The second row of the second table gives you the values of $g^e\pmod{11}$ for $0 \le e \le 10$. Notice that $2^{10}\pmod{11} \equiv 2^{0}\pmod{11}$. This means that any multiple of $2^{10}$ raised to any power is congruent to $1\pmod{11}$.
With that in mind, it shouldn't be hard to see that $2^{2652557887263}\pmod{11} \equiv 2^3\pmod{11}$. So the answer is $8$.
P.S. I suspect your question may be slightly off-topic for this site, hence the down votes.