Triangle inequality of Dirichlet cofficients of Artin L-function.

Question

As for automorphic L-function we know that $$ \left|\lambda_{\pi}(n)\right|^{2} \leq \lambda_{\pi \times \widetilde\pi}(n) $$ is there exist a inequality similarly for Artin L-functions?

For above inequality we can refer the Appendix in Weak subconvexity without a Ramanujan hypothesis by K Soundararajan and J Thorner. Thank you!