}$, we obtain $$\mathrm{vol}({\Gamma\backslash G})f(0) + \frac{ \mathrm{vol}(\mathrm{SL}_{n-0}( {\mathbb{Z}}) \backslash \mathrm{SL}_{n-0}( {\mathbb{R}}))}{\# (\mathrm{SO}_{n-0}({\mathbb{Z}}))}  \zeta(n) \hat{f}(0)