  $^{59}$Co NMR experiments have been performed on single crystals of the
layered cobaltate Na$_{x}$CoO$_{2}$ with x=0.77 which is an antiferromagnet
with N\'eel temperature $T_{N}=22$~K. In this metallic phase six Co sites are
resolved in the NMR spectra, with distinct quadrupole frequencies $\nu _{Q}$,
magnetic shifts $K_{ZZ}$ and nuclear spin lattice relaxation rates $% 1/T_{1}$.
Contrary to the $x=1/2$ or $x=2/3$ phases the 3D stacking of the Na planes is
not perfect for $x=0.77$ but this does not influence markedly the electronic
properties. We evidence that the magnetic and charge properties of the Co sites
are highly correlated with each other as $K_{ZZ}$ and $(1/T_{1})^{1/2}$ scale
linearly with $\nu _{Q}$. The data analysis allows us to separate the
contribution $\nu_{Q}^{latt}$ of the ionic charges to $\nu _{Q}$ from that $\nu
_{Q}^{el}$ due to the hole orbitals on the Co sites. We could extend coherently
this analysis to all the known phases in the Na cobaltate phase diagram. The
variation with $x$ of $\nu _{Q}^{latt}$ is found to fit rather well numerical
computations done in a point charge model. The second term $\nu _{Q}^{el}$
allowed us to deduce the hole concentration on the cobalts. These detailed
experimental results should stimulate theoretical calculations of the
electronic structure involving both the Co orbital configurations and DMFT
approaches to take into account the electronic correlations.
