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\\Gamma = \\partial \\Omega.$ We prove that if $\\gamma(x)$ is nowhere equal to 1, then for every $0 < \\epsilon \\ll 1$ and every $N \\in {\\mathbb N}$ the eigenvalues of $G_b$ lie in the region $\\Lambda_{\\epsilon} \\cup {\\mathcal R}_N,$ where $\\Lambda_{\\epsilon} = \\{ z \\in {\\mathbb C}:\\: |\\Re z | \\leq C_{\\epsilon} (|\\Im z|^{\\frac{1}{2} + \\epsilon} + 1), 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