  $\hat{Z}$ invariants of 3-manifolds were introduced as series in $q=e^{2\pi
i\tau}$ in order to categorify Witten-Reshetikhin-Turaev invariants
corresponding to $\tau=1/k$. However modularity properties suggest that all
roots of unity are on the same footing. The main result of this paper is the
expression connecting Reshetikhin-Turaev invariants with $\hat{Z}$ invariants
for $\tau\in\mathbb{Q}$. We present the reasoning leading to this conjecture
and test it on various 3-manifolds.
