Cohomological invariants of hyperelliptic curves of even genus

Let $g$ be an even positive integer, and $p$ be a prime number. We compute the cohomological invariants with coefficients in $\mathbb{Z}\mathrm{/}p\mathbb{Z}$ of the stacks of hyperelliptic curves ${\mathcal{H}}_g$ over an algebraically closed field $k_0$.