q=499: E|S/q|^2=1.0000  E|S/q|^4=1.9994  E|S/q|^6=4.9941  median|S/q|=0.8062  max=1.999997  median |Im|/|S|=0.0000
q=1009: E|S/q|^2=1.0000  E|S/q|^4=1.9984  E|S/q|^6=4.9917  median|S/q|=0.8088  max=1.999993  median |Im|/|S|=0.0000
q=499: E(S/q)^8=7.068 (Catalan 14); frac S>0=0.5006; max|Im S|/q=2.00e+00; KS distance to semicircle=0.2495 (n=248003)
q=1009: E(S/q)^8=6.988 (Catalan 14); frac S>0=0.5023; max|Im S|/q=2.00e+00; KS distance to semicircle=0.2500 (n=1016063)
