Starting with polynomial:
P : 35/8*t^4 - 15/4*t^2 + 3/8
Extension levels are: 4 11 12
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Trying to find an order 11 Kronrod extension for:
P1 : 35/8*t^4 - 15/4*t^2 + 3/8
Solvable: 1
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Trying to find an order 12 Kronrod extension for:
P2 : 35/8*t^15 - 638415/40664*t^13 + 11181153/503608*t^11 - 55088825/3525256*t^9 + 19993545/3525256*t^7 - 160318323/162665384*t^5 + 10517265/162665384*t^3 - 64053/91941304*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 35/8*t^27 - 353810850417/12121572424*t^25 + 3301833872910204305109/38149138589700635420*t^23 - 28611196629157957218033741147/190355966324645394065153900*t^21 + 426080704462385735828525471740774809/2512922015840108535757927896217000*t^19 - 3375719083305214612498468225500170864716118907/25914403110000146287260867281665716337465000*t^17 + 13458590033211937809911144048007409262347778977567203/193689262137860388232229029661832656737072518118750*t^15 - 12969393486454616392929736605159443680048259769479193/503592081558437009403795477120764907516388547108750*t^13 + 872353768429709170838906097574569596039145598919787/133578801474386474642916572180574246025567253875000*t^11 - 354955749528553277955262987464789950903376757970617/323989311212421013043001285979792807632921303035000*t^9 + 5652118946983909749499571179863895098073190449677/49302721271455371550021934823011948987618459157500*t^7 - 520188378902431254546323392185682554407164812797061/76947461412949990597712805420200791812818809470812500*t^5 + 375066092552102900339783814477721682170566824889/2020242230146949560094390258136545885433080711975000*t^3 - 171636020742601294053925130788477767020868116403/113748421219143464361836321055948996592862587913375000*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:
| (0.99440647375811783848 + 9.8137742782115858385e-414j)  +/-  (2.74e-119, 2.74e-119j)
| (0.22994281668880038296 - 4.4584378948099248301e-420j)  +/-  (1.61e-125, 1.61e-125j)
| (-0.91878233988507960751 + 3.6729109016016441822e-411j)  +/-  (8.3e-119, 8.3e-119j)
| (0.91878233988507960751 - 9.0198923583386192708e-420j)  +/-  (8.12e-119, 8.12e-119j)
| (0.95275482203958774276 - 7.2990410679043594396e-419j)  +/-  (1.54e-118, 1.54e-118j)
| (0.97298173074896685887 - 1.4745094894468697636e-422j)  +/-  (1.22e-118, 1.22e-118j)
| (-0.3399810435848562648 + 2.8937180318216968073e-427j)  +/-  (2.95e-124, 2.95e-124j)
| (-0.86113631159405257522 + 4.1074242372408573799e-420j)  +/-  (2.6e-119, 2.6e-119j)
| (-0.97298173074896685887 + 1.6116753011676781659e-427j)  +/-  (1.13e-118, 1.13e-118j)
| (4.5632723791455396282e-451 + 4.2020662815973716493e-451j)  +/-  (1.67e-449, 1.67e-449j)
| (0.86113631159405257522 - 1.4808509774940221757e-449j)  +/-  (2.68e-119, 2.68e-119j)
| (-0.99440647375811783848 + 1.0605767233828220222e-446j)  +/-  (3e-119, 3e-119j)
| (-0.95275482203958774276 - 5.364317609647365966e-461j)  +/-  (1.55e-118, 1.55e-118j)
| (-0.79361531460634579533 - 2.4048679691902440435e-469j)  +/-  (9.09e-120, 9.09e-120j)
| (0.11513928820520961921 - 5.8062473993526677493e-480j)  +/-  (7.82e-127, 7.82e-127j)
| (0.79361531460634579533 - 5.9012358569213943922e-473j)  +/-  (8.37e-120, 8.37e-120j)
| (0.44438688492749195411 - 3.2717393481063341558e-477j)  +/-  (4.11e-123, 4.11e-123j)
