  We present measurements of the large-scale cosmic-ray anisotropies in right
ascension, using data collected by the surface detector array of the Pierre
Auger Observatory over more than 14 years. We determine the equatorial dipole
component, $\vec{d}_\perp$, through a Fourier analysis in right ascension that
includes weights for each event so as to account for the main detector-induced
systematic effects. For the energies at which the trigger efficiency of the
array is small, the ``East-West'' method is employed. Besides using the data
from the array with detectors separated by 1500 m, we also include data from
the smaller but denser sub-array of detectors with 750 m separation, which
allows us to extend the analysis down to $\sim 0.03$ EeV. The most significant
equatorial dipole amplitude obtained is that in the cumulative bin above 8~EeV,
$d_\perp=6.0^{+1.0}_{-0.9}$%, which is inconsistent with isotropy at the
6$\sigma$ level. In the bins below 8 EeV, we obtain 99% CL upper-bounds on
$d_\perp$ at the level of 1 to 3 percent. At energies below 1 EeV, even though
the amplitudes are not significant, the phases determined in most of the bins
are not far from the right ascension of the Galactic center, at $\alpha_{\rm
GC}=-94^\circ$, suggesting a predominantly Galactic origin for anisotropies at
these energies. The reconstructed dipole phases in the energy bins above 4 EeV
point instead to right ascensions that are almost opposite to the Galactic
center one, indicative of an extragalactic cosmic ray origin.
