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?