Single variable complex functions of a real variable are ubiquitous in engineering contexts such as control engineering and signal processing, and visualizing them is of utmost importance in designing systems such as filters. The functions that we encounter in control systems theory is usually of the following general form: $$s=j\omega\,\,\,\,\,\,\,H(s)=e^{Ts}\frac{s^p+n_1s^{p-1}+n_2s^{p-2}+...+n_p}{d_1s^m+d_2s^{m-1}+...+d_m},\,\,\,\,\,\,\,\ p\leq m\,\,\,\,\,\,,\,\,\omega\in\Re$$
and in many cases $T=0$.
The most widely used method for visualizing the above function is Bode plot, that displays the phase and magnitude of it separately. I'm looking for other, possibly heuristic ways of visualizing functions with the above format. Any suggestion would be appreciated.
(I'm not sure, but maybe this question should be a community wiki question)