  The role of dense-matter properties in the tidal deformability of a cold
nonaccreted neutron star is further investigated. Using the set of
Brussels-Montreal unified equations of state, we have computed the
gravitoelectric Love numbers $k_\ell$ and the gravitomagnetic Love numbers
$j_\ell$ up to $\ell=5$. Their relative importance and their sensitivity to the
symmetry energy and the neutron-matter stiffness are numerically assessed.
Their impact on the phase of the gravitational-wave signal emitted by binary
neutron star inspirals is also discussed.
