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In particular, we prove that $m$ should divide one of the integers: $d-1$, $d$, $d^2-3d+3$, $(d-1)^2$, $d(d-2)$ or $d(d-1)$. Secondly, consider a curve $\\delta\\in M_g^{Pl}$ with $g=(d-1)(d-2)/2$ such that $Aut(\\delta)$ has an element of \"very large\" order, in the sense that this element is of order $d^2-3d+3$, $(d-1)^2$, $d(d-2)$ or $d(d-1)$. 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