  The Jost function method is extended within the framework of the RPA theory
to find poles on the complex energy plane that exhibit complex RPA
eigenenergies. Poles corresponding to the RPA excited states such as the giant
resonance of $^{16}$O electric dipole excitations were successfully found on
the complex energy plane. Although the giant resonance has been known as a
single resonance with large strength and width, it is found that, at least
within the RPA framework, the $^{16}$O electric dipole giant resonance is
formed by multiple poles, each of which is an independent pole with different
widths, origins, response properties to residual interactions, and components
structures of the density fluctuation.
