Is $ \pi\mapsto(s\mapsto L(s,\pi)) $ bijective?

Question

Let $ \pi $ be an automorphic representation of $ \operatorname{GL_{n}}(\mathbb{A}_{\mathbb{Q}}) $ and $ L(s,\pi) $ the associated L-function. Is the map $ \pi\mapsto L(s,\pi) $ bijective ? In other words, is the knowledge of $ L(s,\pi) $ exactly equivalent to the knowledge of $ \pi $ itself ?