Plot of the relationship between Hα from Gaia DR3 including the model (see Eq. A.1) and logP_rot across (G - G_RP)) colour from Gaia DR3, presented as a compliment our analyses in discrepancies between EW Hα measured by ESP-ELS in Gaia DR3 and the values reported in literature. Left: Rotation period distribution with (G - G_RP)) colour-coded by normalised Hα equivalent width. Right: Hα equivalent width against (G - G_RP), colour-coded by logP_rot. Stars with newly determined periods P_rot are plotted as circles with lime-green edges, field stars in the sample are represented as circles with blue edges. The M-dwarf activity boundary plotted as dashed line follows Kiman et al. (2021)