unipotent of ${{\mathrm{SL}}}_3$. Let $\psi_\rho:U_\rho(F) \to {\mathbb{C}}^\times$ be the character given by $$\label{psirho}
\psi_\rho\begin{pmatrix} 1&x+y\tau&\frac{(x^2-y^2\rho)}2+w\tau\\&1&-x+y\tau\\ &&1\end{pmatrix}
= \psi(x).$$ Note that $\psi_\rho|_{N_{2,\rho}}=1$. Given $W\in {{\mathcal {W}}}(\pi,\psi),f_s\in I(s,\chi)$, the local zeta integral of [@G],[@H12] is $$Z(W,f_s)=\int_{N_{2,\rho}\setminus H_\rho(F)}W(g)f_s(w_\beta g)dg.$$ Observe that if $\tilde f_s\in  {{\mathrm{Ind}}}_P^{G_2}(\chi_s)$ is given in terms of $f_s\in  {{\mathrm{ind}}}_{N_{2,\rho} \cdot T_0}^{H_\rho}(\chi_s)$ as in section \[def of tilde f s\] then $$Z(W,\tilde f_s)=\int_{N_{2,\rho}\setminus H_\rho(F)}W(g)f_s( g)dg.$$

Theorem 5.1 of [@H18] states that for each $s_0$, there exists a choice of data $W,f_s$ (depending on $s_0$) such that $Z(W,f_s)$ is holomorphic and nonvanishing at $s_0$. However, there is a gap in the proof of this theorem in the archimedean case, because it is never shown that $f_{s_0} \mapsto Z(W, f_{s_0})$ is a continuous function of $f_{s_0} \in I(s_0, \chi),$ when $s_0$ is outside the domain of convergence. In the split case, it is shown in [@Tianthesis; @Ti18] that $Z$ is, in fact, continuous in both of its arguments. The technique, which was pioneered in [@Soudry-Archimedean], should extend to the non-split case as well. In fact, the non-split case is easier, because the rank of the maximal split torus is only one. Here, we content ourselves with sketching how to close the gap in 