Latin squares with autoparatopism (id,id,gamma;(12)) where gamma is an involution. These represent all possible congugacy classes of autoparatopisms of this type, for orders n \le 17. gamma will be the involution (1,n-1)(2,n-2)(3,n-3)...(r,n-r) where 1 \le r \le (n-1)/2. We do not bother with the trivial case r=0. 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