Arithmetic Sequence coefficients

Algebra Level 5

A linear function f(x)=bx+af(x)=bx+a has the property that f(f(x))=dx+cf\big(f(x)\big)=dx+c is another linear function such that a,b,c,da,b,c,d are integers that are consecutive terms in an arithmetic sequence. Find the last three digits of the sum of all possible values of f(2013)f(2013).

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