We measure the neutral D total forward cross section and the differential cross sections as function of Feynman-x ($x_F$) and transverse momentum squared for 500 GeV/c $\pi^-$-nucleon interactions. The results are obtained from 88990+-460 reconstructed neutral D mesons from Fermilab experiment E791 using the decay channels $D\to K^-\pi^+$ and $D\to K^-\pi^+\pi^-\pi^+$ (and charge conjugates). We extract fit parameters from the differential cross sections and provide the first direct measurement of the turnover point in the $x_F$ distribution, 0.0131+-0.0038. We measure an absolute $D^0 + \bar{D^0}$ ($x_F > 0$) cross section of 15.4+1.8-2.3 microbarns/nucleon (assuming a linear A dependence). The differential and total forward cross sections are compared to theoretical predictions and to results of previous experiments.
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