  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.
