The zeros of an L-function $L(s)$ are the complex numbers $\rho$ for which $L(\rho)=0$.
The lowest zero of an L-function $L(s)$ is the least $\gamma>0$ for which $L(1/2+i\gamma)=0$. Note that even when $L(1/2)=0$, the lowest zero is by definition a positive real number.
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