bounds for, $|L_{\tau}(s)|$, a Dirichlet searies associated with Ramanujan tau function

Question

The Dirichlet searies associated with Ramanujan tau function is defined as:

\begin{equation} L_{\tau}(s)=\sum_{n=0}^{\infty}\frac{\tau(n)}{n^s}=\prod_{p \text{ }\mathrm{prime}}\frac{1}{1-\tau(p)p^{-s}+p^{11-2s}},\qquad \Re(s)>13/2. \end{equation}

It is known that all the zeros of $L_{\tau}(s)$ are inside the critical strip $11/2<\Re(s)<13/2$ and most likely on the critical line $\Re(s)=6$.

Question: What are the bounds of $|L_{\tau}(s)|$ when $11/2<\Re(s)<13/2$ and $\Im(s)$ goes to infinity?

Any comments are welcomed! -mike