  We associate to a unimodular lattice L, endowed with an automorphism of
square -1, a principally polarized abelian variety A:= L_R/L. We show that the
configuration of i-invariant theta divisors of A follows a pattern very similar
to the classical theory of theta characteristics; as a consequence we find that
A has a high number of vanishing thetanulls. When L = E_8 we recover the 10
vanishing thetanulls of the abelian fourfold discovered by R. Varley.
