Starting with polynomial:
P : 2*t^2 - 1
Extension levels are: 2 31
-------------------------------------------------
Trying to find an order 31 Kronrod extension for:
P1 : 2*t^2 - 1
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 2*t^33 - 17*t^31 + 263/4*t^29 - 1225/8*t^27 + 15327/64*t^25 - 33995/128*t^23 + 110055/512*t^21 - 131813/1024*t^19 + 937365/16384*t^17 - 614669/32768*t^15 + 585599/131072*t^13 - 197353/262144*t^11 + 180557/2097152*t^9 - 26265/4194304*t^7 + 4369/16777216*t^5 - 171/33554432*t^3 + 1/33554432*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:
| (0.98078528040323044913 + 4.1707716999968017298e-433j)  +/-  (3.63e-116, 3.63e-116j)
| (-4.0668246421548017081e-449 + 6.5867694398344402397e-448j)  +/-  (2.18e-446, 2.18e-446j)
| (-0.92387953251128675613 - 1.0647218108621864604e-431j)  +/-  (1.05e-116, 1.05e-116j)
| (-0.98078528040323044913 + 8.4438621828809810488e-436j)  +/-  (3.46e-116, 3.46e-116j)
| (0.92387953251128675613 - 4.397344824487869986e-451j)  +/-  (9.25e-117, 9.25e-117j)
| (0.95694033573220886494 + 2.0238106591912846197e-450j)  +/-  (2.44e-116, 2.44e-116j)
| (-0.99518472667219688624 + 1.3169802973571104295e-451j)  +/-  (4.79e-116, 4.79e-116j)
| (-0.88192126434835502971 + 8.5419541809185657133e-468j)  +/-  (2.89e-117, 2.89e-117j)
| (-1 + 7.0445939289814631242e-466j)  +/-  (3.45e-116, 3.45e-116j)
| (1 + 1.3910139474023078213e-468j)  +/-  (3.25e-116, 3.25e-116j)
| (0.88192126434835502971 - 4.4852143524644807541e-480j)  +/-  (3.23e-117, 3.23e-117j)
| (0.99518472667219688624 + 5.6456927171513551583e-483j)  +/-  (5.7e-116, 5.7e-116j)
| (-0.95694033573220886494 - 1.8651410881391020363e-486j)  +/-  (1.96e-116, 1.96e-116j)
| (-0.83146961230254523708 + 6.2705505460221026528e-494j)  +/-  (1.09e-117, 1.09e-117j)
| (-0.29028467725446236764 + 1.1353993299738517063e-503j)  +/-  (1.82e-124, 1.82e-124j)
| (0.77301045336273696081 + 1.3764441276712855016e-493j)  +/-  (1.84e-118, 1.84e-118j)
| (0.83146961230254523708 + 6.1956958612721423574e-496j)  +/-  (9.99e-118, 9.99e-118j)
| (-0.38268343236508977173 + 6.3023854316949521368e-502j)  +/-  (4.17e-123, 4.17e-123j)
| (-0.77301045336273696081 - 2.8138095967211497693e-497j)  +/-  (2.08e-118, 2.08e-118j)
| (-0.7071067811865475244 - 2.162281528918182514e-498j)  +/-  (3.33e-119, 3.33e-119j)
| (0.47139673682599764856 + 4.4797727748477701945e-502j)  +/-  (5.61e-122, 5.61e-122j)
| (0.7071067811865475244 + 1.1864032540849828778e-499j)  +/-  (4.25e-119, 4.25e-119j)
| (0.19509032201612826785 + 5.9576298513108707558e-508j)  +/-  (1.46e-125, 1.46e-125j)
| (-0.55557023301960222474 + 4.3952919214980133942e-501j)  +/-  (6.45e-121, 6.45e-121j)
| (-0.47139673682599764856 + 1.549273102074004737e-502j)  +/-  (5.45e-122, 5.45e-122j)
| (0.098017140329560601994 + 2.4268267797535717328e-508j)  +/-  (5.47e-127, 5.47e-127j)
| (0.63439328416364549822 - 2.6938791533913652299e-501j)  +/-  (5.89e-120, 5.89e-120j)
