unipotentparameter\] Suppose $\left({}^{\vee}{G}^{\Gamma},\mathcal{S}\right)$ is an $E$-group for $G$ with second invariant $z$. Fix a principal morphism $$\begin{aligned} \psi_{0}:\mathbf{SL}(0,\mathbb{C})\longrightarrow {}^{\vee}{G}.\end{aligned}$$ 