  We give a holomorphic quartic polynomial in the overlap variables whose zeros
on the torus are precisely the Weyl-Heisenberg SICs (symmetric informationally
complete positive operator valued measures). By way of comparison, all the
other known systems of equations that determine a Weyl-Heisenberg SIC involve
variables and their complex conjugates. We also give a related interesting
result about the powers of the projective Fourier transform of the group G = Z
d x Z d .
