  We calculate line shapes of correlation functions by use of complete
diagonalization data of finite chains and analytical implications from
conformal field theory, density of states, and Bethe ansatz. The numerical data
have different finite size accuracy in case of the imaginary and real parts in
the frequency and time representations of spin-correlation functions,
respectively. The low temperature, conformally invariant regime crosses over at
$T^*\approx 0.7J$ to a diffusive regime that in turn connects continuously to
the high temperature, interacting fermion regime. The first moment sum rule is
determined.
