  Let $\mathcal{I} \subset \mathbb{N}$ be an infinite subset, and let
$\{a_i\}_{i \in \mathcal{I}}$ be a sequence of nonzero real numbers indexed by
$\mathcal{I}$ such that there exist positive constants $m, C_1$ for which
$|a_i| \leq C_1 \cdot i^m$ for all $i \in \mathcal{I}$. Furthermore, let $c_i
\in [-1,1]$ be defined by $c_i = \frac{a_i}{C_1 \cdot i^m}$ for each $i \in
\mathcal{I}$, and suppose the $c_i$'s are equidistributed in $[-1,1]$ with
respect to a continuous, symmetric probability measure $\mu$. In this paper, we
show that if $\mathcal{I} \subset \mathbb{N}$ is not too sparse, then the
sequence $\{a_i\}_{i \in \mathcal{I}}$ fails to obey Benford's Law with respect
to arithmetic density in any sufficiently large base, and in fact in any base
when $\mu([0,t])$ is a strictly convex function of $t \in (0,1)$. Nonetheless,
we also provide conditions on the density of $\mathcal{I} \subset \mathbb{N}$
under which the sequence $\{a_i\}_{i \in \mathcal{I}}$ satisfies Benford's Law
with respect to logarithmic density in every base.
  As an application, we apply our general result to study Benford's Law-type
behavior in the leading digits of Frobenius traces of newforms of positive,
even weight. Our methods of proof build on the work of Jameson, Thorner, and
Ye, who studied the particular case of newforms without complex multiplication.
