13.3 | Dark matter versus vacuum energy at recombination

The CMB temperature is currently $2.73\,\mathrm K$ and its emission redshift is $z_{\rm CMB}=1100$. Present densities are $\rho_{\rm DE,0}=7.1\times10^{-30}\,\mathrm{g\,cm^{-3}}$, $\rho_{\rm DM,0}=2.4\times10^{-30}\,\mathrm{g\,cm^{-3}}$, and $\rho_{\rm NM,0}=0.5\times10^{-30}\,\mathrm{g\,cm^{-3}}$.

What was the ratio of dark matter density to dark energy density when the CMB was emitted? Assume dark energy is vacuum energy.