Starting with polynomial:
P : 128*t^7 - 1344*t^5 + 3360*t^3 - 1680*t
Extension levels are: 7 20
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Trying to find an order 20 Kronrod extension for:
P1 : 128*t^7 - 1344*t^5 + 3360*t^3 - 1680*t
Solvable: 1
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Ending with final polynomial:
P : 128*t^27 - 41647629984/2190911*t^25 + 2636051101800/2190911*t^23 - 655811201358300/15336377*t^21 + 2074360911914250/2190911*t^19 - 30017405619954675/2190911*t^17 + 289699766277482025/2190911*t^15 - 3735739069226884125/4381822*t^13 + 31703548135043932875/8763644*t^11 - 21384282980847661875/2190911*t^9 + 1103512337933439344625/70109152*t^7 - 1910682259733299177125/140218304*t^5 + 1454477359576101485625/280436608*t^3 - 306293411468461291875/560873216*t
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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
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The nodes are:
| (6.0479050551295344256 - 7.6139330197725818676e-444j)  +/-  (1.15e-122, 1.15e-122j)
| (4.1011264629678223173 - 7.8309034121327158949e-443j)  +/-  (2.6e-121, 2.6e-121j)
| (-4.6671832216386021894 + 3.7735945612039458003e-441j)  +/-  (1.73e-121, 1.73e-121j)
| (-4.1011264629678223173 - 2.4237324485699943983e-451j)  +/-  (2.78e-121, 2.78e-121j)
| (-2.5169069006495475843 - 2.2418482463713543111e-460j)  +/-  (3.99e-121, 3.99e-121j)
| (0.40445396064207384215 - 1.2811971213788401288e-475j)  +/-  (2.64e-126, 2.64e-126j)
| (5.2959173196379115019 + 4.4524766687386015536e-473j)  +/-  (6.77e-122, 6.77e-122j)
| (-1.673551628767471445 + 2.4043771981460916956e-471j)  +/-  (3.91e-123, 3.91e-123j)
| (-5.2959173196379115019 - 2.0258750418210985746e-472j)  +/-  (6.48e-122, 6.48e-122j)
| (4.6671832216386021894 + 1.30312017633700167e-474j)  +/-  (1.89e-121, 1.89e-121j)
| (2.6519613568352334924 - 3.9091919731700542392e-473j)  +/-  (5.81e-121, 5.81e-121j)
| (-6.0479050551295344256 - 2.6850542426434184628e-477j)  +/-  (1.15e-122, 1.15e-122j)
| (-2.6519613568352334924 - 4.4992353284050425751e-480j)  +/-  (5.53e-121, 5.53e-121j)
| (-9.9975568291597976219e-493 - 9.7175740995452201693e-492j)  +/-  (2.64e-490, 2.64e-490j)
| (1.673551628767471445 + 2.6637991571914775352e-491j)  +/-  (3.95e-123, 3.95e-123j)
| (3.0798419631345802719 + 4.3766286632573509957e-490j)  +/-  (3.61e-121, 3.61e-121j)
| (1.2391687433279459505 - 5.1190678875105695672e-495j)  +/-  (3.89e-124, 3.89e-124j)
| (-0.81628788285896466304 + 9.8681127589612772243e-494j)  +/-  (3.43e-125, 3.43e-125j)
| (3.5751675719887767181 - 2.7239187364614570087e-492j)  +/-  (3.17e-121, 3.17e-121j)
| (-3.0798419631345802719 - 5.3521926877206739458e-492j)  +/-  (3.46e-121, 3.46e-121j)
| (-0.40445396064207384215 + 1.6965396934464091093e-501j)  +/-  (2.64e-126, 2.64e-126j)
| (2.5169069006495475843 - 5.2385626146760421594e-496j)  +/-  (3.85e-121, 3.85e-121j)
