The GIsieve function generates a list of Gaussian primes $x+\mathrm{I}y$ whose norms are less than or equal to $m^2$, and who are located in the one-eighth plane defined by $0\le y<x$ .

Any prime found in that area has seven more associated primes: $-x+\mathrm{I}y$, $\pm x-\mathrm{I}y$,  $\pm y-\mathrm{I}x$, except for $1+\mathrm{I}$ which exceptionally lies on $x=y$ and has only three associated primes.

$\mathrm{with}\left(\mathrm{GaussInt}\right)\&colon;$

$\mathrm{GIsieve}\left(10\right)$

$\left[14\&comma;\left[1+\mathrm{I}\&comma;2+\mathrm{I}\&comma;3\&comma;3+2\mathrm{I}\&comma;4+\mathrm{I}\&comma;5+2\mathrm{I}\&comma;6+\mathrm{I}\&comma;5+4\mathrm{I}\&comma;7\&comma;7+2\mathrm{I}\&comma;6+5\mathrm{I}\&comma;8+3\mathrm{I}\&comma;8+5\mathrm{I}\&comma;9+4\mathrm{I}\right]\right]$

$\mathrm{plots}:-\mathrm{display}\left(\mathrm{plots}:-\mathrm{complexplot}\left(\mathrm{GIsieve}\left(100\right)\left[2\right]\&comma;'\mathrm{style}'='\mathrm{point}'\right)\&comma;\mathrm{plot}\left(x\&comma;x=0..100\right)\right)$