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This confirms a conjecture in \\cite{CLW2} and also improves a result of Eremenko and Gabrielov \\cite{EG}. The nonexistence is a delicate problem because the equation always has solutions if $8\\pi n$ in the RHS is replaced by $2\\pi \\rho$ with $0<\\rho\\notin 4\\mathbb{N}$. 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