\[\displaystyle \left( \prod _{\text{ord}(n)<p-1}^{}{ n } \right) \pmod{1601}\]

Consider the prime number \(1601\). Let \(\text{ord}(x)\) denote the least \(j>0\) such that \(x^j\equiv 1 \pmod{1601}\). Evaluate the product above over the set of nonzero residues modulo \(1601\).

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