Lucky number 9!

For every integer \(0 \leq i \leq 9\) and \( a_i \in (0,1,2,3,4)\), given that \(\displaystyle 6\sum_{i=0}^{9} a_i 5^i\) \(\equiv\) \(1\) \(mod\) \((5^{10})\).

Find the value of \(a_{9}\).

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