GLS periodograms of GJ 4276. Panel a: periodogram of the CARMENES RVs. The horizontal lines (dotted, dash-dotted, dashed) indicate FAP levels of 10%, 1%, and 0.1%. The vertical green line marks the orbital period with the highest power at 13.347 d. The left red dashed line at P_rot = 64.3 d (f_rot = 0.0156 d⁻¹) shows the weighted mean of the photometrically derived stellar rotation period and the right red dashed line its first harmonic (2f_rot = 0.0311 d⁻¹). Panel b: periodogram of the residuals after removing the best-fit single-planet Keplerian with eccentricity (see Sect. 4.2.2) signal; panel c: window function of the RV data. Panels d–h: periodograms of the chromatic RV index (CRX), differential line width (dLW), as well as FWHM, contrast, and bisector span from the CCF analysis. Panels i–l: periodograms of the chromospheric line indices of Hα and Ca II IRT.