Starting with polynomial:
P : 3/2*t^2 - 1/2
Extension levels are: 2 4 29
-------------------------------------------------
Trying to find an order 4 Kronrod extension for:
P1 : 3/2*t^2 - 1/2
Solvable: 1
-------------------------------------------------
Trying to find an order 29 Kronrod extension for:
P2 : 3/2*t^6 - 25/14*t^4 + 45/98*t^2 - 1/98
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 3/2*t^35 - 1348884798795788104131608927/104818316823828572099222066*t^33 + 84604034837056929232862290223999/1678403298141555010738793331825*t^31 - 157614610791101210228199503495083/1320343927871356608447850754369*t^29 + 10254864782950919396564121670655819/53756859920476661915376780713595*t^27 - 2782789929759671256838073312062671/12799252362018252836994471598475*t^25 + 34592513659250395791590409548817459/189940905052350872100997958521369*t^23 - 5691457639581010024778697956192169/49984448697987071605525778558255*t^21 + 71018080600283032723162678712040780/1329586335366456104706985709649583*t^19 - 7073864972766194084692257668033556/377423558529390904614838911539873*t^17 + 560067296264190313595446526546136381/115114185351464225907525868019661265*t^15 - 129521395024303765904165442225209513/141425999146084620400674637852726697*t^13 + 501735618684943514152754848938130893/4141761403563906740305471537115567555*t^11 - 62252941431212107481289049646987875/5798465964989469436427660151961794577*t^9 + 127081029023077329336679620550175373/214543240704610369147823425622586399349*t^7 - 19356005636071440906599546500625301/1072716203523051845739117128112931996745*t^5 + 731879907174040061970107041731951/3003605369864545168069527958716209590886*t^3 - 13158428421977335689969135190623/15018026849322725840347639793581047954430*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:
| (-0.98748610447248284002 - 4.7497550702888261244e-444j)  +/-  (4.49e-116, 4.49e-116j)
| (-0.99760970543424740224 - 2.0063059731510660851e-444j)  +/-  (1.55e-116, 1.55e-116j)
| (-0.91248695683407599658 + 2.4582094866731326195e-445j)  +/-  (2.97e-116, 2.97e-116j)
| (0.98748610447248284002 - 6.4200258836353323321e-442j)  +/-  (4.29e-116, 4.29e-116j)
| (0.87393509723304819617 + 9.3890887659791964535e-448j)  +/-  (1.39e-116, 1.39e-116j)
| (0.91248695683407599658 + 3.5869295529642350974e-452j)  +/-  (3.06e-116, 3.06e-116j)
| (0.99760970543424740224 + 2.1727356028227986216e-460j)  +/-  (1.49e-116, 1.49e-116j)
| (-0.87393509723304819617 - 6.9251349595141063101e-472j)  +/-  (1.39e-116, 1.39e-116j)
| (-0.24402958546140932086 - 1.0583753477849564527e-482j)  +/-  (1.6e-124, 1.6e-124j)
| (0.94443029831945333252 + 3.1583767104556526318e-477j)  +/-  (4.83e-116, 4.83e-116j)
| (0.82852300212779487549 + 6.0017804693793278198e-488j)  +/-  (5.54e-117, 5.54e-117j)
| (0.96959513022871262378 + 2.6106814652085986378e-494j)  +/-  (5.52e-116, 5.52e-116j)
| (-0.94443029831945333252 - 7.883785868482298769e-498j)  +/-  (5.07e-116, 5.07e-116j)
| (-0.82852300212779487549 + 4.4724234715637681665e-500j)  +/-  (5.28e-117, 5.28e-117j)
| (-0.41729651639906670022 - 1.9065112594649923103e-507j)  +/-  (3.85e-122, 3.85e-122j)
| (0.77595250415319466515 - 1.9108138323965494452e-504j)  +/-  (1.33e-117, 1.33e-117j)
| (0.6498489178674061656 + 1.8077192787500524815e-506j)  +/-  (4.23e-119, 4.23e-119j)
| (-0.33167317545643584886 + 3.9489702991517793802e-509j)  +/-  (2.45e-123, 2.45e-123j)
| (-0.77595250415319466515 - 1.2623771934490514961e-501j)  +/-  (1.34e-117, 1.34e-117j)
| (-0.96959513022871262378 - 4.5324139034152880058e-504j)  +/-  (5.45e-116, 5.45e-116j)
| (0.41729651639906670022 + 2.7667037606242778862e-510j)  +/-  (3.98e-122, 3.98e-122j)
| (0.71626077567689709711 + 8.7038777914935164914e-508j)  +/-  (2.52e-118, 2.52e-118j)
| (0.15655801081562154215 + 6.6781495275730103512e-516j)  +/-  (9.95e-126, 9.95e-126j)
| (-0.71626077567689709711 + 1.453685624809374895e-507j)  +/-  (2.41e-118, 2.41e-118j)
| (-0.57735026918962576451 - 2.295278405605313578e-509j)  +/-  (5.16e-120, 5.16e-120j)
