  We give an effective algorithm to compute the Euler characteristics
$\chi(\mbar_{1,n}, \otimes_{i=1}^n L_i^{d_i})$. In addition, we give a simple
proof of Pandharipande's vanishing theorem $H^j (\mbar_{0,n}, \otimes_{i=1}^n
L_i^{d_i})=0$ for $j \ge 1, d_i \ge0$.
