Table of Gaussian integer factorizations

A Gaussian integer is either the zero, one of the four units (±1, ±i), a Gaussian prime or composite. The article is a table of Gaussian Integers {{math|x + iy}} followed either by an explicit factorization or followed by the label (p) if the integer is a Gaussian prime. The factorizations take the form of an optional unit multiplied by integer powers of Gaussian primes.

Note that there are rational primes which are not Gaussian primes. A simple example is the rational prime 5, which is factored as {{math|5{{=}}(2+i)(2−i)}} in the table, and therefore not a Gaussian prime.

Conventions

The second column of the table contains only integers in the first quadrant, which means the real part x is positive and the imaginary part y is non-negative. The table might have been further reduced to the integers in the first octant of the

complex plane using the symmetry

{{math|y + ix {{=}}i (x − iy)}}.

The factorizations are often not unique in the sense that the unit could be absorbed into any other factor with exponent equal to one. The entry {{math|4+2i {{=}} −i(1+i)²(2+i)}}, for example, could also be written as {{math|4+2i{{=}} (1+i)²(1−2i)}}. 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 {{math|x² + y²}} {{OEIS|A001481}}. The table is complete up to the maximum norm at the end of the table in the sense that

each composite or prime in the first quadrant appears in the second column.

Gaussian primes occur only for a subset of norms, detailed in sequence {{OEIS2C|A055025}}. This here is a composition of sequences {{OEIS2C|A103431}} and {{OEIS2C|A103432}}.

Factorizations

{{table TOC|allowtoc=yes|title=Norm|1–250|251–500|501–750|751–1000}}

Norm \|\| Integer \|\| Factorization
id="1–250" class="wikitable sortable" style="float:left; margin-right:1em" \|+ Norm 1–250
2	{{math\| 1+i}}	(p)
4	{{math\| 2}}	{{math\| −i·(1+i)²}}
5	{{math\| 2+i}} {{math\| 1+2i}}	(p) (p)
8	{{math\| 2+2i}}	{{math\| −i·(1+i)³}}
9	{{math\| 3}}	(p)
10	{{math\| 1+3i}} {{math\| 3+i}}	{{math\| (1+i)·(2+i)}} {{math\| (1+i)·(2−i)}}
13	{{math\| 3+2i}} {{math\| 2+3i}}	(p) (p)
16	{{math\| 4}}	{{math\| −(1+i)⁴}}
17	{{math\| 1+4i}} {{math\| 4+i}}	(p) (p)
18	{{math\| 3+3i}}	{{math\| (1+i)·3}}
20	{{math\| 2+4i}} {{math\| 4+2i}}	{{math\| (1+i)²·(2−i)}} {{math\| −i·(1+i)²·(2+i)}}
25	{{math\| 3+4i}} {{math\| 4+3i}} {{math\| 5}}	{{math\| (2+i)²}} {{math\| i·(2−i)²}} {{math\| (2+i)·(2−i)}}
26	{{math\| 1+5i}} {{math\| 5+i}}	{{math\| (1+i)·(3+2i)}} {{math\| (1+i)·(3−2i)}}
29	{{math\| 2+5i}} {{math\| 5+2i}}	(p) (p)
32	{{math\| 4+4i}}	{{math\| −(1+i)⁵}}
34	{{math\| 3+5i}} {{math\| 5+3i}}	{{math\| (1+i)·(4+i)}} {{math\| (1+i)·(4−i)}}
36	{{math\| 6}}	{{math\| −i·(1+i)²·3}}
37	{{math\| 1+6i}} {{math\| 6+i}}	(p) (p)
40	{{math\| 2+6i}} {{math\| 6+2i}}	{{math\| −i·(1+i)³·(2+i)}} {{math\| −i·(1+i)³·(2−i)}}
41	{{math\| 4+5i}} {{math\| 5+4i}}	(p) (p)
45	{{math\| 3+6i}} {{math\| 6+3i}}	{{math\| i·(2−i)·3}} {{math\| (2+i)·3}}
49	{{math\| 7}}	(p)
50	{{math\| 1+7i}} {{math\| 5+5i}} {{math\| 7+i}}	{{math\| i·(1+i)·(2−i)²}} {{math\| (1+i)·(2+i)·(2−i)}} {{math\| −i·(1+i)·(2+i)²}}
52	{{math\| 4+6i}} {{math\| 6+4i}}	{{math\| (1+i)²·(3−2i)}} {{math\| −i·(1+i)²·(3+2i)}}
53	{{math\| 2+7i}} {{math\| 7+2i}}	(p) (p)
58	{{math\| 3+7i}} {{math\| 7+3i}}	{{math\| (1+i)·(5+2i)}} {{math\| (1+i)·(5−2i)}}
61	{{math\| 5+6i}} {{math\| 6+5i}}	(p) (p)
64	{{math\| 8}}	{{math\| i·(1+i)⁶}}
65	{{math\| 1+8i}} {{math\| 4+7i}} {{math\| 7+4i}} {{math\| 8+i}}	{{math\| i·(2+i)·(3−2i)}} {{math\| (2+i)·(3+2i)}} {{math\| i·(2−i)·(3−2i)}} {{math\| (2−i)·(3+2i)}}
68	{{math\| 2+8i}} {{math\| 8+2i}}	{{math\| (1+i)²·(4−i)}} {{math\| −i·(1+i)²·(4+i)}}
72	{{math\| 6+6i}}	{{math\| −i·(1+i)³·3}}
73	{{math\| 3+8i}} {{math\| 8+3i}}	(p) (p)
74	{{math\| 5+7i}} {{math\| 7+5i}}	{{math\| (1+i)·(6+i)}} {{math\| (1+i)·(6−i)}}
80	{{math\| 4+8i}} {{math\| 8+4i}}	{{math\| −i·(1+i)⁴·(2−i)}} {{math\| −(1+i)⁴·(2+i)}}
81	{{math\| 9}}	{{math\| 3²}}
82	{{math\| 1+9i}} {{math\| 9+i}}	{{math\| (1+i)·(5+4i)}} {{math\| (1+i)·(5−4i)}}
85	{{math\| 2+9i}} {{math\| 6+7i}} {{math\| 7+6i}} {{math\| 9+2i}}	{{math\| i·(2−i)·(4+i)}} {{math\| i·(2−i)·(4−i)}} {{math\| (2+i)·(4+i)}} {{math\| (2+i)·(4−i)}}
89	{{math\| 5+8i}} {{math\| 8+5i}}	(p) (p)
90	{{math\| 3+9i}} {{math\| 9+3i}}	{{math\| (1+i)·(2+i)·3}} {{math\| (1+i)·(2−i)·3}}
97	{{math\| 4+9i}} {{math\| 9+4i}}	(p) (p)
98	{{math\| 7+7i}}	{{math\| (1+i)·7}}
100	{{math\| 6+8i}} {{math\| 8+6i}} {{math\| 10}}	{{math\| −i·(1+i)²·(2+i)²}} {{math\| (1+i)²·(2−i)²}} {{math\| −i·(1+i)²·(2+i)·(2−i)}}
101	{{math\| 1+10i}} {{math\| 10+i}}	(p) (p)
104	{{math\| 2+10i}} {{math\| 10+2i}}	{{math\| −i·(1+i)³·(3+2i)}} {{math\| −i·(1+i)³·(3−2i)}}
106	{{math\| 5+9i}} {{math\| 9+5i}}	{{math\| (1+i)·(7+2i)}} {{math\| (1+i)·(7−2i)}}
109	{{math\| 3+10i}} {{math\| 10+3i}}	(p) (p)
113	{{math\| 7+8i}} {{math\| 8+7i}}	(p) (p)
116	{{math\| 4+10i}} {{math\| 10+4i}}	{{math\| (1+i)²·(5−2i)}} {{math\| −i·(1+i)²·(5+2i)}}
117	{{math\| 6+9i}} {{math\| 9+6i}}	{{math\| i·3·(3−2i)}} {{math\| 3·(3+2i)}}
121	{{math\| 11}}	(p)
122	{{math\| 1+11i}} {{math\| 11+i}}	{{math\| (1+i)·(6+5i)}} {{math\| (1+i)·(6−5i)}}
125	{{math\| 2+11i}} {{math\| 5+10i}} {{math\| 10+5i}} {{math\| 11+2i}}	{{math\| (2+i)³}} {{math\| i·(2+i)·(2−i)²}} {{math\| (2+i)²·(2−i)}} {{math\| i·(2−i)³}}
128	{{math\| 8+8i}}	{{math\| i·(1+i)⁷}}
130	{{math\| 3+11i}} {{math\| 7+9i}} {{math\| 9+7i}} {{math\| 11+3i}}	{{math\| i·(1+i)·(2−i)·(3−2i)}} {{math\| (1+i)·(2−i)·(3+2i)}} {{math\| (1+i)·(2+i)·(3−2i)}} {{math\| −i·(1+i)·(2+i)·(3+2i)}}
136	{{math\| 6+10i}} {{math\| 10+6i}}	{{math\| −i·(1+i)³·(4+i)}} {{math\| −i·(1+i)³·(4−i)}}
137	{{math\| 4+11i}} {{math\| 11+4i}}	(p) (p)
144	{{math\| 12}}	{{math\| −(1+i)⁴·3}}
145	{{math\| 1+12i}} {{math\| 8+9i}} {{math\| 9+8i}} {{math\| 12+i}}	{{math\| i·(2−i)·(5+2i)}} {{math\| (2+i)·(5+2i)}} {{math\| i·(2−i)·(5−2i)}} {{math\| (2+i)·(5−2i)}}
146	{{math\| 5+11i}} {{math\| 11+5i}}	{{math\| (1+i)·(8+3i)}} {{math\| (1+i)·(8−3i)}}
148	{{math\| 2+12i}} {{math\| 12+2i}}	{{math\| (1+i)²·(6−i)}} {{math\| −i·(1+i)²·(6+i)}}
149	{{math\| 7+10i}} {{math\| 10+7i}}	(p) (p)
153	{{math\| 3+12i}} {{math\| 12+3i}}	{{math\| i·3·(4−i)}} {{math\| 3·(4+i)}}
157	{{math\| 6+11i}} {{math\| 11+6i}}	(p) (p)
160	{{math\| 4+12i}} {{math\| 12+4i}}	{{math\| −(1+i)⁵·(2+i)}} {{math\| −(1+i)⁵·(2−i)}}
162	{{math\| 9+9i}}	{{math\| (1+i)·3²}}
164	{{math\| 8+10i}} {{math\| 10+8i}}	{{math\| (1+i)²·(5−4i)}} {{math\| −i·(1+i)²·(5+4i)}}
169	{{math\| 5+12i}} {{math\| 12+5i}} {{math\| 13}}	{{math\| (3+2i)²}} {{math\| i·(3−2i)²}} {{math\| (3+2i)·(3−2i)}}
170	{{math\| 1+13i}} {{math\| 7+11i}} {{math\| 11+7i}} {{math\| 13+i}}	{{math\| (1+i)·(2+i)·(4+i)}} {{math\| (1+i)·(2+i)·(4−i)}} {{math\| (1+i)·(2−i)·(4+i)}} {{math\| (1+i)·(2−i)·(4−i)}}
173	{{math\| 2+13i}} {{math\| 13+2i}}	(p) (p)
178	{{math\| 3+13i}} {{math\| 13+3i}}	{{math\| (1+i)·(8+5i)}} {{math\| (1+i)·(8−5i)}}
180	{{math\| 6+12i}} {{math\| 12+6i}}	{{math\| (1+i)²·(2−i)·3}} {{math\| −i·(1+i)²·(2+i)·3}}
181	{{math\| 9+10i}} {{math\| 10+9i}}	(p) (p)
185	{{math\| 4+13i}} {{math\| 8+11i}} {{math\| 11+8i}} {{math\| 13+4i}}	{{math\| i·(2−i)·(6+i)}} {{math\| i·(2−i)·(6−i)}} {{math\| (2+i)·(6+i)}} {{math\| (2+i)·(6−i)}}
193	{{math\| 7+12i}} {{math\| 12+7i}}	(p) (p)
194	{{math\| 5+13i}} {{math\| 13+5i}}	{{math\| (1+i)·(9+4i)}} {{math\| (1+i)·(9−4i)}}
196	{{math\| 14}}	{{math\| −i·(1+i)²·7}}
197	{{math\| 1+14i}} {{math\| 14+i}}	(p) (p)
200	{{math\| 2+14i}} {{math\| 10+10i}} {{math\| 14+2i}}	{{math\| (1+i)³·(2−i)²}} {{math\| −i·(1+i)³·(2+i)·(2−i)}} {{math\| −(1+i)³·(2+i)²}}
202	{{math\| 9+11i}} {{math\| 11+9i}}	{{math\| (1+i)·(10+i)}} {{math\| (1+i)·(10−i)}}
205	{{math\| 3+14i}} {{math\| 6+13i}} {{math\| 13+6i}} {{math\| 14+3i}}	{{math\| i·(2+i)·(5−4i)}} {{math\| (2+i)·(5+4i)}} {{math\| i·(2−i)·(5−4i)}} {{math\| (2−i)·(5+4i)}}
208	{{math\| 8+12i}} {{math\| 12+8i}}	{{math\| −i·(1+i)⁴·(3−2i)}} {{math\| −(1+i)⁴·(3+2i)}}
212	{{math\| 4+14i}} {{math\| 14+4i}}	{{math\| (1+i)²·(7−2i)}} {{math\| −i·(1+i)²·(7+2i)}}
218	{{math\| 7+13i}} {{math\| 13+7i}}	{{math\| (1+i)·(10+3i)}} {{math\| (1+i)·(10−3i)}}
221	{{math\| 5+14i}} {{math\| 10+11i}} {{math\| 11+10i}} {{math\| 14+5i}}	{{math\| i·(3−2i)·(4+i)}} {{math\| (3+2i)·(4+i)}} {{math\| i·(3−2i)·(4−i)}} {{math\| (3+2i)·(4−i)}}
225	{{math\| 9+12i}} {{math\| 12+9i}} {{math\| 15}}	{{math\| (2+i)²·3}} {{math\| i·(2−i)²·3}} {{math\| (2+i)·(2−i)·3}}
226	{{math\| 1+15i}} {{math\| 15+i}}	{{math\| (1+i)·(8+7i)}} {{math\| (1+i)·(8−7i)}}
229	{{math\| 2+15i}} {{math\| 15+2i}}	(p) (p)
232	{{math\| 6+14i}} {{math\| 14+6i}}	{{math\| −i·(1+i)³·(5+2i)}} {{math\| −i·(1+i)³·(5−2i)}}
233	{{math\| 8+13i}} {{math\| 13+8i}}	(p) (p)
234	{{math\| 3+15i}} {{math\| 15+3i}}	{{math\| (1+i)·3·(3+2i)}} {{math\| (1+i)·3·(3−2i)}}
241	{{math\| 4+15i}} {{math\| 15+4i}}	(p) (p)
242	{{math\| 11+11i}}	{{math\| (1+i)·11}}
244	{{math\| 10+12i}} {{math\| 12+10i}}	{{math\| (1+i)²·(6−5i)}} {{math\| −i·(1+i)²·(6+5i)}}
245	{{math\| 7+14i}} {{math\| 14+7i}}	{{math\| i·(2−i)·7}} {{math\| (2+i)·7}}
250	{{math\| 5+15i}} {{math\| 9+13i}} {{math\| 13+9i}} {{math\| 15+5i}}	{{math\| (1+i)·(2+i)²·(2−i)}} {{math\| i·(1+i)·(2−i)³}} {{math\| −i·(1+i)·(2+i)³}} {{math\| (1+i)·(2+i)·(2−i)²}}

