Unlucky Polynomial

Algebra Level 5

Suppose f(x)f(x) is a polynomial of degree 1313 that satisfies the functional equation f(2x21)=2(f(x))21f(2x^2-1)=2(f(x))^2-1 Find the last three digits of the coefficient of x5x^5 in ff.

Details and assumptions

The coefficient of x5x^5 is a positive integer.

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