An ellipse \( E:\; \displaystyle\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1 \) passes through the vertices of the hyperbola \( H:\; \displaystyle\frac{x^{2}}{49}-\frac{y^{2}}{64}=-1 \). Let the major and minor axes of the ellipse \( E \) coincide with the transverse and conjugate axes of the hyperbola \( H \), respectively. Let the product of the eccentricities of \( E \) and \( H \) be \( {1}/{2} \). If \( l \) is the length of the latus rectum of the ellipse \( E \), then the value of \( 113l \) is equal to ______.
