Upper panel: mean magnetic field modulus of HD 166473 against rotation phase. The different symbols identify the instrumental configuration from which the ⟨B⟩ value was obtained, as follows: filled circles (dark blue): CAT + CES LC; asterisk (turquoise): CAT + CES LC, lower resolution; open circle (steel blue): CAT + CES SC; filled triangles (violet): CFHT + Gecko (all previous symbols identical to Mathys 2017); five-pointed open star (orange): 3.6 m + CES VLC; four-pointed open stars (light green): UT2 + UVES; filled pentagons (yellow): 3.6 m + HARPS; filled squares (salmon): CFHT + ESPaDOnS. The long-dashed line (red) is the best fit of the observations by a cosine wave (see Eq. (4)). The short-dashed line (dark green) corresponds to the superposition of low-order multipoles discussed in Sect. 4. Lower panel: differences O–C between the individual ⟨B⟩ measurements and the best-fit curve, against rotation phase. The dotted lines (blue) correspond to ±1 rms deviation of the observational data about the fit (red dashed line). The symbols are the same as in the upper panel.