  Let $M$ be a 1-cusped hyperbolic 3-manifold. In this paper, we investigate
the behavior of the number $N_M(v)$ of Dehn fillings of $M$ with a given volume
$v$. Our study focuses on 236 manifolds with cusp shapes characterized by
rational real parts. We establish necessary conditions for Dehn fillings that
share the same complex volume or exhibit conjugate complex volume differences.
Additionally, we demonstrate the transcendental nature of the Neumann-Zagier
volume formula, proving that the growth of $N_M$ is slower than any power of
its filling coefficient.
