Starting with polynomial:
P : 8*t^3 - 12*t
Extension levels are: 3 28
-------------------------------------------------
Trying to find an order 28 Kronrod extension for:
P1 : 8*t^3 - 12*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 8*t^31 - 226942741276/94518463*t^29 + 28225235849258/94518463*t^27 - 150371025565509/7270651*t^25 + 13029636735701775/14541302*t^23 - 747941195631912975/29082604*t^21 + 29280397035306064725/58165208*t^19 - 791066818602524997225/116330416*t^17 + 14736541235109459883425/232660832*t^15 - 186957709796386606163625/465321664*t^13 + 1575515020428670206760875/930643328*t^11 - 8463799522227624427227375/1861286656*t^9 + 27150071826935693461951125/3722573312*t^7 - 46698742063919906652817125/7445146624*t^5 + 35385482708586154410564375/14890293248*t^3 - 7482944217160189385251875/29780586496*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:   31 out of 31
Indefinite weights: 0 out of 31
Negative weights:   0 out of 31
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (0.40670148944933477364 + 1.2653342959698175627e-431j)  +/-  (3.67e-126, 3.67e-126j)
| (-6.6741902582934452344 - 1.468348677233596624e-427j)  +/-  (1.22e-121, 1.22e-121j)
| (6.6741902582934452344 + 6.5316040188470597985e-427j)  +/-  (1.18e-121, 1.18e-121j)
| (2.9173780732339647739 - 1.9935571274195407283e-426j)  +/-  (3.4e-121, 3.4e-121j)
| (10.001289610832486052 - 1.5068697746458039502e-429j)  +/-  (1.34e-123, 1.34e-123j)
| (-5.9538378597044861915 - 1.6450352136723130819e-426j)  +/-  (6.79e-121, 6.79e-121j)
| (-4.3024922552489947966 + 5.2521837970506577342e-425j)  +/-  (2.21e-120, 2.21e-120j)
| (-1.6385632780281483633 + 1.4420023726723977296e-432j)  +/-  (3.77e-123, 3.77e-123j)
| (5.9538378597044861915 + 1.1516177914051767628e-429j)  +/-  (6.35e-121, 6.35e-121j)
| (3.8231257617379700565 - 2.828010556854157927e-440j)  +/-  (1.6e-120, 1.6e-120j)
| (1.6385632780281483633 - 2.7111251015219905894e-450j)  +/-  (3.72e-123, 3.72e-123j)
| (2.4830447844160796544 + 4.2862137781015851713e-449j)  +/-  (9.85e-122, 9.85e-122j)
| (-10.001289610832486052 - 3.6116803177753375312e-453j)  +/-  (1.37e-123, 1.37e-123j)
| (-2.9173780732339647739 + 7.6116645588605569791e-450j)  +/-  (3.63e-121, 3.63e-121j)
| (-3.8231257617379700565 - 2.9443155773898787518e-451j)  +/-  (1.55e-120, 1.55e-120j)
| (4.3024922552489947966 + 8.7346690059154535492e-460j)  +/-  (2.09e-120, 2.09e-120j)
| (4.8079895941051616207 + 1.6799533851355321023e-471j)  +/-  (2.27e-120, 2.27e-120j)
| (5.3510645640869972732 + 1.2994296268122241411e-478j)  +/-  (1.6e-120, 1.6e-120j)
| (-2.4830447844160796544 - 1.2563279152579885344e-480j)  +/-  (9.75e-122, 9.75e-122j)
| (1.1665947067274060524e-491 - 3.0409768047007958591e-492j)  +/-  (3.74e-490, 3.74e-490j)
| (1.2247448713915890491 + 7.7845923692252729721e-484j)  +/-  (4.47e-124, 4.47e-124j)
| (0.81455226404587909708 + 9.2521596764369078608e-485j)  +/-  (4.83e-125, 4.83e-125j)
| (-2.0574419649029150434 + 2.186933051088075496e-481j)  +/-  (2.23e-122, 2.23e-122j)
| (-1.2247448713915890491 + 1.639990446088044337e-484j)  +/-  (4.47e-124, 4.47e-124j)
| (-4.8079895941051616207 + 8.5176616639269972656e-480j)  +/-  (2.38e-120, 2.38e-120j)
| (2.0574419649029150434 + 6.8742968613521811376e-484j)  +/-  (2.13e-122, 2.13e-122j)
