In books/papers, we often see the notation that the zeros of the $\zeta$-function with positive imaginary part are denoted $\rho_n$ in order of increasing height.
However, because of the equation $\zeta(\bar{s})=\overline{\zeta(s)}$ and the functional equation it is easy to see that any zeros off the critical line in the critical strip occur in pairs, symmetric about the critical line.
So why are zeros denoted this way when there may be zeros with the same imaginary part?