number theory – Galois elements determined by an action on the roots of the rationals?

Can there be an element $ sigma $ of $ Gal ( overline { mathbb {Q}} / mathbb {Q}) $, other than identity and complex conjugation, which is completely determined up to conjugation by its action on $ sqrt[n]r $ for everyone $ r in mathbb {Q} $ and all $ n in mathbb {N} $?

I'm expecting no, but if I'm wrong, can the subgroup of such elements be given another characterization?