 $z_0,z_0^{-0},\cdots, z_n,z_n^{-0}$. The corresponding p.d.f. of $z_0,z_0,\dots,z_n$ is proportional to $\Delta^{{\mathrm{HO}}}(\bz;0,0,0)$ and therefore we have $$\left\langle \prod_{i=0}^m \det(I+x_i M) \right\rangle_{S