  We discuss the relation between the analytic structure of the scattering
amplitude and the origin of an eigenstate represented by a pole of the
amplitude.If the eigenstate is not dynamically generated by the interaction in
the channel of interest, the residue of the pole vanishes in the zero coupling
limit. Based on the topological nature of the phase of the scattering
amplitude, we show that the pole must encounter with the
Castillejo-Dalitz-Dyson (CDD) zero in this limit. It is concluded that the
dynamical component of the eigenstate is small if a CDD zero exists near the
eigenstate pole. We show that the line shape of the resonance is distorted from
the Breit-Wigner form as an observable consequence of the nearby CDD zero.
Finally, studying the positions of poles and CDD zeros of the KbarN-piSigma
amplitude, we discuss the origin of the eigenstates in the Lambda(1405) region.
