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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 = ½ Heisenberg model to calculate and numerically evaluate transition rates pertaining to dynamic spin structure factors. For real solutions z1,..., zr of the Bethe ansatz equations, the size of the determinants is of order rxr. We present applications to the zero-temperature spin fluctuations parallel and perpendicular to an external magnetic field.