Starting with polynomial:
P : t^12 - 66*t^10 + 1485*t^8 - 13860*t^6 + 51975*t^4 - 62370*t^2 + 10395
Extension levels are: 12 21
-------------------------------------------------
Trying to find an order 21 Kronrod extension for:
P1 : t^12 - 66*t^10 + 1485*t^8 - 13860*t^6 + 51975*t^4 - 62370*t^2 + 10395
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^33 - 1324463019/3091984*t^31 + 200577548160/2512237*t^29 - 343933605133635/40195792*t^27 + 11800013774900175/20097896*t^25 - 1093070447790596055/40195792*t^23 + 1254116412737264835/1435564*t^21 - 113144489909606783925/5742256*t^19 + 47216958813223825725/151112*t^17 - 1044815980504160192625/302224*t^15 + 991113838582300856775/37778*t^13 - 3086482588843958417025/23248*t^11 + 4986513451688993222625/11624*t^9 - 19245077839616143717125/23248*t^7 + 4975584239837721943125/5812*t^5 - 9059923977142930439625/23248*t^3 + 573488939085422196375/11624*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: 0
  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:   33 out of 33
Indefinite weights: 0 out of 33
Negative weights:   0 out of 33
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (-5.5009017044677476008 - 1.0558148900434536775e-460j)  +/-  (4.58e-120, 4.58e-120j)
| (-4.8655991678763826087 + 4.2744955191068259556e-474j)  +/-  (3.54e-120, 3.54e-120j)
| (-8.5924213544905429774 + 1.1797325506818303761e-475j)  +/-  (6.38e-121, 6.38e-121j)
| (-7.6950847096487529197 - 3.0151667548043700042e-476j)  +/-  (2.13e-120, 2.13e-120j)
| (9.7170945544746670212 + 1.6517637157178631074e-480j)  +/-  (7.74e-122, 7.74e-122j)
| (-6.9032512392201122593 + 3.1152855821805949873e-478j)  +/-  (4.09e-120, 4.09e-120j)
| (6.9032512392201122593 - 1.0098600442516559826e-481j)  +/-  (4.04e-120, 4.04e-120j)
| (-9.7170945544746670212 - 1.2146186782003209064e-485j)  +/-  (8.54e-122, 8.54e-122j)
| (-1.7900108872750493005 + 1.6545328672552911858e-483j)  +/-  (4.27e-123, 4.27e-123j)
| (2.7413880669757772047 + 2.5026691766878500293e-484j)  +/-  (1.17e-121, 1.17e-121j)
| (3.7251423458907299374 + 8.6965394500037895961e-483j)  +/-  (1.22e-120, 1.22e-120j)
| (5.5009017044677476008 - 3.8148867480453888793e-483j)  +/-  (4.88e-120, 4.88e-120j)
| (-4.271825847932281723 + 1.1312630932196656346e-483j)  +/-  (2.41e-120, 2.41e-120j)
| (6.1776748673297394834 + 3.4124653054211421755e-489j)  +/-  (5.12e-120, 5.12e-120j)
| (-2.7413880669757772047 + 1.1653213606146383851e-489j)  +/-  (1.06e-121, 1.06e-121j)
| (1.7900108872750493005 + 2.2424891017709484947e-495j)  +/-  (3.54e-123, 3.54e-123j)
| (7.6950847096487529197 + 2.2724026378970809984e-492j)  +/-  (2.09e-120, 2.09e-120j)
| (2.2594644510007991239 - 4.4302570119376414725e-494j)  +/-  (2.16e-122, 2.16e-122j)
| (-1.3403751971516167215 - 1.383458470167635538e-494j)  +/-  (5.59e-124, 5.59e-124j)
| (4.271825847932281723 - 4.2343792185588214136e-492j)  +/-  (2.39e-120, 2.39e-120j)
| (1.3403751971516167215 + 3.7230618491810045299e-497j)  +/-  (4.76e-124, 4.76e-124j)
| (4.8655991678763826087 + 1.3828342221439158216e-494j)  +/-  (3.41e-120, 3.41e-120j)
| (-6.1776748673297394834 + 2.6714319626271032518e-492j)  +/-  (5.28e-120, 5.28e-120j)
| (-0.89397002524891343288 - 1.8412651782503719356e-502j)  +/-  (4.48e-125, 4.48e-125j)
| (-1.2666264572193705448e-510 + 1.3081404235070923087e-511j)  +/-  (4.2e-509, 4.2e-509j)
| (8.5924213544905429774 - 6.4255082794300492317e-499j)  +/-  (6.29e-121, 6.29e-121j)
| (0.89397002524891343288 + 9.1787105181110193246e-503j)  +/-  (4.94e-125, 4.94e-125j)
