Starting with polynomial:
P : 128*t^8 - 256*t^6 + 160*t^4 - 32*t^2 + 1
Extension levels are: 8 32
-------------------------------------------------
Trying to find an order 32 Kronrod extension for:
P1 : 128*t^8 - 256*t^6 + 160*t^4 - 32*t^2 + 1
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 128*t^40 - 1280*t^38 + 5920*t^36 - 16800*t^34 + 32725*t^32 - 46376*t^30 + 49445*t^28 - 40455*t^26 + 13147875/512*t^24 - 3251625/256*t^22 + 10015005/2048*t^20 - 2982525/2048*t^18 + 21729825/65536*t^16 - 928625/16384*t^14 + 928625/131072*t^12 - 81719/131072*t^10 + 1225785/33554432*t^8 - 21945/16777216*t^6 + 3325/134217728*t^4 - 25/134217728*t^2 + 1/4294967296
-------------------------------------------------
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:   40 out of 40
Indefinite weights: 0 out of 40
Negative weights:   0 out of 40
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (-0.99922903624072293474 - 2.0093346212571726571e-430j)  +/-  (1.78e-114, 1.78e-114j)
| (-0.93819133592248413445 - 2.5707514321970186544e-431j)  +/-  (2.4e-114, 2.4e-114j)
| (-0.90814317382508129926 + 3.5253127535882814247e-433j)  +/-  (1.25e-114, 1.25e-114j)
| (0.96245523645364728763 + 5.3456374932505038862e-432j)  +/-  (3.79e-114, 3.79e-114j)
| (0.90814317382508129926 - 1.4669861126416898556e-437j)  +/-  (1.34e-114, 1.34e-114j)
| (0.99922903624072293474 - 1.8651682037474896325e-443j)  +/-  (1.95e-114, 1.95e-114j)
| (-0.99306845695492629564 - 2.4782747252331259201e-455j)  +/-  (4.1e-114, 4.1e-114j)
| (-0.87249600707279711453 - 2.2783580874732036972e-461j)  +/-  (4.71e-115, 4.71e-115j)
| (-0.96245523645364728763 + 1.818634455660839831e-460j)  +/-  (3.34e-114, 3.34e-114j)
| (0.98078528040323044913 + 3.7591638540303554069e-463j)  +/-  (4.69e-114, 4.69e-114j)
| (0.87249600707279711453 - 7.5949435297300277214e-475j)  +/-  (4.86e-115, 4.86e-115j)
| (-0.11753739745783764411 - 1.5634835400622463602e-490j)  +/-  (2.36e-126, 2.36e-126j)
| (-0.98078528040323044913 - 3.0361963136803182982e-478j)  +/-  (4.91e-114, 4.91e-114j)
| (-0.83146961230254523708 + 4.470162617986363131e-480j)  +/-  (1.43e-115, 1.43e-115j)
| (0.48862124149695494742 + 1.3196217494709612238e-484j)  +/-  (2.84e-120, 2.84e-120j)
| (0.83146961230254523708 + 3.2404335092728900762e-479j)  +/-  (1.69e-115, 1.69e-115j)
| (0.19509032201612826785 + 2.3831784312829603133e-491j)  +/-  (5.18e-125, 5.18e-125j)
| (0.99306845695492629564 + 6.6706005168959760842e-480j)  +/-  (4.45e-114, 4.45e-114j)
| (-0.78531693088074492747 - 6.031734318298352032e-491j)  +/-  (3.67e-116, 3.67e-116j)
| (-0.19509032201612826785 + 5.5518896422437380294e-500j)  +/-  (5.12e-125, 5.12e-125j)
| (0.27144044986507425334 + 1.8942282397488494974e-499j)  +/-  (9.72e-124, 9.72e-124j)
| (0.73432250943568553564 + 3.0194949383176623856e-489j)  +/-  (9.58e-117, 9.58e-117j)
| (0.93819133592248413445 - 1.0228675091609365234e-491j)  +/-  (2.18e-114, 2.18e-114j)
| (-0.73432250943568553564 - 9.6539806986778484461e-493j)  +/-  (1.09e-116, 1.09e-116j)
| (-0.67880074553294174139 + 1.4270856519144705993e-494j)  +/-  (1.64e-117, 1.64e-117j)
| (-0.039259815759068609021 - 1.0595245519505042004e-504j)  +/-  (1.36e-127, 1.36e-127j)
| (0.67880074553294174139 + 1.2686952764454011784e-494j)  +/-  (1.63e-117, 1.63e-117j)
| (0.78531693088074492747 + 1.2300909096291814692e-497j)  +/-  (3.97e-116, 3.97e-116j)
| (-0.41865973753742808668 - 3.3956636938559840103e-503j)  +/-  (2.1e-121, 2.1e-121j)
| (-0.61909394930983398694 + 6.1645998966151519828e-499j)  +/-  (2.32e-118, 2.32e-118j)
| (-0.27144044986507425334 - 1.4493261170703282596e-504j)  +/-  (1.34e-123, 1.34e-123j)