Norm \|\| Integer \|\| Factorization
id="251–500" class="wikitable sortable" style="float:left; margin-right:1em" \|+ Norm 251–500
256	{{math\| 16}}	{{math\| (1+i)⁸}}
257	{{math\| 1+16i}} {{math\| 16+i}}	(p) (p)
260	{{math\| 2+16i}} {{math\| 8+14i}} {{math\| 14+8i}} {{math\| 16+2i}}	{{math\| (1+i)²·(2+i)·(3−2i)}} {{math\| −i·(1+i)²·(2+i)·(3+2i)}} {{math\| (1+i)²·(2−i)·(3−2i)}} {{math\| −i·(1+i)²·(2−i)·(3+2i)}}
261	{{math\| 6+15i}} {{math\| 15+6i}}	{{math\| i·3·(5−2i)}} {{math\| 3·(5+2i)}}
265	{{math\| 3+16i}} {{math\| 11+12i}} {{math\| 12+11i}} {{math\| 16+3i}}	{{math\| i·(2−i)·(7+2i)}} {{math\| i·(2−i)·(7−2i)}} {{math\| (2+i)·(7+2i)}} {{math\| (2+i)·(7−2i)}}
269	{{math\| 10+13i}} {{math\| 13+10i}}	(p) (p)
272	{{math\| 4+16i}} {{math\| 16+4i}}	{{math\| −i·(1+i)⁴·(4−i)}} {{math\| −(1+i)⁴·(4+i)}}
274	{{math\| 7+15i}} {{math\| 15+7i}}	{{math\| (1+i)·(11+4i)}} {{math\| (1+i)·(11−4i)}}
277	{{math\| 9+14i}} {{math\| 14+9i}}	(p) (p)
281	{{math\| 5+16i}} {{math\| 16+5i}}	(p) (p)
288	{{math\| 12+12i}}	{{math\| −(1+i)⁵·3}}
289	{{math\| 8+15i}} {{math\| 15+8i}} {{math\| 17}}	{{math\| i·(4−i)²}} {{math\| (4+i)²}} {{math\| (4+i)·(4−i)}}
290	{{math\| 1+17i}} {{math\| 11+13i}} {{math\| 13+11i}} {{math\| 17+i}}	{{math\| i·(1+i)·(2−i)·(5−2i)}} {{math\| (1+i)·(2+i)·(5−2i)}} {{math\| (1+i)·(2−i)·(5+2i)}} {{math\| −i·(1+i)·(2+i)·(5+2i)}}
292	{{math\| 6+16i}} {{math\| 16+6i}}	{{math\| (1+i)²·(8−3i)}} {{math\| −i·(1+i)²·(8+3i)}}
293	{{math\| 2+17i}} {{math\| 17+2i}}	(p) (p)
296	{{math\| 10+14i}} {{math\| 14+10i}}	{{math\| −i·(1+i)³·(6+i)}} {{math\| −i·(1+i)³·(6−i)}}
298	{{math\| 3+17i}} {{math\| 17+3i}}	{{math\| (1+i)·(10+7i)}} {{math\| (1+i)·(10−7i)}}
305	{{math\| 4+17i}} {{math\| 7+16i}} {{math\| 16+7i}} {{math\| 17+4i}}	{{math\| i·(2+i)·(6−5i)}} {{math\| (2+i)·(6+5i)}} {{math\| i·(2−i)·(6−5i)}} {{math\| (2−i)·(6+5i)}}
306	{{math\| 9+15i}} {{math\| 15+9i}}	{{math\| (1+i)·3·(4+i)}} {{math\| (1+i)·3·(4−i)}}
313	{{math\| 12+13i}} {{math\| 13+12i}}	(p) (p)
314	{{math\| 5+17i}} {{math\| 17+5i}}	{{math\| (1+i)·(11+6i)}} {{math\| (1+i)·(11−6i)}}
317	{{math\| 11+14i}} {{math\| 14+11i}}	(p) (p)
320	{{math\| 8+16i}} {{math\| 16+8i}}	{{math\| −(1+i)⁶·(2−i)}} {{math\| i·(1+i)⁶·(2+i)}}
324	{{math\| 18}}	{{math\| −i·(1+i)²·3²}}
325	{{math\| 1+18i}} {{math\| 6+17i}} {{math\| 10+15i}} {{math\| 15+10i}} {{math\| 17+6i}} {{math\| 18+i}}	{{math\| (2+i)²·(3+2i)}} {{math\| i·(2−i)²·(3+2i)}} {{math\| i·(2+i)·(2−i)·(3−2i)}} {{math\| (2+i)·(2−i)·(3+2i)}} {{math\| (2+i)²·(3−2i)}} {{math\| i·(2−i)²·(3−2i)}}
328	{{math\| 2+18i}} {{math\| 18+2i}}	{{math\| −i·(1+i)³·(5+4i)}} {{math\| −i·(1+i)³·(5−4i)}}
333	{{math\| 3+18i}} {{math\| 18+3i}}	{{math\| i·3·(6−i)}} {{math\| 3·(6+i)}}
337	{{math\| 9+16i}} {{math\| 16+9i}}	(p) (p)
338	{{math\| 7+17i}} {{math\| 13+13i}} {{math\| 17+7i}}	{{math\| i·(1+i)·(3−2i)²}} {{math\| (1+i)·(3+2i)·(3−2i)}} {{math\| −i·(1+i)·(3+2i)²}}
340	{{math\| 4+18i}} {{math\| 12+14i}} {{math\| 14+12i}} {{math\| 18+4i}}	{{math\| (1+i)²·(2−i)·(4+i)}} {{math\| (1+i)²·(2−i)·(4−i)}} {{math\| −i·(1+i)²·(2+i)·(4+i)}} {{math\| −i·(1+i)²·(2+i)·(4−i)}}
346	{{math\| 11+15i}} {{math\| 15+11i}}	{{math\| (1+i)·(13+2i)}} {{math\| (1+i)·(13−2i)}}
349	{{math\| 5+18i}} {{math\| 18+5i}}	(p) (p)
353	{{math\| 8+17i}} {{math\| 17+8i}}	(p) (p)
356	{{math\| 10+16i}} {{math\| 16+10i}}	{{math\| (1+i)²·(8−5i)}} {{math\| −i·(1+i)²·(8+5i)}}
360	{{math\| 6+18i}} {{math\| 18+6i}}	{{math\| −i·(1+i)³·(2+i)·3}} {{math\| −i·(1+i)³·(2−i)·3}}
361	{{math\| 19}}	(p)
362	{{math\| 1+19i}} {{math\| 19+i}}	{{math\| (1+i)·(10+9i)}} {{math\| (1+i)·(10−9i)}}
365	{{math\| 2+19i}} {{math\| 13+14i}} {{math\| 14+13i}} {{math\| 19+2i}}	{{math\| i·(2−i)·(8+3i)}} {{math\| (2+i)·(8+3i)}} {{math\| i·(2−i)·(8−3i)}} {{math\| (2+i)·(8−3i)}}
369	{{math\| 12+15i}} {{math\| 15+12i}}	{{math\| i·3·(5−4i)}} {{math\| 3·(5+4i)}}
370	{{math\| 3+19i}} {{math\| 9+17i}} {{math\| 17+9i}} {{math\| 19+3i}}	{{math\| (1+i)·(2+i)·(6+i)}} {{math\| (1+i)·(2+i)·(6−i)}} {{math\| (1+i)·(2−i)·(6+i)}} {{math\| (1+i)·(2−i)·(6−i)}}
373	{{math\| 7+18i}} {{math\| 18+7i}}	(p) (p)
377	{{math\| 4+19i}} {{math\| 11+16i}} {{math\| 16+11i}} {{math\| 19+4i}}	{{math\| i·(3−2i)·(5+2i)}} {{math\| (3+2i)·(5+2i)}} {{math\| i·(3−2i)·(5−2i)}} {{math\| (3+2i)·(5−2i)}}
386	{{math\| 5+19i}} {{math\| 19+5i}}	{{math\| (1+i)·(12+7i)}} {{math\| (1+i)·(12−7i)}}
388	{{math\| 8+18i}} {{math\| 18+8i}}	{{math\| (1+i)²·(9−4i)}} {{math\| −i·(1+i)²·(9+4i)}}
389	{{math\| 10+17i}} {{math\| 17+10i}}	(p) (p)
392	{{math\| 14+14i}}	{{math\| −i·(1+i)³·7}}
394	{{math\| 13+15i}} {{math\| 15+13i}}	{{math\| (1+i)·(14+i)}} {{math\| (1+i)·(14−i)}}
397	{{math\| 6+19i}} {{math\| 19+6i}}	(p) (p)
400	{{math\| 12+16i}} {{math\| 16+12i}} {{math\| 20}}	{{math\| −(1+i)⁴·(2+i)²}} {{math\| −i·(1+i)⁴·(2−i)²}} {{math\| −(1+i)⁴·(2+i)·(2−i)}}
401	{{math\| 1+20i}} {{math\| 20+i}}	(p) (p)
404	{{math\| 2+20i}} {{math\| 20+2i}}	{{math\| (1+i)²·(10−i)}} {{math\| −i·(1+i)²·(10+i)}}
405	{{math\| 9+18i}} {{math\| 18+9i}}	{{math\| i·(2−i)·3²}} {{math\| (2+i)·3²}}
409	{{math\| 3+20i}} {{math\| 20+3i}}	(p) (p)
410	{{math\| 7+19i}} {{math\| 11+17i}} {{math\| 17+11i}} {{math\| 19+7i}}	{{math\| i·(1+i)·(2−i)·(5−4i)}} {{math\| (1+i)·(2−i)·(5+4i)}} {{math\| (1+i)·(2+i)·(5−4i)}} {{math\| −i·(1+i)·(2+i)·(5+4i)}}
416	{{math\| 4+20i}} {{math\| 20+4i}}	{{math\| −(1+i)⁵·(3+2i)}} {{math\| −(1+i)⁵·(3−2i)}}
421	{{math\| 14+15i}} {{math\| 15+14i}}	(p) (p)
424	{{math\| 10+18i}} {{math\| 18+10i}}	{{math\| −i·(1+i)³·(7+2i)}} {{math\| −i·(1+i)³·(7−2i)}}
425	{{math\| 5+20i}} {{math\| 8+19i}} {{math\| 13+16i}} {{math\| 16+13i}} {{math\| 19+8i}} {{math\| 20+5i}}	{{math\| i·(2+i)·(2−i)·(4−i)}} {{math\| (2+i)²·(4+i)}} {{math\| i·(2−i)²·(4+i)}} {{math\| (2+i)²·(4−i)}} {{math\| i·(2−i)²·(4−i)}} {{math\| (2+i)·(2−i)·(4+i)}}
433	{{math\| 12+17i}} {{math\| 17+12i}}	(p) (p)
436	{{math\| 6+20i}} {{math\| 20+6i}}	{{math\| (1+i)²·(10−3i)}} {{math\| −i·(1+i)²·(10+3i)}}
441	{{math\| 21}}	{{math\| 3·7}}
442	{{math\| 1+21i}} {{math\| 9+19i}} {{math\| 19+9i}} {{math\| 21+i}}	{{math\| i·(1+i)·(3−2i)·(4−i)}} {{math\| (1+i)·(3+2i)·(4−i)}} {{math\| (1+i)·(3−2i)·(4+i)}} {{math\| −i·(1+i)·(3+2i)·(4+i)}}
445	{{math\| 2+21i}} {{math\| 11+18i}} {{math\| 18+11i}} {{math\| 21+2i}}	{{math\| i·(2+i)·(8−5i)}} {{math\| (2+i)·(8+5i)}} {{math\| i·(2−i)·(8−5i)}} {{math\| (2−i)·(8+5i)}}
449	{{math\| 7+20i}} {{math\| 20+7i}}	(p) (p)
450	{{math\| 3+21i}} {{math\| 15+15i}} {{math\| 21+3i}}	{{math\| i·(1+i)·(2−i)²·3}} {{math\| (1+i)·(2+i)·(2−i)·3}} {{math\| −i·(1+i)·(2+i)²·3}}
452	{{math\| 14+16i}} {{math\| 16+14i}}	{{math\| (1+i)²·(8−7i)}} {{math\| −i·(1+i)²·(8+7i)}}
457	{{math\| 4+21i}} {{math\| 21+4i}}	(p) (p)
458	{{math\| 13+17i}} {{math\| 17+13i}}	{{math\| (1+i)·(15+2i)}} {{math\| (1+i)·(15−2i)}}
461	{{math\| 10+19i}} {{math\| 19+10i}}	(p) (p)
464	{{math\| 8+20i}} {{math\| 20+8i}}	{{math\| −i·(1+i)⁴·(5−2i)}} {{math\| −(1+i)⁴·(5+2i)}}
466	{{math\| 5+21i}} {{math\| 21+5i}}	{{math\| (1+i)·(13+8i)}} {{math\| (1+i)·(13−8i)}}
468	{{math\| 12+18i}} {{math\| 18+12i}}	{{math\| (1+i)²·3·(3−2i)}} {{math\| −i·(1+i)²·3·(3+2i)}}
477	{{math\| 6+21i}} {{math\| 21+6i}}	{{math\| i·3·(7−2i)}} {{math\| 3·(7+2i)}}
481	{{math\| 9+20i}} {{math\| 15+16i}} {{math\| 16+15i}} {{math\| 20+9i}}	{{math\| i·(3−2i)·(6+i)}} {{math\| i·(3−2i)·(6−i)}} {{math\| (3+2i)·(6+i)}} {{math\| (3+2i)·(6−i)}}
482	{{math\| 11+19i}} {{math\| 19+11i}}	{{math\| (1+i)·(15+4i)}} {{math\| (1+i)·(15−4i)}}
484	{{math\| 22}}	{{math\| −i·(1+i)²·11}}
485	{{math\| 1+22i}} {{math\| 14+17i}} {{math\| 17+14i}} {{math\| 22+i}}	{{math\| i·(2−i)·(9+4i)}} {{math\| (2+i)·(9+4i)}} {{math\| i·(2−i)·(9−4i)}} {{math\| (2+i)·(9−4i)}}
488	{{math\| 2+22i}} {{math\| 22+2i}}	{{math\| −i·(1+i)³·(6+5i)}} {{math\| −i·(1+i)³·(6−5i)}}
490	{{math\| 7+21i}} {{math\| 21+7i}}	{{math\| (1+i)·(2+i)·7}} {{math\| (1+i)·(2−i)·7}}
493	{{math\| 3+22i}} {{math\| 13+18i}} {{math\| 18+13i}} {{math\| 22+3i}}	{{math\| i·(4+i)·(5−2i)}} {{math\| i·(4−i)·(5−2i)}} {{math\| (4+i)·(5+2i)}} {{math\| (4−i)·(5+2i)}}
500	{{math\| 4+22i}} {{math\| 10+20i}} {{math\| 20+10i}} {{math\| 22+4i}}	{{math\| −i·(1+i)²·(2+i)³}} {{math\| (1+i)²·(2+i)·(2−i)²}} {{math\| −i·(1+i)²·(2+i)²·(2−i)}} {{math\| (1+i)²·(2−i)³}}

