Let \(N\) be the sum of all positive integers \(q\) of the form \(q=p^k\) with prime \(p\), such that for at least four different integer values of \(x\) from \(1\) to \(q\),

\[x^3-3x\equiv 123 \pmod{q}.\]

What are the last 3 digits of \(N?\)

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