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).



explicit lower bounds on $|L(1,\chi)|$
This is discussed on page 47 of Narkiewicz's new book (Rational Number Theory in the 20th Century); see


<http://books.google.ca/books?id=3SWNZaDM6iMC&lpg=PP1&dq=rational%20number%20theory%20in%20the&pg=PA47#v=onepage&q&f=false>


Reference [4268] is to 


Metsankyla, T.: Estimations for L-functions and the class numbers of certain imaginary cyclic fields, Ann. Univ. Turku, Ser. AI 140, 1--11 (1970)


[3995] is


Louboutin, Stéphane(F-CAEN)
Minoration au point 1 des fonctions L et détermination des corps sextiques abéliens totalement imaginaires principaux. (French) [Lower bound at the point 1 of L-functions and determination of the principal totally imaginary abelian sextic fields]
Acta Arith. 62 (1992), no. 2, 109–124. 


and [338] is


Barrucand, Pierre; Louboutin, Stéphane(F-CAEN)
Minoration au point 1 des fonctions L attachées à des caractères de Dirichlet. (French) [Lower bound at the point 1 of L-functions associated with Dirichlet characters]
Colloq. Math. 65 (1993), no. 2, 301–306. 


