Uproot this recurrence

Algebra Level 5

Let \({a_n}\) be the sequence of real numbers defined by \(a_1 = t\) and \(a_{n+1} = 4a_n(1 - a_n)\) for \(n \geq 1\).

If the number of distinct values of \(t\) such that \(a_{1998} = 0\) is \(x\), find the value of \(x \pmod {1000}\).

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