| (-2.1173182181845577955 + 5.4312016532457983995e-497j)  +/-  (3.7e-122, 3.7e-122j)
| (-3.5751675719887767181 - 3.9386062581950648466e-504j)  +/-  (3.66e-121, 3.66e-121j)
| (-1.2391687433279459505 - 1.8348091934107763435e-508j)  +/-  (4.04e-124, 4.04e-124j)
| (2.1173182181845577955 - 2.6088124914095687622e-507j)  +/-  (3.33e-122, 3.33e-122j)
| (0.81628788285896466304 - 4.9487558643986186121e-511j)  +/-  (3.46e-125, 3.46e-125j)
-------------------------------------------------
The weights are:
| (6.3508929056755576049e-17 + 2.1370429616169093472e-455j)  +/-  (1.05e-47, 1.93e-107j)
| (1.5211932191571769754e-08 + 5.1494795113113422071e-450j)  +/-  (2.01e-43, 3.69e-103j)
| (1.1579724106364961183e-10 + 2.3876860097712259488e-450j)  +/-  (7.18e-46, 1.32e-105j)
| (1.5211932191571769754e-08 - 1.4653965003885060148e-449j)  +/-  (1.28e-44, 2.36e-104j)
| (0.00023112896829255611227 - 1.4164278549410085468e-446j)  +/-  (2.02e-40, 3.71e-100j)
| (0.19505668069615854297 + 2.2700839483506255172e-446j)  +/-  (1.39e-37, 2.55e-97j)
| (2.5088428225441960657e-13 - 2.8073352512091391714e-453j)  +/-  (1.37e-47, 2.52e-107j)
| (0.015077371440022784028 - 1.364807832543941121e-446j)  +/-  (1.37e-37, 2.52e-97j)
| (2.5088428225441960657e-13 + 2.0545634899450918639e-452j)  +/-  (5.72e-48, 1.05e-107j)
| (1.1579724106364961183e-10 + 1.5658644465715644978e-451j)  +/-  (1.66e-46, 3.05e-106j)
| (0.00013548201932480794815 + 8.0179011663735354302e-448j)  +/-  (3.24e-43, 5.95e-103j)
| (6.3508929056755576049e-17 - 9.4817543259145701256e-455j)  +/-  (3.03e-50, 5.57e-110j)
| (0.00013548201932480794815 + 9.8946738175771000757e-447j)  +/-  (2.1e-42, 3.85e-102j)
| (0.22739211457097574536 - 2.8214524809139302738e-446j)  +/-  (1.14e-39, 2.09e-99j)
| (0.015077371440022784028 - 4.3727070014111806358e-447j)  +/-  (2.13e-41, 3.91e-101j)
| (2.0556078807406430869e-05 + 1.42097727538536048e-449j)  +/-  (1.58e-44, 2.9e-104j)
| (0.052086648283233455594 + 8.6573797457877445874e-447j)  +/-  (9.84e-41, 1.81e-100j)
| (0.12085544844482172293 - 2.5210679100949071431e-446j)  +/-  (8.65e-41, 1.59e-100j)
| (8.0886563430968495738e-07 - 1.7014971643243270452e-449j)  +/-  (1.6e-45, 2.94e-105j)
| (2.0556078807406430869e-05 - 8.5399763323245183801e-448j)  +/-  (2.13e-45, 3.89e-105j)
| (0.19505668069615854297 + 2.9040498096578808955e-446j)  +/-  (1.34e-41, 2.45e-101j)
| (0.00023112896829255611227 - 1.5786610421364372459e-447j)  +/-  (7.44e-44, 1.37e-103j)
| (0.0028398025902361611888 + 1.0675668156206001729e-446j)  +/-  (6.41e-44, 1.17e-103j)
| (8.0886563430968495738e-07 + 1.0243183652800205853e-448j)  +/-  (1.15e-46, 2.1e-106j)
| (0.052086648283233455594 + 1.9184775732737004367e-446j)  +/-  (2.56e-43, 4.66e-103j)
| (0.0028398025902361611888 + 2.1887127143279931528e-447j)  +/-  (1.13e-44, 2.23e-104j)
| (0.12085544844482172293 - 1.5194095491093322672e-446j)  +/-  (1.32e-43, 2.2e-103j)
