Table 1 Examples for ${\mathbf{\sum }}_{\mathit{m}\mathbf{=}\mathbf{1}}^{\mathbf{2}\mathit{q}}\stackrel{\mathbf{ˆ}}{\mathit{\sigma }}\mathbf{(}\mathit{m}\mathbf{)}\stackrel{\mathbf{ˆ}}{\mathit{\sigma }}\mathbf{(}\mathbf{2}\mathit{q}\mathbf{+}\mathbf{1}\mathbf{-}\mathit{m}\mathbf{)}$ and $\mathbf{2}{\mathit{T}}_{\mathbf{2}}\mathbf{(}\mathit{q}\mathbf{)}$ ( $\mathbf{1}\mathbf{\le }\mathit{q}\mathbf{\le }\mathbf{11}$ )

${\sum }_{m=1}^{2q}\hat{\sigma }(m)\hat{\sigma }(2q+1-m)$

2

10

28

62

110

182

292

408

570

800

$1\text{,}012$

$2T_2(q)$

2

10

28

60

110

182

280

408

570

770

$1\text{,}012$