3. $(-32,0)$. Let $k=-b^{2}$, then $c=\sqrt{a^{2}+b^{2}}=\sqrt{4-k}$, from $1<\frac{\sqrt{4-k}}{2}<3$, we know $-32<k<0$.
3. For the hyperbola $\frac{x^{2}}{4}+\frac{y^{2}}{k}=1$, the eccentricity $e \in(1,3)$, then the range of $k$ is $\qquad$ .