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Quasinormal modes of asymptotically AdS black holes can be interpreted aspoles of retarded correlators in the dual gauge theory. To determine theresponse of the system to small external perturbations it is not enough to knowthe location of the poles: one also needs to know the residues. We compute themfor R-charge currents and find that they are complex except for thehydrodynamic mode, whose residue is purely imaginary. For different quasinormalmodes the residue grows with momentum q, whereas for the hydrodynamic mode itbehaves as a damped oscillation with distinct zeroes at finite q. Similar tocollective excitations at weak coupling the hydrodynamic mode decouples atshort wavelengths. Knowledge of the residues allows as well to define the timescale t_H from when on the system enters the hydrodynamic regime, restrictingthe validity of hydrodynamic simulations to times t>t_H.

Residues of Correlators in the Strongly Coupled N=4 Plasma