Bash Me Not

Let \(g_{0},g_{1},g_{2},...,g_{n}\) be a sequence satisfying the Fibonacci recurrence relation such that\[g_{n}=g_{n-1}+g_{n-2}\]\[g_{0}=2, g_{1}=-1\] where \(2 \leq n\) Find \(g_{496}\) and enter the last two digits. You may use a computational engine if and only if you found the general formula. Before it was the first perfect number now it's the third!

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