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We construct a matrix $A(\\mathfrak{d})$ of size $(m-1) \\times (m-1)$ depending on only of $\\mathfrak{d}$ with the following property: For any tame $\\mathbb{Z}/m\\mathbb{Z}$-number field $K$ of discriminant $\\mathfrak{d}$ the matrix $A(\\mathfrak{d})$ represents the Gram matrix of the integral trace zero form of $K$. In particular, we have that the integral trace zero form of tame cyclic number fields is determined by the degree and discriminant of the field. 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We construct a matrix $A(\\mathfrak{d})$ of size $(m-1) \\times (m-1)$ depending on only of $\\mathfrak{d}$ with the following property: For any tame $\\mathbb{Z}/m\\mathbb{Z}$-number field $K$ of discriminant $\\mathfrak{d}$ the matrix $A(\\mathfrak{d})$ represents the Gram matrix of the integral trace zero form of $K$. In particular, we have that the integral trace zero form of tame cyclic number fields is determined by the degree and discriminant of the field. 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