The number of coefficients of automorphic $L$-functions for $G{L}_m$ of same signs

Let $\pi$ be an irreducible unitary cuspidal representation for $GL_m({\Bbb A}_{\Bbb Q})$,andlet$L(s, \pi)$betheautomorphic$L$-functionattachedto$\pi$,whichhasaDirichletseriesexpressioninthehalf-plane$\mbox{Re} s>1$\mathrm{.}When$\pi$ is self-contragredient, all the coefficients in the Dirichlet series expression are real. In this paper we give non-trivial lower bounds for the number of positive and negative coefficients, respectively.