Norm \|\| Integer \|\| Factorization
id="501–750" class="wikitable sortable" style="float:left; margin-right:1em" \|+ Norm 501–750
505	{{math\| 8+21i}} {{math\| 12+19i}} {{math\| 19+12i}} {{math\| 21+8i}}	{{math\| i·(2−i)·(10+i)}} {{math\| i·(2−i)·(10−i)}} {{math\| (2+i)·(10+i)}} {{math\| (2+i)·(10−i)}}
509	{{math\| 5+22i}} {{math\| 22+5i}}	(p) (p)
512	{{math\| 16+16i}}	{{math\| (1+i)⁹}}
514	{{math\| 15+17i}} {{math\| 17+15i}}	{{math\| (1+i)·(16+i)}} {{math\| (1+i)·(16−i)}}
520	{{math\| 6+22i}} {{math\| 14+18i}} {{math\| 18+14i}} {{math\| 22+6i}}	{{math\| (1+i)³·(2−i)·(3−2i)}} {{math\| −i·(1+i)³·(2−i)·(3+2i)}} {{math\| −i·(1+i)³·(2+i)·(3−2i)}} {{math\| −(1+i)³·(2+i)·(3+2i)}}
521	{{math\| 11+20i}} {{math\| 20+11i}}	(p) (p)
522	{{math\| 9+21i}} {{math\| 21+9i}}	{{math\| (1+i)·3·(5+2i)}} {{math\| (1+i)·3·(5−2i)}}
529	{{math\| 23}}	(p)
530	{{math\| 1+23i}} {{math\| 13+19i}} {{math\| 19+13i}} {{math\| 23+i}}	{{math\| (1+i)·(2+i)·(7+2i)}} {{math\| (1+i)·(2+i)·(7−2i)}} {{math\| (1+i)·(2−i)·(7+2i)}} {{math\| (1+i)·(2−i)·(7−2i)}}
533	{{math\| 2+23i}} {{math\| 7+22i}} {{math\| 22+7i}} {{math\| 23+2i}}	{{math\| i·(3+2i)·(5−4i)}} {{math\| (3+2i)·(5+4i)}} {{math\| i·(3−2i)·(5−4i)}} {{math\| (3−2i)·(5+4i)}}
538	{{math\| 3+23i}} {{math\| 23+3i}}	{{math\| (1+i)·(13+10i)}} {{math\| (1+i)·(13−10i)}}
541	{{math\| 10+21i}} {{math\| 21+10i}}	(p) (p)
544	{{math\| 12+20i}} {{math\| 20+12i}}	{{math\| −(1+i)⁵·(4+i)}} {{math\| −(1+i)⁵·(4−i)}}
545	{{math\| 4+23i}} {{math\| 16+17i}} {{math\| 17+16i}} {{math\| 23+4i}}	{{math\| i·(2−i)·(10+3i)}} {{math\| i·(2−i)·(10−3i)}} {{math\| (2+i)·(10+3i)}} {{math\| (2+i)·(10−3i)}}
548	{{math\| 8+22i}} {{math\| 22+8i}}	{{math\| (1+i)²·(11−4i)}} {{math\| −i·(1+i)²·(11+4i)}}
549	{{math\| 15+18i}} {{math\| 18+15i}}	{{math\| i·3·(6−5i)}} {{math\| 3·(6+5i)}}
554	{{math\| 5+23i}} {{math\| 23+5i}}	{{math\| (1+i)·(14+9i)}} {{math\| (1+i)·(14−9i)}}
557	{{math\| 14+19i}} {{math\| 19+14i}}	(p) (p)
562	{{math\| 11+21i}} {{math\| 21+11i}}	{{math\| (1+i)·(16+5i)}} {{math\| (1+i)·(16−5i)}}
565	{{math\| 6+23i}} {{math\| 9+22i}} {{math\| 22+9i}} {{math\| 23+6i}}	{{math\| i·(2+i)·(8−7i)}} {{math\| (2+i)·(8+7i)}} {{math\| i·(2−i)·(8−7i)}} {{math\| (2−i)·(8+7i)}}
569	{{math\| 13+20i}} {{math\| 20+13i}}	(p) (p)
576	{{math\| 24}}	{{math\| i·(1+i)⁶·3}}
577	{{math\| 1+24i}} {{math\| 24+i}}	(p) (p)
578	{{math\| 7+23i}} {{math\| 17+17i}} {{math\| 23+7i}}	{{math\| (1+i)·(4+i)²}} {{math\| (1+i)·(4+i)·(4−i)}} {{math\| (1+i)·(4−i)²}}
580	{{math\| 2+24i}} {{math\| 16+18i}} {{math\| 18+16i}} {{math\| 24+2i}}	{{math\| (1+i)²·(2−i)·(5+2i)}} {{math\| −i·(1+i)²·(2+i)·(5+2i)}} {{math\| (1+i)²·(2−i)·(5−2i)}} {{math\| −i·(1+i)²·(2+i)·(5−2i)}}
584	{{math\| 10+22i}} {{math\| 22+10i}}	{{math\| −i·(1+i)³·(8+3i)}} {{math\| −i·(1+i)³·(8−3i)}}
585	{{math\| 3+24i}} {{math\| 12+21i}} {{math\| 21+12i}} {{math\| 24+3i}}	{{math\| i·(2+i)·3·(3−2i)}} {{math\| (2+i)·3·(3+2i)}} {{math\| i·(2−i)·3·(3−2i)}} {{math\| (2−i)·3·(3+2i)}}
586	{{math\| 15+19i}} {{math\| 19+15i}}	{{math\| (1+i)·(17+2i)}} {{math\| (1+i)·(17−2i)}}
592	{{math\| 4+24i}} {{math\| 24+4i}}	{{math\| −i·(1+i)⁴·(6−i)}} {{math\| −(1+i)⁴·(6+i)}}
593	{{math\| 8+23i}} {{math\| 23+8i}}	(p) (p)
596	{{math\| 14+20i}} {{math\| 20+14i}}	{{math\| (1+i)²·(10−7i)}} {{math\| −i·(1+i)²·(10+7i)}}
601	{{math\| 5+24i}} {{math\| 24+5i}}	(p) (p)
605	{{math\| 11+22i}} {{math\| 22+11i}}	{{math\| i·(2−i)·11}} {{math\| (2+i)·11}}
610	{{math\| 9+23i}} {{math\| 13+21i}} {{math\| 21+13i}} {{math\| 23+9i}}	{{math\| i·(1+i)·(2−i)·(6−5i)}} {{math\| (1+i)·(2−i)·(6+5i)}} {{math\| (1+i)·(2+i)·(6−5i)}} {{math\| −i·(1+i)·(2+i)·(6+5i)}}
612	{{math\| 6+24i}} {{math\| 24+6i}}	{{math\| (1+i)²·3·(4−i)}} {{math\| −i·(1+i)²·3·(4+i)}}
613	{{math\| 17+18i}} {{math\| 18+17i}}	(p) (p)
617	{{math\| 16+19i}} {{math\| 19+16i}}	(p) (p)
625	{{math\| 7+24i}} {{math\| 15+20i}} {{math\| 20+15i}} {{math\| 24+7i}} {{math\| 25}}	{{math\| −(2−i)⁴}} {{math\| (2+i)³·(2−i)}} {{math\| i·(2+i)·(2−i)³}} {{math\| −i·(2+i)⁴}} {{math\| (2+i)²·(2−i)²}}
626	{{math\| 1+25i}} {{math\| 25+i}}	{{math\| (1+i)·(13+12i)}} {{math\| (1+i)·(13−12i)}}
628	{{math\| 12+22i}} {{math\| 22+12i}}	{{math\| (1+i)²·(11−6i)}} {{math\| −i·(1+i)²·(11+6i)}}
629	{{math\| 2+25i}} {{math\| 10+23i}} {{math\| 23+10i}} {{math\| 25+2i}}	{{math\| i·(4−i)·(6+i)}} {{math\| i·(4−i)·(6−i)}} {{math\| (4+i)·(6+i)}} {{math\| (4+i)·(6−i)}}
634	{{math\| 3+25i}} {{math\| 25+3i}}	{{math\| (1+i)·(14+11i)}} {{math\| (1+i)·(14−11i)}}
637	{{math\| 14+21i}} {{math\| 21+14i}}	{{math\| i·(3−2i)·7}} {{math\| (3+2i)·7}}
640	{{math\| 8+24i}} {{math\| 24+8i}}	{{math\| i·(1+i)⁷·(2+i)}} {{math\| i·(1+i)⁷·(2−i)}}
641	{{math\| 4+25i}} {{math\| 25+4i}}	(p) (p)
648	{{math\| 18+18i}}	{{math\| −i·(1+i)³·3²}}
650	{{math\| 5+25i}} {{math\| 11+23i}} {{math\| 17+19i}} {{math\| 19+17i}} {{math\| 23+11i}} {{math\| 25+5i}}	{{math\| (1+i)·(2+i)·(2−i)·(3+2i)}} {{math\| (1+i)·(2+i)²·(3−2i)}} {{math\| i·(1+i)·(2−i)²·(3−2i)}} {{math\| −i·(1+i)·(2+i)²·(3+2i)}} {{math\| (1+i)·(2−i)²·(3+2i)}} {{math\| (1+i)·(2+i)·(2−i)·(3−2i)}}
653	{{math\| 13+22i}} {{math\| 22+13i}}	(p) (p)
656	{{math\| 16+20i}} {{math\| 20+16i}}	{{math\| −i·(1+i)⁴·(5−4i)}} {{math\| −(1+i)⁴·(5+4i)}}
657	{{math\| 9+24i}} {{math\| 24+9i}}	{{math\| i·3·(8−3i)}} {{math\| 3·(8+3i)}}
661	{{math\| 6+25i}} {{math\| 25+6i}}	(p) (p)
666	{{math\| 15+21i}} {{math\| 21+15i}}	{{math\| (1+i)·3·(6+i)}} {{math\| (1+i)·3·(6−i)}}
673	{{math\| 12+23i}} {{math\| 23+12i}}	(p) (p)
674	{{math\| 7+25i}} {{math\| 25+7i}}	{{math\| (1+i)·(16+9i)}} {{math\| (1+i)·(16−9i)}}
676	{{math\| 10+24i}} {{math\| 24+10i}} {{math\| 26}}	{{math\| −i·(1+i)²·(3+2i)²}} {{math\| (1+i)²·(3−2i)²}} {{math\| −i·(1+i)²·(3+2i)·(3−2i)}}
677	{{math\| 1+26i}} {{math\| 26+i}}	(p) (p)
680	{{math\| 2+26i}} {{math\| 14+22i}} {{math\| 22+14i}} {{math\| 26+2i}}	{{math\| −i·(1+i)³·(2+i)·(4+i)}} {{math\| −i·(1+i)³·(2+i)·(4−i)}} {{math\| −i·(1+i)³·(2−i)·(4+i)}} {{math\| −i·(1+i)³·(2−i)·(4−i)}}
685	{{math\| 3+26i}} {{math\| 18+19i}} {{math\| 19+18i}} {{math\| 26+3i}}	{{math\| i·(2−i)·(11+4i)}} {{math\| (2+i)·(11+4i)}} {{math\| i·(2−i)·(11−4i)}} {{math\| (2+i)·(11−4i)}}
689	{{math\| 8+25i}} {{math\| 17+20i}} {{math\| 20+17i}} {{math\| 25+8i}}	{{math\| i·(3−2i)·(7+2i)}} {{math\| (3+2i)·(7+2i)}} {{math\| i·(3−2i)·(7−2i)}} {{math\| (3+2i)·(7−2i)}}
692	{{math\| 4+26i}} {{math\| 26+4i}}	{{math\| (1+i)²·(13−2i)}} {{math\| −i·(1+i)²·(13+2i)}}
697	{{math\| 11+24i}} {{math\| 16+21i}} {{math\| 21+16i}} {{math\| 24+11i}}	{{math\| i·(4+i)·(5−4i)}} {{math\| (4+i)·(5+4i)}} {{math\| i·(4−i)·(5−4i)}} {{math\| (4−i)·(5+4i)}}
698	{{math\| 13+23i}} {{math\| 23+13i}}	{{math\| (1+i)·(18+5i)}} {{math\| (1+i)·(18−5i)}}
701	{{math\| 5+26i}} {{math\| 26+5i}}	(p) (p)
706	{{math\| 9+25i}} {{math\| 25+9i}}	{{math\| (1+i)·(17+8i)}} {{math\| (1+i)·(17−8i)}}
709	{{math\| 15+22i}} {{math\| 22+15i}}	(p) (p)
712	{{math\| 6+26i}} {{math\| 26+6i}}	{{math\| −i·(1+i)³·(8+5i)}} {{math\| −i·(1+i)³·(8−5i)}}
720	{{math\| 12+24i}} {{math\| 24+12i}}	{{math\| −i·(1+i)⁴·(2−i)·3}} {{math\| −(1+i)⁴·(2+i)·3}}
722	{{math\| 19+19i}}	{{math\| (1+i)·19}}
724	{{math\| 18+20i}} {{math\| 20+18i}}	{{math\| (1+i)²·(10−9i)}} {{math\| −i·(1+i)²·(10+9i)}}
725	{{math\| 7+26i}} {{math\| 10+25i}} {{math\| 14+23i}} {{math\| 23+14i}} {{math\| 25+10i}} {{math\| 26+7i}}	{{math\| (2+i)²·(5+2i)}} {{math\| i·(2+i)·(2−i)·(5−2i)}} {{math\| i·(2−i)²·(5+2i)}} {{math\| (2+i)²·(5−2i)}} {{math\| (2+i)·(2−i)·(5+2i)}} {{math\| i·(2−i)²·(5−2i)}}
729	{{math\| 27}}	{{math\| 3³}}
730	{{math\| 1+27i}} {{math\| 17+21i}} {{math\| 21+17i}} {{math\| 27+i}}	{{math\| i·(1+i)·(2−i)·(8−3i)}} {{math\| (1+i)·(2+i)·(8−3i)}} {{math\| (1+i)·(2−i)·(8+3i)}} {{math\| −i·(1+i)·(2+i)·(8+3i)}}
733	{{math\| 2+27i}} {{math\| 27+2i}}	(p) (p)
738	{{math\| 3+27i}} {{math\| 27+3i}}	{{math\| (1+i)·3·(5+4i)}} {{math\| (1+i)·3·(5−4i)}}
740	{{math\| 8+26i}} {{math\| 16+22i}} {{math\| 22+16i}} {{math\| 26+8i}}	{{math\| (1+i)²·(2−i)·(6+i)}} {{math\| (1+i)²·(2−i)·(6−i)}} {{math\| −i·(1+i)²·(2+i)·(6+i)}} {{math\| −i·(1+i)²·(2+i)·(6−i)}}
745	{{math\| 4+27i}} {{math\| 13+24i}} {{math\| 24+13i}} {{math\| 27+4i}}	{{math\| i·(2+i)·(10−7i)}} {{math\| (2+i)·(10+7i)}} {{math\| i·(2−i)·(10−7i)}} {{math\| (2−i)·(10+7i)}}
746	{{math\| 11+25i}} {{math\| 25+11i}}	{{math\| (1+i)·(18+7i)}} {{math\| (1+i)·(18−7i)}}

