  We use the exact determinantal representation derived by Kitanine, Maillet,
and Terras for matrix elements of local spin operators between Bethe wave
functions of the one-dimensional s=1/2 Heisenberg model to calculate and
numerically evaluate transition rates pertaining to dynamic spin structure
factors. For real solutions z_1,...,z_r of the Bethe ansatz equations, the size
of the determinants is of order r x r. We present applications to the
zero-temperature spin fluctuations parallel and perpendicular to an external
magnetic field.
