Starting with polynomial:
P : 3/2*t^2 - 1/2
Extension levels are: 2 6 18
-------------------------------------------------
Trying to find an order 6 Kronrod extension for:
P1 : 3/2*t^2 - 1/2
Solvable: 1
-------------------------------------------------
Trying to find an order 18 Kronrod extension for:
P2 : 3/2*t^8 - 161/52*t^6 + 105/52*t^4 - 245/572*t^2 + 25/1716
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 3/2*t^26 - 24516004014371226905143525/2272458258739826193262772*t^24 + 41808543066376067434493895675/1211220251908327361009057476*t^22 - 1601193989682126500758170265925/24743499431841544660613602724*t^20 + 216406397377752248654653917711025/2746528436934411457328109902364*t^18 - 104549118403227731747727231264600/1602141588211740016774730776379*t^16 + 1318796740797867615374295818082975/35247114940658280369044077080338*t^14 - 5741726638553301227618915418175/387330933413827256802682165718*t^12 + 440785467665159013586361125753725/110794252907873405775421766766517*t^10 - 3455625613213688655736239979925/4979516984623523855075135585012*t^8 + 338596566399496219366208198903/4632512316705508255418331711492*t^6 - 257549464917181923272887335595/63311001661641946157383866723724*t^4 + 1355710879858116415961576105/14938550953870571565225406755036*t^2 - 4791398699021968260548525/13946129736655393733969173439142
-------------------------------------------------
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:
| (-0.99938427483443948435 + 1.1370710199643141488e-259j)  +/-  (2.11e-117, 2.11e-117j)
| (-0.98219129046748981137 - 3.015962224494437369e-281j)  +/-  (1.8e-117, 1.8e-117j)
| (-0.68239011718365358647 - 2.4334258272846405603e-301j)  +/-  (3.96e-121, 3.96e-121j)
| (0.99938427483443948435 + 2.102740602905797897e-296j)  +/-  (2.04e-117, 2.04e-117j)
| (0.91170554006328717675 - 1.0097943104109976846e-298j)  +/-  (1.24e-118, 1.24e-118j)
| (0.95526936302604635714 - 1.2815604949215654058e-298j)  +/-  (5.55e-118, 5.55e-118j)
| (0.99517513040458488078 - 9.785447481317383155e-297j)  +/-  (3.66e-117, 3.66e-117j)
| (-0.91170554006328717675 + 3.2320057982025924489e-295j)  +/-  (1.34e-118, 1.34e-118j)
| (-0.95526936302604635714 - 8.4755771927863131642e-314j)  +/-  (5.96e-118, 5.96e-118j)
| (0.98219129046748981137 - 5.6325180541189420778e-329j)  +/-  (1.71e-117, 1.71e-117j)
| (0.85110112875893547946 + 4.5553503687461312424e-335j)  +/-  (2.46e-119, 2.46e-119j)
| (-0.33591637530927440701 + 1.7367616429573148966e-338j)  +/-  (1.11e-124, 1.11e-124j)
| (-0.99517513040458488078 + 1.0129816423405117722e-348j)  +/-  (3.43e-117, 3.43e-117j)
| (-0.85110112875893547946 - 2.7396400667497132673e-369j)  +/-  (2.29e-119, 2.29e-119j)
| (0.2041968861768067152 - 1.773152942854569755e-376j)  +/-  (5.78e-126, 5.78e-126j)
| (0.77421495376050439073 - 8.3640763959461009649e-377j)  +/-  (3.33e-120, 3.33e-120j)
| (0.57735026918962576451 + 2.0329867082865130258e-379j)  +/-  (2.9e-122, 2.9e-122j)
| (0.068509439373879866294 + 2.6850478530141024352e-374j)  +/-  (2.04e-127, 2.04e-127j)
