Let $\pi$ be a unitary cuspidal representation of $\mathrm{GL}_n(\mathbb{A})$.

It is written is some paper that using the results towards the generalized Ramanujan conjecture in the paper "On the generalized Ramanujan conjecture for GL" by Luo, Rudnick and Saran (https://www.researchgate.net/publication/247040108_On_the_generalized_Ramanujan_conjecture_for_GL), one can prove that $L(s,\pi,\mathrm{Sym}^2)$ and $L(s,\pi,\bigwedge^2)$ are nonzero for $Re(s) \ge 2$. But I don't know why it does.

I would appreciate if you let me know this point.