Starting with polynomial:
P : 1/2*t^2 - 2*t + 1
Extension levels are: 2 6
-------------------------------------------------
Trying to find an order 6 Kronrod extension for:
P1 : 1/2*t^2 - 2*t + 1
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 1/2*t^8 - 4663/167*t^7 + 392807/668*t^6 - 993633/167*t^5 + 10206975/334*t^4 - 12943920/167*t^3 + 14566410/167*t^2 - 5684760/167*t + 397260/167
-------------------------------------------------
Computing nodes and weights
  current precision for roots: 53
  current precision for roots: 106
 current precision for weights: 53
Linear system for weights solvable: 1
  current precision for roots: 106
  current precision for roots: 212
 current precision for weights: 106
Linear system for weights solvable: 1
Sufficient bits for target precision reached
Positive weights:   8 out of 8
Indefinite weights: 0 out of 8
Negative weights:   0 out of 8
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (20.799370790425286883 + 1.6518878012110690686e-187j)  +/-  (3.98e-60, 3.98e-60j)
| (9.3459518428118469803 - 5.6987043074218479034e-192j)  +/-  (1.21e-59, 1.21e-59j)
| (3.4142135623730950488 + 1.1772413495650602264e-195j)  +/-  (1.62e-60, 1.62e-60j)
| (14.023914954138327016 - 2.939445397418085837e-199j)  +/-  (1.21e-59, 1.21e-59j)
| (0.5857864376269049512 + 1.9392174496855427397e-201j)  +/-  (2.44e-62, 2.44e-62j)
| (1.6682880962583043051 - 2.3206684158876462689e-215j)  +/-  (2.74e-61, 2.74e-61j)
| (0.08837702141245734094 + 1.2882297539194266616e-230j)  +/-  (1.19e-63, 1.19e-63j)
| (5.9184086721992864573 + 8.4211491014647245998e-243j)  +/-  (5.69e-60, 5.69e-60j)
-------------------------------------------------
The weights are:
| (7.8936707537787857204e-09 - 6.6528097397080986753e-196j)  +/-  (4e-31, 2.78e-60j)
| (0.00034718110539956278496 - 2.5976310940754770984e-194j)  +/-  (4.71e-29, 3.27e-58j)
| (0.0692635852360207144 - 2.6301998646412505056e-193j)  +/-  (2.76e-27, 1.92e-56j)
| (4.4644641245099157966e-06 + 4.9520475285191040477e-195j)  +/-  (2.93e-30, 2.05e-59j)
| (0.43103991140737761267 - 5.2887618116549007534e-193j)  +/-  (5.51e-27, 4.13e-56j)
| (0.26435000551464918648 + 4.6834740939496521032e-193j)  +/-  (2.75e-27, 2e-56j)
| (0.22711592136394294911 + 2.4511499757418045346e-193j)  +/-  (2.47e-27, 1.93e-56j)
| (0.0078789230148147108598 + 1.0012330504667593892e-193j)  +/-  (2.05e-28, 1.42e-57j)
Starting with polynomial:
P : 1/2*t^2 - 2*t + 1
Extension levels are: 2 6
-------------------------------------------------
Trying to find an order 6 Kronrod extension for:
P1 : 1/2*t^2 - 2*t + 1
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 1/2*t^8 - 4663/167*t^7 + 392807/668*t^6 - 993633/167*t^5 + 10206975/334*t^4 - 12943920/167*t^3 + 14566410/167*t^2 - 5684760/167*t + 397260/167
-------------------------------------------------
Computing nodes and weights
  current precision for roots: 53
  current precision for roots: 106
 current precision for weights: 53
Linear system for weights solvable: 1
  current precision for roots: 106
  current precision for roots: 212
 current precision for weights: 106
Linear system for weights solvable: 1
Sufficient bits for target precision reached
Positive weights:   8 out of 8
Indefinite weights: 0 out of 8
Negative weights:   0 out of 8
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (20.799370790425286883 + 1.6518878012110690686e-187j)  +/-  (3.98e-60, 3.98e-60j)
| (9.3459518428118469803 - 5.6987043074218479034e-192j)  +/-  (1.21e-59, 1.21e-59j)
| (3.4142135623730950488 + 1.1772413495650602264e-195j)  +/-  (1.62e-60, 1.62e-60j)
| (14.023914954138327016 - 2.939445397418085837e-199j)  +/-  (1.21e-59, 1.21e-59j)
| (0.5857864376269049512 + 1.9392174496855427397e-201j)  +/-  (2.44e-62, 2.44e-62j)
| (1.6682880962583043051 - 2.3206684158876462689e-215j)  +/-  (2.74e-61, 2.74e-61j)
| (0.08837702141245734094 + 1.2882297539194266616e-230j)  +/-  (1.19e-63, 1.19e-63j)
| (5.9184086721992864573 + 8.4211491014647245998e-243j)  +/-  (5.69e-60, 5.69e-60j)
-------------------------------------------------
The weights are:
| (7.8936707537787857204e-09 - 6.6528097397080986753e-196j)  +/-  (4e-31, 2.78e-60j)
| (0.00034718110539956278496 - 2.5976310940754770984e-194j)  +/-  (4.71e-29, 3.27e-58j)
| (0.0692635852360207144 - 2.6301998646412505056e-193j)  +/-  (2.76e-27, 1.92e-56j)
| (4.4644641245099157966e-06 + 4.9520475285191040477e-195j)  +/-  (2.93e-30, 2.05e-59j)
| (0.43103991140737761267 - 5.2887618116549007534e-193j)  +/-  (5.51e-27, 4.13e-56j)
| (0.26435000551464918648 + 4.6834740939496521032e-193j)  +/-  (2.75e-27, 2e-56j)
| (0.22711592136394294911 + 2.4511499757418045346e-193j)  +/-  (2.47e-27, 1.93e-56j)
| (0.0078789230148147108598 + 1.0012330504667593892e-193j)  +/-  (2.05e-28, 1.42e-57j)