Norm \|\| Integer \|\| Factorization
id="751–1000" class="wikitable sortable" style="float:left; margin-right:1em" \|+ Norm 751–1000
754	{{math\| 5+27i}} {{math\| 15+23i}} {{math\| 23+15i}} {{math\| 27+5i}}	{{math\| i·(1+i)·(3−2i)·(5−2i)}} {{math\| (1+i)·(3+2i)·(5−2i)}} {{math\| (1+i)·(3−2i)·(5+2i)}} {{math\| −i·(1+i)·(3+2i)·(5+2i)}}
757	{{math\| 9+26i}} {{math\| 26+9i}}	(p) (p)
761	{{math\| 19+20i}} {{math\| 20+19i}}	(p) (p)
765	{{math\| 6+27i}} {{math\| 18+21i}} {{math\| 21+18i}} {{math\| 27+6i}}	{{math\| i·(2−i)·3·(4+i)}} {{math\| i·(2−i)·3·(4−i)}} {{math\| (2+i)·3·(4+i)}} {{math\| (2+i)·3·(4−i)}}
769	{{math\| 12+25i}} {{math\| 25+12i}}	(p) (p)
772	{{math\| 14+24i}} {{math\| 24+14i}}	{{math\| (1+i)²·(12−7i)}} {{math\| −i·(1+i)²·(12+7i)}}
773	{{math\| 17+22i}} {{math\| 22+17i}}	(p) (p)
776	{{math\| 10+26i}} {{math\| 26+10i}}	{{math\| −i·(1+i)³·(9+4i)}} {{math\| −i·(1+i)³·(9−4i)}}
778	{{math\| 7+27i}} {{math\| 27+7i}}	{{math\| (1+i)·(17+10i)}} {{math\| (1+i)·(17−10i)}}
784	{{math\| 28}}	{{math\| −(1+i)⁴·7}}
785	{{math\| 1+28i}} {{math\| 16+23i}} {{math\| 23+16i}} {{math\| 28+i}}	{{math\| i·(2+i)·(11−6i)}} {{math\| (2+i)·(11+6i)}} {{math\| i·(2−i)·(11−6i)}} {{math\| (2−i)·(11+6i)}}
788	{{math\| 2+28i}} {{math\| 28+2i}}	{{math\| (1+i)²·(14−i)}} {{math\| −i·(1+i)²·(14+i)}}
793	{{math\| 3+28i}} {{math\| 8+27i}} {{math\| 27+8i}} {{math\| 28+3i}}	{{math\| i·(3+2i)·(6−5i)}} {{math\| (3+2i)·(6+5i)}} {{math\| i·(3−2i)·(6−5i)}} {{math\| (3−2i)·(6+5i)}}
794	{{math\| 13+25i}} {{math\| 25+13i}}	{{math\| (1+i)·(19+6i)}} {{math\| (1+i)·(19−6i)}}
797	{{math\| 11+26i}} {{math\| 26+11i}}	(p) (p)
800	{{math\| 4+28i}} {{math\| 20+20i}} {{math\| 28+4i}}	{{math\| −i·(1+i)⁵·(2−i)²}} {{math\| −(1+i)⁵·(2+i)·(2−i)}} {{math\| i·(1+i)⁵·(2+i)²}}
801	{{math\| 15+24i}} {{math\| 24+15i}}	{{math\| i·3·(8−5i)}} {{math\| 3·(8+5i)}}
802	{{math\| 19+21i}} {{math\| 21+19i}}	{{math\| (1+i)·(20+i)}} {{math\| (1+i)·(20−i)}}
808	{{math\| 18+22i}} {{math\| 22+18i}}	{{math\| −i·(1+i)³·(10+i)}} {{math\| −i·(1+i)³·(10−i)}}
809	{{math\| 5+28i}} {{math\| 28+5i}}	(p) (p)
810	{{math\| 9+27i}} {{math\| 27+9i}}	{{math\| (1+i)·(2+i)·3²}} {{math\| (1+i)·(2−i)·3²}}
818	{{math\| 17+23i}} {{math\| 23+17i}}	{{math\| (1+i)·(20+3i)}} {{math\| (1+i)·(20−3i)}}
820	{{math\| 6+28i}} {{math\| 12+26i}} {{math\| 26+12i}} {{math\| 28+6i}}	{{math\| (1+i)²·(2+i)·(5−4i)}} {{math\| −i·(1+i)²·(2+i)·(5+4i)}} {{math\| (1+i)²·(2−i)·(5−4i)}} {{math\| −i·(1+i)²·(2−i)·(5+4i)}}
821	{{math\| 14+25i}} {{math\| 25+14i}}	(p) (p)
829	{{math\| 10+27i}} {{math\| 27+10i}}	(p) (p)
832	{{math\| 16+24i}} {{math\| 24+16i}}	{{math\| −(1+i)⁶·(3−2i)}} {{math\| i·(1+i)⁶·(3+2i)}}
833	{{math\| 7+28i}} {{math\| 28+7i}}	{{math\| i·(4−i)·7}} {{math\| (4+i)·7}}
841	{{math\| 20+21i}} {{math\| 21+20i}} {{math\| 29}}	{{math\| i·(5−2i)²}} {{math\| (5+2i)²}} {{math\| (5+2i)·(5−2i)}}
842	{{math\| 1+29i}} {{math\| 29+i}}	{{math\| (1+i)·(15+14i)}} {{math\| (1+i)·(15−14i)}}
845	{{math\| 2+29i}} {{math\| 13+26i}} {{math\| 19+22i}} {{math\| 22+19i}} {{math\| 26+13i}} {{math\| 29+2i}}	{{math\| −(2−i)·(3−2i)²}} {{math\| i·(2−i)·(3+2i)·(3−2i)}} {{math\| i·(2+i)·(3−2i)²}} {{math\| (2−i)·(3+2i)²}} {{math\| (2+i)·(3+2i)·(3−2i)}} {{math\| −i·(2+i)·(3+2i)²}}
848	{{math\| 8+28i}} {{math\| 28+8i}}	{{math\| −i·(1+i)⁴·(7−2i)}} {{math\| −(1+i)⁴·(7+2i)}}
850	{{math\| 3+29i}} {{math\| 11+27i}} {{math\| 15+25i}} {{math\| 25+15i}} {{math\| 27+11i}} {{math\| 29+3i}}	{{math\| (1+i)·(2+i)²·(4−i)}} {{math\| i·(1+i)·(2−i)²·(4−i)}} {{math\| (1+i)·(2+i)·(2−i)·(4+i)}} {{math\| (1+i)·(2+i)·(2−i)·(4−i)}} {{math\| −i·(1+i)·(2+i)²·(4+i)}} {{math\| (1+i)·(2−i)²·(4+i)}}
853	{{math\| 18+23i}} {{math\| 23+18i}}	(p) (p)
857	{{math\| 4+29i}} {{math\| 29+4i}}	(p) (p)
865	{{math\| 9+28i}} {{math\| 17+24i}} {{math\| 24+17i}} {{math\| 28+9i}}	{{math\| i·(2−i)·(13+2i)}} {{math\| i·(2−i)·(13−2i)}} {{math\| (2+i)·(13+2i)}} {{math\| (2+i)·(13−2i)}}
866	{{math\| 5+29i}} {{math\| 29+5i}}	{{math\| (1+i)·(17+12i)}} {{math\| (1+i)·(17−12i)}}
872	{{math\| 14+26i}} {{math\| 26+14i}}	{{math\| −i·(1+i)³·(10+3i)}} {{math\| −i·(1+i)³·(10−3i)}}
873	{{math\| 12+27i}} {{math\| 27+12i}}	{{math\| i·3·(9−4i)}} {{math\| 3·(9+4i)}}
877	{{math\| 6+29i}} {{math\| 29+6i}}	(p) (p)
881	{{math\| 16+25i}} {{math\| 25+16i}}	(p) (p)
882	{{math\| 21+21i}}	{{math\| (1+i)·3·7}}
884	{{math\| 10+28i}} {{math\| 20+22i}} {{math\| 22+20i}} {{math\| 28+10i}}	{{math\| (1+i)²·(3−2i)·(4+i)}} {{math\| −i·(1+i)²·(3+2i)·(4+i)}} {{math\| (1+i)²·(3−2i)·(4−i)}} {{math\| −i·(1+i)²·(3+2i)·(4−i)}}
890	{{math\| 7+29i}} {{math\| 19+23i}} {{math\| 23+19i}} {{math\| 29+7i}}	{{math\| i·(1+i)·(2−i)·(8−5i)}} {{math\| (1+i)·(2−i)·(8+5i)}} {{math\| (1+i)·(2+i)·(8−5i)}} {{math\| −i·(1+i)·(2+i)·(8+5i)}}
898	{{math\| 13+27i}} {{math\| 27+13i}}	{{math\| (1+i)·(20+7i)}} {{math\| (1+i)·(20−7i)}}
900	{{math\| 18+24i}} {{math\| 24+18i}} {{math\| 30}}	{{math\| −i·(1+i)²·(2+i)²·3}} {{math\| (1+i)²·(2−i)²·3}} {{math\| −i·(1+i)²·(2+i)·(2−i)·3}}
901	{{math\| 1+30i}} {{math\| 15+26i}} {{math\| 26+15i}} {{math\| 30+i}}	{{math\| i·(4+i)·(7−2i)}} {{math\| i·(4−i)·(7−2i)}} {{math\| (4+i)·(7+2i)}} {{math\| (4−i)·(7+2i)}}
904	{{math\| 2+30i}} {{math\| 30+2i}}	{{math\| −i·(1+i)³·(8+7i)}} {{math\| −i·(1+i)³·(8−7i)}}
905	{{math\| 8+29i}} {{math\| 11+28i}} {{math\| 28+11i}} {{math\| 29+8i}}	{{math\| i·(2+i)·(10−9i)}} {{math\| (2+i)·(10+9i)}} {{math\| i·(2−i)·(10−9i)}} {{math\| (2−i)·(10+9i)}}
909	{{math\| 3+30i}} {{math\| 30+3i}}	{{math\| i·3·(10−i)}} {{math\| 3·(10+i)}}
914	{{math\| 17+25i}} {{math\| 25+17i}}	{{math\| (1+i)·(21+4i)}} {{math\| (1+i)·(21−4i)}}
916	{{math\| 4+30i}} {{math\| 30+4i}}	{{math\| (1+i)²·(15−2i)}} {{math\| −i·(1+i)²·(15+2i)}}
922	{{math\| 9+29i}} {{math\| 29+9i}}	{{math\| (1+i)·(19+10i)}} {{math\| (1+i)·(19−10i)}}
925	{{math\| 5+30i}} {{math\| 14+27i}} {{math\| 21+22i}} {{math\| 22+21i}} {{math\| 27+14i}} {{math\| 30+5i}}	{{math\| i·(2+i)·(2−i)·(6−i)}} {{math\| (2+i)²·(6+i)}} {{math\| i·(2−i)²·(6+i)}} {{math\| (2+i)²·(6−i)}} {{math\| i·(2−i)²·(6−i)}} {{math\| (2+i)·(2−i)·(6+i)}}
928	{{math\| 12+28i}} {{math\| 28+12i}}	{{math\| −(1+i)⁵·(5+2i)}} {{math\| −(1+i)⁵·(5−2i)}}
929	{{math\| 20+23i}} {{math\| 23+20i}}	(p) (p)
932	{{math\| 16+26i}} {{math\| 26+16i}}	{{math\| (1+i)²·(13−8i)}} {{math\| −i·(1+i)²·(13+8i)}}
936	{{math\| 6+30i}} {{math\| 30+6i}}	{{math\| −i·(1+i)³·3·(3+2i)}} {{math\| −i·(1+i)³·3·(3−2i)}}
937	{{math\| 19+24i}} {{math\| 24+19i}}	(p) (p)
941	{{math\| 10+29i}} {{math\| 29+10i}}	(p) (p)
949	{{math\| 7+30i}} {{math\| 18+25i}} {{math\| 25+18i}} {{math\| 30+7i}}	{{math\| i·(3−2i)·(8+3i)}} {{math\| (3+2i)·(8+3i)}} {{math\| i·(3−2i)·(8−3i)}} {{math\| (3+2i)·(8−3i)}}
953	{{math\| 13+28i}} {{math\| 28+13i}}	(p) (p)
954	{{math\| 15+27i}} {{math\| 27+15i}}	{{math\| (1+i)·3·(7+2i)}} {{math\| (1+i)·3·(7−2i)}}
961	{{math\| 31}}	(p)
962	{{math\| 1+31i}} {{math\| 11+29i}} {{math\| 29+11i}} {{math\| 31+i}}	{{math\| (1+i)·(3+2i)·(6+i)}} {{math\| (1+i)·(3+2i)·(6−i)}} {{math\| (1+i)·(3−2i)·(6+i)}} {{math\| (1+i)·(3−2i)·(6−i)}}
964	{{math\| 8+30i}} {{math\| 30+8i}}	{{math\| (1+i)²·(15−4i)}} {{math\| −i·(1+i)²·(15+4i)}}
965	{{math\| 2+31i}} {{math\| 17+26i}} {{math\| 26+17i}} {{math\| 31+2i}}	{{math\| i·(2+i)·(12−7i)}} {{math\| (2+i)·(12+7i)}} {{math\| i·(2−i)·(12−7i)}} {{math\| (2−i)·(12+7i)}}
968	{{math\| 22+22i}}	{{math\| −i·(1+i)³·11}}
970	{{math\| 3+31i}} {{math\| 21+23i}} {{math\| 23+21i}} {{math\| 31+3i}}	{{math\| i·(1+i)·(2−i)·(9−4i)}} {{math\| (1+i)·(2+i)·(9−4i)}} {{math\| (1+i)·(2−i)·(9+4i)}} {{math\| −i·(1+i)·(2+i)·(9+4i)}}
976	{{math\| 20+24i}} {{math\| 24+20i}}	{{math\| −i·(1+i)⁴·(6−5i)}} {{math\| −(1+i)⁴·(6+5i)}}
977	{{math\| 4+31i}} {{math\| 31+4i}}	(p) (p)
980	{{math\| 14+28i}} {{math\| 28+14i}}	{{math\| (1+i)²·(2−i)·7}} {{math\| −i·(1+i)²·(2+i)·7}}
981	{{math\| 9+30i}} {{math\| 30+9i}}	{{math\| i·3·(10−3i)}} {{math\| 3·(10+3i)}}
985	{{math\| 12+29i}} {{math\| 16+27i}} {{math\| 27+16i}} {{math\| 29+12i}}	{{math\| i·(2−i)·(14+i)}} {{math\| i·(2−i)·(14−i)}} {{math\| (2+i)·(14+i)}} {{math\| (2+i)·(14−i)}}
986	{{math\| 5+31i}} {{math\| 19+25i}} {{math\| 25+19i}} {{math\| 31+5i}}	{{math\| (1+i)·(4+i)·(5+2i)}} {{math\| (1+i)·(4−i)·(5+2i)}} {{math\| (1+i)·(4+i)·(5−2i)}} {{math\| (1+i)·(4−i)·(5−2i)}}
997	{{math\| 6+31i}} {{math\| 31+6i}}	(p) (p)
1000	{{math\| 10+30i}} {{math\| 18+26i}} {{math\| 26+18i}} {{math\| 30+10i}}	{{math\| −i·(1+i)³·(2+i)²·(2−i)}} {{math\| (1+i)³·(2−i)³}} {{math\| −(1+i)³·(2+i)³}} {{math\| −i·(1+i)³·(2+i)·(2−i)²}}

