  Let $M_{\tau_0}$ be the Grauert tube (of some fixed radius $\tau_0$) of a
compact, negatively curved, real analytic Riemannian manifold $M$ without
boundary. Let $\phi_\lambda$ be a Laplacian eigenfunction on $M$ of eigenvalues
$-\lambda^2$ and let $\phi_\lambda^\mathbb{C}$ be its holomorphic extension to
$M_{\tau_0}$. In this article, we prove that on $M_{\tau_0} \setminus M$, there
exists a dimensional constant $\alpha > 0$ and a full density subsequence $
\{\lambda_{j_k}\}_{k=1}^{\infty}$ of the spectrum for which the masses of the
complexified eigenfunctions $\phi_{\lambda_{j_k}}^\mathbb{C}$ are
asymptotically equidistributed at length scale $(\log
\lambda_{j_k})^{-\alpha}$. Moreover, the complex zeros of
$\phi_{\lambda_{j_k}}^\mathbb{C}$ also become equidistributed on this
logarithmic length scale.
