Does anyone know of an explicit effective lower bound for $|L(1,\chi)|$, where $\chi$ is an odd complex (primitive) Dirichlet character?

I know of Landau's paper Uber Dirichletsche Reihen mit komplexen Charakteren, where he bounds $$ |L(1,\chi)|>\frac{1}{c \log(q)},$$

where $q$ is the conductor of $\chi$, but the constant $c$ he gets is on the order of $e^{50}$, and is totally useless for computations.

I know of many papers dealing with quadratic characters but very few that address complex characters (explicitly).