| (0.073618824281943662477 - 6.4653474300151522821e-519j)  +/-  (5.95e-127, 5.95e-127j)
| (0.57735026918962576451 - 2.375475067423669868e-512j)  +/-  (5.7e-120, 5.7e-120j)
| (0.33167317545643584886 - 4.0135123354491212132e-516j)  +/-  (2.66e-123, 2.66e-123j)
| (-0.15655801081562154215 + 1.8453230086545453235e-517j)  +/-  (1.03e-125, 1.03e-125j)
| (-0.6498489178674061656 + 4.6368800615367489997e-512j)  +/-  (4.31e-119, 4.31e-119j)
| (-0.073618824281943662477 + 6.6405288969595362891e-520j)  +/-  (5.95e-127, 5.95e-127j)
| (0.24402958546140932086 + 1.0319307264562200745e-517j)  +/-  (1.45e-124, 1.45e-124j)
| (0.49953703163638994193 - 8.0606329554461645031e-515j)  +/-  (4.99e-121, 4.99e-121j)
| (-2.8842070853084335377e-528 + 3.9654484739085370511e-528j)  +/-  (1.72e-526, 1.72e-526j)
| (-0.49953703163638994193 + 3.6140435148667157235e-515j)  +/-  (5.28e-121, 5.28e-121j)
-------------------------------------------------
The weights are:
| (0.014076082875155708463 + 6.0651799974226626323e-444j)  +/-  (8.05e-22, 1.7e-76j)
| (0.0061250704893262166142 - 5.7238118508912888415e-444j)  +/-  (4.84e-22, 1.02e-76j)
| (0.035235224104451308535 - 2.1018292181829610229e-443j)  +/-  (1.13e-22, 2.38e-77j)
| (0.014076082875155708463 + 3.92160891652625345e-442j)  +/-  (9.89e-23, 2.09e-77j)
| (0.041918452857268253082 + 4.8878133900400385114e-442j)  +/-  (4.49e-23, 9.47e-78j)
| (0.035235224104451308535 - 5.7897966237458201822e-442j)  +/-  (3.99e-23, 8.41e-78j)
| (0.0061250704893262166142 + 2.4813683741118421883e-442j)  +/-  (8.66e-24, 1.83e-78j)
| (0.041918452857268253082 + 2.811356594431324291e-443j)  +/-  (1.84e-24, 3.89e-79j)
| (0.088041578648195566084 - 1.4478953594492219015e-442j)  +/-  (1.42e-25, 2.99e-80j)
| (0.02862040187372442433 + 7.0481273273544009117e-442j)  +/-  (6.87e-24, 1.45e-78j)
| (0.048962848733672145139 - 4.0815576365540538722e-442j)  +/-  (3.87e-25, 8.16e-80j)
| (0.021620254458846725454 - 1.0316691610834143499e-441j)  +/-  (6.46e-24, 1.36e-78j)
| (0.02862040187372442433 + 1.347527904558822287e-443j)  +/-  (4.67e-26, 9.86e-81j)
| (0.048962848733672145139 - 3.4439317541651060009e-443j)  +/-  (5.99e-27, 1.26e-81j)
| (0.084124004970057881688 - 8.1958484508249792666e-443j)  +/-  (2.52e-28, 5.32e-83j)
| (0.056171566199685526496 + 3.384796757937123568e-442j)  +/-  (1.35e-26, 2.84e-81j)
| (0.069574237148345161711 + 2.448137962644513219e-442j)  +/-  (5.49e-28, 1.16e-82j)
| (0.086902620698195322072 + 1.0550183905145887267e-442j)  +/-  (1.64e-28, 3.46e-83j)
| (0.056171566199685526496 + 3.9586885883114156323e-443j)  +/-  (3.85e-28, 8.13e-83j)
| (0.021620254458846725454 - 5.0862448848743117623e-444j)  +/-  (5.74e-27, 1.21e-81j)
| (0.084124004970057881688 - 2.0310827343314634101e-442j)  +/-  (2.15e-30, 4.54e-85j)
| (0.06314236647949409579 - 2.8389941245147655917e-442j)  +/-  (2.21e-28, 4.67e-83j)
| (0.086204726117080084128 + 2.9481484805759285226e-442j)  +/-  (3.25e-31, 6.86e-86j)
| (0.06314236647949409579 - 4.4374544254139716796e-443j)  +/-  (1.3e-29, 2.75e-84j)
| (0.07529399883782686725 - 5.6903772853307024367e-443j)  +/-  (1.86e-30, 3.93e-85j)
| (0.078493707320938677283 - 3.7433829344277668729e-442j)  +/-  (1.91e-31, 4.04e-86j)
| (0.07529399883782686725 - 2.1935537690779120559e-442j)  +/-  (6.83e-31, 1.44e-85j)
| (0.086902620698195322072 + 2.1312781221577715931e-442j)  +/-  (1.26e-31, 2.65e-86j)
| (0.086204726117080084128 + 2.1373428555564176157e-442j)  +/-  (3.59e-32, 7.57e-87j)
| (0.069574237148345161711 + 4.9800392158952806268e-443j)  +/-  (5.59e-32, 1.18e-86j)
| (0.078493707320938677283 - 3.2212363799221005362e-442j)  +/-  (1.52e-32, 3.2e-87j)
| (0.088041578648195566084 - 2.4055381218604218241e-442j)  +/-  (6.15e-33, 1.29e-87j)
| (0.080185199694851118503 + 2.0566385172372571668e-442j)  +/-  (4.46e-33, 9.34e-88j)
| (0.07061531698576983476 + 4.0244597804152848043e-442j)  +/-  (7.35e-33, 1.56e-87j)
| (0.080185199694851118503 + 6.6962207010176660448e-443j)  +/-  (1.43e-33, 2.89e-88j)
