Starting with polynomial:
P : t^8 - 28*t^6 + 210*t^4 - 420*t^2 + 105
Extension levels are: 8 22
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Trying to find an order 22 Kronrod extension for:
P1 : t^8 - 28*t^6 + 210*t^4 - 420*t^2 + 105
Solvable: 1
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Ending with final polynomial:
P : t^30 - 6293846973611/18480916529*t^28 + 920636615220012/18480916529*t^26 - 76275612520750650/18480916529*t^24 + 3976311393915680775/18480916529*t^22 - 137103210398023202025/18480916529*t^20 + 188302269395303528850/1087112737*t^18 - 2998483272238319296200/1087112737*t^16 + 32370599322094287783375/1087112737*t^14 - 232354608261896447452125/1087112737*t^12 + 15054285343794980283000/15311447*t^10 - 2958969575127402325739250/1087112737*t^8 + 4427866251098037244121625/1087112737*t^6 - 2944702489166228915499375/1087112737*t^4 + 568275793353555633596250/1087112737*t^2 - 6105340625746309447500/1087112737
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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:   30 out of 30
Indefinite weights: 0 out of 30
Negative weights:   0 out of 30
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (5.500169678405946515 + 9.8081492473580985185e-364j)  +/-  (9.51e-121, 9.51e-121j)
| (-7.9005857813502380742 + 4.2075107457430975768e-371j)  +/-  (1.96e-121, 1.96e-121j)
| (-8.9503856871195767617 - 1.9378648942732038271e-372j)  +/-  (2.74e-122, 2.74e-122j)
| (7.9005857813502380742 - 4.8166011597011999722e-370j)  +/-  (1.77e-121, 1.77e-121j)
| (8.9503856871195767617 + 8.9939875150520607775e-373j)  +/-  (2.98e-122, 2.98e-122j)
| (4.1445471861258943321 + 4.0977976414819663082e-379j)  +/-  (6.61e-121, 6.61e-121j)
| (-3.5268525359911109167 - 1.0488286713578544662e-385j)  +/-  (5.16e-121, 5.16e-121j)
| (-2.2223763129000755597 - 3.6809314965582025689e-390j)  +/-  (6.97e-123, 6.97e-123j)
| (-5.500169678405946515 + 2.3494966250921325335e-388j)  +/-  (9.03e-121, 9.03e-121j)
| (4.8061035437663571886 + 2.4507628906190668926e-397j)  +/-  (8.44e-121, 8.44e-121j)
| (2.8024858612875416991 - 3.7402032068571465585e-404j)  +/-  (8.58e-122, 8.58e-122j)
| (-6.2339892447528273444 + 6.9522408399992297697e-405j)  +/-  (8.87e-121, 8.87e-121j)
| (-7.0234290877169996175 - 1.6505608418732354351e-412j)  +/-  (4.65e-121, 4.65e-121j)
| (-1.6365190424351079992 + 7.1727307437967998867e-419j)  +/-  (6.94e-124, 6.94e-124j)
| (7.0234290877169996175 + 4.7825132077836923197e-418j)  +/-  (5.59e-121, 5.59e-121j)
| (2.2223763129000755597 - 1.7135389029813576322e-430j)  +/-  (7.07e-123, 7.07e-123j)
| (0.53907981135137510807 - 3.0559288295904103658e-434j)  +/-  (3.87e-126, 3.87e-126j)
| (-4.8061035437663571886 + 3.8922873472271418575e-428j)  +/-  (8.15e-121, 8.15e-121j)
| (-4.1445471861258943321 - 1.6524444862033551279e-427j)  +/-  (6.59e-121, 6.59e-121j)
| (3.5268525359911109167 - 4.0645813336815267446e-428j)  +/-  (6.13e-121, 6.13e-121j)
| (1.0698782640929084781 - 3.3426802328944558793e-441j)  +/-  (4.97e-125, 4.97e-125j)
| (1.6365190424351079992 - 6.0145045252266144208e-441j)  +/-  (7.14e-124, 7.14e-124j)
| (0.10680039256797057303 + 1.7806064504159851422e-443j)  +/-  (3.44e-127, 3.44e-127j)
| (-0.10680039256797057303 - 1.95026364572307237e-443j)  +/-  (3.44e-127, 3.44e-127j)
