So's spectral characterization conjecture for integral circulant graphs

Let $n\in\mathbb{N}$, and let $S,T\subseteq\mathbb{Z}_n$ be integral symbols, so that $\Gamma_S=Cay(\mathbb{Z}_n,S)$ and $\Gamma_T=Cay(\mathbb{Z}_n,T)$ are integral circulant graphs. Write $sp(\Gamma)$ for the spectrum of a graph $\Gamma$. So's conjecture. If $S\neq T$, then

$$sp(\Gamma_S)\neq sp(\Gamma_T),$$

and hence $\Gamma_S$ and $\Gamma_T$ are not isomorphic. This would imply that distinct integral symbols always produce non-isomorphic integral circulant graphs. The conjecture remains open except for some special choices of $n$, including cases resolved by M{"o}nius and So.