| (-2.2594644510007991239 - 2.4302056718699729987e-499j)  +/-  (2.31e-122, 2.31e-122j)
| (-3.2237098287700974717 - 2.2107768144722183693e-497j)  +/-  (4.21e-121, 4.21e-121j)
| (-0.4444030019441389453 + 2.0707711298439050226e-513j)  +/-  (3.72e-126, 3.72e-126j)
| (-3.7251423458907299374 + 1.848675579360744664e-513j)  +/-  (1.11e-120, 1.11e-120j)
| (3.2237098287700974717 + 3.2640822754427904922e-527j)  +/-  (4.46e-121, 4.46e-121j)
| (0.4444030019441389453 + 1.3076545765037996908e-535j)  +/-  (3.36e-126, 3.36e-126j)
-------------------------------------------------
The weights are:
| (7.0241986351229608354e-08 - 2.7511884189702387949e-467j)  +/-  (1.02e-27, 1.18e-86j)
| (1.7746949078648174161e-06 + 1.134751614988458814e-466j)  +/-  (3.61e-26, 4.2e-85j)
| (3.6163947593646578788e-17 + 6.7939386970751937569e-474j)  +/-  (7.5e-35, 8.71e-94j)
| (4.6169328763194783924e-14 - 5.3297106023177670994e-472j)  +/-  (2.56e-33, 2.97e-92j)
| (1.7031980757140935515e-21 + 6.7615947301255932831e-477j)  +/-  (6.08e-40, 7.06e-99j)
| (1.3505848071778103229e-11 + 2.339026831002238114e-470j)  +/-  (3.99e-32, 4.63e-91j)
| (1.3505848071778103229e-11 - 2.6443830571265121099e-471j)  +/-  (8.14e-36, 9.45e-95j)
| (1.7031980757140935515e-21 - 2.4405411936355155833e-476j)  +/-  (1.41e-37, 1.63e-96j)
| (0.036840944498752074726 + 7.0591085493498466107e-464j)  +/-  (1.14e-20, 1.32e-79j)
| (0.0044894929212943745126 + 5.2422236702619411903e-465j)  +/-  (4.78e-26, 5.55e-85j)
| (0.00020190394859705160263 + 3.4680111858468497735e-466j)  +/-  (1.92e-29, 2.23e-88j)
| (7.0241986351229608354e-08 - 6.740943492557945251e-469j)  +/-  (7e-34, 8.12e-93j)
| (2.4841170013685313486e-05 - 4.4745461832517102811e-466j)  +/-  (2.57e-30, 2.99e-89j)
| (1.4402041153833014942e-09 + 4.9959559300416605705e-470j)  +/-  (3.69e-35, 4.29e-94j)
| (0.0044894929212943745126 + 1.5657805038532206589e-464j)  +/-  (5.94e-28, 6.9e-87j)
| (0.036840944498752074726 + 3.5929083998367890768e-464j)  +/-  (8.81e-26, 1.02e-84j)
| (4.6169328763194783924e-14 + 8.8620585526132984761e-473j)  +/-  (2.43e-38, 2.81e-97j)
| (0.014876927885944634827 - 1.486468338275043324e-464j)  +/-  (1.01e-27, 1.18e-86j)
| (0.072244625679194799292 - 1.1628438318237949718e-463j)  +/-  (1.52e-25, 1.76e-84j)
| (2.4841170013685313486e-05 - 5.6274531887839350081e-467j)  +/-  (1.26e-32, 1.46e-91j)
| (0.072244625679194799292 - 7.0718414935473983868e-464j)  +/-  (1.31e-26, 1.52e-85j)
| (1.7746949078648174161e-06 + 6.9542325639163251042e-468j)  +/-  (9.65e-34, 1.12e-92j)
| (1.4402041153833014942e-09 - 8.6211535976954553788e-469j)  +/-  (1.22e-36, 1.42e-95j)
| (0.12018767238488778267 + 1.5828968067651187044e-463j)  +/-  (5.12e-28, 5.94e-87j)
| (0.17646715825421950581 + 1.8491814477586206293e-463j)  +/-  (6.81e-28, 7.9e-87j)
| (3.6163947593646578788e-17 - 1.4903223955905821257e-474j)  +/-  (1.04e-40, 1.21e-99j)
| (0.12018767238488778267 + 1.1403352173795082633e-463j)  +/-  (9.02e-29, 1.05e-87j)
| (0.014876927885944634827 - 3.558772754643738069e-464j)  +/-  (3.29e-31, 3.82e-90j)
| (0.0010740729027396747919 - 5.9296164246027885948e-465j)  +/-  (3.68e-33, 4.27e-92j)
| (0.16182409309081578436 - 1.845257282149171432e-463j)  +/-  (1.06e-30, 1.27e-89j)
| (0.00020190394859705160263 + 1.8018220663299903982e-465j)  +/-  (6.75e-34, 7.83e-93j)
| (0.0010740729027396747919 - 1.5476762829688124498e-465j)  +/-  (1.95e-33, 2.18e-92j)
| (0.16182409309081578436 - 1.5693966102270097569e-463j)  +/-  (5.52e-31, 6.61e-90j)
