Given a function f for which

f(x)=f(398-x)=f(2158-x)=f(3214-x)

holds for all real x, what is the largest number of different values that can appear in the list f(0), f(1), f(2), \ldots, f(999) ?

Given a function f for which

f(x)=f(398-x)=f(2158-x)=f(3214-x)

holds for all real x, what is the largest number of different values that can appear in the list f(0), f(1), f(2), \ldots, f(999) ?