Let $F$ be a quadratic number field with class number $h_F = 1$. Let $\lambda (n) = \left( \frac{n}{|n|}\right) ^{w_F}$ be the Grossencharacter, where $w_F$ denotes the number of units. The associated L-function is defined by $$ L(s,\lambda ^m) = \frac{1}{w_F} \sum_n \lambda ^m(n) |n|^{-2s}.$$
I need some (subconvexity) bound of the L-function on the line $\Re(s) = 1/2$. Thanks a lot!