| (-0.77421495376050439073 + 7.0126088882224350407e-373j)  +/-  (3.42e-120, 3.42e-120j)
| (-0.068509439373879866294 - 6.5426629981802762608e-374j)  +/-  (2.04e-127, 2.04e-127j)
| (0.46111006295702354451 + 3.1017543373961182501e-380j)  +/-  (2.19e-123, 2.19e-123j)
| (0.68239011718365358647 - 3.3064305528087311996e-379j)  +/-  (3.78e-121, 3.78e-121j)
| (0.33591637530927440701 - 2.8564757627772128168e-380j)  +/-  (1.15e-124, 1.15e-124j)
| (-0.46111006295702354451 + 2.4752486267355718214e-375j)  +/-  (1.85e-123, 1.85e-123j)
| (-0.57735026918962576451 - 5.0429392369511314863e-376j)  +/-  (3.17e-122, 3.17e-122j)
| (-0.2041968861768067152 - 9.4161452372874597677e-374j)  +/-  (5.78e-126, 5.78e-126j)
-------------------------------------------------
The weights are:
| (0.0017496116510385145027 + 7.1678384685236542073e-260j)  +/-  (1.42e-31, 1.55e-86j)
| (0.019254617468731128508 + 1.3105817290932699025e-260j)  +/-  (1.14e-31, 1.25e-86j)
| (0.098746068903222853215 - 5.3708203361033891336e-263j)  +/-  (1.14e-32, 1.24e-87j)
| (0.0017496116510385145027 - 9.9532920153130576099e-263j)  +/-  (7.58e-33, 8.25e-88j)
| (0.052143421819533995334 - 3.2099976453813344206e-263j)  +/-  (2.36e-33, 2.57e-88j)
| (0.035028493754615654824 + 5.8990806349851135217e-263j)  +/-  (1.71e-33, 1.86e-88j)
| (0.0076187057476192636331 + 1.745155736860741371e-262j)  +/-  (3.91e-33, 4.26e-88j)
| (0.052143421819533995334 + 6.9966723652498819444e-262j)  +/-  (3.94e-35, 4.29e-90j)
| (0.035028493754615654824 - 2.6137781875860442423e-261j)  +/-  (8.64e-35, 9.41e-90j)
| (0.019254617468731128508 - 1.1371159179830305774e-262j)  +/-  (7.94e-34, 8.65e-89j)
| (0.068930656613177309183 + 1.9605809679396251494e-263j)  +/-  (5.82e-36, 6.33e-91j)
| (0.1288737473981338203 + 1.4046320351880902758e-263j)  +/-  (8.05e-38, 8.77e-93j)
| (0.0076187057476192636331 - 8.2696539559766767927e-260j)  +/-  (1.63e-34, 1.77e-89j)
| (0.068930656613177309183 - 2.4466883524901065234e-262j)  +/-  (1.73e-36, 1.88e-91j)
| (0.13413806524341969696 + 7.0561669203704675353e-264j)  +/-  (8.95e-39, 9.75e-94j)
| (0.084614989604825690137 - 1.3412416641553639549e-263j)  +/-  (2.03e-37, 2.21e-92j)
| (0.1109969147350048782 - 8.3163614671011679385e-264j)  +/-  (9.24e-39, 1.01e-93j)
| (0.13679653361630247261 - 7.5973726500463832791e-264j)  +/-  (1.97e-39, 2.15e-94j)
| (0.084614989604825690137 + 1.0564606090917053284e-262j)  +/-  (1.18e-38, 1.28e-93j)
| (0.13679653361630247261 + 8.7156577752675570322e-264j)  +/-  (7.49e-40, 8.16e-95j)
| (0.1211081734443747226 + 7.3627397331973464949e-264j)  +/-  (7e-40, 7.62e-95j)
| (0.098746068903222853215 + 1.0123347557301184032e-263j)  +/-  (2.01e-39, 2.19e-94j)
| (0.1288737473981338203 - 6.9791643244665516349e-264j)  +/-  (3.4e-40, 3.71e-95j)
| (0.1211081734443747226 - 1.9977252213999515244e-263j)  +/-  (2.58e-41, 2.81e-96j)
| (0.1109969147350048782 + 3.1070231854266232792e-263j)  +/-  (3.03e-41, 3.31e-96j)
| (0.13413806524341969696 - 1.0680085845734090664e-263j)  +/-  (2.04e-41, 2.21e-96j)
