The factorizations take the form of an optional unit multiplied by integer powers of Gaussian primes.
The table might have been further reduced to the integers in the first octant of the complex plane using the symmetry y + ix =i (x − iy).
The entries in the table resolve this ambiguity by the following convention: the factors are primes in the right complex half plane with absolute value of the real part larger than or equal to the absolute value of the imaginary part.
The entries are sorted according to increasing norm x2 + y2 (sequence A001481 in the OEIS).
Gaussian primes occur only for a subset of norms, detailed in sequence OEIS: A055025.