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Three types of possible asymptotic behavior of the modes eigenfrequencies are found for the case of large skyrmion radius $R_s$, namely $\\omega_0\\sim R_s^{-2}$ for the breathing mode, $\\omega_{-|\\mu|}\\sim R_s^{-1}$ and $\\omega_{|\\mu|}\\sim R_s^{-3}$ for modes with negative and positive azimuthal quantum numbers, respectively. A number of properties of the magnon eigenfunctions are determined. 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