Starting with polynomial:
P : t^2 - 1
Extension levels are: 2 3 28
-------------------------------------------------
Trying to find an order 3 Kronrod extension for:
P1 : t^2 - 1
Solvable: 1
-------------------------------------------------
Trying to find an order 28 Kronrod extension for:
P2 : t^5 - 7*t^3 + 6*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^33 - 349246284179083625724887063/731920585313098339748759*t^31 + 657240022528862881909056388207/6587285267817885057738831*t^29 - 79573517733554730166815688400197/6587285267817885057738831*t^27 + 53086809779399742747204235893153/56301583485622949211443*t^25 - 2815792603462840072802797930921575/56301583485622949211443*t^23 + 104259628011825322249806556571921775/56301583485622949211443*t^21 - 2726722453179241400708773447915895325/56301583485622949211443*t^19 + 50418890049627922435926888445784835075/56301583485622949211443*t^17 - 653738087220368272409176338360331953225/56301583485622949211443*t^15 + 5841037283776106711891660906763634025625/56301583485622949211443*t^13 - 34959311577941753940030323657853442891875/56301583485622949211443*t^11 + 134277521292479385225611437351493801302875/56301583485622949211443*t^9 - 310086668501896173612636021864409855324125/56301583485622949211443*t^7 + 387657021039988449995973810264977526241125/56301583485622949211443*t^5 - 216899480153462061317271227602400628579375/56301583485622949211443*t^3 + 34775825040432273294844140776560629108750/56301583485622949211443*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:   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:
| (6.6063248505268155481 + 1.2442164619426129496e-455j)  +/-  (9.78e-120, 9.78e-120j)
| (-8.0695543101543246546 + 1.0459866247383368182e-454j)  +/-  (3.86e-120, 3.86e-120j)
| (8.0695543101543246546 + 8.0275187186901195748e-461j)  +/-  (3.82e-120, 3.82e-120j)
| (-6.6063248505268155481 - 3.8670103596928298947e-461j)  +/-  (1.08e-119, 1.08e-119j)
| (8.9151158541140833189 - 6.600944135450609434e-466j)  +/-  (1.14e-120, 1.14e-120j)
| (-9.9298370350741959833 - 2.3169847733657272055e-465j)  +/-  (1.53e-121, 1.53e-121j)
| (-8.9151158541140833189 + 4.383148124464589606e-464j)  +/-  (1.22e-120, 1.22e-120j)
| (-7.310433298452702449 - 2.9264636327647518977e-468j)  +/-  (7.37e-120, 7.37e-120j)
| (9.9298370350741959833 + 8.5539941401056644794e-479j)  +/-  (1.46e-121, 1.46e-121j)
| (3.5298626496166927728 - 2.3767399159342025071e-476j)  +/-  (4.85e-121, 4.85e-121j)
| (2.4494897427831780982 + 3.013669299784481451e-479j)  +/-  (2.84e-122, 2.84e-122j)
| (2.9774319258524154311 - 2.2292563664654449643e-478j)  +/-  (1.31e-121, 1.31e-121j)
| (-4.6938607947742638794 - 2.9557367865442935372e-476j)  +/-  (3.49e-120, 3.49e-120j)
| (-1.476762586756873728 + 4.0784406639180631189e-490j)  +/-  (7.27e-124, 7.27e-124j)
| (-3.5298626496166927728 + 8.3878018783105711591e-489j)  +/-  (4.3e-121, 4.3e-121j)
| (5.9411940996132860726 + 1.3945329297474746928e-490j)  +/-  (9.92e-120, 9.92e-120j)
| (-1.9514660360272807957 + 2.9856121958120356058e-499j)  +/-  (5.39e-123, 5.39e-123j)
| (-5.3056471232641363766 + 1.1512163810477592649e-496j)  +/-  (6.63e-120, 6.63e-120j)
| (-2.4494897427831780982 - 1.4249533782627338422e-508j)  +/-  (2.89e-122, 2.89e-122j)
| (7.310433298452702449 + 6.0985959801562616221e-507j)  +/-  (7.46e-120, 7.46e-120j)
| (4.6938607947742638794 - 4.0592866878711315553e-506j)  +/-  (3.34e-120, 3.34e-120j)
| (1 + 6.1512921040477542636e-512j)  +/-  (6.73e-125, 6.73e-125j)
| (-5.9411940996132860726 - 5.3216607842779436916e-508j)  +/-  (9.53e-120, 9.53e-120j)
| (-1 - 1.1311922066158942959e-519j)  +/-  (6.72e-125, 6.72e-125j)
| (-2.9774319258524154311 + 5.8840526211196590463e-515j)  +/-  (1.39e-121, 1.39e-121j)
