sage: G = GaussianIntegers()
sage: r = 30
sage: good = [] # prime and equal to 1 modulo (8 * ZZ[i])
sage: nope = [] # others
sage: for a in (-r .. r):
....:     for b in (-r .. r):
....:         g = G((a, b))
....:         if a % 8 ==1 and g.is_prime():
....:             good.append(g)
....:         else:
....:             nope.append(g)
....:

sage: plot_good = point2d(good, color='red', size=10)
sage: plot_nope = point2d(nope, color='blue', size=1)
sage: (plot_good + plot_nope).show(aspect_ratio=1, figsize=7)
Launched png viewer for Graphics object consisting of 2 graphics primitives

sage: (plot_good + plot_nope).save('gaussian_primes.png', aspect_ratio=1, figsize=7)

sage: [g for g in good if not g.norm().is_prime()]
[-23, -7]