| (0.34611705707749297647 - 1.7181737319160114119e-503j)  +/-  (1.37e-122, 1.37e-122j)
| (0.61909394930983398694 + 2.864492426919418296e-500j)  +/-  (2.3e-118, 2.3e-118j)
| (0.039259815759068609021 + 2.6727991548421161374e-509j)  +/-  (1.36e-127, 1.36e-127j)
| (-0.55557023301960222474 - 1.7935547935465680426e-502j)  +/-  (2.48e-119, 2.48e-119j)
| (-0.48862124149695494742 + 5.0163675989205552557e-503j)  +/-  (3.14e-120, 3.14e-120j)
| (0.11753739745783764411 - 6.1398193917515909035e-509j)  +/-  (1.84e-126, 1.84e-126j)
| (0.55557023301960222474 - 5.066334955728911047e-504j)  +/-  (3.16e-119, 3.16e-119j)
| (0.41865973753742808668 - 8.0130523098327533407e-506j)  +/-  (2.29e-121, 2.29e-121j)
| (-0.34611705707749297647 + 1.0463652426814982159e-506j)  +/-  (1.4e-122, 1.4e-122j)
-------------------------------------------------
The weights are:
| (0.025 - 1.627092901923336694e-429j)  +/-  (9.25e-18, 9.21e-71j)
| (0.025 - 7.2791630806934368426e-430j)  +/-  (4.05e-18, 4.03e-71j)
| (0.025 + 6.1410859480799875486e-430j)  +/-  (2.54e-18, 2.53e-71j)
| (0.025 - 1.8845834339115122651e-431j)  +/-  (5.87e-20, 5.84e-73j)
| (0.025 - 3.2305752127108706273e-431j)  +/-  (3.99e-20, 3.98e-73j)
| (0.025 + 2.0260436117228456465e-432j)  +/-  (9.63e-21, 9.58e-74j)
| (0.025 + 2.4371962866481656531e-429j)  +/-  (1.42e-18, 1.41e-71j)
| (0.025 - 5.0754785832197131614e-430j)  +/-  (1.45e-19, 1.44e-72j)
| (0.025 + 9.2364401608526766929e-430j)  +/-  (4.95e-19, 4.93e-72j)
| (0.025 + 7.5578701821846053289e-432j)  +/-  (1.86e-21, 1.86e-74j)
| (0.025 + 3.6583170458804989027e-431j)  +/-  (4.73e-22, 4.71e-75j)
| (0.025 - 1.4684022252811861532e-430j)  +/-  (2.14e-23, 2.14e-76j)
| (0.025 - 1.3449011887536092897e-429j)  +/-  (4.87e-19, 4.85e-72j)
| (0.025 + 4.3370805768557954582e-430j)  +/-  (5.5e-21, 5.47e-74j)
| (0.025 - 7.7087480348069873889e-431j)  +/-  (1.95e-24, 1.95e-77j)
| (0.025 - 4.1507785871117074287e-431j)  +/-  (3.19e-23, 3.18e-76j)
| (0.025 - 1.0732951072566041266e-430j)  +/-  (8.37e-25, 8.34e-78j)
| (0.025 - 5.7725970985423650147e-432j)  +/-  (1.46e-22, 1.45e-75j)
| (0.025 - 3.7810998281548095812e-430j)  +/-  (3.52e-23, 3.51e-76j)
| (0.025 + 1.5895522770813003755e-430j)  +/-  (3.28e-25, 3.27e-78j)
| (0.025 + 9.9095548080055640637e-431j)  +/-  (2.93e-25, 2.92e-78j)
| (0.025 - 5.2328617654331242991e-431j)  +/-  (2.66e-25, 2.65e-78j)
| (0.025 + 3.0227805594668403486e-431j)  +/-  (2.42e-23, 2.41e-76j)
| (0.025 + 3.3432568660759274025e-430j)  +/-  (4.06e-25, 4.04e-78j)
| (0.025 - 2.9876867340390605005e-430j)  +/-  (5.37e-26, 5.34e-79j)
| (0.025 + 1.3576326243833528074e-430j)  +/-  (1.06e-26, 1.05e-79j)
| (0.025 + 5.81202252822953891e-431j)  +/-  (1.37e-26, 1.37e-79j)
| (0.025 + 4.6784140436100336795e-431j)  +/-  (1.44e-25, 1.43e-78j)
| (0.025 - 2.0375335709560434405e-430j)  +/-  (1.59e-28, 1.58e-81j)
| (0.025 + 2.6920426045661450641e-430j)  +/-  (1.09e-27, 1.09e-80j)
| (0.025 - 1.7230360468311622193e-430j)  +/-  (2.35e-28, 2.34e-81j)
| (0.025 - 9.1349673903186954476e-431j)  +/-  (4.66e-29, 4.65e-82j)
| (0.025 - 6.4163561061776668764e-431j)  +/-  (8.02e-29, 8e-82j)
| (0.025 - 1.255672512368029558e-430j)  +/-  (4.27e-29, 4.25e-82j)
| (0.025 - 2.4415006455425192164e-430j)  +/-  (2.6e-29, 2.58e-82j)
| (0.025 + 2.2257863740089668656e-430j)  +/-  (1.44e-29, 1.43e-82j)
| (0.025 + 1.1612436153326533819e-430j)  +/-  (6.65e-30, 6.72e-83j)
| (0.025 + 7.0476827695255838467e-431j)  +/-  (1.33e-30, 1.34e-83j)
| (0.025 + 8.4030775378028623071e-431j)  +/-  (1.22e-30, 1.25e-83j)
| (0.025 + 1.8713142842348758768e-430j)  +/-  (1.01e-30, 8.5e-84j)
