quotient $Z^*(W_v,f_{s,v})/L(s,\pi_v,{{\mathrm{Ad}}}\times \chi_v)$ has no zeros on the region ${{\mathrm{Re}}}(s)\ge \frac{1}{2}$. The main obstacle here is that, at this time, we can not rule out the existence of a place $v\in S-S_\infty$ such that $\chi_v$ is unramified $\pi_v$ is both ramified and non-tempered. In this case, $\pi_v$ is of the form ${{\mathrm{Ind}}}_{B_3}^{{{\mathrm{GL}}}_3(F_v)}(||^{\alpha}\otimes \mu_2\otimes ||^{-\alpha})$, where $B_3$ is the upper triangular Borel subgroup of ${{\mathrm{GL}}}_3(F_v)$, $\alpha$ is a real number with $0<\alpha<1/2 $, and $\mu_2$ is a ramified character of $F_v^\times$. It turns out that the required “test" Whittaker function comes from a certain new form of $\pi_v$. More precisely, let $\psi_v$ be an unramified additive character, and let $W_c\in {{\mathcal {W}}}(\pi_v,\psi_v)$ be the Whittaker function associated with a new vector of $\pi_v$ with respect to the group $$K_c=\begin{pmatrix}{{\mathfrak{o}}}& {{\mathfrak{o}}}& {{\mathfrak{p}}}^{-c} \\ {{\mathfrak{p}}}^c & 1+{{\mathfrak{p}}}^c & {{\mathfrak{o}}}\\ {{\mathfrak{p}}}^c & {{\mathfrak{p}}}^c &{{\mathfrak{o}}}\end{pmatrix}^\times,$$ where ${{\mathfrak{o}}}$ is the ring of integers of $F_v$, ${{\mathfrak{p}}}$ is the maximal ideal of ${{\mathfrak{o}}}$ and $c$ is the conductor of $\pi_v$ in the sense of [@JPSS81]. Here a new vector of $\pi_v$ with respect to $K_c$ is a nonzero vector in the space $\pi_v^{K_c}$. It is known that $W_c$ is unique (up to scalar). The main local ingredient 