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

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