Let $z=\frac{1-i\sqrt{3}}{2},i=\sqrt{-1}$. Then the value of $21+{\left(z+\frac{1}{z}\right)}^3+{\left(z^2+\frac{1}{z^2}\right)}^3+{\left(z^3+\frac{1}{z^3}\right)}^3+\dots +{\left(z^{21}+\frac{1}{z^{21}}\right)}^3$ is______.

Let $Z$ be the set of all integers,
$A=\left\{(x,y)\in Z\times Z:(x-2{)}^2+y^2\le 4\right\}$

$B=\left\{(x,y)\in Z\times Z:x^2+y^2\le 4\right\}\text{ and }$

$C=\left\{(x,y)\in Z\times Z:(x-2{)}^2+(y-2{)}^2\le 4\right\}$
If the total number of relations from $A\cap B$ to $A\cap C$ is $2^p$, then the value of $p$ is: