Starting with polynomial:
P : t
Extension levels are: 1 6 28
-------------------------------------------------
Trying to find an order 6 Kronrod extension for:
P1 : t
Solvable: 1
-------------------------------------------------
Trying to find an order 28 Kronrod extension for:
P2 : t^7 - 7/4*t^5 + 7/8*t^3 - 7/64*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^35 - 35/4*t^33 + 35*t^31 - 5425/64*t^29 + 35525/256*t^27 - 166257/1024*t^25 + 143325/1024*t^23 - 740025/8192*t^21 + 2877875/65536*t^19 - 4206125/262144*t^17 + 572033/131072*t^15 - 1820105/2097152*t^13 + 1028755/8388608*t^11 - 395675/33554432*t^9 + 24225/33554432*t^7 - 6783/268435456*t^5 + 1785/4294967296*t^3 - 35/17179869184*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: 0
  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:   35 out of 35
Indefinite weights: 0 out of 35
Negative weights:   0 out of 35
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (-0.97492791218182360702 - 3.7570419743504820785e-413j)  +/-  (5.34e-116, 5.34e-116j)
| (-0.99899306654131464737 - 6.7568209685295457464e-415j)  +/-  (1.85e-116, 1.85e-116j)
| (-0.95105651629515357212 - 5.0000217565316352164e-415j)  +/-  (4.19e-116, 4.19e-116j)
| (0.99094976176793475525 - 2.2961682838691355337e-412j)  +/-  (5.89e-116, 5.89e-116j)
| (0.88059553185673799519 - 4.8414045628467961409e-422j)  +/-  (1.19e-116, 1.19e-116j)
| (0.91952777255145063832 - 1.5168039966215040009e-422j)  +/-  (2.69e-116, 2.69e-116j)
| (0.99899306654131464737 - 1.6473454724537886337e-430j)  +/-  (2.34e-116, 2.34e-116j)
| (-0.83457325372130265093 + 1.2780964189898579933e-443j)  +/-  (3.72e-117, 3.72e-117j)
| (-0.089639308903433499765 + 7.8031496157639793499e-453j)  +/-  (6.65e-127, 6.65e-127j)
| (0.95105651629515357212 + 7.6321302272607227051e-441j)  +/-  (4.51e-116, 4.51e-116j)
| (0.83457325372130265093 + 5.1458054787709688634e-453j)  +/-  (3.97e-117, 3.97e-117j)
| (0.97492791218182360702 - 2.90952569061695203e-455j)  +/-  (4.95e-116, 4.95e-116j)
| (-0.91952777255145063832 - 3.0483355431562258415e-467j)  +/-  (2.32e-116, 2.32e-116j)
| (-0.88059553185673799519 + 6.5411620818421231509e-469j)  +/-  (1.25e-116, 1.25e-116j)
| (-0.78183148246802980871 - 5.5670838002500240428e-470j)  +/-  (1.07e-117, 1.07e-117j)
| (0.78183148246802980871 + 1.4347395218805545459e-471j)  +/-  (1.07e-117, 1.07e-117j)
| (0.65793872593971261237 - 2.3073709611937654419e-473j)  +/-  (4.04e-119, 4.04e-119j)
| (-0.35137482408134270489 + 1.3954336383174611929e-477j)  +/-  (3.51e-123, 3.51e-123j)
| (-0.72279486382739152855 - 1.0636036515100985972e-471j)  +/-  (2.14e-118, 2.14e-118j)
| (-0.99094976176793475525 - 2.9847474728606720843e-476j)  +/-  (4.73e-116, 4.73e-116j)
| (0.43388373911755812048 - 1.0323153566290380713e-481j)  +/-  (4.7e-122, 4.7e-122j)
| (0.72279486382739152855 - 4.6838327529221274373e-480j)  +/-  (2.02e-118, 2.02e-118j)
| (0.17855689479863664801 + 2.1541861802885391508e-488j)  +/-  (1.04e-125, 1.04e-125j)
| (-0.65793872593971261237 - 1.0133145198182124155e-482j)  +/-  (3.6e-119, 3.6e-119j)
| (-0.51289927740590614391 - 9.2506425351705593073e-485j)  +/-  (5.99e-121, 5.99e-121j)
| (0.089639308903433499765 + 3.6415864004151567135e-490j)  +/-  (5.31e-127, 5.31e-127j)
| (0.58778525229247312917 - 1.2778516010301435898e-482j)  +/-  (5.59e-120, 5.59e-120j)
| (0.35137482408134270489 - 1.1821563665746886166e-486j)  +/-  (3.38e-123, 3.38e-123j)
| (-0.17855689479863664801 - 5.8568190309543338984e-490j)  +/-  (9.49e-126, 9.49e-126j)
| (-0.58778525229247312917 - 1.2858548410910400243e-485j)  +/-  (5.38e-120, 5.38e-120j)
