$$\frac { 2 ^ { - 9 } \pi } { 2 \sin 11 - \sqrt { 14 \pi } }$$
$-\frac{\pi \left(\sqrt{14\pi }+0.3816179907530896\right)}{512\left(14\pi -0.14563229086642517945095194562816\right)}\approx -0.000981701$