125j)
| (5.6545621267720157303 + 1.0762143272812650064e-467j)  +/-  (1.56e-120, 1.56e-120j)
| (-6.3725842092196922567 + 1.0932798334587284315e-480j)  +/-  (1.27e-120, 1.27e-120j)
| (-2.2210157242456798448 - 1.6333412564688016775e-485j)  +/-  (1.34e-122, 1.34e-122j)
| (1.4511588231512457452e-485 - 2.724827181466255983e-485j)  +/-  (9.57e-484, 9.57e-484j)
| (-0.84628809835102169611 - 2.5017408372097602023e-486j)  +/-  (4.9e-125, 4.9e-125j)
| (0.47371420996884380468 - 2.3029789981228527395e-484j)  +/-  (5.47e-126, 5.47e-126j)
| (4.9791465117195582423 + 5.2067873498399808906e-483j)  +/-  (1.12e-120, 1.12e-120j)
| (-1.243545700652809326 - 9.2023547386562945374e-492j)  +/-  (3.11e-124, 3.11e-124j)
| (2.2210157242456798448 + 4.819740837284954474e-488j)  +/-  (1.2e-122, 1.2e-122j)
| (3.1782891110545300949 - 7.6985986411808438391e-487j)  +/-  (1.64e-121, 1.64e-121j)
| (-5.6545621267720157303 + 5.048788495067270759e-487j)  +/-  (1.57e-120, 1.57e-120j)
| (2.6840395601585691766 + 1.4833375578808372763e-487j)  +/-  (6.1e-122, 6.1e-122j)
| (-3.7355715460409572598 - 9.6572205621039189255e-489j)  +/-  (3.52e-121, 3.52e-121j)
| (-0.47371420996884380468 - 3.0404780305298438057e-496j)  +/-  (4.8e-126, 4.8e-126j)
| (-3.1782891110545300949 - 2.3984857567358944428e-494j)  +/-  (1.39e-121, 1.39e-121j)
-------------------------------------------------
The weights are:
| (2.0232543534503754413e-05 - 6.9678584442089142198e-375j)  +/-  (5.14e-33, 1.95e-92j)
| (4.226469169022273101e-15 + 1.0839300195289400548e-382j)  +/-  (1.41e-41, 5.35e-101j)
| (4.226469169022273101e-15 - 3.6447340442788146248e-382j)  +/-  (1.73e-41, 6.58e-101j)
| (0.044481385621128847499 + 9.7694481459070465377e-373j)  +/-  (1.02e-23, 3.88e-83j)
| (7.7644167578883331338e-19 - 7.3953096247041301853e-385j)  +/-  (1.14e-43, 4.32e-103j)
| (2.6008512932958704308e-12 + 2.0890096812218540246e-380j)  +/-  (3.03e-40, 1.15e-99j)
| (2.0232543534503754413e-05 - 2.3793916918044292224e-376j)  +/-  (2.16e-36, 8.19e-96j)
| (7.7644167578883331338e-19 + 2.1018193755737718113e-384j)  +/-  (1.2e-43, 4.56e-103j)
| (0.0050719932375344830764 + 5.0769550641249753311e-374j)  +/-  (4.71e-32, 1.79e-91j)
| (0.084745366521723195011 - 2.0999874631154896862e-372j)  +/-  (1.27e-24, 4.81e-84j)
| (0.00021715076230543381016 + 2.4716338420170452321e-374j)  +/-  (2.22e-34, 8.42e-94j)
| (4.5065599115684821853e-10 - 6.7479896906462226122e-379j)  +/-  (1.73e-39, 6.58e-99j)
| (2.6008512932958704308e-12 - 5.107826513346314266e-381j)  +/-  (2.94e-42, 1.12e-101j)
| (0.044481385621128847499 + 4.1954527855648996814e-373j)  +/-  (1.2e-30, 4.55e-90j)
| (1.0838265985708568313e-06 + 2.5177880694614355959e-377j)  +/-  (4.09e-39, 1.55e-98j)
| (0.095370664742481130158 + 3.4708175020815860066e-372j)  +/-  (6.03e-29, 2.29e-88j)
| (3.1609310509441943207e-08 + 1.5948169676877175647e-377j)  +/-  (2.6e-39, 9.87e-99j)
| (4.5065599115684821853e-10 + 1.2807821594807288412e-379j)  +/-  (1.35e-41, 5.14e-101j)
| (0.016004991112877288561 - 1.556058594146885022e-373j)  +/-  (1.04e-33, 3.96e-93j)
| (0.1965496921139127001 + 2.9445379997558550371e-372j)  +/-  (2.02e-30, 7.68e-90j)
| (0.095370664742481130158 + 2.3379691649413583006e-372j)  +/-  (4.83e-31, 1.83e-90j)
| (0.15446510655576585012 - 3.575208841096307244e-372j)  +/-  (1.81e-30, 6.86e-90j)
| (1.0838265985708568313e-06 - 3.667546583536950636e-376j)  +/-  (1.61e-38, 6.1e-98j)
| (0.084745366521723195011 - 1.1644884797514042272e-372j)  +/-  (4.84e-32, 1.84e-91j)
| (0.016004991112877288561 - 4.8189183273572894414e-373j)  +/-  (9.01e-35, 3.42e-94j)
| (0.0013471469565227679705 - 7.4824048837841299934e-374j)  +/-  (1.16e-36, 4.41e-96j)
| (3.1609310509441943207e-08 - 2.0986690558322419214e-378j)  +/-  (1.72e-41, 6.53e-101j)
| (0.0050719932375344830764 + 2.1540522299882992479e-373j)  +/-  (3.57e-36, 1.36e-95j)
| (0.00021715076230543381016 + 1.8482952411727604866e-375j)  +/-  (3.53e-39, 1.35e-98j)
| (0.15446510655576585012 - 2.8714567897732731153e-372j)  +/-  (1.09e-35, 5.33e-95j)
| (0.0013471469565227679705 - 1.1556796419055513519e-374j)  +/-  (2.27e-38, 8.53e-98j)
