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\begin{abstract}  Magnetic fields play a role in almost all stages of stellar evolution. evolution \citep{Landstreet_1992}.  Most low-mass stars, including the Sun, show surface fields that are  generated by dynamo processes in their convective envelopes. envelopes \citep{Parker_1955}.  Intermediate-mass stars do not have deep convective envelopes, envelopes \citep{Kippenhahn_1990},  yet 10\% exhibit strong surface fields that are presumed to be residuals from the stellar  formation process. process \citep{2008CoSka..38..443P}.  These stars do have convective cores that might produce internal magnetic fields, fields \citep{Brun_2005},  and these might even survive into later stages of stellar evolution, but information is limited by our inability to measure the  fields below the stellar surface. Here we use asteroseismology to study  the occurrence of magnetic fields in the cores of low- and