| (3.3629640889632544128 + 1.3519572038318996157e-485j)  +/-  (9.22e-121, 9.22e-121j)
| (-3.3629640889632544128 - 5.6623052665756424085e-488j)  +/-  (8.65e-121, 8.65e-121j)
| (-0.40670148944933477364 - 5.1762646126838885845e-494j)  +/-  (3.67e-126, 3.67e-126j)
| (-0.81455226404587909708 - 7.3083962226590544236e-493j)  +/-  (4.83e-125, 4.83e-125j)
| (-5.3510645640869972732 + 1.233112978060038312e-490j)  +/-  (1.53e-120, 1.53e-120j)
-------------------------------------------------
The weights are:
| (0.19465811031822222685 + 2.1455132138367976406e-429j)  +/-  (7.56e-28, 1.39e-88j)
| (2.1065114176090465763e-20 - 4.6716874507314307378e-439j)  +/-  (1.18e-41, 2.17e-102j)
| (2.1065114176090465763e-20 + 7.3695371027495690595e-439j)  +/-  (4.97e-42, 9.16e-103j)
| (4.9893874928891735125e-05 + 2.8463682893582979983e-430j)  +/-  (4.09e-32, 7.53e-93j)
| (9.4835669981857129774e-35 - 1.635273498769421803e-445j)  +/-  (1.75e-47, 3.23e-108j)
| (1.4676531380266198679e-16 + 4.4520606386295952256e-437j)  +/-  (5.32e-41, 9.8e-102j)
| (2.5298680969126843842e-09 + 4.6102732160839838123e-433j)  +/-  (1.01e-37, 1.85e-98j)
| (0.016017073434852904946 - 2.6406085927111167005e-430j)  +/-  (7.43e-28, 1.37e-88j)
| (1.4676531380266198679e-16 - 7.0133292758113316005e-437j)  +/-  (2.63e-41, 4.84e-102j)
| (1.1876304984643165151e-07 - 5.6516014983031954626e-432j)  +/-  (6.61e-37, 1.22e-97j)
| (0.016017073434852904946 - 1.3009133523846134785e-429j)  +/-  (1.36e-29, 2.5e-90j)
| (0.00050914272891309765751 - 7.1437417337132696209e-430j)  +/-  (6.85e-33, 1.26e-93j)
| (9.4835669981857129774e-35 + 1.1554526950538360207e-445j)  +/-  (7.01e-50, 1.29e-110j)
| (4.9893874928891735125e-05 + 4.3084264765112463826e-432j)  +/-  (2.28e-36, 4.19e-97j)
| (1.1876304984643165151e-07 - 1.1118056757389878605e-432j)  +/-  (2.35e-38, 4.32e-99j)
| (2.5298680969126843842e-09 + 5.5661991311973013064e-433j)  +/-  (3.19e-39, 5.88e-100j)
| (2.6881609235015196618e-11 - 4.3597928741921768164e-434j)  +/-  (1.13e-40, 2.08e-101j)
| (1.1750018958907576053e-13 + 2.340006828452362874e-435j)  +/-  (7.28e-42, 1.34e-102j)
| (0.00050914272891309765751 - 2.7499646875849785801e-431j)  +/-  (5.66e-38, 1.04e-98j)
| (0.22934946967356771219 - 1.9400800178086796195e-429j)  +/-  (1.91e-34, 3.51e-95j)
| (0.05183819212449018945 + 1.7289999955243165869e-429j)  +/-  (3.6e-35, 6.62e-96j)
| (0.11879596213888437904 - 2.059772347805957668e-429j)  +/-  (7.31e-35, 1.34e-95j)
| (0.003453642263434136493 + 9.8661062028872697853e-431j)  +/-  (4.15e-37, 7.67e-98j)
| (0.05183819212449018945 + 5.6749005832811170776e-430j)  +/-  (1.06e-35, 1.95e-96j)
| (2.6881609235015196618e-11 + 3.8166262532498202477e-434j)  +/-  (2.26e-43, 4.17e-104j)
| (0.003453642263434136493 + 9.1859686047864278641e-430j)  +/-  (1.02e-37, 1.79e-98j)
| (3.1269595731181732663e-06 + 5.7324113449557915997e-431j)  +/-  (1.2e-39, 2.12e-100j)
| (3.1269595731181732663e-06 + 7.4632824511622616035e-433j)  +/-  (1.13e-40, 1.92e-101j)
| (0.19465811031822222685 + 1.5166108816056609471e-429j)  +/-  (8.47e-38, 1.36e-98j)
| (0.11879596213888437904 - 1.0104369138448467016e-429j)  +/-  (4.25e-38, 6.45e-99j)
| (1.1750018958907576053e-13 - 1.5806054351888795271e-435j)  +/-  (6.59e-45, 1.31e-105j)
