Square modulo \(7\)

Number Theory Level pending

Consider the function \(f: \mathbb Z \to \mathbb Z_7\) below:

\[ f(n)=n^2 \mod 7 \]

where \(\mathbb Z_7= \{0,1,2,3,4,5,6\}\).

Find the sum of distinct values of \(f\).

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