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Stars above $1.6 M_\odot$ show a 50-60\% suppression rate, much larger than  can be accounted for by A-type stars known to show strong surface fields,  which represent only up to 10\% of A-type stars (Power2008). This shows  that the previously known magnetic A stars detected through their surface  fields are only the tip of the iceberg and a much larger fraction of A  stars host strong magnetic fields hidden in their core.   %The rapid fractional increase reaching 50-60\% for stars above 1.6\msol, coincides  %with the mass beyond which about 10\% of hydrogen-core burning A-stars are  %known to show strong magnetic fields on the surface [Power2008].   %[The large fraction of suppressed stars above 1.6\msol\ coinsides with  %the masses of A stars, of which up to 10\% are known to have strong  %surface fields[REFS].]   %This further supports that the suppression arises from a magnetic field.  %Even more interesting, it shows that the previously known magnetic A   %stars detected through their surface fields are only the tip of the  %iceberg and a much larger fraction of A stars host strong magnetic fields  %hidden in their core.   %, than anticipated purely from their observable surface fields.   In Figure 4, we show the observed \numax\ and inferred mass of all the  stars superimposed on a contour plot of theoretically predicted magnetic field strengths  at the hydrogen-burning shell[REF theory paper]. The location of a star  with suppressed modes (filled circles) provides a lower limit to the field  strength in the core given by the colour band it falls in.   For stars without suppressed modes (open circles) we can only derive an  upper limit to the field at the hydrogen-burning shell; on either side of this  region the field could potentially be larger.   From this diagram we conclude that magnetic fields above 10 kG  are not present at the hydrogen-burning shell for stars below 1.1\msol when  they are near the red giant luminosity bump (\numax\ $\sim50$\muhz). By  assuming flux conservation this corresponds to 1 kG near the  hydrogen-burning cores of Sun like stars [in agreement  with observed surface fields in Sun-like stars[REFDonati] OR do we not want  to make any comparison with known (surface) fields???].   %For stars with suppressed modes we derive the lower limit of how  %strong the field in the core [at least] needs to be for suppression to  %be observed.  For a given \numax, stars more massive than 1.4 times solar require  increasingly stronger magnetic fields to suppress their dipole modes[REF  Fig. 4]. [DO WE WANT TO PHRASE NEXT SENTENCE EVEN MORE CAREFULLY?] The  hint of a fractional decline of suppressed stars beyond   2\msol seen in Fig. 3, are suggestive we might see the effect of an  upper limit to the typical dynamo-generated magnetic field of 3000 kG  in the cores of intermediate-mass stars.