Let $m$ be a positive integer and $\chi$ a primitive character mod $m$. Let $x$ be such that $\chi(p)\ne 1$ for all primes $p<x$. Assume GRH. How can one bound $x$ in terms of $m$ ? I do not need the best possible bound, but I need a good quality bound which is **totally explicit** in all parameters. 


A related question: what is an **explicit** lower bound for $L(1,\chi)$ under GRH? 



Least quadratic residue under GRH: an explicit bound
See the work of [Lamzouri, Li, and Soundararajan](https://arxiv.org/abs/1309.3595) (I link the arXiv version; the paper appeared in Math. Comp.). Assuming that $\chi$ is a primitive quadratic character (as the title suggests) then Theorem 1.4 of that paper gives an explicit bound on the least prime quadratic residue on GRH. (Indeed that theorem gives an explicit bound on the least prime in any coset of a subgroup of $({\Bbb Z}/q{\Bbb Z})^\times$.) Theorem 1.5 there gives explicit upper and lower bounds for $|L(1,\chi)|$ for any primitive character $\chi \pmod q$ (not necessarily quadratic).


