Loog at this Familiar Recursive!

Consider the sequence \(a_1, a_2, a_3, \ldots\) where

\[a_1= 1, a_2 = 3, a_n = a_{n - 1} a_{n - 2}\]

for \(n \geq 3\). Calculate the remainder when \(a_{514}\) is divided by \(11\).

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