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More precisely, given a particle label \\(p\\in\\T^3\\), a time \\(T>0\\), and \\(F_*\\in\\SL(3,\\R)\\), every sufficiently large odd integer \\(N\\) admits a real-analytic curl eigenfield \\(W_N\\) with \\(\\operatorname{curl}W_N=NW_N\\). 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