References

{{Cite journal

|last=Dresden

|first=Greg

|last2=Dymacek

|first2=Wayne

|journal=American Mathematical Monthly

|title=Finding factors of factor rings over the Gaussian integers

|volume=112

|year=2005

|issue=7

|pages=602–611

|mr=2158894

|jstor = 30037545

|doi=10.2307/30037545}}

{{Cite journal

|first1=Ellen

|last1=Gethner

|first2=Stan

|last2=Wagner

|first3=Brian

|last3=Wick

|title=A stroll through the Gaussian primes

|journal=Amer. Math. Monthly

|jstor=2589708

|volume=105

|issue=4

|year=1998

|pages=327–337

|mr=1614871

|doi=10.2307/2589708

}}

{{Cite journal

|last=Matsui

|first=Hajime

|title=A bound for the least Gaussian prime omega with alpha < arg(omega) < beta

|journal=Arch. Math.

|volume=74

|issue=6

|year=2000

|doi=10.1007/s000130050463

|pages=423–431

|mr=1753540

}}

External links

{{Mathworld|title= Gaussian prime| urlname=GaussianPrime}}
{{Mathworld|title= Prime Factorization |urlname= PrimeFactorization}}
[https://oeis.org/search?q=Gaussian+prime OEIS: Gaussian Primes]

Category:Complex numbers

Gaussian integer factorizations

Norm \|\| Integer \|\| Factorization
id="1–250" class="wikitable sortable" style="float:left; margin-right:1em" \|+ Norm 1–250
2	{{math\| 1+i}}	(p)
4	{{math\| 2}}	{{math\| −i·(1+i)²}}
5	{{math\| 2+i}} {{math\| 1+2i}}	(p) (p)
8	{{math\| 2+2i}}	{{math\| −i·(1+i)³}}
9	{{math\| 3}}	(p)
10	{{math\| 1+3i}} {{math\| 3+i}}	{{math\| (1+i)·(2+i)}} {{math\| (1+i)·(2−i)}}
13	{{math\| 3+2i}} {{math\| 2+3i}}	(p) (p)
16	{{math\| 4}}	{{math\| −(1+i)⁴}}
17	{{math\| 1+4i}} {{math\| 4+i}}	(p) (p)
18	{{math\| 3+3i}}	{{math\| (1+i)·3}}
20	{{math\| 2+4i}} {{math\| 4+2i}}	{{math\| (1+i)²·(2−i)}} {{math\| −i·(1+i)²·(2+i)}}
25	{{math\| 3+4i}} {{math\| 4+3i}} {{math\| 5}}	{{math\| (2+i)²}} {{math\| i·(2−i)²}} {{math\| (2+i)·(2−i)}}
26	{{math\| 1+5i}} {{math\| 5+i}}	{{math\| (1+i)·(3+2i)}} {{math\| (1+i)·(3−2i)}}
29	{{math\| 2+5i}} {{math\| 5+2i}}	(p) (p)
32	{{math\| 4+4i}}	{{math\| −(1+i)⁵}}
34	{{math\| 3+5i}} {{math\| 5+3i}}	{{math\| (1+i)·(4+i)}} {{math\| (1+i)·(4−i)}}
36	{{math\| 6}}	{{math\| −i·(1+i)²·3}}
37	{{math\| 1+6i}} {{math\| 6+i}}	(p) (p)
40	{{math\| 2+6i}} {{math\| 6+2i}}	{{math\| −i·(1+i)³·(2+i)}} {{math\| −i·(1+i)³·(2−i)}}
41	{{math\| 4+5i}} {{math\| 5+4i}}	(p) (p)
45	{{math\| 3+6i}} {{math\| 6+3i}}	{{math\| i·(2−i)·3}} {{math\| (2+i)·3}}
49	{{math\| 7}}	(p)
50	{{math\| 1+7i}} {{math\| 5+5i}} {{math\| 7+i}}	{{math\| i·(1+i)·(2−i)²}} {{math\| (1+i)·(2+i)·(2−i)}} {{math\| −i·(1+i)·(2+i)²}}
52	{{math\| 4+6i}} {{math\| 6+4i}}	{{math\| (1+i)²·(3−2i)}} {{math\| −i·(1+i)²·(3+2i)}}
53	{{math\| 2+7i}} {{math\| 7+2i}}	(p) (p)
58	{{math\| 3+7i}} {{math\| 7+3i}}	{{math\| (1+i)·(5+2i)}} {{math\| (1+i)·(5−2i)}}
61	{{math\| 5+6i}} {{math\| 6+5i}}	(p) (p)
64	{{math\| 8}}	{{math\| i·(1+i)⁶}}
65	{{math\| 1+8i}} {{math\| 4+7i}} {{math\| 7+4i}} {{math\| 8+i}}	{{math\| i·(2+i)·(3−2i)}} {{math\| (2+i)·(3+2i)}} {{math\| i·(2−i)·(3−2i)}} {{math\| (2−i)·(3+2i)}}
68	{{math\| 2+8i}} {{math\| 8+2i}}	{{math\| (1+i)²·(4−i)}} {{math\| −i·(1+i)²·(4+i)}}
72	{{math\| 6+6i}}	{{math\| −i·(1+i)³·3}}
73	{{math\| 3+8i}} {{math\| 8+3i}}	(p) (p)
74	{{math\| 5+7i}} {{math\| 7+5i}}	{{math\| (1+i)·(6+i)}} {{math\| (1+i)·(6−i)}}
80	{{math\| 4+8i}} {{math\| 8+4i}}	{{math\| −i·(1+i)⁴·(2−i)}} {{math\| −(1+i)⁴·(2+i)}}
81	{{math\| 9}}	{{math\| 3²}}
82	{{math\| 1+9i}} {{math\| 9+i}}	{{math\| (1+i)·(5+4i)}} {{math\| (1+i)·(5−4i)}}
85	{{math\| 2+9i}} {{math\| 6+7i}} {{math\| 7+6i}} {{math\| 9+2i}}	{{math\| i·(2−i)·(4+i)}} {{math\| i·(2−i)·(4−i)}} {{math\| (2+i)·(4+i)}} {{math\| (2+i)·(4−i)}}
89	{{math\| 5+8i}} {{math\| 8+5i}}	(p) (p)
90	{{math\| 3+9i}} {{math\| 9+3i}}	{{math\| (1+i)·(2+i)·3}} {{math\| (1+i)·(2−i)·3}}
97	{{math\| 4+9i}} {{math\| 9+4i}}	(p) (p)
98	{{math\| 7+7i}}	{{math\| (1+i)·7}}
100	{{math\| 6+8i}} {{math\| 8+6i}} {{math\| 10}}	{{math\| −i·(1+i)²·(2+i)²}} {{math\| (1+i)²·(2−i)²}} {{math\| −i·(1+i)²·(2+i)·(2−i)}}
101	{{math\| 1+10i}} {{math\| 10+i}}	(p) (p)
104	{{math\| 2+10i}} {{math\| 10+2i}}	{{math\| −i·(1+i)³·(3+2i)}} {{math\| −i·(1+i)³·(3−2i)}}
106	{{math\| 5+9i}} {{math\| 9+5i}}	{{math\| (1+i)·(7+2i)}} {{math\| (1+i)·(7−2i)}}
109	{{math\| 3+10i}} {{math\| 10+3i}}	(p) (p)
113	{{math\| 7+8i}} {{math\| 8+7i}}	(p) (p)
116	{{math\| 4+10i}} {{math\| 10+4i}}	{{math\| (1+i)²·(5−2i)}} {{math\| −i·(1+i)²·(5+2i)}}
117	{{math\| 6+9i}} {{math\| 9+6i}}	{{math\| i·3·(3−2i)}} {{math\| 3·(3+2i)}}
121	{{math\| 11}}	(p)
122	{{math\| 1+11i}} {{math\| 11+i}}	{{math\| (1+i)·(6+5i)}} {{math\| (1+i)·(6−5i)}}
125	{{math\| 2+11i}} {{math\| 5+10i}} {{math\| 10+5i}} {{math\| 11+2i}}	{{math\| (2+i)³}} {{math\| i·(2+i)·(2−i)²}} {{math\| (2+i)²·(2−i)}} {{math\| i·(2−i)³}}
128	{{math\| 8+8i}}	{{math\| i·(1+i)⁷}}
130	{{math\| 3+11i}} {{math\| 7+9i}} {{math\| 9+7i}} {{math\| 11+3i}}	{{math\| i·(1+i)·(2−i)·(3−2i)}} {{math\| (1+i)·(2−i)·(3+2i)}} {{math\| (1+i)·(2+i)·(3−2i)}} {{math\| −i·(1+i)·(2+i)·(3+2i)}}
136	{{math\| 6+10i}} {{math\| 10+6i}}	{{math\| −i·(1+i)³·(4+i)}} {{math\| −i·(1+i)³·(4−i)}}
137	{{math\| 4+11i}} {{math\| 11+4i}}	(p) (p)
144	{{math\| 12}}	{{math\| −(1+i)⁴·3}}
145	{{math\| 1+12i}} {{math\| 8+9i}} {{math\| 9+8i}} {{math\| 12+i}}	{{math\| i·(2−i)·(5+2i)}} {{math\| (2+i)·(5+2i)}} {{math\| i·(2−i)·(5−2i)}} {{math\| (2+i)·(5−2i)}}
146	{{math\| 5+11i}} {{math\| 11+5i}}	{{math\| (1+i)·(8+3i)}} {{math\| (1+i)·(8−3i)}}
148	{{math\| 2+12i}} {{math\| 12+2i}}	{{math\| (1+i)²·(6−i)}} {{math\| −i·(1+i)²·(6+i)}}
149	{{math\| 7+10i}} {{math\| 10+7i}}	(p) (p)
153	{{math\| 3+12i}} {{math\| 12+3i}}	{{math\| i·3·(4−i)}} {{math\| 3·(4+i)}}
157	{{math\| 6+11i}} {{math\| 11+6i}}	(p) (p)
160	{{math\| 4+12i}} {{math\| 12+4i}}	{{math\| −(1+i)⁵·(2+i)}} {{math\| −(1+i)⁵·(2−i)}}
162	{{math\| 9+9i}}	{{math\| (1+i)·3²}}
164	{{math\| 8+10i}} {{math\| 10+8i}}	{{math\| (1+i)²·(5−4i)}} {{math\| −i·(1+i)²·(5+4i)}}
169	{{math\| 5+12i}} {{math\| 12+5i}} {{math\| 13}}	{{math\| (3+2i)²}} {{math\| i·(3−2i)²}} {{math\| (3+2i)·(3−2i)}}
170	{{math\| 1+13i}} {{math\| 7+11i}} {{math\| 11+7i}} {{math\| 13+i}}	{{math\| (1+i)·(2+i)·(4+i)}} {{math\| (1+i)·(2+i)·(4−i)}} {{math\| (1+i)·(2−i)·(4+i)}} {{math\| (1+i)·(2−i)·(4−i)}}
173	{{math\| 2+13i}} {{math\| 13+2i}}	(p) (p)
178	{{math\| 3+13i}} {{math\| 13+3i}}	{{math\| (1+i)·(8+5i)}} {{math\| (1+i)·(8−5i)}}
180	{{math\| 6+12i}} {{math\| 12+6i}}	{{math\| (1+i)²·(2−i)·3}} {{math\| −i·(1+i)²·(2+i)·3}}
181	{{math\| 9+10i}} {{math\| 10+9i}}	(p) (p)
185	{{math\| 4+13i}} {{math\| 8+11i}} {{math\| 11+8i}} {{math\| 13+4i}}	{{math\| i·(2−i)·(6+i)}} {{math\| i·(2−i)·(6−i)}} {{math\| (2+i)·(6+i)}} {{math\| (2+i)·(6−i)}}
193	{{math\| 7+12i}} {{math\| 12+7i}}	(p) (p)
194	{{math\| 5+13i}} {{math\| 13+5i}}	{{math\| (1+i)·(9+4i)}} {{math\| (1+i)·(9−4i)}}
196	{{math\| 14}}	{{math\| −i·(1+i)²·7}}
197	{{math\| 1+14i}} {{math\| 14+i}}	(p) (p)
200	{{math\| 2+14i}} {{math\| 10+10i}} {{math\| 14+2i}}	{{math\| (1+i)³·(2−i)²}} {{math\| −i·(1+i)³·(2+i)·(2−i)}} {{math\| −(1+i)³·(2+i)²}}
202	{{math\| 9+11i}} {{math\| 11+9i}}	{{math\| (1+i)·(10+i)}} {{math\| (1+i)·(10−i)}}
205	{{math\| 3+14i}} {{math\| 6+13i}} {{math\| 13+6i}} {{math\| 14+3i}}	{{math\| i·(2+i)·(5−4i)}} {{math\| (2+i)·(5+4i)}} {{math\| i·(2−i)·(5−4i)}} {{math\| (2−i)·(5+4i)}}
208	{{math\| 8+12i}} {{math\| 12+8i}}	{{math\| −i·(1+i)⁴·(3−2i)}} {{math\| −(1+i)⁴·(3+2i)}}
212	{{math\| 4+14i}} {{math\| 14+4i}}	{{math\| (1+i)²·(7−2i)}} {{math\| −i·(1+i)²·(7+2i)}}
218	{{math\| 7+13i}} {{math\| 13+7i}}	{{math\| (1+i)·(10+3i)}} {{math\| (1+i)·(10−3i)}}
221	{{math\| 5+14i}} {{math\| 10+11i}} {{math\| 11+10i}} {{math\| 14+5i}}	{{math\| i·(3−2i)·(4+i)}} {{math\| (3+2i)·(4+i)}} {{math\| i·(3−2i)·(4−i)}} {{math\| (3+2i)·(4−i)}}
225	{{math\| 9+12i}} {{math\| 12+9i}} {{math\| 15}}	{{math\| (2+i)²·3}} {{math\| i·(2−i)²·3}} {{math\| (2+i)·(2−i)·3}}
226	{{math\| 1+15i}} {{math\| 15+i}}	{{math\| (1+i)·(8+7i)}} {{math\| (1+i)·(8−7i)}}
229	{{math\| 2+15i}} {{math\| 15+2i}}	(p) (p)
232	{{math\| 6+14i}} {{math\| 14+6i}}	{{math\| −i·(1+i)³·(5+2i)}} {{math\| −i·(1+i)³·(5−2i)}}
233	{{math\| 8+13i}} {{math\| 13+8i}}	(p) (p)
234	{{math\| 3+15i}} {{math\| 15+3i}}	{{math\| (1+i)·3·(3+2i)}} {{math\| (1+i)·3·(3−2i)}}
241	{{math\| 4+15i}} {{math\| 15+4i}}	(p) (p)
242	{{math\| 11+11i}}	{{math\| (1+i)·11}}
244	{{math\| 10+12i}} {{math\| 12+10i}}	{{math\| (1+i)²·(6−5i)}} {{math\| −i·(1+i)²·(6+5i)}}
245	{{math\| 7+14i}} {{math\| 14+7i}}	{{math\| i·(2−i)·7}} {{math\| (2+i)·7}}
250	{{math\| 5+15i}} {{math\| 9+13i}} {{math\| 13+9i}} {{math\| 15+5i}}	{{math\| (1+i)·(2+i)²·(2−i)}} {{math\| i·(1+i)·(2−i)³}} {{math\| −i·(1+i)·(2+i)³}} {{math\| (1+i)·(2+i)·(2−i)²}}

