Let $$\alpha, \beta$$ be the roots of the equation $$x^2-x+2=0$$ with $$\operatorname{Im}(\alpha)>\operatorname{Im}(\beta)$$. Then $$\alpha^6+\alpha^4+\beta^4-5 \alpha^2$$ is equal to ___________.

Let the complex numbers $$\alpha$$ and $$\frac{1}{\bar{\alpha}}$$ lie on the circles $$\left|z-z_0\right|^2=4$$ and $$\left|z-z_0\right|^2=16$$ respectively, where $$z_0=1+i$$. Then, the value of $$100|\alpha|^2$$ is __________.

Let $$w=z \bar{z}+k_{1} z+k_{2} i z+\lambda(1+i), k_{1}, k_{2} \in \mathbb{R}$$. Let $$\operatorname{Re}(w)=0$$ be the circle $$\mathrm{C}$$ of radius 1 in the first quadrant touching the line $$y=1$$ and the $$y$$-axis. If the curve $$\operatorname{Im}(w)=0$$ intersects $$\mathrm{C}$$ at $$\mathrm{A}$$ and $$\mathrm{B}$$, then $$30(A B)^{2}$$ is equal to __________