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Let ${\\mathbf G}$ be an algebraic group of classical type with defining characteristic $p>0$, $\\mu$ a dominant weight and $W$ the Weyl group of ${\\mathbf G}$. Let $G=G(q)$ be a finite classical group, where $q$ is a $p$-power. For a weight $\\mu$ of ${\\mathbf G}$ the sum $s_\\mu$ of distinct weights $w(\\mu)$ with $w\\in W$ viewed as a function on the semisimple elements of $G$ is known to be a generalized Brauer character of $G$ called an orbit character of $G$. 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