We present measurements of the large-scale cosmic-ray (CR) anisotropies in R.A., using data collected by the surface detector array of the Pierre Auger Observatory over more than 14 yr. We determine the equatorial dipole component, through a Fourier analysis in R.A. 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 subarray of detectors with 750 m separation, which allows us to extend the analysis down to ∼0.03 EeV. The most significant equatorial dipole amplitude obtained is that in the cumulative bin above 8 EeV, %, which is inconsistent with isotropy at the 6σ level. In the bins below 8 EeV, we obtain 99% CL upper bounds on d ⊥ at the level of 1%-3%. 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 R.A. of the Galactic center, at GC =-94°, suggesting a predominantly Galactic origin for anisotropies at these energies. The reconstructed dipole phases in the energy bins above 4 EeV point instead to R.A. that are almost opposite to the Galactic center one, indicative of an extragalactic CR origin.