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\\lambda^d(\\alpha{\\Bbb Z}[i]) = (\\alpha /|\\alpha|)^{4d}$, for $0\\neq\\alpha\\in{\\Bbb Z}[i]$, and $\\zeta(s,\\lambda^d)$ is the Hecke zeta function that satisfies $\\zeta(s,\\lambda^d) =(1/4)\\sum_{0\\neq\\alpha\\in{\\Bbb Z}[i]} \\lambda^d((\\alpha)) |\\alpha|^{-2s}$ for $\\Re(s)>1$, while the numbers $D,M\\in(0,\\infty)$ 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