Table 9 Convolution sum when N is prime

N : prime

${\mathbf{\sum }}_{\mathit{k}\mathbf{=}\mathbf{1}}^{\mathit{N}\mathbf{-}\mathbf{1}}{\mathit{\sigma }}_{\mathbf{1}}^{\mathbf{\ast }}\mathbf{(}\mathit{k}\mathbf{)}{\mathit{\sigma }}_{\mathbf{1}}^{\mathbf{\ast }}\mathbf{(}\mathit{N}\mathbf{-}\mathit{k}\mathbf{)}$

${\mathbf{\sum }}_{\mathit{k}\mathbf{=}\mathbf{1}}^{\mathit{N}\mathbf{-}\mathbf{1}}{\mathit{\sigma }}_{\mathbf{1}}^{\mathbf{\ast }}\mathbf{(}\mathit{k}\mathbf{;}\mathbf{4}\mathbf{)}{\mathit{\sigma }}_{\mathbf{1}}^{\mathbf{\ast }}\mathbf{(}\mathit{N}\mathbf{-}\mathit{k}\mathbf{;}\mathbf{4}\mathbf{)}$