| (0.72322064929065662618 + 1.74213257257183066e-474j)  +/-  (2.36e-120, 2.36e-120j)
| (-0.72322064929065662618 + 1.7987717793341840994e-474j)  +/-  (2.31e-120, 2.31e-120j)
| (-0.44438688492749195411 - 1.63922525563074199e-478j)  +/-  (4.1e-123, 4.1e-123j)
| (0.3399810435848562648 - 5.1228764643570304419e-480j)  +/-  (2.85e-124, 2.85e-124j)
| (0.64196104725310865483 - 2.3650429012357226955e-478j)  +/-  (3.78e-121, 3.78e-121j)
| (-0.11513928820520961921 - 1.0431543598400995775e-482j)  +/-  (7.82e-127, 7.82e-127j)
| (-0.54633537010580514983 + 7.6512612101337192926e-477j)  +/-  (3.89e-122, 3.89e-122j)
| (-0.64196104725310865483 + 2.5712450232825418694e-479j)  +/-  (3.74e-121, 3.74e-121j)
| (-0.22994281668880038296 + 1.3440517605980712754e-484j)  +/-  (1.88e-125, 1.88e-125j)
| (0.54633537010580514983 - 1.1766015846546649018e-482j)  +/-  (4.38e-122, 4.38e-122j)
-------------------------------------------------
The weights are:
| (0.014181092508994001171 - 2.4292006947027625348e-413j)  +/-  (4.77e-33, 8.09e-90j)
| (0.11320563753276791661 + 3.6718219821013649058e-412j)  +/-  (7.56e-34, 1.28e-90j)
| (0.048848815601805347773 - 1.4646011918851010743e-411j)  +/-  (2.08e-34, 3.52e-91j)
| (0.048848815601805347773 + 1.2041137211792024665e-412j)  +/-  (1.55e-33, 2.63e-90j)
| (0.01906584419803717349 - 1.3388584034352591517e-412j)  +/-  (1.16e-33, 1.97e-90j)
| (0.025390323439237773294 + 9.1076629825636403047e-413j)  +/-  (1.08e-33, 1.83e-90j)
| (0.10667298773250746554 - 7.0621896344473734312e-412j)  +/-  (1.51e-36, 2.57e-93j)
| (0.064401678420415574472 - 3.2741876667937245399e-411j)  +/-  (4.24e-36, 7.19e-93j)
| (0.025390323439237773294 - 1.7201620558047826013e-411j)  +/-  (8.32e-37, 1.41e-93j)
| (0.11486552572811872533 + 4.6913815084829652504e-412j)  +/-  (2.93e-37, 4.98e-94j)
| (0.064401678420415574472 - 1.1959921897498073341e-412j)  +/-  (2.85e-36, 4.83e-93j)
| (0.014181092508994001171 + 1.9165278089853858671e-412j)  +/-  (1.74e-37, 2.95e-94j)
| (0.01906584419803717349 + 5.1523211107823304642e-411j)  +/-  (9.5e-37, 1.61e-93j)
| (0.069051627789997482141 + 2.0276178352489433336e-411j)  +/-  (3.87e-38, 6.57e-95j)
| (0.11547156694976768735 - 4.1294004531780477781e-412j)  +/-  (3.78e-38, 6.41e-95j)
| (0.069051627789997482141 + 1.6023254420390588245e-412j)  +/-  (1.77e-38, 3e-95j)
| (0.10298430587701938649 + 2.8408106061462232421e-412j)  +/-  (1.44e-39, 2.43e-96j)
| (0.073694313194438421341 - 2.0148766166108113806e-412j)  +/-  (4.3e-39, 7.3e-96j)
| (0.073694313194438421341 - 1.6005839551333746468e-411j)  +/-  (5.29e-40, 9e-97j)
| (0.10298430587701938649 + 7.9985861579670222151e-412j)  +/-  (1.44e-40, 2.45e-97j)
| (0.10667298773250746554 - 3.2935590964646869511e-412j)  +/-  (5.84e-40, 9.88e-97j)
| (0.089422128017012735385 + 2.1938275374317638442e-412j)  +/-  (1.68e-40, 2.85e-97j)
| (0.11547156694976768735 - 5.2898810630520984269e-412j)  +/-  (1.18e-40, 2.01e-97j)
| (0.10017691587393967227 - 9.2100440697850250444e-412j)  +/-  (2.72e-41, 4.62e-98j)
| (0.089422128017012735385 + 1.188394224635780398e-411j)  +/-  (2.71e-41, 4.61e-98j)
| (0.11320563753276791661 + 6.0687526214966322372e-412j)  +/-  (2.23e-41, 3.83e-98j)
| (0.10017691587393967227 - 2.4091750983933104673e-412j)  +/-  (1.32e-41, 2.04e-98j)
