I need to evaluate L-functions of the form ∞∑n=0(Dn)n−s at integers, where (⋅⋅) is the Kronecker symbol. This is apparently what quadratic_L_function__exact(k,D) does. However I find this unreliable when D is not squarefree.
For example, the value quadratic_L_function__exact(2,4) = pi^2 / 6 is incorrect; the sum should actually be pi^2 / 8. However, the value quadratic_L_function__exact(2,12) = 1/18 * sqrt(3) * pi^2 seems correct. I can't tell what's going on.