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"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)."
That symmetry maps between the 1st and 4th quadrants. It rotates by +/- 90 degrees so maps between the 1st and 7th octant and between the 2nd and 8th octant.
e.g. 2+i == i(1-2i) is a first octant term compared to a 7th octant term.
"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 ambiguity is not resolved. Consider 1+i == i(1 - i) Both of these have x > 0 and hence are in the right complex half plane. Both of these have the absolute value of the real part larger than or equal to the absolute value of the imaginary part.
