Starting with polynomial:
P : 4*t^2 - 2
Extension levels are: 2 7 22
-------------------------------------------------
Trying to find an order 7 Kronrod extension for:
P1 : 4*t^2 - 2
Solvable: 1
-------------------------------------------------
Trying to find an order 22 Kronrod extension for:
P2 : 4*t^9 - 346/5*t^7 + 1743/5*t^5 - 1113/2*t^3 + 399/2*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 4*t^31 - 2920374384609013514657792078653/3904915415107666622223936915*t^29 + 8041901676266676382436760385583753/132767124113660665155613855110*t^27 - 331195052269676336499181178054457197/118015221434365035693878982320*t^25 + 82055247883143004461000450083856017165/991327860048666299828583451488*t^23 - 3246140248777571012182912994628889581935/1982655720097332599657166902976*t^21 + 4210438466998417746953493509541979108465/188824354294984057110206371712*t^19 - 586953887803066500665781963577244487195/2776828739632118486914799584*t^17 + 30960600010240643947552909561046053882545/22214629917056947895318396672*t^15 - 280716368844760760210308125539800415363325/44429259834113895790636793344*t^13 + 1708461983397182388502263244930665088920675/88858519668227791581273586688*t^11 - 13401282238554224335199442158767674246255225/355434078672911166325094346752*t^9 + 31706871247875302668932220875649590073946925/710868157345822332650188693504*t^7 - 40576475554716825828648518123433562033330575/1421736314691644665300377387008*t^5 + 23056085060108313266668173710515747405147125/2843472629383289330600754774016*t^3 - 1849077059374323896631123075777392766559875/2843472629383289330600754774016*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:
| (-3.1316817004388926669 + 7.2253296263700787103e-433j)  +/-  (1.21e-120, 1.21e-120j)
| (-4.0759802498934410429 - 5.7336988175312561135e-438j)  +/-  (1.63e-120, 1.63e-120j)
| (5.7523211588684976193 - 3.0488780665455901318e-443j)  +/-  (2.76e-121, 2.76e-121j)
| (4.5876877939005054751 - 1.9827263570576822853e-450j)  +/-  (1.25e-120, 1.25e-120j)
| (-5.7523211588684976193 - 1.8869321458918927721e-456j)  +/-  (2.64e-121, 2.64e-121j)
| (-6.4873329877730356082 + 3.9725140579519151075e-461j)  +/-  (3.63e-122, 3.63e-122j)
| (-4.5876877939005054751 - 2.4102246938464335458e-460j)  +/-  (1.4e-120, 1.4e-120j)
| (-2.2201724783418921227 - 1.28909634487923038e-469j)  +/-  (4.9e-121, 4.9e-121j)
| (4.0759802498934410429 + 2.7068242874743975364e-473j)  +/-  (1.52e-120, 1.52e-120j)
| (5.1389653722216878794 - 1.6308461335509303406e-475j)  +/-  (7.66e-121, 7.66e-121j)
| (0.7071067811865475244 + 9.8533556792161875757e-480j)  +/-  (3.92e-125, 3.92e-125j)
| (2.2201724783418921227 - 3.554556241481398265e-474j)  +/-  (5.38e-121, 5.38e-121j)
| (6.4873329877730356082 + 6.7353233073663239862e-480j)  +/-  (3.68e-122, 3.68e-122j)
| (-1.0630378696698020148 + 7.0978683551496454502e-482j)  +/-  (4.67e-124, 4.67e-124j)
| (-2.3793271081551065923 + 6.7742606872294247218e-478j)  +/-  (9.64e-121, 9.64e-121j)
| (0.35569202951777278278 + 5.7577156077917787302e-486j)  +/-  (2.83e-126, 2.83e-126j)
| (1.8288875098724870322 - 1.2078548939537341117e-481j)  +/-  (4.06e-122, 4.06e-122j)
| (-3.5926078682648708514 - 2.3461759089132368836e-480j)  +/-  (1.49e-120, 1.49e-120j)
| (-1.4364553225037617879 + 4.7927787755476524601e-483j)  +/-  (3.87e-123, 3.87e-123j)
| (-5.1389653722216878794 - 9.5252086481511076727e-482j)  +/-  (7.09e-121, 7.09e-121j)
| (2.3793271081551065923 - 9.4147720432751186237e-481j)  +/-  (9.52e-121, 9.52e-121j)
| (1.4364553225037617879 - 5.4313397143108667422e-488j)  +/-  (3.95e-123, 3.95e-123j)
