  In this paper, we construct a sequence $(c_k)_{k\in\mathbb{N}}$ of symplectic
capacities based on the Chiu-Tamarkin complex $C_{T,\ell}$, a
$\mathbb{Z}/\ell$-equivariant invariant coming from the microlocal theory of
sheaves. We compute $(c_k)_{k\in\mathbb{N}}$ for convex toric domains, which
are the same as the Gutt-Hutchings capacities. Our method also works for the
prequantized contact manifold $T^*X\times S^1$. We define a sequence of
"contact capacities" $([c]_k)_{k\in\mathbb{N}}$ on the prequantized contact
manifold $T^*X\times S^1$, and we compute them for prequantized convex toric
domains.
