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We analyze the spectral density of a single level quantum dot coupled to superconducting leads focusing on the Andreev states appearing within the superconducting gap. We use two complementary approaches: the numerical renormalization group and the Hartree-Fock approximation. Our results show the existence of up to four bound states within the gap when the ground state is a spin doublet (\pi\ phase). Furthermore the results demonstrate the reliability of the mean field description within thisdoi:10.1088/0953-8984/24/38/385303 pmid:22945559 fatcat:pyvbczx5dzbpxd5rox5xvmbugu