Let $$y=y(x)$$ be the solution curve of the differential equation

$$\sin \left( {2{x^2}} \right){\log _e}\left( {\tan {x^2}} \right)dy + \left( {4xy - 4\sqrt 2 x\sin \left( {{x^2} - {\pi \over 4}} \right)} \right)dx = 0$$, $$0 < x < \sqrt {{\pi \over 2}} $$, which passes through the point $$\left(\sqrt{\frac{\pi}{6}}, 1\right)$$. Then $$\left|y\left(\sqrt{\frac{\pi}{3}}\right)\right|$$ is equal to ______________.

Let $$f(x)=2 x^{2}-x-1$$ and $$\mathrm{S}=\{n \in \mathbb{Z}:|f(n)| \leq 800\}$$. Then, the value of $$\sum\limits_{n \in S} f(n)$$ is equal to ___________.

Let $$S$$ be the set containing all $$3 \times 3$$ matrices with entries from $$\{-1,0,1\}$$. The total number of matrices $$A \in S$$ such that the sum of all the diagonal elements of $$A^{\mathrm{T}} A$$ is 6 is ____________.

If the length of the latus rectum of the ellipse $$x^{2}+4 y^{2}+2 x+8 y-\lambda=0$$ is 4 , and $$l$$ is the length of its major axis, then $$\lambda+l$$ is equal to ____________.