Norm \|\| Integer \|\| Factorization
id="251–500" class="wikitable sortable" style="float:left; margin-right:1em" \|+ Norm 251–500
256	{{math\| 16}}	{{math\| (1+i)⁸}}
257	{{math\| 1+16i}} {{math\| 16+i}}	(p) (p)
260	{{math\| 2+16i}} {{math\| 8+14i}} {{math\| 14+8i}} {{math\| 16+2i}}	{{math\| (1+i)²·(2+i)·(3−2i)}} {{math\| −i·(1+i)²·(2+i)·(3+2i)}} {{math\| (1+i)²·(2−i)·(3−2i)}} {{math\| −i·(1+i)²·(2−i)·(3+2i)}}
261	{{math\| 6+15i}} {{math\| 15+6i}}	{{math\| i·3·(5−2i)}} {{math\| 3·(5+2i)}}
265	{{math\| 3+16i}} {{math\| 11+12i}} {{math\| 12+11i}} {{math\| 16+3i}}	{{math\| i·(2−i)·(7+2i)}} {{math\| i·(2−i)·(7−2i)}} {{math\| (2+i)·(7+2i)}} {{math\| (2+i)·(7−2i)}}
269	{{math\| 10+13i}} {{math\| 13+10i}}	(p) (p)
272	{{math\| 4+16i}} {{math\| 16+4i}}	{{math\| −i·(1+i)⁴·(4−i)}} {{math\| −(1+i)⁴·(4+i)}}
274	{{math\| 7+15i}} {{math\| 15+7i}}	{{math\| (1+i)·(11+4i)}} {{math\| (1+i)·(11−4i)}}
277	{{math\| 9+14i}} {{math\| 14+9i}}	(p) (p)
281	{{math\| 5+16i}} {{math\| 16+5i}}	(p) (p)
288	{{math\| 12+12i}}	{{math\| −(1+i)⁵·3}}
289	{{math\| 8+15i}} {{math\| 15+8i}} {{math\| 17}}	{{math\| i·(4−i)²}} {{math\| (4+i)²}} {{math\| (4+i)·(4−i)}}
290	{{math\| 1+17i}} {{math\| 11+13i}} {{math\| 13+11i}} {{math\| 17+i}}	{{math\| i·(1+i)·(2−i)·(5−2i)}} {{math\| (1+i)·(2+i)·(5−2i)}} {{math\| (1+i)·(2−i)·(5+2i)}} {{math\| −i·(1+i)·(2+i)·(5+2i)}}
292	{{math\| 6+16i}} {{math\| 16+6i}}	{{math\| (1+i)²·(8−3i)}} {{math\| −i·(1+i)²·(8+3i)}}
293	{{math\| 2+17i}} {{math\| 17+2i}}	(p) (p)
296	{{math\| 10+14i}} {{math\| 14+10i}}	{{math\| −i·(1+i)³·(6+i)}} {{math\| −i·(1+i)³·(6−i)}}
298	{{math\| 3+17i}} {{math\| 17+3i}}	{{math\| (1+i)·(10+7i)}} {{math\| (1+i)·(10−7i)}}
305	{{math\| 4+17i}} {{math\| 7+16i}} {{math\| 16+7i}} {{math\| 17+4i}}	{{math\| i·(2+i)·(6−5i)}} {{math\| (2+i)·(6+5i)}} {{math\| i·(2−i)·(6−5i)}} {{math\| (2−i)·(6+5i)}}
306	{{math\| 9+15i}} {{math\| 15+9i}}	{{math\| (1+i)·3·(4+i)}} {{math\| (1+i)·3·(4−i)}}
313	{{math\| 12+13i}} {{math\| 13+12i}}	(p) (p)
314	{{math\| 5+17i}} {{math\| 17+5i}}	{{math\| (1+i)·(11+6i)}} {{math\| (1+i)·(11−6i)}}
317	{{math\| 11+14i}} {{math\| 14+11i}}	(p) (p)
320	{{math\| 8+16i}} {{math\| 16+8i}}	{{math\| −(1+i)⁶·(2−i)}} {{math\| i·(1+i)⁶·(2+i)}}
324	{{math\| 18}}	{{math\| −i·(1+i)²·3²}}
325	{{math\| 1+18i}} {{math\| 6+17i}} {{math\| 10+15i}} {{math\| 15+10i}} {{math\| 17+6i}} {{math\| 18+i}}	{{math\| (2+i)²·(3+2i)}} {{math\| i·(2−i)²·(3+2i)}} {{math\| i·(2+i)·(2−i)·(3−2i)}} {{math\| (2+i)·(2−i)·(3+2i)}} {{math\| (2+i)²·(3−2i)}} {{math\| i·(2−i)²·(3−2i)}}
328	{{math\| 2+18i}} {{math\| 18+2i}}	{{math\| −i·(1+i)³·(5+4i)}} {{math\| −i·(1+i)³·(5−4i)}}
333	{{math\| 3+18i}} {{math\| 18+3i}}	{{math\| i·3·(6−i)}} {{math\| 3·(6+i)}}
337	{{math\| 9+16i}} {{math\| 16+9i}}	(p) (p)
338	{{math\| 7+17i}} {{math\| 13+13i}} {{math\| 17+7i}}	{{math\| i·(1+i)·(3−2i)²}} {{math\| (1+i)·(3+2i)·(3−2i)}} {{math\| −i·(1+i)·(3+2i)²}}
340	{{math\| 4+18i}} {{math\| 12+14i}} {{math\| 14+12i}} {{math\| 18+4i}}	{{math\| (1+i)²·(2−i)·(4+i)}} {{math\| (1+i)²·(2−i)·(4−i)}} {{math\| −i·(1+i)²·(2+i)·(4+i)}} {{math\| −i·(1+i)²·(2+i)·(4−i)}}
346	{{math\| 11+15i}} {{math\| 15+11i}}	{{math\| (1+i)·(13+2i)}} {{math\| (1+i)·(13−2i)}}
349	{{math\| 5+18i}} {{math\| 18+5i}}	(p) (p)
353	{{math\| 8+17i}} {{math\| 17+8i}}	(p) (p)
356	{{math\| 10+16i}} {{math\| 16+10i}}	{{math\| (1+i)²·(8−5i)}} {{math\| −i·(1+i)²·(8+5i)}}
360	{{math\| 6+18i}} {{math\| 18+6i}}	{{math\| −i·(1+i)³·(2+i)·3}} {{math\| −i·(1+i)³·(2−i)·3}}
361	{{math\| 19}}	(p)
362	{{math\| 1+19i}} {{math\| 19+i}}	{{math\| (1+i)·(10+9i)}} {{math\| (1+i)·(10−9i)}}
365	{{math\| 2+19i}} {{math\| 13+14i}} {{math\| 14+13i}} {{math\| 19+2i}}	{{math\| i·(2−i)·(8+3i)}} {{math\| (2+i)·(8+3i)}} {{math\| i·(2−i)·(8−3i)}} {{math\| (2+i)·(8−3i)}}
369	{{math\| 12+15i}} {{math\| 15+12i}}	{{math\| i·3·(5−4i)}} {{math\| 3·(5+4i)}}
370	{{math\| 3+19i}} {{math\| 9+17i}} {{math\| 17+9i}} {{math\| 19+3i}}	{{math\| (1+i)·(2+i)·(6+i)}} {{math\| (1+i)·(2+i)·(6−i)}} {{math\| (1+i)·(2−i)·(6+i)}} {{math\| (1+i)·(2−i)·(6−i)}}
373	{{math\| 7+18i}} {{math\| 18+7i}}	(p) (p)
377	{{math\| 4+19i}} {{math\| 11+16i}} {{math\| 16+11i}} {{math\| 19+4i}}	{{math\| i·(3−2i)·(5+2i)}} {{math\| (3+2i)·(5+2i)}} {{math\| i·(3−2i)·(5−2i)}} {{math\| (3+2i)·(5−2i)}}
386	{{math\| 5+19i}} {{math\| 19+5i}}	{{math\| (1+i)·(12+7i)}} {{math\| (1+i)·(12−7i)}}
388	{{math\| 8+18i}} {{math\| 18+8i}}	{{math\| (1+i)²·(9−4i)}} {{math\| −i·(1+i)²·(9+4i)}}
389	{{math\| 10+17i}} {{math\| 17+10i}}	(p) (p)
392	{{math\| 14+14i}}	{{math\| −i·(1+i)³·7}}
394	{{math\| 13+15i}} {{math\| 15+13i}}	{{math\| (1+i)·(14+i)}} {{math\| (1+i)·(14−i)}}
397	{{math\| 6+19i}} {{math\| 19+6i}}	(p) (p)
400	{{math\| 12+16i}} {{math\| 16+12i}} {{math\| 20}}	{{math\| −(1+i)⁴·(2+i)²}} {{math\| −i·(1+i)⁴·(2−i)²}} {{math\| −(1+i)⁴·(2+i)·(2−i)}}
401	{{math\| 1+20i}} {{math\| 20+i}}	(p) (p)
404	{{math\| 2+20i}} {{math\| 20+2i}}	{{math\| (1+i)²·(10−i)}} {{math\| −i·(1+i)²·(10+i)}}
405	{{math\| 9+18i}} {{math\| 18+9i}}	{{math\| i·(2−i)·3²}} {{math\| (2+i)·3²}}
409	{{math\| 3+20i}} {{math\| 20+3i}}	(p) (p)
410	{{math\| 7+19i}} {{math\| 11+17i}} {{math\| 17+11i}} {{math\| 19+7i}}	{{math\| i·(1+i)·(2−i)·(5−4i)}} {{math\| (1+i)·(2−i)·(5+4i)}} {{math\| (1+i)·(2+i)·(5−4i)}} {{math\| −i·(1+i)·(2+i)·(5+4i)}}
416	{{math\| 4+20i}} {{math\| 20+4i}}	{{math\| −(1+i)⁵·(3+2i)}} {{math\| −(1+i)⁵·(3−2i)}}
421	{{math\| 14+15i}} {{math\| 15+14i}}	(p) (p)
424	{{math\| 10+18i}} {{math\| 18+10i}}	{{math\| −i·(1+i)³·(7+2i)}} {{math\| −i·(1+i)³·(7−2i)}}
425	{{math\| 5+20i}} {{math\| 8+19i}} {{math\| 13+16i}} {{math\| 16+13i}} {{math\| 19+8i}} {{math\| 20+5i}}	{{math\| i·(2+i)·(2−i)·(4−i)}} {{math\| (2+i)²·(4+i)}} {{math\| i·(2−i)²·(4+i)}} {{math\| (2+i)²·(4−i)}} {{math\| i·(2−i)²·(4−i)}} {{math\| (2+i)·(2−i)·(4+i)}}
433	{{math\| 12+17i}} {{math\| 17+12i}}	(p) (p)
436	{{math\| 6+20i}} {{math\| 20+6i}}	{{math\| (1+i)²·(10−3i)}} {{math\| −i·(1+i)²·(10+3i)}}
441	{{math\| 21}}	{{math\| 3·7}}
442	{{math\| 1+21i}} {{math\| 9+19i}} {{math\| 19+9i}} {{math\| 21+i}}	{{math\| i·(1+i)·(3−2i)·(4−i)}} {{math\| (1+i)·(3+2i)·(4−i)}} {{math\| (1+i)·(3−2i)·(4+i)}} {{math\| −i·(1+i)·(3+2i)·(4+i)}}
445	{{math\| 2+21i}} {{math\| 11+18i}} {{math\| 18+11i}} {{math\| 21+2i}}	{{math\| i·(2+i)·(8−5i)}} {{math\| (2+i)·(8+5i)}} {{math\| i·(2−i)·(8−5i)}} {{math\| (2−i)·(8+5i)}}
449	{{math\| 7+20i}} {{math\| 20+7i}}	(p) (p)
450	{{math\| 3+21i}} {{math\| 15+15i}} {{math\| 21+3i}}	{{math\| i·(1+i)·(2−i)²·3}} {{math\| (1+i)·(2+i)·(2−i)·3}} {{math\| −i·(1+i)·(2+i)²·3}}
452	{{math\| 14+16i}} {{math\| 16+14i}}	{{math\| (1+i)²·(8−7i)}} {{math\| −i·(1+i)²·(8+7i)}}
457	{{math\| 4+21i}} {{math\| 21+4i}}	(p) (p)
458	{{math\| 13+17i}} {{math\| 17+13i}}	{{math\| (1+i)·(15+2i)}} {{math\| (1+i)·(15−2i)}}
461	{{math\| 10+19i}} {{math\| 19+10i}}	(p) (p)
464	{{math\| 8+20i}} {{math\| 20+8i}}	{{math\| −i·(1+i)⁴·(5−2i)}} {{math\| −(1+i)⁴·(5+2i)}}
466	{{math\| 5+21i}} {{math\| 21+5i}}	{{math\| (1+i)·(13+8i)}} {{math\| (1+i)·(13−8i)}}
468	{{math\| 12+18i}} {{math\| 18+12i}}	{{math\| (1+i)²·3·(3−2i)}} {{math\| −i·(1+i)²·3·(3+2i)}}
477	{{math\| 6+21i}} {{math\| 21+6i}}	{{math\| i·3·(7−2i)}} {{math\| 3·(7+2i)}}
481	{{math\| 9+20i}} {{math\| 15+16i}} {{math\| 16+15i}} {{math\| 20+9i}}	{{math\| i·(3−2i)·(6+i)}} {{math\| i·(3−2i)·(6−i)}} {{math\| (3+2i)·(6+i)}} {{math\| (3+2i)·(6−i)}}
482	{{math\| 11+19i}} {{math\| 19+11i}}	{{math\| (1+i)·(15+4i)}} {{math\| (1+i)·(15−4i)}}
484	{{math\| 22}}	{{math\| −i·(1+i)²·11}}
485	{{math\| 1+22i}} {{math\| 14+17i}} {{math\| 17+14i}} {{math\| 22+i}}	{{math\| i·(2−i)·(9+4i)}} {{math\| (2+i)·(9+4i)}} {{math\| i·(2−i)·(9−4i)}} {{math\| (2+i)·(9−4i)}}
488	{{math\| 2+22i}} {{math\| 22+2i}}	{{math\| −i·(1+i)³·(6+5i)}} {{math\| −i·(1+i)³·(6−5i)}}
490	{{math\| 7+21i}} {{math\| 21+7i}}	{{math\| (1+i)·(2+i)·7}} {{math\| (1+i)·(2−i)·7}}
493	{{math\| 3+22i}} {{math\| 13+18i}} {{math\| 18+13i}} {{math\| 22+3i}}	{{math\| i·(4+i)·(5−2i)}} {{math\| i·(4−i)·(5−2i)}} {{math\| (4+i)·(5+2i)}} {{math\| (4−i)·(5+2i)}}
500	{{math\| 4+22i}} {{math\| 10+20i}} {{math\| 20+10i}} {{math\| 22+4i}}	{{math\| −i·(1+i)²·(2+i)³}} {{math\| (1+i)²·(2+i)·(2−i)²}} {{math\| −i·(1+i)²·(2+i)²·(2−i)}} {{math\| (1+i)²·(2−i)³}}

