Many many tuples

Find the last three digits of the number of 599-tuples (x1,x2,,x599)(x_1,x_2, \ldots, x_{599}) of integers where 0xi5980\leq x_i \leq 598, for i=1i=1 to 599, such that x12x22+x32x42+x5982+x59921(mod599).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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