Starting with polynomial:
P : 4*t^2 - 2
Extension levels are: 2 7 18
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Trying to find an order 7 Kronrod extension for:
P1 : 4*t^2 - 2
Solvable: 1
-------------------------------------------------
Trying to find an order 18 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^27 - 23713059798960210194599/40133743389473733395*t^25 + 38490928736959356647640159/1043477328126317068270*t^23 - 2669596356929556607160822889/2086954656252634136540*t^21 + 1251302066060699168832390282579/45913002437557951003880*t^19 - 8560045570713565284471721748121/22956501218778975501940*t^17 + 305729943623714833393266252893961/91826004875115902007760*t^15 - 54678536972190494062088435867835/2825415534618950831008*t^13 + 50763533942882437096743705288123/706353883654737707752*t^11 - 337716694675472793580850976022851/2054847661541055149824*t^9 + 893850191374390231079302957672731/4109695323082110299648*t^7 - 1231431587235049993945122648792933/8219390646164220599296*t^5 + 723505001219868112063866791914905/16438781292328441198592*t^3 - 56456117968234496017092998491395/16438781292328441198592*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:   27 out of 27
Indefinite weights: 0 out of 27
Negative weights:   0 out of 27
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (2.2201724783418921227 - 9.7110283816725565429e-441j)  +/-  (2.3e-122, 2.3e-122j)
| (-5.35493947967242833 - 1.329906729885323732e-439j)  +/-  (5.37e-122, 5.37e-122j)
| (-6.1146809802577541845 + 6.4508598420023404432e-442j)  +/-  (9.57e-123, 9.57e-123j)
| (-4.1536549176290219175 + 7.7773847882871112752e-441j)  +/-  (1.89e-121, 1.89e-121j)
| (3.6271949889961452522 + 6.6400799319665334339e-445j)  +/-  (1.71e-121, 1.71e-121j)
| (4.1536549176290219175 + 1.3776326582380882712e-448j)  +/-  (1.83e-121, 1.83e-121j)
| (-2.2201724783418921227 + 2.740735485664252764e-455j)  +/-  (2.37e-122, 2.37e-122j)
| (-3.1316817004388926669 - 5.5974746402741179025e-469j)  +/-  (1.14e-121, 1.14e-121j)
| (4.7219036866476203619 + 1.6663915896962166103e-481j)  +/-  (1.29e-121, 1.29e-121j)
| (5.35493947967242833 + 7.5807968522953626338e-482j)  +/-  (5.62e-122, 5.62e-122j)
| (0.34350364112563201909 - 9.6091514497442304862e-483j)  +/-  (2.35e-126, 2.35e-126j)
| (6.1146809802577541845 - 7.1255289839656949137e-483j)  +/-  (9.99e-123, 9.99e-123j)
| (-3.6271949889961452522 - 2.0144295642622670703e-480j)  +/-  (1.75e-121, 1.75e-121j)
| (-0.7071067811865475244 + 3.9135193300355037975e-490j)  +/-  (2.85e-125, 2.85e-125j)
| (1.4364553225037617879 - 1.2025787519366468872e-488j)  +/-  (1.51e-123, 1.51e-123j)
| (-4.7219036866476203619 - 1.0702571240768639739e-488j)  +/-  (1.24e-121, 1.24e-121j)
| (-2.315179857970498286e-496 + 1.9214354170092871518e-495j)  +/-  (5.23e-494, 5.23e-494j)
| (-2.6624812406647748761 + 2.411036068175271929e-498j)  +/-  (5.82e-122, 5.82e-122j)
| (-1.0755726275498348925 + 9.209000222124446323e-503j)  +/-  (2.49e-124, 2.49e-124j)
| (2.6624812406647748761 + 1.4097397996600041304e-500j)  +/-  (5.85e-122, 5.85e-122j)