Norm \|\| Integer \|\| Factorization
id="501–750" class="wikitable sortable" style="float:left; margin-right:1em" \|+ Norm 501–750
505	{{math\| 8+21i}} {{math\| 12+19i}} {{math\| 19+12i}} {{math\| 21+8i}}	{{math\| i·(2−i)·(10+i)}} {{math\| i·(2−i)·(10−i)}} {{math\| (2+i)·(10+i)}} {{math\| (2+i)·(10−i)}}
509	{{math\| 5+22i}} {{math\| 22+5i}}	(p) (p)
512	{{math\| 16+16i}}	{{math\| (1+i)⁹}}
514	{{math\| 15+17i}} {{math\| 17+15i}}	{{math\| (1+i)·(16+i)}} {{math\| (1+i)·(16−i)}}
520	{{math\| 6+22i}} {{math\| 14+18i}} {{math\| 18+14i}} {{math\| 22+6i}}	{{math\| (1+i)³·(2−i)·(3−2i)}} {{math\| −i·(1+i)³·(2−i)·(3+2i)}} {{math\| −i·(1+i)³·(2+i)·(3−2i)}} {{math\| −(1+i)³·(2+i)·(3+2i)}}
521	{{math\| 11+20i}} {{math\| 20+11i}}	(p) (p)
522	{{math\| 9+21i}} {{math\| 21+9i}}	{{math\| (1+i)·3·(5+2i)}} {{math\| (1+i)·3·(5−2i)}}
529	{{math\| 23}}	(p)
530	{{math\| 1+23i}} {{math\| 13+19i}} {{math\| 19+13i}} {{math\| 23+i}}	{{math\| (1+i)·(2+i)·(7+2i)}} {{math\| (1+i)·(2+i)·(7−2i)}} {{math\| (1+i)·(2−i)·(7+2i)}} {{math\| (1+i)·(2−i)·(7−2i)}}
533	{{math\| 2+23i}} {{math\| 7+22i}} {{math\| 22+7i}} {{math\| 23+2i}}	{{math\| i·(3+2i)·(5−4i)}} {{math\| (3+2i)·(5+4i)}} {{math\| i·(3−2i)·(5−4i)}} {{math\| (3−2i)·(5+4i)}}
538	{{math\| 3+23i}} {{math\| 23+3i}}	{{math\| (1+i)·(13+10i)}} {{math\| (1+i)·(13−10i)}}
541	{{math\| 10+21i}} {{math\| 21+10i}}	(p) (p)
544	{{math\| 12+20i}} {{math\| 20+12i}}	{{math\| −(1+i)⁵·(4+i)}} {{math\| −(1+i)⁵·(4−i)}}
545	{{math\| 4+23i}} {{math\| 16+17i}} {{math\| 17+16i}} {{math\| 23+4i}}	{{math\| i·(2−i)·(10+3i)}} {{math\| i·(2−i)·(10−3i)}} {{math\| (2+i)·(10+3i)}} {{math\| (2+i)·(10−3i)}}
548	{{math\| 8+22i}} {{math\| 22+8i}}	{{math\| (1+i)²·(11−4i)}} {{math\| −i·(1+i)²·(11+4i)}}
549	{{math\| 15+18i}} {{math\| 18+15i}}	{{math\| i·3·(6−5i)}} {{math\| 3·(6+5i)}}
554	{{math\| 5+23i}} {{math\| 23+5i}}	{{math\| (1+i)·(14+9i)}} {{math\| (1+i)·(14−9i)}}
557	{{math\| 14+19i}} {{math\| 19+14i}}	(p) (p)
562	{{math\| 11+21i}} {{math\| 21+11i}}	{{math\| (1+i)·(16+5i)}} {{math\| (1+i)·(16−5i)}}
565	{{math\| 6+23i}} {{math\| 9+22i}} {{math\| 22+9i}} {{math\| 23+6i}}	{{math\| i·(2+i)·(8−7i)}} {{math\| (2+i)·(8+7i)}} {{math\| i·(2−i)·(8−7i)}} {{math\| (2−i)·(8+7i)}}
569	{{math\| 13+20i}} {{math\| 20+13i}}	(p) (p)
576	{{math\| 24}}	{{math\| i·(1+i)⁶·3}}
577	{{math\| 1+24i}} {{math\| 24+i}}	(p) (p)
578	{{math\| 7+23i}} {{math\| 17+17i}} {{math\| 23+7i}}	{{math\| (1+i)·(4+i)²}} {{math\| (1+i)·(4+i)·(4−i)}} {{math\| (1+i)·(4−i)²}}
580	{{math\| 2+24i}} {{math\| 16+18i}} {{math\| 18+16i}} {{math\| 24+2i}}	{{math\| (1+i)²·(2−i)·(5+2i)}} {{math\| −i·(1+i)²·(2+i)·(5+2i)}} {{math\| (1+i)²·(2−i)·(5−2i)}} {{math\| −i·(1+i)²·(2+i)·(5−2i)}}
584	{{math\| 10+22i}} {{math\| 22+10i}}	{{math\| −i·(1+i)³·(8+3i)}} {{math\| −i·(1+i)³·(8−3i)}}
585	{{math\| 3+24i}} {{math\| 12+21i}} {{math\| 21+12i}} {{math\| 24+3i}}	{{math\| i·(2+i)·3·(3−2i)}} {{math\| (2+i)·3·(3+2i)}} {{math\| i·(2−i)·3·(3−2i)}} {{math\| (2−i)·3·(3+2i)}}
586	{{math\| 15+19i}} {{math\| 19+15i}}	{{math\| (1+i)·(17+2i)}} {{math\| (1+i)·(17−2i)}}
592	{{math\| 4+24i}} {{math\| 24+4i}}	{{math\| −i·(1+i)⁴·(6−i)}} {{math\| −(1+i)⁴·(6+i)}}
593	{{math\| 8+23i}} {{math\| 23+8i}}	(p) (p)
596	{{math\| 14+20i}} {{math\| 20+14i}}	{{math\| (1+i)²·(10−7i)}} {{math\| −i·(1+i)²·(10+7i)}}
601	{{math\| 5+24i}} {{math\| 24+5i}}	(p) (p)
605	{{math\| 11+22i}} {{math\| 22+11i}}	{{math\| i·(2−i)·11}} {{math\| (2+i)·11}}
610	{{math\| 9+23i}} {{math\| 13+21i}} {{math\| 21+13i}} {{math\| 23+9i}}	{{math\| i·(1+i)·(2−i)·(6−5i)}} {{math\| (1+i)·(2−i)·(6+5i)}} {{math\| (1+i)·(2+i)·(6−5i)}} {{math\| −i·(1+i)·(2+i)·(6+5i)}}
612	{{math\| 6+24i}} {{math\| 24+6i}}	{{math\| (1+i)²·3·(4−i)}} {{math\| −i·(1+i)²·3·(4+i)}}
613	{{math\| 17+18i}} {{math\| 18+17i}}	(p) (p)
617	{{math\| 16+19i}} {{math\| 19+16i}}	(p) (p)
625	{{math\| 7+24i}} {{math\| 15+20i}} {{math\| 20+15i}} {{math\| 24+7i}} {{math\| 25}}	{{math\| −(2−i)⁴}} {{math\| (2+i)³·(2−i)}} {{math\| i·(2+i)·(2−i)³}} {{math\| −i·(2+i)⁴}} {{math\| (2+i)²·(2−i)²}}
626	{{math\| 1+25i}} {{math\| 25+i}}	{{math\| (1+i)·(13+12i)}} {{math\| (1+i)·(13−12i)}}
628	{{math\| 12+22i}} {{math\| 22+12i}}	{{math\| (1+i)²·(11−6i)}} {{math\| −i·(1+i)²·(11+6i)}}
629	{{math\| 2+25i}} {{math\| 10+23i}} {{math\| 23+10i}} {{math\| 25+2i}}	{{math\| i·(4−i)·(6+i)}} {{math\| i·(4−i)·(6−i)}} {{math\| (4+i)·(6+i)}} {{math\| (4+i)·(6−i)}}
634	{{math\| 3+25i}} {{math\| 25+3i}}	{{math\| (1+i)·(14+11i)}} {{math\| (1+i)·(14−11i)}}
637	{{math\| 14+21i}} {{math\| 21+14i}}	{{math\| i·(3−2i)·7}} {{math\| (3+2i)·7}}
640	{{math\| 8+24i}} {{math\| 24+8i}}	{{math\| i·(1+i)⁷·(2+i)}} {{math\| i·(1+i)⁷·(2−i)}}
641	{{math\| 4+25i}} {{math\| 25+4i}}	(p) (p)
648	{{math\| 18+18i}}	{{math\| −i·(1+i)³·3²}}
650	{{math\| 5+25i}} {{math\| 11+23i}} {{math\| 17+19i}} {{math\| 19+17i}} {{math\| 23+11i}} {{math\| 25+5i}}	{{math\| (1+i)·(2+i)·(2−i)·(3+2i)}} {{math\| (1+i)·(2+i)²·(3−2i)}} {{math\| i·(1+i)·(2−i)²·(3−2i)}} {{math\| −i·(1+i)·(2+i)²·(3+2i)}} {{math\| (1+i)·(2−i)²·(3+2i)}} {{math\| (1+i)·(2+i)·(2−i)·(3−2i)}}
653	{{math\| 13+22i}} {{math\| 22+13i}}	(p) (p)
656	{{math\| 16+20i}} {{math\| 20+16i}}	{{math\| −i·(1+i)⁴·(5−4i)}} {{math\| −(1+i)⁴·(5+4i)}}
657	{{math\| 9+24i}} {{math\| 24+9i}}	{{math\| i·3·(8−3i)}} {{math\| 3·(8+3i)}}
661	{{math\| 6+25i}} {{math\| 25+6i}}	(p) (p)
666	{{math\| 15+21i}} {{math\| 21+15i}}	{{math\| (1+i)·3·(6+i)}} {{math\| (1+i)·3·(6−i)}}
673	{{math\| 12+23i}} {{math\| 23+12i}}	(p) (p)
674	{{math\| 7+25i}} {{math\| 25+7i}}	{{math\| (1+i)·(16+9i)}} {{math\| (1+i)·(16−9i)}}
676	{{math\| 10+24i}} {{math\| 24+10i}} {{math\| 26}}	{{math\| −i·(1+i)²·(3+2i)²}} {{math\| (1+i)²·(3−2i)²}} {{math\| −i·(1+i)²·(3+2i)·(3−2i)}}
677	{{math\| 1+26i}} {{math\| 26+i}}	(p) (p)
680	{{math\| 2+26i}} {{math\| 14+22i}} {{math\| 22+14i}} {{math\| 26+2i}}	{{math\| −i·(1+i)³·(2+i)·(4+i)}} {{math\| −i·(1+i)³·(2+i)·(4−i)}} {{math\| −i·(1+i)³·(2−i)·(4+i)}} {{math\| −i·(1+i)³·(2−i)·(4−i)}}
685	{{math\| 3+26i}} {{math\| 18+19i}} {{math\| 19+18i}} {{math\| 26+3i}}	{{math\| i·(2−i)·(11+4i)}} {{math\| (2+i)·(11+4i)}} {{math\| i·(2−i)·(11−4i)}} {{math\| (2+i)·(11−4i)}}
689	{{math\| 8+25i}} {{math\| 17+20i}} {{math\| 20+17i}} {{math\| 25+8i}}	{{math\| i·(3−2i)·(7+2i)}} {{math\| (3+2i)·(7+2i)}} {{math\| i·(3−2i)·(7−2i)}} {{math\| (3+2i)·(7−2i)}}
692	{{math\| 4+26i}} {{math\| 26+4i}}	{{math\| (1+i)²·(13−2i)}} {{math\| −i·(1+i)²·(13+2i)}}
697	{{math\| 11+24i}} {{math\| 16+21i}} {{math\| 21+16i}} {{math\| 24+11i}}	{{math\| i·(4+i)·(5−4i)}} {{math\| (4+i)·(5+4i)}} {{math\| i·(4−i)·(5−4i)}} {{math\| (4−i)·(5+4i)}}
698	{{math\| 13+23i}} {{math\| 23+13i}}	{{math\| (1+i)·(18+5i)}} {{math\| (1+i)·(18−5i)}}
701	{{math\| 5+26i}} {{math\| 26+5i}}	(p) (p)
706	{{math\| 9+25i}} {{math\| 25+9i}}	{{math\| (1+i)·(17+8i)}} {{math\| (1+i)·(17−8i)}}
709	{{math\| 15+22i}} {{math\| 22+15i}}	(p) (p)
712	{{math\| 6+26i}} {{math\| 26+6i}}	{{math\| −i·(1+i)³·(8+5i)}} {{math\| −i·(1+i)³·(8−5i)}}
720	{{math\| 12+24i}} {{math\| 24+12i}}	{{math\| −i·(1+i)⁴·(2−i)·3}} {{math\| −(1+i)⁴·(2+i)·3}}
722	{{math\| 19+19i}}	{{math\| (1+i)·19}}
724	{{math\| 18+20i}} {{math\| 20+18i}}	{{math\| (1+i)²·(10−9i)}} {{math\| −i·(1+i)²·(10+9i)}}
725	{{math\| 7+26i}} {{math\| 10+25i}} {{math\| 14+23i}} {{math\| 23+14i}} {{math\| 25+10i}} {{math\| 26+7i}}	{{math\| (2+i)²·(5+2i)}} {{math\| i·(2+i)·(2−i)·(5−2i)}} {{math\| i·(2−i)²·(5+2i)}} {{math\| (2+i)²·(5−2i)}} {{math\| (2+i)·(2−i)·(5+2i)}} {{math\| i·(2−i)²·(5−2i)}}
729	{{math\| 27}}	{{math\| 3³}}
730	{{math\| 1+27i}} {{math\| 17+21i}} {{math\| 21+17i}} {{math\| 27+i}}	{{math\| i·(1+i)·(2−i)·(8−3i)}} {{math\| (1+i)·(2+i)·(8−3i)}} {{math\| (1+i)·(2−i)·(8+3i)}} {{math\| −i·(1+i)·(2+i)·(8+3i)}}
733	{{math\| 2+27i}} {{math\| 27+2i}}	(p) (p)
738	{{math\| 3+27i}} {{math\| 27+3i}}	{{math\| (1+i)·3·(5+4i)}} {{math\| (1+i)·3·(5−4i)}}
740	{{math\| 8+26i}} {{math\| 16+22i}} {{math\| 22+16i}} {{math\| 26+8i}}	{{math\| (1+i)²·(2−i)·(6+i)}} {{math\| (1+i)²·(2−i)·(6−i)}} {{math\| −i·(1+i)²·(2+i)·(6+i)}} {{math\| −i·(1+i)²·(2+i)·(6−i)}}
745	{{math\| 4+27i}} {{math\| 13+24i}} {{math\| 24+13i}} {{math\| 27+4i}}	{{math\| i·(2+i)·(10−7i)}} {{math\| (2+i)·(10+7i)}} {{math\| i·(2−i)·(10−7i)}} {{math\| (2−i)·(10+7i)}}
746	{{math\| 11+25i}} {{math\| 25+11i}}	{{math\| (1+i)·(18+7i)}} {{math\| (1+i)·(18−7i)}}

