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Specifically, we study the sum\n  \\begin{equation*}\n  \\sum_{\\substack{\\chi\\ primitive\\ quartic\\\\ \\chi^2 primitive\\\\ genus(\\chi)=g}}L_q(\\frac{1}{2}, \\chi),\n  \\end{equation*} where $L_q(s,\\chi)$ denotes the $L$-function associated with primitive quartic character $\\chi$. 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Specifically, we study the sum\n  \\begin{equation*}\n  \\sum_{\\substack{\\chi\\ primitive\\ quartic\\\\ \\chi^2 primitive\\\\ genus(\\chi)=g}}L_q(\\frac{1}{2}, \\chi),\n  \\end{equation*} where $L_q(s,\\chi)$ denotes the $L$-function associated with primitive quartic character $\\chi$. 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