Generalized Lomb-Scargle periodograms of the HARPS RVs and spectral activity indicators from serval (blue) andTERRA (red). The horizontal dashed lines mark, from bottom to top, the 5, 1, and 0.1% FAP levels, respectively. The vertical dashed lines mark the orbital frequencies of the two transiting planets (f _b = 0.121 d⁻¹ and f _c = 0.064 d⁻¹) and of the stellar signal at ~0.03 d⁻¹. Upper panel: HARPS RVs. Second panel: RV residuals following the subtraction of the signal of TOI-776 c. Third panel: RV residuals following the subtraction of the reflex motion of TOI-776 c and of the activity-induced stellar signal. Fourth panel: S-index. Fifth panel: Hα line. Sixth panel: Na D lines. Seventh panel: differential line width (dLW). Eighth panel: chromatic index (CRX). Bottom panel: window function. The arrow in the bottom panel indicates the peak at 0.07 d⁻¹ referred to in the discussion of Sect. 5.1.