If the line joining the foci of the hyperbola $S_1\equiv \frac{x^2}{a^2}-\frac{y^2}{b^2}+1=0$ does not subtend a right angle at any point on the hyperbola $S_2\equiv \frac{x^2}{4a^2}-\frac{y^2}{b^2}=1,$ then number of integral values of  $4e^2$ is/are (e is eccentricity of $S_2=0$)