  We present a method for accurate evaluation of the Green function
$G(\omega,r_1,...,r_d)$ at any real frequency $\omega$ and any lattice vector
$(r_1,...,r_d)$ for a $d$-dimensional hypercubic lattice that may have
anisotropic couplings $(\Omega_1,...,\Omega_d)$. In this method, we start with
an integral representation of $G$, split the oscillatory integrand into
combinations of Hankel functions, and deform the integration paths into the
complex plane to obtain rapidly convergent integrals. We also discuss an
alternative approach using the Levin collocation method. We report values of
the Green function at selected frequencies on the branch cut and selected
lattice vectors.
