Fourier spectrum of KIC 8375138. Frequencies that fulfil our detection criterion, are indicated in black, whereas frequencies marked in red fulfil the detection criterion, and have the first-order harmonic within the extracted frequency list. The derived near-core rotation frequency and its harmonic are indicated with the dashed and dotted lines, respectively, while the cumulative distribution function of the red frequency peaks is shown by the blue curve. Signatures of rotational modulation occur within the shaded grey frequency range. Inset: a close-up of the Fourier spectrum around the near-core rotation rate f_rot,i (dashed line). The 1σ (dotted lines) and 3σ (grey area) uncertainties on f_rot,i are indicated. The ten highest-amplitude pulsation frequencies have been prewhitened for clarity.