  We present further results on a class of sums which involve complex powers of
the distance to points in a two-dimensional square lattice and trigonometric
functions of their angle, supplementing those in a previous paper (McPhedran et
al, Porc. Roy. Soc., 2008). We give a general expression which permits
numerical evaluation of members of the class of sums to arbitrary order. We use
this to illustrate numerically the properties of trajectories along which the
real and imaginary parts of the sums are zero, and we show results for the
first two of a particular set of angular sums which indicate their density of
zeros on the critical line of the complex exponent is the same as that for the
product of the Riemann zeta function and the Catalan beta function.
