Uproot this recurrence

Algebra Level 5

Let an{a_n} be the sequence of real numbers defined by a1=ta_1 = t and an+1=4an(1an)a_{n+1} = 4a_n(1 - a_n) for n1n \geq 1.

If the number of distinct values of tt such that a1998=0a_{1998} = 0 is xx, find the value of x(mod1000)x \pmod {1000}.

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