| (3.5926078682648708514 - 8.2809839923527758381e-487j)  +/-  (1.57e-120, 1.57e-120j)
| (-2.6933746190492254305 - 1.1811072247828420198e-492j)  +/-  (1.03e-120, 1.03e-120j)
| (-1.8288875098724870322 + 1.2800018451965669351e-493j)  +/-  (4.47e-122, 4.47e-122j)
| (8.5876252576417059044e-502 - 7.245529750522397707e-502j)  +/-  (3.48e-500, 3.48e-500j)
| (1.0630378696698020148 - 1.2718819390280327237e-494j)  +/-  (4.67e-124, 4.67e-124j)
| (2.6933746190492254305 + 7.7605343843790671314e-495j)  +/-  (9.93e-121, 9.93e-121j)
| (-0.35569202951777278278 + 1.7409777705283727569e-502j)  +/-  (2.83e-126, 2.83e-126j)
| (-0.7071067811865475244 + 5.8121628189793672193e-501j)  +/-  (3.98e-125, 3.98e-125j)
| (3.1316817004388926669 - 5.3608927857915390179e-499j)  +/-  (1.17e-120, 1.17e-120j)
-------------------------------------------------
The weights are:
| (1.399131634274591996e-05 + 5.2645716727561239314e-437j)  +/-  (3.54e-33, 8.8e-93j)
| (1.7056121392545558908e-08 - 8.6374701415254473834e-440j)  +/-  (1.04e-36, 2.58e-96j)
| (1.5819728188163908176e-15 - 5.6915803577451608126e-445j)  +/-  (2.03e-42, 5.03e-102j)
| (2.159449531464712658e-10 - 6.7274169555921181679e-442j)  +/-  (1.29e-39, 3.21e-99j)
| (1.5819728188163908176e-15 + 1.9294518379091593476e-444j)  +/-  (2.16e-42, 5.37e-102j)
| (2.5183121869419399865e-19 - 1.1286642841257089415e-446j)  +/-  (3.26e-44, 8.09e-104j)
| (2.159449531464712658e-10 + 3.5666949310100416047e-441j)  +/-  (1.53e-39, 3.8e-99j)
| (0.0014143246321165330212 - 1.2821768611807703096e-435j)  +/-  (2.79e-33, 6.93e-93j)
| (1.7056121392545558908e-08 + 1.1316142531215323879e-440j)  +/-  (1.9e-40, 4.72e-100j)
| (1.1049506440399598007e-12 + 2.6670480597128669302e-443j)  +/-  (9.59e-43, 2.38e-102j)
| (0.12015281099649103846 - 1.4232877031943952698e-435j)  +/-  (2.23e-31, 5.53e-91j)
| (0.0014143246321165330212 - 2.1837581731903010963e-436j)  +/-  (1.93e-36, 4.79e-96j)
| (2.5183121869419399865e-19 + 3.9374156969725289624e-447j)  +/-  (2.54e-46, 6.3e-106j)
| (0.066202901802475877359 + 1.7643962180369395929e-435j)  +/-  (1.61e-31, 4.01e-91j)
| (0.00021681118797937011786 + 1.0540761594330391136e-435j)  +/-  (7.25e-36, 1.8e-95j)
| (0.17567188671080612155 + 1.9560660471677045454e-435j)  +/-  (6.12e-32, 1.52e-91j)
| (0.0079461844221479157528 + 2.4835490594403875578e-436j)  +/-  (9.81e-36, 2.44e-95j)
| (6.6001917665216114145e-07 + 2.1175891530360900673e-438j)  +/-  (2.58e-39, 6.4e-99j)
| (0.027499029984673614711 - 1.2465556724178225981e-435j)  +/-  (6.57e-35, 1.63e-94j)
| (1.1049506440399598007e-12 - 1.0989073110382209719e-442j)  +/-  (5.52e-43, 1.37e-102j)
| (0.00021681118797937011786 + 1.4390081318829811253e-436j)  +/-  (3.03e-38, 7.52e-98j)
| (0.027499029984673614711 - 4.625941766674549766e-436j)  +/-  (1.8e-36, 4.46e-96j)
| (6.6001917665216114145e-07 - 1.451528970062437897e-439j)  +/-  (9.1e-42, 2.27e-101j)
| (0.00016824225363881697811 - 2.6189353976075792645e-436j)  +/-  (1.34e-38, 3.37e-98j)
| (0.0079461844221479157528 + 9.4564597624021401818e-436j)  +/-  (2.11e-37, 5.31e-97j)
| (0.20142627880195687082 - 2.3279958253325611027e-435j)  +/-  (5.05e-37, 1.32e-96j)
| (0.066202901802475877359 + 8.7011937819201019106e-436j)  +/-  (3.55e-37, 8.86e-97j)
| (0.00016824225363881697811 - 1.9706198867273263773e-437j)  +/-  (2.85e-40, 7.14e-100j)
| (0.17567188671080612155 + 2.4573339561245274426e-435j)  +/-  (7.51e-38, 2.11e-97j)
| (0.12015281099649103846 - 2.2534675833702216618e-435j)  +/-  (4.64e-38, 1.31e-97j)
| (1.399131634274591996e-05 + 1.6140172728788808021e-438j)  +/-  (1.69e-41, 4.08e-101j)
