nt.number theory – Explicit version of Burgess theorem

There is totally explicit Version of Burgess's theorem? Precisely, let's go $$m$$ be a positive integer, and leave $$chi$$ be a mod of primitive character $$m$$. A special case (sufficient for my purposes) of Burgess's theorem states that

$$left | sum_ {a le n le a + x} chi (n) right | ll_ varepsilon x ^ {1/2} m ^ 3/16 + varepsilon}$$

I wonder if this ever became totally explicit. If $$m = p$$ The first Iwaniec and Kowalski demonstrate in their book the inequality with the right side $$cx ^ {1/2} p ^ 3/16 ( log p) ^ {1/2}$$ and claim (without going into details) that $$c = 30$$ it's good.

I need, however, the case of the composite module as well. Did something like this ever happen?