Starting with polynomial:
P : t^2 - 1
Extension levels are: 2 7 22
-------------------------------------------------
Trying to find an order 7 Kronrod extension for:
P1 : t^2 - 1
Solvable: 1
-------------------------------------------------
Trying to find an order 22 Kronrod extension for:
P2 : t^9 - 173/5*t^7 + 1743/5*t^5 - 1113*t^3 + 798*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^31 - 2920374384609013514657792078653/7809830830215333244447873830*t^29 + 8041901676266676382436760385583753/132767124113660665155613855110*t^27 - 331195052269676336499181178054457197/59007610717182517846939491160*t^25 + 82055247883143004461000450083856017165/247831965012166574957145862872*t^23 - 3246140248777571012182912994628889581935/247831965012166574957145862872*t^21 + 4210438466998417746953493509541979108465/11801522143436503569387898232*t^19 - 586953887803066500665781963577244487195/86775898113503702716087487*t^17 + 30960600010240643947552909561046053882545/347103592454014810864349948*t^15 - 280716368844760760210308125539800415363325/347103592454014810864349948*t^13 + 1708461983397182388502263244930665088920675/347103592454014810864349948*t^11 - 13401282238554224335199442158767674246255225/694207184908029621728699896*t^9 + 31706871247875302668932220875649590073946925/694207184908029621728699896*t^7 - 40576475554716825828648518123433562033330575/694207184908029621728699896*t^5 + 23056085060108313266668173710515747405147125/694207184908029621728699896*t^3 - 1849077059374323896631123075777392766559875/347103592454014810864349948*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
  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:
| (3.3648766656749077059 + 1.0595781550863254979e-536j)  +/-  (2.9e-248, 2.9e-248j)
| (2.5864375205164289264 - 1.1918054935117584145e-537j)  +/-  (1.33e-249, 1.33e-249j)
| (4.4288667337963182986 + 2.8237235195050492892e-536j)  +/-  (3.79e-248, 3.79e-248j)
| (7.267594525961611606 + 7.0980903381590483481e-537j)  +/-  (2.71e-248, 2.71e-248j)
| (3.1397980296785904718 - 9.7712307124411719018e-537j)  +/-  (1.63e-248, 1.63e-248j)
| (5.7643065493641814279 - 1.8065973295248413375e-536j)  +/-  (5.46e-248, 5.46e-248j)
| (3.8090069148108828844 - 1.3486850819493668455e-536j)  +/-  (3.12e-248, 3.12e-248j)
| (6.4879702980675993229 - 1.5369245118177811232e-537j)  +/-  (4.55e-248, 4.55e-248j)
| (8.1350105979975484512 - 3.7187913423735921171e-538j)  +/-  (8.17e-249, 8.17e-249j)
| (5.0807147715884739741 + 3.4748471651545906366e-536j)  +/-  (5.06e-248, 5.06e-248j)
| (9.1744742949389989527 - 3.0409511116185680347e-538j)  +/-  (1.21e-249, 1.21e-249j)
| (2.0314545988278380851 + 1.2602708945065885483e-539j)  +/-  (1.36e-250, 1.36e-250j)
| (-8.1350105979975484512 + 4.1857773616534247939e-535j)  +/-  (8.37e-249, 8.37e-249j)
| (-9.1744742949389989527 + 5.5368580676085287935e-542j)  +/-  (1.25e-249, 1.25e-249j)
| (-5.0807147715884739741 - 1.390442054901013431e-559j)  +/-  (5.13e-248, 5.13e-248j)
| (-4.4288667337963182986 + 1.6176303523794089638e-585j)  +/-  (3.82e-248, 3.82e-248j)
| (-1.5033625726032366371 - 3.0735251729395422321e-601j)  +/-  (1.4e-251, 1.4e-251j)
| (-3.8090069148108828844 + 2.5008243094279506994e-623j)  +/-  (3.23e-248, 3.23e-248j)
| (1 + 4.3893339839388703602e-645j)  +/-  (1.09e-252, 1.09e-252j)
| (-7.267594525961611606 - 9.7415222604255820596e-656j)  +/-  (2.35e-248, 2.35e-248j)
| (-1 + 9.4491194015735450293e-674j)  +/-  (1.17e-252, 1.17e-252j)
| (-3.1397980296785904718 + 1.6086225804285018778e-687j)  +/-  (1.67e-248, 1.67e-248j)
