Explicit bound for the eventuality threshold

Find an explicit upper bound for the positive integer N, in terms of the balanced coprime pair (a, b), such that D_n(a, b; q) is positive and unimodal for all n ≥ N.

Background

In addition to establishing eventual positivity and unimodality, the authors ask for quantitative control of the threshold beyond which these properties hold. The bound should depend explicitly on the data defining the balanced coprime pair (a, b).

Such a bound would strengthen the asymptotic existence assertion and provide an effective version of the proposed eventual positivity/unimodality result.