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The aim of this article is to get non-trivial bound on non-linearly additively twisted sums of the Fourier coefficients $\\lambda_g (n)$. Precisely, we prove for any $3/4 < \\beta < 3/2$, $\\beta \\neq 1 $, the following non-trivial estimate $$ \\sum_{n \\leq N}\\lambda_g(n)\\,e(\\alpha\\, n^{\\beta})\\ll_{g, \\alpha, \\beta, \\varepsilon} N^{\\frac{1}{2}+ \\frac{\\beta}{3} +\\varepsilon} + N^{\\frac{3}{2}-\\frac {2\\beta}{3} + \\varepsilon}, $$ for any $\\varepsilon > 0$. 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