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We prove that for finite a point set $P\\subset F^2\\setminus\\{0\\}$, the set $T_\\omega(P)$ of nonzero values of $\\omega$ in $P\\times P$, if nonempty, has cardinality $\\Omega(N^{9/13}).$\n  A presumably near-sharp estimate $\\Omega(N/\\log N)$ was claimed in the abovemnetioned paper over the reals for a symmetric or skew-symmetric form $\\omega$. 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