Norm \|\| Integer \|\| Factorization
id="751–1000" class="wikitable sortable" style="float:left; margin-right:1em" \|+ Norm 751–1000
754	{{math\| 5+27i}} {{math\| 15+23i}} {{math\| 23+15i}} {{math\| 27+5i}}	{{math\| i·(1+i)·(3−2i)·(5−2i)}} {{math\| (1+i)·(3+2i)·(5−2i)}} {{math\| (1+i)·(3−2i)·(5+2i)}} {{math\| −i·(1+i)·(3+2i)·(5+2i)}}
757	{{math\| 9+26i}} {{math\| 26+9i}}	(p) (p)
761	{{math\| 19+20i}} {{math\| 20+19i}}	(p) (p)
765	{{math\| 6+27i}} {{math\| 18+21i}} {{math\| 21+18i}} {{math\| 27+6i}}	{{math\| i·(2−i)·3·(4+i)}} {{math\| i·(2−i)·3·(4−i)}} {{math\| (2+i)·3·(4+i)}} {{math\| (2+i)·3·(4−i)}}
769	{{math\| 12+25i}} {{math\| 25+12i}}	(p) (p)
772	{{math\| 14+24i}} {{math\| 24+14i}}	{{math\| (1+i)²·(12−7i)}} {{math\| −i·(1+i)²·(12+7i)}}
773	{{math\| 17+22i}} {{math\| 22+17i}}	(p) (p)
776	{{math\| 10+26i}} {{math\| 26+10i}}	{{math\| −i·(1+i)³·(9+4i)}} {{math\| −i·(1+i)³·(9−4i)}}
778	{{math\| 7+27i}} {{math\| 27+7i}}	{{math\| (1+i)·(17+10i)}} {{math\| (1+i)·(17−10i)}}
784	{{math\| 28}}	{{math\| −(1+i)⁴·7}}
785	{{math\| 1+28i}} {{math\| 16+23i}} {{math\| 23+16i}} {{math\| 28+i}}	{{math\| i·(2+i)·(11−6i)}} {{math\| (2+i)·(11+6i)}} {{math\| i·(2−i)·(11−6i)}} {{math\| (2−i)·(11+6i)}}
788	{{math\| 2+28i}} {{math\| 28+2i}}	{{math\| (1+i)²·(14−i)}} {{math\| −i·(1+i)²·(14+i)}}
793	{{math\| 3+28i}} {{math\| 8+27i}} {{math\| 27+8i}} {{math\| 28+3i}}	{{math\| i·(3+2i)·(6−5i)}} {{math\| (3+2i)·(6+5i)}} {{math\| i·(3−2i)·(6−5i)}} {{math\| (3−2i)·(6+5i)}}
794	{{math\| 13+25i}} {{math\| 25+13i}}	{{math\| (1+i)·(19+6i)}} {{math\| (1+i)·(19−6i)}}
797	{{math\| 11+26i}} {{math\| 26+11i}}	(p) (p)
800	{{math\| 4+28i}} {{math\| 20+20i}} {{math\| 28+4i}}	{{math\| −i·(1+i)⁵·(2−i)²}} {{math\| −(1+i)⁵·(2+i)·(2−i)}} {{math\| i·(1+i)⁵·(2+i)²}}
801	{{math\| 15+24i}} {{math\| 24+15i}}	{{math\| i·3·(8−5i)}} {{math\| 3·(8+5i)}}
802	{{math\| 19+21i}} {{math\| 21+19i}}	{{math\| (1+i)·(20+i)}} {{math\| (1+i)·(20−i)}}
808	{{math\| 18+22i}} {{math\| 22+18i}}	{{math\| −i·(1+i)³·(10+i)}} {{math\| −i·(1+i)³·(10−i)}}
809	{{math\| 5+28i}} {{math\| 28+5i}}	(p) (p)
810	{{math\| 9+27i}} {{math\| 27+9i}}	{{math\| (1+i)·(2+i)·3²}} {{math\| (1+i)·(2−i)·3²}}
818	{{math\| 17+23i}} {{math\| 23+17i}}	{{math\| (1+i)·(20+3i)}} {{math\| (1+i)·(20−3i)}}
820	{{math\| 6+28i}} {{math\| 12+26i}} {{math\| 26+12i}} {{math\| 28+6i}}	{{math\| (1+i)²·(2+i)·(5−4i)}} {{math\| −i·(1+i)²·(2+i)·(5+4i)}} {{math\| (1+i)²·(2−i)·(5−4i)}} {{math\| −i·(1+i)²·(2−i)·(5+4i)}}
821	{{math\| 14+25i}} {{math\| 25+14i}}	(p) (p)
829	{{math\| 10+27i}} {{math\| 27+10i}}	(p) (p)
832	{{math\| 16+24i}} {{math\| 24+16i}}	{{math\| −(1+i)⁶·(3−2i)}} {{math\| i·(1+i)⁶·(3+2i)}}
833	{{math\| 7+28i}} {{math\| 28+7i}}	{{math\| i·(4−i)·7}} {{math\| (4+i)·7}}
841	{{math\| 20+21i}} {{math\| 21+20i}} {{math\| 29}}	{{math\| i·(5−2i)²}} {{math\| (5+2i)²}} {{math\| (5+2i)·(5−2i)}}
842	{{math\| 1+29i}} {{math\| 29+i}}	{{math\| (1+i)·(15+14i)}} {{math\| (1+i)·(15−14i)}}
845	{{math\| 2+29i}} {{math\| 13+26i}} {{math\| 19+22i}} {{math\| 22+19i}} {{math\| 26+13i}} {{math\| 29+2i}}	{{math\| −(2−i)·(3−2i)²}} {{math\| i·(2−i)·(3+2i)·(3−2i)}} {{math\| i·(2+i)·(3−2i)²}} {{math\| (2−i)·(3+2i)²}} {{math\| (2+i)·(3+2i)·(3−2i)}} {{math\| −i·(2+i)·(3+2i)²}}
848	{{math\| 8+28i}} {{math\| 28+8i}}	{{math\| −i·(1+i)⁴·(7−2i)}} {{math\| −(1+i)⁴·(7+2i)}}
850	{{math\| 3+29i}} {{math\| 11+27i}} {{math\| 15+25i}} {{math\| 25+15i}} {{math\| 27+11i}} {{math\| 29+3i}}	{{math\| (1+i)·(2+i)²·(4−i)}} {{math\| i·(1+i)·(2−i)²·(4−i)}} {{math\| (1+i)·(2+i)·(2−i)·(4+i)}} {{math\| (1+i)·(2+i)·(2−i)·(4−i)}} {{math\| −i·(1+i)·(2+i)²·(4+i)}} {{math\| (1+i)·(2−i)²·(4+i)}}
853	{{math\| 18+23i}} {{math\| 23+18i}}	(p) (p)
857	{{math\| 4+29i}} {{math\| 29+4i}}	(p) (p)
865	{{math\| 9+28i}} {{math\| 17+24i}} {{math\| 24+17i}} {{math\| 28+9i}}	{{math\| i·(2−i)·(13+2i)}} {{math\| i·(2−i)·(13−2i)}} {{math\| (2+i)·(13+2i)}} {{math\| (2+i)·(13−2i)}}
866	{{math\| 5+29i}} {{math\| 29+5i}}	{{math\| (1+i)·(17+12i)}} {{math\| (1+i)·(17−12i)}}
872	{{math\| 14+26i}} {{math\| 26+14i}}	{{math\| −i·(1+i)³·(10+3i)}} {{math\| −i·(1+i)³·(10−3i)}}
873	{{math\| 12+27i}} {{math\| 27+12i}}	{{math\| i·3·(9−4i)}} {{math\| 3·(9+4i)}}
877	{{math\| 6+29i}} {{math\| 29+6i}}	(p) (p)
881	{{math\| 16+25i}} {{math\| 25+16i}}	(p) (p)
882	{{math\| 21+21i}}	{{math\| (1+i)·3·7}}
884	{{math\| 10+28i}} {{math\| 20+22i}} {{math\| 22+20i}} {{math\| 28+10i}}	{{math\| (1+i)²·(3−2i)·(4+i)}} {{math\| −i·(1+i)²·(3+2i)·(4+i)}} {{math\| (1+i)²·(3−2i)·(4−i)}} {{math\| −i·(1+i)²·(3+2i)·(4−i)}}
890	{{math\| 7+29i}} {{math\| 19+23i}} {{math\| 23+19i}} {{math\| 29+7i}}	{{math\| i·(1+i)·(2−i)·(8−5i)}} {{math\| (1+i)·(2−i)·(8+5i)}} {{math\| (1+i)·(2+i)·(8−5i)}} {{math\| −i·(1+i)·(2+i)·(8+5i)}}
898	{{math\| 13+27i}} {{math\| 27+13i}}	{{math\| (1+i)·(20+7i)}} {{math\| (1+i)·(20−7i)}}
900	{{math\| 18+24i}} {{math\| 24+18i}} {{math\| 30}}	{{math\| −i·(1+i)²·(2+i)²·3}} {{math\| (1+i)²·(2−i)²·3}} {{math\| −i·(1+i)²·(2+i)·(2−i)·3}}
901	{{math\| 1+30i}} {{math\| 15+26i}} {{math\| 26+15i}} {{math\| 30+i}}	{{math\| i·(4+i)·(7−2i)}} {{math\| i·(4−i)·(7−2i)}} {{math\| (4+i)·(7+2i)}} {{math\| (4−i)·(7+2i)}}
904	{{math\| 2+30i}} {{math\| 30+2i}}	{{math\| −i·(1+i)³·(8+7i)}} {{math\| −i·(1+i)³·(8−7i)}}
905	{{math\| 8+29i}} {{math\| 11+28i}} {{math\| 28+11i}} {{math\| 29+8i}}	{{math\| i·(2+i)·(10−9i)}} {{math\| (2+i)·(10+9i)}} {{math\| i·(2−i)·(10−9i)}} {{math\| (2−i)·(10+9i)}}
909	{{math\| 3+30i}} {{math\| 30+3i}}	{{math\| i·3·(10−i)}} {{math\| 3·(10+i)}}
914	{{math\| 17+25i}} {{math\| 25+17i}}	{{math\| (1+i)·(21+4i)}} {{math\| (1+i)·(21−4i)}}
916	{{math\| 4+30i}} {{math\| 30+4i}}	{{math\| (1+i)²·(15−2i)}} {{math\| −i·(1+i)²·(15+2i)}}
922	{{math\| 9+29i}} {{math\| 29+9i}}	{{math\| (1+i)·(19+10i)}} {{math\| (1+i)·(19−10i)}}
925	{{math\| 5+30i}} {{math\| 14+27i}} {{math\| 21+22i}} {{math\| 22+21i}} {{math\| 27+14i}} {{math\| 30+5i}}	{{math\| i·(2+i)·(2−i)·(6−i)}} {{math\| (2+i)²·(6+i)}} {{math\| i·(2−i)²·(6+i)}} {{math\| (2+i)²·(6−i)}} {{math\| i·(2−i)²·(6−i)}} {{math\| (2+i)·(2−i)·(6+i)}}
928	{{math\| 12+28i}} {{math\| 28+12i}}	{{math\| −(1+i)⁵·(5+2i)}} {{math\| −(1+i)⁵·(5−2i)}}
929	{{math\| 20+23i}} {{math\| 23+20i}}	(p) (p)
932	{{math\| 16+26i}} {{math\| 26+16i}}	{{math\| (1+i)²·(13−8i)}} {{math\| −i·(1+i)²·(13+8i)}}
936	{{math\| 6+30i}} {{math\| 30+6i}}	{{math\| −i·(1+i)³·3·(3+2i)}} {{math\| −i·(1+i)³·3·(3−2i)}}
937	{{math\| 19+24i}} {{math\| 24+19i}}	(p) (p)
941	{{math\| 10+29i}} {{math\| 29+10i}}	(p) (p)
949	{{math\| 7+30i}} {{math\| 18+25i}} {{math\| 25+18i}} {{math\| 30+7i}}	{{math\| i·(3−2i)·(8+3i)}} {{math\| (3+2i)·(8+3i)}} {{math\| i·(3−2i)·(8−3i)}} {{math\| (3+2i)·(8−3i)}}
953	{{math\| 13+28i}} {{math\| 28+13i}}	(p) (p)
954	{{math\| 15+27i}} {{math\| 27+15i}}	{{math\| (1+i)·3·(7+2i)}} {{math\| (1+i)·3·(7−2i)}}
961	{{math\| 31}}	(p)
962	{{math\| 1+31i}} {{math\| 11+29i}} {{math\| 29+11i}} {{math\| 31+i}}	{{math\| (1+i)·(3+2i)·(6+i)}} {{math\| (1+i)·(3+2i)·(6−i)}} {{math\| (1+i)·(3−2i)·(6+i)}} {{math\| (1+i)·(3−2i)·(6−i)}}
964	{{math\| 8+30i}} {{math\| 30+8i}}	{{math\| (1+i)²·(15−4i)}} {{math\| −i·(1+i)²·(15+4i)}}
965	{{math\| 2+31i}} {{math\| 17+26i}} {{math\| 26+17i}} {{math\| 31+2i}}	{{math\| i·(2+i)·(12−7i)}} {{math\| (2+i)·(12+7i)}} {{math\| i·(2−i)·(12−7i)}} {{math\| (2−i)·(12+7i)}}
968	{{math\| 22+22i}}	{{math\| −i·(1+i)³·11}}
970	{{math\| 3+31i}} {{math\| 21+23i}} {{math\| 23+21i}} {{math\| 31+3i}}	{{math\| i·(1+i)·(2−i)·(9−4i)}} {{math\| (1+i)·(2+i)·(9−4i)}} {{math\| (1+i)·(2−i)·(9+4i)}} {{math\| −i·(1+i)·(2+i)·(9+4i)}}
976	{{math\| 20+24i}} {{math\| 24+20i}}	{{math\| −i·(1+i)⁴·(6−5i)}} {{math\| −(1+i)⁴·(6+5i)}}
977	{{math\| 4+31i}} {{math\| 31+4i}}	(p) (p)
980	{{math\| 14+28i}} {{math\| 28+14i}}	{{math\| (1+i)²·(2−i)·7}} {{math\| −i·(1+i)²·(2+i)·7}}
981	{{math\| 9+30i}} {{math\| 30+9i}}	{{math\| i·3·(10−3i)}} {{math\| 3·(10+3i)}}
985	{{math\| 12+29i}} {{math\| 16+27i}} {{math\| 27+16i}} {{math\| 29+12i}}	{{math\| i·(2−i)·(14+i)}} {{math\| i·(2−i)·(14−i)}} {{math\| (2+i)·(14+i)}} {{math\| (2+i)·(14−i)}}
986	{{math\| 5+31i}} {{math\| 19+25i}} {{math\| 25+19i}} {{math\| 31+5i}}	{{math\| (1+i)·(4+i)·(5+2i)}} {{math\| (1+i)·(4−i)·(5+2i)}} {{math\| (1+i)·(4+i)·(5−2i)}} {{math\| (1+i)·(4−i)·(5−2i)}}
997	{{math\| 6+31i}} {{math\| 31+6i}}	(p) (p)
1000	{{math\| 10+30i}} {{math\| 18+26i}} {{math\| 26+18i}} {{math\| 30+10i}}	{{math\| −i·(1+i)³·(2+i)²·(2−i)}} {{math\| (1+i)³·(2−i)³}} {{math\| −(1+i)³·(2+i)³}} {{math\| −i·(1+i)³·(2+i)·(2−i)²}}

Table of Gaussian integer factorizations

Conventions

Factorizations

See also

References

External links