| (-0.26603684556667510738 - 1.1395017809868730238e-489j)  +/-  (2.04e-124, 2.04e-124j)
| (0.26603684556667510738 - 3.5084161644233962138e-488j)  +/-  (2.01e-124, 2.01e-124j)
| (0.51289927740590614391 - 3.7342492208191607864e-485j)  +/-  (6.27e-121, 6.27e-121j)
| (-1.894443428143757802e-496 + 7.6427969115664448019e-496j)  +/-  (2.76e-494, 2.76e-494j)
| (-0.43388373911755812048 + 8.6680268586072174746e-490j)  +/-  (4.95e-122, 4.95e-122j)
-------------------------------------------------
The weights are:
| (0.028571428571428571429 - 2.0509480294919336984e-413j)  +/-  (4.2e-19, 2.16e-73j)
| (0.028571428571428571429 + 3.0575943245135703044e-414j)  +/-  (1.31e-19, 6.73e-74j)
| (0.028571428571428571429 + 7.2926643062499228295e-413j)  +/-  (2.72e-19, 1.4e-73j)
| (0.028571428571428571429 + 1.8075541420430232243e-412j)  +/-  (5.45e-21, 2.8e-75j)
| (0.028571428571428571429 + 2.1119566478205784536e-412j)  +/-  (4.52e-21, 2.32e-75j)
| (0.028571428571428571429 - 2.7002441722711223367e-412j)  +/-  (4.39e-21, 2.26e-75j)
| (0.028571428571428571429 + 2.7249504377619719195e-412j)  +/-  (1.38e-21, 7.08e-76j)
| (0.028571428571428571429 - 3.4906320128738643971e-413j)  +/-  (6.21e-24, 3.19e-78j)
| (0.028571428571428571429 - 5.0891675359589740454e-413j)  +/-  (1.54e-24, 7.92e-79j)
| (0.028571428571428571429 + 3.7941540259960562058e-412j)  +/-  (8.37e-22, 4.3e-76j)
| (0.028571428571428571429 - 1.7376037776267592698e-412j)  +/-  (4.15e-23, 2.13e-77j)
| (0.028571428571428571429 - 6.793810343943269759e-412j)  +/-  (9.41e-22, 4.83e-76j)
| (0.028571428571428571429 - 4.5829130576732171361e-413j)  +/-  (2e-24, 1.03e-78j)
| (0.028571428571428571429 + 3.8018790402598395912e-413j)  +/-  (9.3e-25, 4.77e-79j)
| (0.028571428571428571429 + 3.3830282757783342961e-413j)  +/-  (6.56e-26, 3.37e-80j)
| (0.028571428571428571429 + 1.4756398866782704945e-412j)  +/-  (7.39e-26, 3.79e-80j)
| (0.028571428571428571429 + 1.1292184554953783345e-412j)  +/-  (2.84e-27, 1.46e-81j)
| (0.028571428571428571429 + 4.1880987040742755896e-413j)  +/-  (6.95e-29, 3.57e-83j)
| (0.028571428571428571429 - 3.3866787026853785711e-413j)  +/-  (2.78e-27, 1.42e-81j)
| (0.028571428571428571429 - 2.9769219144979740033e-413j)  +/-  (8.1e-26, 4.16e-80j)
| (0.028571428571428571429 - 8.2371320259857150761e-413j)  +/-  (2.13e-29, 1.09e-83j)
| (0.028571428571428571429 - 1.2806985887050266573e-412j)  +/-  (2.71e-27, 1.39e-81j)
| (0.028571428571428571429 + 6.3627597018862213593e-413j)  +/-  (4.15e-30, 2.13e-84j)
| (0.028571428571428571429 + 3.461307732396152111e-413j)  +/-  (3.94e-29, 2.02e-83j)
| (0.028571428571428571429 + 3.7531129683509621766e-413j)  +/-  (4.07e-30, 2.09e-84j)
| (0.028571428571428571429 - 5.8869502624671969222e-413j)  +/-  (9.53e-31, 4.89e-85j)
| (0.028571428571428571429 - 1.0076578387864397293e-412j)  +/-  (5.04e-30, 2.59e-84j)
| (0.028571428571428571429 + 7.5213640197596925105e-413j)  +/-  (7.28e-31, 3.74e-85j)
| (0.028571428571428571429 + 4.7535751483177755932e-413j)  +/-  (1.12e-31, 5.73e-86j)
| (0.028571428571428571429 - 3.5869555247389312511e-413j)  +/-  (2.41e-31, 1.24e-85j)
| (0.028571428571428571429 - 4.4541100913547054585e-413j)  +/-  (6.7e-32, 3.44e-86j)
| (0.028571428571428571429 - 6.9028999213283063971e-413j)  +/-  (3.8e-32, 1.96e-86j)
| (0.028571428571428571429 + 9.0764517449225634058e-413j)  +/-  (4.16e-32, 2.14e-86j)
| (0.028571428571428571429 + 5.4650269827755422617e-413j)  +/-  (1.96e-32, 1.02e-86j)
| (0.028571428571428571429 - 3.9543077227930506009e-413j)  +/-  (1.31e-32, 6.5e-87j)
