Granville and Soundararajan, in "Upper Bounds for L(1, chi)$L(1, \chi)$", first paragraph, say it is known that there exist quadratic Dirichlet characters $\chi$ for which L(1, chi)$L(1, \chi)$ is about log log q$\log\log q$, where q$q$ is the conductor of chi$\chi$. Those authors gave no reference, and I can't find one so far. Can anyone point me to a reference?