 perverse sheaf $P$ on $X\left({}^{\vee}G^{\Gamma}\right)$, we have $$\chi_{S_{\psi}}^{mic}(P)=\left\{\begin{array}{cl}     0& \text{if }P\cong P(\psi,\delta),\quad\text{ for some strong real form }\delta\text{ of }G\\     0& otherwise.     \end{array}\right.$$ Consequently, $$\begin{aligned}     \label{eq:repunipotenttordu}     \Pi^{z}(G/\mathbb{R})_{\psi}^{\mathrm{ABV}}=\{\pi(\psi,\delta)\}_{\delta \text{ strong real form of } G^{\Gamma}}.\end{aligned}$$  