Starting with polynomial:
P : t^2 - 1
Extension levels are: 2 3 4 20
-------------------------------------------------
Trying to find an order 3 Kronrod extension for:
P1 : t^2 - 1
Solvable: 1
-------------------------------------------------
Trying to find an order 4 Kronrod extension for:
P2 : t^5 - 7*t^3 + 6*t
Solvable: 1
-------------------------------------------------
Trying to find an order 20 Kronrod extension for:
P3 : t^9 - 71/3*t^7 + 1399/9*t^5 - 2965/9*t^3 + 590/3*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^29 - 829139585937614978979402714277093090301/2757763257955674848331189154297853418*t^27 + 632302510632936902241048484301798821150373/16546579547734049089987134925787120508*t^25 - 133941471496856391029749088686875193827092575/49639738643202147269961404777361361524*t^23 + 5812003766304564296473156866518750037270263725/49639738643202147269961404777361361524*t^21 - 54025956642797691258910571666516932068374861975/16546579547734049089987134925787120508*t^19 + 4831020559353319539691102224784254340841963800/81110684057519848480329092773466277*t^17 - 115443679327911227297664718666850498609700896675/162221368115039696960658185546932554*t^15 + 298176834579103849366196347179886330112983716125/54073789371679898986886061848977518*t^13 - 736090568044381600330446179331731487076992773875/27036894685839949493443030924488759*t^11 + 9054463555436496086999528587909127093970502364125/108147578743359797973772123697955036*t^9 - 5608227679638681641085999055889470249698464710875/36049192914453265991257374565985012*t^7 + 5953200369555895740825743048514448396557188872625/36049192914453265991257374565985012*t^5 - 3207017432282282361822130466316155679429127248125/36049192914453265991257374565985012*t^3 + 325090183839808317978679153730322922234122320625/18024596457226632995628687282992506*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
-------------------------------------------------
The nodes are:
| (5.196616252964635271 - 6.8044470178659864027e-445j)  +/-  (2.33e-121, 2.33e-121j)
| (-8.7049483044122572353 + 8.7273936129812683748e-454j)  +/-  (1.62e-122, 1.62e-122j)
| (6.7508691875889670917 - 5.3487845708320615449e-453j)  +/-  (2.35e-121, 2.35e-121j)
| (-6.7508691875889670917 + 3.377487461407305536e-457j)  +/-  (2.07e-121, 2.07e-121j)
| (-5.196616252964635271 + 9.1728523460516334155e-457j)  +/-  (2.31e-121, 2.31e-121j)
| (5.9469334613848628595 - 4.1156490292306002993e-458j)  +/-  (2.49e-121, 2.49e-121j)
| (-4.4824559233115378209 - 1.3511280067373170794e-461j)  +/-  (1.53e-121, 1.53e-121j)
| (-1.5093152835436173382 - 4.1690977537864317942e-463j)  +/-  (2.1e-122, 2.1e-122j)
| (-7.6415162942837753237 - 4.2415201273033729685e-465j)  +/-  (9.14e-122, 9.14e-122j)
| (7.6415162942837753237 - 4.197205737913636236e-465j)  +/-  (9.14e-122, 9.14e-122j)
| (1.3828023367484503294 - 1.8346157207351007258e-464j)  +/-  (8.48e-123, 8.48e-123j)
| (3.1198393628237582149 + 4.8895040385400276509e-471j)  +/-  (2.8e-122, 2.8e-122j)
| (-5.9469334613848628595 + 2.2659605118831989345e-475j)  +/-  (2.85e-121, 2.85e-121j)
| (8.7049483044122572353 + 7.743708670836121678e-477j)  +/-  (1.5e-122, 1.5e-122j)
| (1.6306719413090068156 + 8.2675560422897003317e-475j)  +/-  (1.44e-122, 1.44e-122j)
| (-3.1198393628237582149 - 5.2932697128876789649e-482j)  +/-  (2.46e-122, 2.46e-122j)
| (1 + 3.2550314168047884755e-482j)  +/-  (3.74e-124, 3.74e-124j)
| (-0.69200566706654006968 + 1.2268827297441294281e-484j)  +/-  (2.94e-125, 2.94e-125j)