| (0.38268343236508977173 - 3.3290295317715633291e-504j)  +/-  (4.29e-123, 4.29e-123j)
| (-0.19509032201612826785 + 1.3485539877016279547e-506j)  +/-  (1.13e-125, 1.13e-125j)
| (-0.63439328416364549822 - 2.1939848002089285807e-503j)  +/-  (6.26e-120, 6.26e-120j)
| (-0.098017140329560601994 - 2.8489119709685759422e-511j)  +/-  (6.22e-127, 6.22e-127j)
| (0.29028467725446236764 - 3.127235226446709034e-508j)  +/-  (2.01e-124, 2.01e-124j)
| (0.55557023301960222474 + 2.3758828461360835546e-505j)  +/-  (6.19e-121, 6.19e-121j)
-------------------------------------------------
The weights are:
| (0.03125 - 6.7422586778807729807e-435j)  +/-  (2e-20, 1.71e-75j)
| (0.03125 - 3.7340165942763073251e-433j)  +/-  (1.19e-20, 1.01e-75j)
| (0.03125 + 1.0431442590665119122e-432j)  +/-  (3.16e-21, 2.69e-76j)
| (0.03125 + 5.8399743526122722862e-432j)  +/-  (2.3e-21, 1.96e-76j)
| (0.03125 - 4.0909538115084502662e-433j)  +/-  (8.29e-22, 7.07e-77j)
| (0.03125 + 7.2349153924786054675e-433j)  +/-  (1.31e-21, 1.12e-76j)
| (0.03125 - 4.6577892068213625515e-432j)  +/-  (3.18e-22, 2.71e-77j)
| (0.03125 + 7.936646829054973879e-432j)  +/-  (2.25e-23, 1.92e-78j)
| (0.015625 + 2.1815430613466966231e-432j)  +/-  (1.94e-22, 1.65e-77j)
| (0.015625 + 2.5269235919605354171e-433j)  +/-  (3.22e-24, 2.75e-79j)
| (0.03125 + 3.160738138598375068e-433j)  +/-  (1.52e-25, 1.29e-80j)
| (0.03125 - 7.3178448204023726334e-433j)  +/-  (5.37e-24, 4.57e-79j)
| (0.03125 - 1.0058430017264319066e-431j)  +/-  (8.78e-25, 7.48e-80j)
| (0.03125 - 3.6075547164999463083e-432j)  +/-  (1.96e-26, 1.67e-81j)
| (0.03125 + 5.3535518354673354762e-433j)  +/-  (1.17e-28, 9.98e-84j)
| (0.03125 + 2.5879433073054111909e-433j)  +/-  (5.76e-28, 4.91e-83j)
| (0.03125 - 2.7682425662665215576e-433j)  +/-  (3.21e-27, 2.73e-82j)
| (0.03125 - 6.243117562505432404e-433j)  +/-  (3.18e-29, 2.71e-84j)
| (0.03125 + 2.2126973895124342022e-432j)  +/-  (2.11e-28, 1.8e-83j)
| (0.03125 - 1.5425303764710972926e-432j)  +/-  (3.32e-29, 2.83e-84j)
| (0.03125 + 2.6403442959235530307e-433j)  +/-  (2.24e-31, 1.91e-86j)
| (0.03125 - 2.5161102679157713944e-433j)  +/-  (3.43e-30, 2.92e-85j)
| (0.03125 - 3.1391615667842632736e-433j)  +/-  (1.03e-31, 8.77e-87j)
| (0.03125 - 9.1180771178483773592e-433j)  +/-  (9.52e-31, 8.11e-86j)
| (0.03125 + 7.4425650017229081898e-433j)  +/-  (7.67e-31, 6.54e-86j)
| (0.03125 + 3.4033617065855193695e-433j)  +/-  (4.39e-32, 3.74e-87j)
| (0.03125 + 2.5113260031149537145e-433j)  +/-  (2.53e-32, 2.15e-87j)
| (0.03125 - 2.7642947951756864333e-433j)  +/-  (7.32e-33, 6.24e-88j)
| (0.03125 - 4.6759631396010516666e-433j)  +/-  (6.99e-33, 5.96e-88j)
| (0.03125 + 1.1573590144728057621e-432j)  +/-  (7.41e-33, 6.31e-88j)
| (0.03125 + 4.1493428426339839889e-433j)  +/-  (4.93e-33, 4.2e-88j)
| (0.03125 + 2.9289162070264048797e-433j)  +/-  (1.31e-33, 1.13e-88j)
| (0.03125 - 2.5553293838442382135e-433j)  +/-  (9.98e-34, 8.31e-89j)