| (-6.4879702980675993229 - 2.789448204018369028e-708j)  +/-  (4.81e-248, 4.81e-248j)
| (-1.6550562328754219482e-724 + 3.7462969195678135306e-724j)  +/-  (1.27e-722, 1.27e-722j)
| (1.5033625726032366371 + 4.4081650111414099313e-725j)  +/-  (1.4e-251, 1.4e-251j)
| (-2.5864375205164289264 + 6.5983553956949907258e-726j)  +/-  (1.36e-249, 1.36e-249j)
| (-2.0314545988278380851 + 8.1425634306592202963e-744j)  +/-  (1.42e-250, 1.42e-250j)
| (0.50302449217204552456 - 1.6135636154586470937e-754j)  +/-  (1.14e-253, 1.14e-253j)
| (-3.3648766656749077059 + 2.1182477500470100587e-757j)  +/-  (3.06e-248, 3.06e-248j)
| (-0.50302449217204552456 - 2.9223375052325525955e-777j)  +/-  (1.14e-253, 1.14e-253j)
| (-5.7643065493641814279 + 3.222308988600406321e-776j)  +/-  (5.68e-248, 5.68e-248j)
-------------------------------------------------
The weights are:
| (0.00021681118797937011786 - 3.0425902804278570836e-539j)  +/-  (4.66e-77, 3.53e-200j)
| (0.0079461844221479157528 - 5.6812146433273422001e-539j)  +/-  (5.42e-74, 4.1e-197j)
| (1.399131634274591996e-05 - 6.6260638382532190745e-541j)  +/-  (3.69e-81, 2.79e-204j)
| (1.1049506440399598007e-12 + 1.7823355661380782833e-546j)  +/-  (1.61e-88, 1.22e-211j)
| (0.0014143246321165330212 + 6.1596919624456981228e-539j)  +/-  (5.02e-77, 3.8e-200j)
| (1.7056121392545558908e-08 + 1.8163998138294278665e-543j)  +/-  (1.36e-85, 1.03e-208j)
| (0.00016824225363881697811 + 1.3172150892479354165e-539j)  +/-  (4.27e-80, 3.23e-203j)
| (2.159449531464712658e-10 - 3.4193868283532857599e-545j)  +/-  (2.61e-87, 1.97e-210j)
| (1.5819728188163908176e-15 - 3.7725193975624236723e-548j)  +/-  (2.51e-91, 1.9e-214j)
| (6.6001917665216114145e-07 - 1.6640587912359793903e-541j)  +/-  (6.03e-85, 4.56e-208j)
| (2.5183121869419399865e-19 + 2.4144571697413561182e-550j)  +/-  (1.04e-93, 7.85e-217j)
| (0.027499029984673614711 + 3.7075620579387804589e-539j)  +/-  (1.25e-79, 9.48e-203j)
| (1.5819728188163908176e-15 + 1.9686075397582030832e-548j)  +/-  (1.95e-98, 1.47e-221j)
| (2.5183121869419399865e-19 - 1.0973696149916345578e-550j)  +/-  (6.93e-100, 5.25e-223j)
| (6.6001917665216114145e-07 + 4.3722460197536573389e-543j)  +/-  (2.51e-94, 1.9e-217j)
| (1.399131634274591996e-05 - 4.8798629927490138241e-542j)  +/-  (2.7e-93, 2.04e-216j)
| (0.066202901802475877359 - 2.7256735581830196166e-539j)  +/-  (2.99e-86, 2.26e-209j)
| (0.00016824225363881697811 + 5.9876003130609280306e-541j)  +/-  (1.63e-92, 1.24e-215j)
| (0.12015281099649103846 + 7.4643661627882685339e-539j)  +/-  (3.04e-86, 2.29e-209j)
| (1.1049506440399598007e-12 - 8.1660370876283480688e-547j)  +/-  (1.6e-98, 1.21e-221j)
| (0.12015281099649103846 + 4.5021687960763631535e-539j)  +/-  (1.82e-86, 1.37e-209j)
| (0.0014143246321165330212 + 6.6804184500682099406e-540j)  +/-  (3.09e-92, 2.33e-215j)
| (2.159449531464712658e-10 + 2.0268676948517299547e-545j)  +/-  (9.35e-98, 7.08e-221j)
| (0.20142627880195687082 + 7.5373339297308853185e-539j)  +/-  (4.26e-89, 3.19e-212j)
| (0.066202901802475877359 - 5.7973956416940974293e-539j)  +/-  (5.85e-89, 4.39e-212j)
| (0.0079461844221479157528 - 7.6493782872871052402e-540j)  +/-  (3.68e-92, 2.76e-215j)
| (0.027499029984673614711 + 1.4362702679207776341e-539j)  +/-  (1.25e-91, 9.39e-215j)
| (0.17567188671080612155 - 8.0588255856316351428e-539j)  +/-  (1.08e-90, 7.56e-214j)
| (0.00021681118797937011786 - 4.3913374912287765627e-540j)  +/-  (8.16e-93, 6.08e-216j)
| (0.17567188671080612155 - 6.2555572812360514926e-539j)  +/-  (4.53e-91, 2.66e-214j)
| (1.7056121392545558908e-08 - 3.4023493576331285518e-544j)  +/-  (4.11e-97, 3.19e-220j)