| (-2.8024858612875416991 + 1.7217162172841079566e-436j)  +/-  (8.23e-122, 8.23e-122j)
| (3.1551890731254908841 + 6.3078697466392254324e-446j)  +/-  (3.09e-121, 3.09e-121j)
| (-0.53907981135137510807 + 3.3613730477526446941e-463j)  +/-  (3.87e-126, 3.87e-126j)
| (6.2339892447528273444 - 1.7840388249897554201e-469j)  +/-  (9.3e-121, 9.3e-121j)
| (-3.1551890731254908841 - 2.0368326144993850477e-480j)  +/-  (3.03e-121, 3.03e-121j)
| (-1.0698782640929084781 - 2.6322938128881078773e-488j)  +/-  (5.59e-125, 5.59e-125j)
-------------------------------------------------
The weights are:
| (7.6618628028699658849e-08 - 2.7401628957788890693e-370j)  +/-  (3.7e-37, 1.06e-97j)
| (1.0472848867557932628e-14 - 3.9347904995311277981e-376j)  +/-  (4.48e-42, 1.28e-102j)
| (1.9368935294110277211e-18 + 2.8982901264422965774e-378j)  +/-  (1.19e-43, 3.39e-104j)
| (1.0472848867557932628e-14 - 2.1966676895549917954e-375j)  +/-  (6.73e-43, 1.92e-103j)
| (1.9368935294110277211e-18 + 1.2138921702825239585e-377j)  +/-  (1.45e-44, 4.15e-105j)
| (4.7926327224862004538e-05 - 6.6815510776866444737e-369j)  +/-  (3.22e-36, 9.2e-97j)
| (0.00045164986443460891584 - 1.1310165968864533319e-368j)  +/-  (9.1e-36, 2.6e-96j)
| (0.019936564390868084308 + 1.1215033205775456202e-367j)  +/-  (1.68e-31, 4.8e-92j)
| (7.6618628028699658849e-08 + 6.8314886910293541341e-372j)  +/-  (1.72e-40, 4.91e-101j)
| (2.6054597639986646052e-06 + 1.2658797385594039088e-369j)  +/-  (9.69e-39, 2.77e-99j)
| (0.004279177645236311323 + 2.1504958285513322072e-367j)  +/-  (5.39e-35, 1.54e-95j)
| (1.1008273997595023641e-09 - 4.2185758566265342765e-373j)  +/-  (4.86e-42, 1.39e-102j)
| (6.4001518167242771637e-12 + 1.7499285950205489283e-374j)  +/-  (2.69e-43, 7.71e-104j)
| (0.060488085890408312398 - 2.5124418610167186869e-367j)  +/-  (4.81e-33, 1.37e-93j)
| (6.4001518167242771637e-12 + 1.4387177542963290702e-373j)  +/-  (2.54e-44, 7.27e-105j)
| (0.019936564390868084308 - 2.6422840020723962574e-367j)  +/-  (5.28e-36, 1.51e-96j)
| (0.17384131366758802608 + 2.2315259496606619955e-366j)  +/-  (5.8e-34, 1.66e-94j)
| (2.6054597639986646052e-06 - 8.5249462960369094295e-371j)  +/-  (1.45e-40, 4.14e-101j)
| (4.7926327224862004538e-05 + 9.3913186394203842212e-370j)  +/-  (1.09e-39, 3.11e-100j)
| (0.00045164986443460891584 + 5.1738829627546718722e-368j)  +/-  (2.22e-39, 6.35e-100j)
| (0.12429453268421805608 - 9.4552168449400966409e-367j)  +/-  (2.57e-35, 7.35e-96j)
| (0.060488085890408312398 + 4.6408221600570722936e-367j)  +/-  (1.02e-36, 2.93e-97j)
| (0.11612500485822044829 - 5.6979223789548794904e-366j)  +/-  (4.38e-35, 1.25e-95j)
| (0.11612500485822044829 + 5.4808567127824617576e-366j)  +/-  (2.55e-35, 7.32e-96j)
| (0.004279177645236311323 - 6.9873521410455868321e-368j)  +/-  (5.26e-39, 1.51e-99j)
| (0.00053306148617123687384 - 1.5760630354662138028e-367j)  +/-  (5.06e-39, 1.44e-99j)
| (0.17384131366758802608 - 1.8331418160374023935e-366j)  +/-  (1.7e-37, 4.79e-98j)
| (1.1008273997595023641e-09 - 6.7457235770747821525e-372j)  +/-  (2.1e-44, 5.98e-105j)
| (0.00053306148617123687384 + 4.2699989191509731427e-368j)  +/-  (1.17e-39, 3.37e-100j)
| (0.12429453268421805608 + 6.3758082706461292503e-367j)  +/-  (2.08e-38, 5.69e-99j)
