Modular fusion categories with few twists

We classify modular fusion categories up to braided equivalence with less than four distinct twists of simple objects by observing that under this assumption, for each positive integer <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>N</mml:mi> </mml:math> , there are finitely many modular fusion categories of Frobenius–Schur exponent <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>N</mml:mi> </mml:math> up to braided equivalence whose twists are a proper subset of the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mi>N</mml:mi> <mml:mi mathvariant="normal">th</mml:mi> </mml:msup> </mml:math> roots of unity.