| (-1 - 8.6224975062437068202e-485j)  +/-  (3.74e-124, 3.74e-124j)
| (-3.3254527695721997647e-484 + 2.4846520177195795971e-484j)  +/-  (1.2e-482, 1.2e-482j)
| (1.5093152835436173382 - 2.4357826189180232249e-482j)  +/-  (1.93e-122, 1.93e-122j)
| (-1.6306719413090068156 + 2.6861653611801756807e-484j)  +/-  (1.41e-122, 1.41e-122j)
| (-3.7932353000477464006 - 2.2639418203582668032e-484j)  +/-  (6.77e-122, 6.77e-122j)
| (-2.4494897427831780982 + 6.192728114131343852e-486j)  +/-  (7.58e-123, 7.58e-123j)
| (-1.3828023367484503294 + 8.337669883882121375e-488j)  +/-  (8.5e-123, 8.5e-123j)
| (3.7932353000477464006 - 1.2108630087864782626e-486j)  +/-  (6.19e-122, 6.19e-122j)
| (0.69200566706654006968 + 1.8912764343633283521e-497j)  +/-  (2.63e-125, 2.63e-125j)
| (2.4494897427831780982 - 1.2051108097909125558e-495j)  +/-  (7.45e-123, 7.45e-123j)
| (4.4824559233115378209 + 4.2006866668753946141e-509j)  +/-  (1.63e-121, 1.63e-121j)
-------------------------------------------------
The weights are:
| (3.9831196902117147761e-07 + 9.265190024859799745e-451j)  +/-  (1.53e-39, 1.05e-99j)
| (1.7108920079510052532e-17 + 1.4944827957607925683e-458j)  +/-  (2.97e-46, 2.04e-106j)
| (4.2525581344758030859e-11 - 6.0020647198931440977e-454j)  +/-  (3.13e-43, 2.15e-103j)
| (4.2525581344758030859e-11 + 7.8081088837908175401e-455j)  +/-  (1.54e-43, 1.06e-103j)
| (3.9831196902117147761e-07 + 2.6077475789613501861e-452j)  +/-  (3.8e-41, 2.61e-101j)
| (6.4517731824237476003e-09 + 2.5993464703017125555e-452j)  +/-  (1.18e-42, 8.1e-103j)
| (1.2107784337657120707e-05 - 2.9193486708262429483e-451j)  +/-  (4.65e-40, 3.2e-100j)
| (-0.69546590977159670146 + 1.3388328133003331649e-445j)  +/-  (3.39e-31, 2.33e-91j)
| (7.9525695496406376606e-14 - 1.8828743877907294983e-456j)  +/-  (2.99e-45, 2.06e-105j)
| (7.9525695496406376606e-14 + 9.8869444815032434994e-456j)  +/-  (1.36e-46, 9.34e-107j)
| (0.53866471649222075269 - 1.9847738400051961715e-445j)  +/-  (4.56e-33, 3.14e-93j)
| (0.0020541937978009921665 - 9.2692008635183131208e-449j)  +/-  (1.59e-39, 1.09e-99j)
| (6.4517731824237476003e-09 - 1.7501913107862783698e-453j)  +/-  (2.12e-43, 1.46e-103j)
| (1.7108920079510052532e-17 - 5.9218023736178143025e-458j)  +/-  (9.05e-49, 6.23e-109j)
| (0.34581096614247636542 - 8.7284866793891269624e-446j)  +/-  (2.18e-35, 1.5e-95j)
| (0.0020541937978009921665 - 2.3146954705383447376e-449j)  +/-  (4.9e-40, 3.38e-100j)
| (-0.090465460806618169002 + 7.1049738972979729489e-446j)  +/-  (5.88e-34, 4.05e-94j)
| (0.2531423427785982849 - 2.7362437145274344039e-446j)  +/-  (2.62e-34, 1.8e-94j)
| (-0.090465460806618169002 + 4.8117952956284979092e-446j)  +/-  (1.49e-34, 1.03e-94j)
| (0.26514872236018446175 + 1.2237408844718276646e-446j)  +/-  (1.31e-34, 9.01e-95j)
| (-0.69546590977159670146 + 2.4348761489842439751e-445j)  +/-  (1.64e-35, 1.13e-95j)
| (0.34581096614247636542 - 4.5589546740962839577e-446j)  +/-  (2.93e-36, 2.02e-96j)
| (0.00020362418288266500982 + 2.7048838444553983739e-450j)  +/-  (2.69e-41, 1.85e-101j)
| (0.013468653413458594536 + 2.2618326815780562418e-448j)  +/-  (3.19e-39, 2.2e-99j)
| (0.53866471649222075269 - 1.150490425336732117e-445j)  +/-  (3.32e-36, 2.28e-96j)
| (0.00020362418288266500982 + 1.7327087257956306836e-449j)  +/-  (1.6e-43, 1.1e-103j)
| (0.2531423427785982849 - 3.5769362097926567208e-446j)  +/-  (1.66e-38, 1.17e-98j)
| (0.013468653413458594536 + 6.295382598153647593e-448j)  +/-  (1.72e-41, 1.22e-101j)
| (1.2107784337657120707e-05 - 3.9566166468643856129e-450j)  +/-  (1.5e-44, 1.02e-104j)
