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\section*{Methods}  \subsection{HOW WE MADE FIG2}   For each star in our sample we derived the frequency power spectrum as the  Fourier transform of the \kepler\ light curve (up to observing quarter 14)  and adopted the values of the large frequency separation, \dnu, the  frequency of maximum power, \numax, and mass from \citep{Stello_2013}. To correct the  spectrum for the background noise, we measured and subtracted a linear  slope anchored on the median power on either side of the central  power excess, defined by the frequency ranges 0.75(4\dnu\ $-$ \numax) to  (4\dnu\ $-$ \numax) and (4\dnu\ $-$ \numax) to 1.25(4\dnu\ $-$ \numax).  We then selected a 4\dnu-wide range of the spectrum centred on \numax.  The location of each mode was found by first folding this central part of  the spectrum using \dnu\ as the folding frequency such that modes of the  same spherical degree each formed a single peak. The folded spectrum was  smoothed by a Gaussian filter with a width of 0.1\dnu. We finally   correlated the folded spectrum with a model spectrum comprising of three  Lorenzian profiles, one for each degree $\ell$, 1, and 2 with relative  heights 1.0, 0.5, and 0.8, and width of 5\%, 10\%, and 5\% of  \dnu, respectively.  The centres of each Lorenzian profile was fixed relative to one  another such that the one representing the $\ell=2$ modes was 0.12\dnu to the  left (lower frequency) of the $\ell=0$ profile, and the $\ell=1$ profile was  0.52\dnu to the right (higher frequency) [Huber10_800RGs].   The shift between the model and the observed folded spectrum that gave the  larges correlation, provide the location of each mode.   %With this method the pattern of the multiple mixed   %modes around the acoustic resonance is smoothed away, creating a single  %broad peak centred at the resonant frequency.  %Separations between mixed   %modes could therefore not be mistaken for the small separation betweeen  %radial and quadrupole modes, which ensured a unique mode identification.  The region of the power spectrum associated with each spherical degree were  set to be 0.16, 0.53, and 0.16 times \dnu\ wide for $\ell=0$--2,  respectively, with the regions located according to the mode location found  by the correlation with the model spectrum. The remaining region was  associated with $\ell=3$ modes (Fig. 1).  The dipole-mode visibility was derived as the integrated power of the  dipole modes relative to that of the radial modes.  %For normal stars the integrated power in the dipole modes is typically  %about 50\% larger than for the radial modes ($V^2\simeq 1.5$)   %[This 'frequency  %of maximum power' shows tight correlation with stellar surface gravity[REF  %Brown]].   \subsection{DISUCSSION OF WHY NOT 100\% SUPPRESSED AND OR LINKS TO ROTATION AS REFEREE ALLUDES TO}   The resulting strong magnetic fields must have survived long after the  dynamo terminated at the end of hydrogen-core burning in order to be  detected during the red giant phase. Therefore, dynamo-generated fields are  frequently able to settle into long-lived stable configurations  \citep{Braithwaite_2004,Braithwaite_2006,Duez_2010}, a result that was not  certain from the 3D hydrodynamical simulations.   The gradual increase in suppression may result from the increasing size of  the convective core in more massive stars, which generates stronger  magnetic fields that survive after hydrogen burning ceases in the core.   [Jim/Matteo elaborate?]