  Nuclear spins and precise values of the magnetic dipole and electric
quadrupole moments of the ground-states of neutron-rich $^{76-78}$Cu isotopes
were measured using the Collinear Resonance Ionization Spectroscopy (CRIS)
experiment at ISOLDE, CERN. The nuclear moments of the less exotic $^{73,75}$Cu
isotopes were re-measured with similar precision, yielding values that are
consistent with earlier measurements. The moments of the odd-odd isotopes, and
$^{78}_{29}$Cu ($N=49$) in particular, are used to investigate excitations of
the assumed doubly-magic $^{78}$Ni core through comparisons with large-scale
shell-model calculations. Despite the narrowing of the $Z=28$ shell gap between
$N\sim45$ and $N=50$, the magicity of $Z=28$ and $N=50$ is restored towards
$^{78}$Ni. This is due to weakened dynamical correlations, as clearly probed by
the present moment measurements.
