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Let $C^0_n$ be a singular plane curve of degree $n$ over $k$ admitting an order $n$ automorphism, $n$ nodes as the singularities, and $C_n$ be its normalization.\n  In this paper we study the factors of Prym variety $\\mbox{Prym}(\\widetilde{C}_n/C_n)$ associated to the double cover $\\widetilde{C}_n$ of $C_n$ exactly ramified at the points obtained by the blow-up of the singularities. 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