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For $V\\in L_{\\rm loc}^p(\\R^2)$, $p\\in(2,\\infty]$, and $b\\in L_{\\rm loc}^q(\\R^2)$, $q\\in(1,\\infty]$, both decaying at infinity, we show that states in the discrete spectrum of $H$ are superexponentially localized. We establish the existence of such states between the zeroth and the first Landau level assuming that V=0. 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