Let \( S=\left\{ z\in\mathbb{C}-\{i,2i\}:\dfrac{z^{2}+8iz-15}{z^{2}-3iz-2}\in\mathbb{R}\right\}. \) If \( \alpha-\dfrac{13}{11}i\in S,\; \alpha\in\mathbb{R}-\{0\} \), then \( 242\alpha^{2} \) is equal to ______.
