  Assuming GRH and the Ramanujan-Petersson conjecture we prove explicit bounds
for $L(1,f)$ for a large class of $L$-functions $L(s,f)$, which includes
$L$-functions attached to automorphic cuspidal forms on $GL(n)$. The proof
generalizes work of Lamzouri, Li and Soundararajan. Furthermore, the main
results improve the classical bounds of Littlewood
\[(1+o(1))\left(\frac{12e^{\gamma}}{\pi^2}\log\log C(f)\right)^{-d} \leq
|L(1,f)|\leq (1+o(1))\Big(2e^{\gamma}\log\log C(f)\Big)^d,\] where $C(f)$ is
the analytic conductor of $L(s,f)$.
