Let $\chi$ denote the Legendre symbol of conductor $q$. A Siegel zero for the $ L $ series associated to $ \chi $, which we denote by $ L(s,\chi) $ is a real zero $ \sigma $  satisfying $ 1-\frac{c}{\log |q|} < \sigma < 1$ for some constant $c$.


I have read in many places (see for example the second page of the article by Ajit Bhand and Ram Murty available [here][1]) that the non-existence of Siegel zeros for $ L(s,\chi) $ can be used to prove the bound
$$
h(d) > c_1 \frac{\sqrt{d}}{\log(d)},
$$
where $ h(d)$ is the class number of the associated imaginary quadratic field and $c_1$ is another *effective constant* which can be calculated depending on $c$.

> **My Question :** How to explicitly compute $c_1$ from $c$?

If anyone can direct me to a proof of the above statement, I think that would also suffice.

Thank you,
Krishnarjun

  [1]: https://mast.queensu.ca/~murty/class-groups_final_revised.pdf