(Color online) (a) Typical integration paths for case 2; (b) and (c): Re[a_ad] and Im[a_ad] as functions of a_BB, for the systems of case 2. The parameters are same as in Fig. 2. Here we show the results given by path-I (red dashed-dotted line), path-II (blue open circles), and path-III (magenta solid line).