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=13.973 (Catalan 14); classes among |S|>0.2q: real=0.5008 imag=0.4992 other=0.0000
   real-class fraction | chi(-1)=+1: 0.5005; | chi(-1)=-1: 0.5011
   imag-class fraction | chi(-1)=+1: 0.4995; | chi(-1)=-1: 0.4989
q=1009: E|S/q|^8=13.968 (Catalan 14); classes among |S|>0.2q: real=0.5007 imag=0.4993 other=0.0000
   real-class fraction | chi(-1)=+1: 0.5015; | chi(-1)=-1: 0.4999
   imag-class fraction | chi(-1)=+1: 0.4985; | chi(-1)=-1: 0.5001
