Find the last three digits of the number of 599-tuples \((x_1,x_2, \ldots, x_{599})\) of integers where \(0\leq x_i \leq 598\), for \(i=1\) to 599, such that \[x_1^2-x_2^2+x_3^2-x_4^2+\cdots-x_{598}^2+x_{599}^2 \equiv 1 \pmod{599}.\]

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