  We compute all dynamical spin-spin correlation functions for the spin-1/2
$XXZ$ anisotropic Heisenberg model in the gapless antiferromagnetic regime,
using numerical sums of exact determinant representations for form factors of
spin operators on the lattice. Contributions from intermediate states
containing many particles and string (bound) states are included. We present
modified determinant representations for the form factors valid in the general
case with string solutions to the Bethe equations. Our results are such that
the available sum rules are saturated to high precision. We Fourier transform
our results back to real space, allowing us in particular to make a comparison
with known exact formulas for equal-time correlation functions for small
separations in zero field, and with predictions for the zero-field asymptotics
from conformal field theory.
