N$_{out}$, they can be neglected. In what follows, among the CFS of a state, if some of them have N$_{out}\geq 8$, then those with N$_{out}\leq 7$ are neglected; if all the CFS has N$_{out}\leq 7,$ then all of them would be neglected except the one with the largest N$_{out}$; all the CFS with N$_{out}=12$ are neglected without exception. After the neglect, the remaining CFS  are call the favorable structures (FSs), they are listed in Table 2. E.g., the $L=86$ state has four CFS ,  namely the (5)$_{c}$-8, (9)$_{c}$-4, (11)$_{c}$-2, and (12)$_{c}$-1 .  Among them only the (5)$_{c}$-8 as a FS is listed in Table 2.   When a state has more than three FS, only the most competitive three are listed.

\(iv) [** Excitation of the core**]{}

This paper concerns only the low-lying states with $L\geq N(N-1)$ $/2$ ( or the filling factor $\nu \leq 1$ ), they contain mainly the BFs belonging to the LLL. In these BFs, the angular momenta of any pair of electrons can not be the same due to the Pauli Principle. Therefore, they can be denoted as $%
\psi _{\alpha }=\{l_{1}l_{2}\cdot \cdot \cdot l_{N}\}$ with  $l_{i}<l_{i+1}$.

 Since we have

$<\phi _{l0}|r^{2}|\phi _{l0}>=(l+1)\frac{\hbar }{m^{\ast
}\Omega _{o}},\qquad 