Generalized Riemann Hypothesis for Dirichlet L-functions

Let $q$ be a positive integer and let $\chi$ be a primitive Dirichlet character modulo $q$. The Dirichlet $L$-function associated to $\chi$ is denoted $L(\chi, s)$. The trivial zeros of $L(\chi, s)$ are defined as follows: if $q = 1$ (so $\chi = 1$ and $L(\chi, s)$ is the Riemann zeta function $\zeta(s)$), the trivial zeros are the negative even integers $-2, -4, -6, \ldots$; if $\chi$ is odd, the trivial zeros are the negative odd integers $-1, -3, -5, \ldots$; and if $\chi \neq 1$ is even, the trivial zeros are the non-positive even integers $0, -2, -4, \ldots$. A complex number $s$ is called a non-trivial zero of $L(\chi, s)$ if $L(\chi, s) = 0$ and $s$ is not equal to any trivial zero (under the canonical embedding $\mathbb{Z} \hookrightarrow \mathbb{C}$). Prove that for every primitive Dirichlet character $\chi$ and every non-trivial zero $s$ of $L(\chi, s)$, the real part of $s$ equals $\frac{1}{2}$.