How many \(20\)-element subsets of \(\{0,1,2,...,1024\}\) can be ordered to form a geometric progression modulo \(1025\) with common ratio \(2?\)

**Details and assumptions**

The sequence \( \{a_i \} \) is a geometric progression modulo \(1025\) with common ratio \(2\) if \( a_i \equiv a_1 \times 2^{i-1} \pmod{1025} \).

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