Explicit upper bound for $\left|L(1, χ)\right|$ when $χ(2)=1$ and $χ$ is even

Let $χ$ be a primitive Dirichlet character of conductor $q$ and let us denote by $L(z, χ)$ the associated $L$-series. In this paper, we provide an explicit upper bound for $\left|L(1, χ)\right|$ when $χ$ is a primitive even Dirichlet character with $χ(2)=1$.

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