| (1.9514660360272807957 + 1.145010318464619738e-515j)  +/-  (5.22e-123, 5.22e-123j)
| (0.50586066992431242685 - 9.2021883110717279338e-519j)  +/-  (5.99e-126, 5.99e-126j)
| (4.1023861416814739846 + 2.851783601658101809e-513j)  +/-  (1.54e-120, 1.54e-120j)
| (5.3056471232641363766 - 3.8414005619786084931e-518j)  +/-  (6.94e-120, 6.94e-120j)
| (-0.50586066992431242685 + 1.2452822535623111571e-524j)  +/-  (5.99e-126, 5.99e-126j)
| (-4.1023861416814739846 + 4.33517884712541683e-521j)  +/-  (1.4e-120, 1.4e-120j)
| (5.019446091858372073e-543 + 6.2033056216384283134e-542j)  +/-  (2.05e-540, 2.05e-540j)
| (1.476762586756873728 - 1.7015201062258111637e-525j)  +/-  (7.05e-124, 7.05e-124j)
-------------------------------------------------
The weights are:
| (9.0789918861280717237e-11 - 4.0771895946278086787e-465j)  +/-  (1.45e-32, 7.04e-92j)
| (2.2968144752571563734e-15 + 7.7278058064919646349e-469j)  +/-  (6.18e-36, 3e-95j)
| (2.2968144752571563734e-15 + 2.594577773369275425e-468j)  +/-  (9.21e-36, 4.46e-95j)
| (9.0789918861280717237e-11 - 3.6373079661774383142e-467j)  +/-  (9.06e-34, 4.39e-93j)
| (1.9959225720430142957e-18 - 3.9693501249351290643e-470j)  +/-  (1.65e-37, 7.99e-97j)
| (1.8088489901647612703e-22 - 6.5814650038578876909e-473j)  +/-  (1.14e-39, 5.51e-99j)
| (1.9959225720430142957e-18 + 1.2692531372152361499e-470j)  +/-  (6.1e-38, 2.96e-97j)
| (7.2149841394574596895e-13 - 9.813202043667906948e-469j)  +/-  (1.86e-35, 8.99e-95j)
| (1.8088489901647612703e-22 + 2.1159954571026122459e-472j)  +/-  (6.37e-41, 3.08e-100j)
| (0.00044229899191857281043 + 2.9125367946740093997e-462j)  +/-  (1.67e-30, 8.1e-90j)
| (0.010200222048394422649 + 2.0727653157820450961e-461j)  +/-  (1.64e-27, 7.96e-87j)
| (0.002565881292891860923 - 8.3470663316669995929e-462j)  +/-  (4.55e-29, 2.2e-88j)
| (3.9417515385930762654e-06 + 3.3195073268322123151e-464j)  +/-  (9.92e-35, 4.81e-94j)
| (0.063163891977581285508 + 4.1273795052834795326e-461j)  +/-  (7.49e-26, 3.63e-85j)
| (0.00044229899191857281043 + 7.7139935541891758398e-463j)  +/-  (6.76e-33, 3.28e-92j)
| (5.6030563033844427635e-09 + 1.6543926770567976106e-464j)  +/-  (2.15e-37, 1.04e-96j)
| (0.028719276567807718149 - 2.1683442647281133284e-461j)  +/-  (6.73e-29, 3.26e-88j)
| (1.9172031651066930097e-07 - 4.968212727736791444e-465j)  +/-  (4.83e-36, 2.34e-95j)
| (0.010200222048394422649 + 8.7590804764861925938e-462j)  +/-  (6.1e-31, 2.95e-90j)
| (7.2149841394574596895e-13 - 1.1657407020873841592e-466j)  +/-  (1.47e-39, 7.12e-99j)
| (3.9417515385930762654e-06 + 2.4685995984606573392e-463j)  +/-  (1.24e-36, 6.03e-96j)
| (0.11738418496671283079 - 8.643542739343550132e-461j)  +/-  (9.83e-30, 4.76e-89j)
| (5.6030563033844427635e-09 + 5.4963051466426124682e-466j)  +/-  (1.59e-37, 7.73e-97j)
| (0.11738418496671283079 - 6.1776098940177344203e-461j)  +/-  (1.31e-30, 6.34e-90j)
| (0.002565881292891860923 - 2.8414497940388317826e-462j)  +/-  (1.84e-33, 8.91e-93j)
| (0.028719276567807718149 - 4.2466093020162122111e-461j)  +/-  (4.27e-33, 2.07e-92j)
| (0.17616452354773206301 + 9.2460929758321628777e-461j)  +/-  (1.5e-31, 7.27e-91j)
| (5.1440465623093344548e-05 - 8.9778105181030018321e-463j)  +/-  (4.02e-36, 1.95e-95j)
| (1.9172031651066930097e-07 - 6.2308316601179731293e-464j)  +/-  (9.67e-38, 4.68e-97j)
| (0.17616452354773206301 + 7.8097990667649694685e-461j)  +/-  (2.08e-33, 1.02e-92j)
| (5.1440465623093344548e-05 - 1.7616576581077850172e-463j)  +/-  (2.65e-36, 1.29e-95j)
| (0.20260828194982605919 - 8.8736107142948970565e-461j)  +/-  (1.29e-33, 6.43e-93j)
| (0.063163891977581285508 + 6.8130602540617122297e-461j)  +/-  (2.84e-34, 1.29e-93j)
