  We prove that any odd-dimensional modular category of rank at most 23 is
pointed. We also show that an odd-dimensional modular category of rank 25 is
either pointed, perfect, or equivalent to $\operatorname{Rep}(D^\omega(\mathbb
Z_7\rtimes \mathbb Z_3))$. Finally, we give partial classification results for
modular categories of rank up to 73.