| (1.8106928800784913879 - 2.8129309769398308768e-503j)  +/-  (6.56e-123, 6.56e-123j)
| (0.7071067811865475244 + 6.4489163487320341438e-505j)  +/-  (2.97e-125, 2.97e-125j)
| (3.1316817004388926669 + 5.7497648659591543042e-502j)  +/-  (1.21e-121, 1.21e-121j)
| (-0.34350364112563201909 + 3.4891660603278880925e-506j)  +/-  (2.35e-126, 2.35e-126j)
| (-1.4364553225037617879 - 1.9662145676278331732e-504j)  +/-  (1.82e-123, 1.82e-123j)
| (-1.8106928800784913879 + 1.8281558699322766952e-507j)  +/-  (6.7e-123, 6.7e-123j)
| (1.0755726275498348925 - 2.4775202414338423691e-508j)  +/-  (2.24e-124, 2.24e-124j)
-------------------------------------------------
The weights are:
| (0.0017433044574893640728 + 6.0502524192098352374e-443j)  +/-  (1.03e-33, 4.11e-94j)
| (1.3492009003117934119e-13 + 1.2425005405510367062e-450j)  +/-  (5.84e-44, 2.33e-104j)
| (2.8541324863367743767e-17 - 1.3425932152715700519e-452j)  +/-  (1.41e-45, 5.6e-106j)
| (9.8832215076674869394e-09 + 1.3137598303499121771e-447j)  +/-  (1.04e-41, 4.16e-102j)
| (5.5589672450307278045e-07 + 4.7884425370056246992e-446j)  +/-  (1.33e-41, 5.31e-102j)
| (9.8832215076674869394e-09 - 3.1212310401104149801e-447j)  +/-  (3.16e-43, 1.26e-103j)
| (0.0017433044574893640728 + 3.9151177100403173342e-444j)  +/-  (4.47e-38, 1.78e-98j)
| (1.4968037093525062101e-05 + 1.0835012278372878643e-445j)  +/-  (8.32e-41, 3.31e-101j)
| (6.9642078277768414493e-11 + 1.4086105257614062603e-448j)  +/-  (2.54e-45, 1.01e-105j)
| (1.3492009003117934119e-13 - 3.5261411189201615414e-450j)  +/-  (2.97e-47, 1.19e-107j)
| (0.17740053584341527688 - 4.9229856413925728835e-442j)  +/-  (8.48e-39, 3.37e-99j)
| (2.8541324863367743767e-17 + 2.9687502136401607834e-452j)  +/-  (3.11e-49, 1.24e-109j)
| (5.5589672450307278045e-07 - 1.3112196784737258837e-446j)  +/-  (3.65e-44, 1.46e-104j)
| (0.12659263371237718764 + 2.201006649769124485e-442j)  +/-  (3.15e-39, 1.25e-99j)
| (0.025934682592751693492 + 2.3464372991395745824e-442j)  +/-  (9.67e-40, 3.85e-100j)
| (6.9642078277768414493e-11 - 4.211751418980578085e-449j)  +/-  (1.56e-46, 6.22e-107j)
| (0.19034964838266794687 + 4.7896008632955844898e-442j)  +/-  (3.47e-39, 1.38e-99j)
| (0.00021481447658721927718 - 7.2462083993232610424e-445j)  +/-  (1.21e-42, 4.84e-103j)
| (0.064616713007727776208 - 1.1647144929714433593e-442j)  +/-  (6.96e-40, 2.77e-100j)
| (0.00021481447658721927718 + 7.6956267680555174046e-444j)  +/-  (1.06e-43, 4.22e-104j)
| (0.0083069578315009462832 - 1.5996484067155659063e-442j)  +/-  (2.68e-42, 1.06e-102j)
| (0.12659263371237718764 + 4.2319815518765264865e-442j)  +/-  (3.78e-41, 1.49e-101j)
| (1.4968037093525062101e-05 - 5.9781625708055467743e-445j)  +/-  (1.35e-44, 5.38e-105j)
| (0.17740053584341527688 - 3.6143249261388950797e-442j)  +/-  (5.67e-41, 2.26e-101j)
| (0.025934682592751693492 + 5.0993339423146099802e-443j)  +/-  (1.45e-42, 5.81e-103j)
| (0.0083069578315009462832 - 1.6562591514103999201e-443j)  +/-  (3.69e-43, 1.48e-103j)
| (0.064616713007727776208 - 3.3209828052477535366e-442j)  +/-  (2.24e-42, 7.92e-103j)
