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For each $K \\in \\mathcal{C}_{d}$, we construct a weight 1 modular form $f_{K}$ with level $3^{\\pm 1}d$ and nebentypus $\\left( \\frac{-3^{\\pm 1}d}{\\cdot} \\right)$. We show that the form $f_{K}$ completely determines the field $K$. 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