Tabela rozkładu liczb całkowitych Gaussa na czynniki pierwsze

Liczba całkowita Gaussa jest zerem, jedną z czterech jedności ${\displaystyle (\pm 1,\pm i),}$ liczbą pierwszą Gaussa lub liczbą złożoną. Artykuł stanowi tabela liczb całkowitych Gaussa ${\displaystyle x+yi,}$ których norma nie przekracza 1000 i ich rozkład na czynniki pierwsze. Liczby pierwsze Gaussa oznaczone są w tabeli etykietą (p). Rozkład na czynniki obejmuje również opcjonalną jedność pomnożoną przez potęgi liczb pierwszych Gaussa dla większej przejrzystości zapisu.

Zwrócić uwagę należy na istnienie wymiernych liczb pierwszych (tzn. liczb pierwszych ze zbioru liczb całkowitych), które nie są liczbami pierwszymi Gaussa^[1]. Przykładem jest wymierna liczba pierwsza 5, która w zbiorze ${\displaystyle \mathbb {Z} [i]}$ jest rozkładalna na czynniki: ${\displaystyle 5=(2-i)(2+i),}$ nie jest w związku z tym liczbą pierwszą Gaussa.

Druga kolumna tabeli zawiera tylko liczby z pierwszej ćwiartki, tzn. liczby, których część rzeczywista ${\displaystyle x}$ jest dodatnia, a część urojona ${\displaystyle y}$ jest nieujemna. Tabelę można było jeszcze bardziej uprościć sprowadzając liczby do tych z pierwszej oktanty płaszczyzny zespolonej przy użyciu obserwacji, że ${\displaystyle y+xi=i(x-yi).}$

Rozkłady na czynniki nie są wyjątkowe w tym sensie, że jednostka może zostać wchłonięta przez dowolny inny czynnik z wykładnikiem równym jeden. Na przykład ${\displaystyle 4+2i=-i(1+i)^{2}(2+i)}$ można zapisać również jako ${\displaystyle 4+2i=(1+i)^{2}(1-2i).}$ Ta niejednoznaczność została rozwiązana zgodnie z następującą konwencją: czynniki są liczbami pierwszymi z prawej półpłaszczyzny zespolonej o wartości bezwzględnej części rzeczywistej większej lub równej wartości bezwzględnej części urojonej.

Wpisy są sortowane według rosnącej normy ${\displaystyle x^{2}+y^{2}}$ (ciąg 001481 w OEIS). Tabela jest kompletna do maksymalnej normy na końcu tabeli w tym sensie, że każda liczba złożona lub pierwsza z pierwszej ćwiartki pojawia się w drugiej kolumnie.

Liczby pierwsze Gaussa występują tylko dla pewnego podzbioru norm (ciąg A055025 w OEIS). Jest to bardziej przejrzysta wersja dwóch innych ciągów: (ciąg A103431 w OEIS), (ciąg A103432 w OEIS).

Norma	Liczba	Czynniki
${\displaystyle 2}$	${\displaystyle 1+i}$	(p)
${\displaystyle 4}$	${\displaystyle 2}$	${\displaystyle -i(1+i)^{2}}$
${\displaystyle 5}$	${\displaystyle 2+i}$ ${\displaystyle 1+2i}$	(p) (p)
${\displaystyle 8}$	${\displaystyle 2+2i}$	${\displaystyle -i(1+i)^{3}}$
${\displaystyle 9}$	${\displaystyle 3}$	(p)
${\displaystyle 10}$	${\displaystyle 1+3i}$ ${\displaystyle 3+i}$	${\displaystyle (1+i)(2+i)}$ ${\displaystyle (1+i)(2-i)}$
${\displaystyle 13}$	${\displaystyle 3+2i}$ ${\displaystyle 2+3i}$	(p) (p)
${\displaystyle 16}$	${\displaystyle 4}$	${\displaystyle -(1+i)^{4}}$
${\displaystyle 17}$	${\displaystyle 1+4i}$ ${\displaystyle 4+i}$	(p) (p)
${\displaystyle 18}$	${\displaystyle 3+3i}$	${\displaystyle (1+i)\cdot 3}$
${\displaystyle 20}$	${\displaystyle 2+4i}$ ${\displaystyle 4+2i}$	${\displaystyle (1+i)^{2}(2-i)}$ ${\displaystyle -i(1+i)^{2}(2+i)}$
${\displaystyle 25}$	${\displaystyle 3+4i}$ ${\displaystyle 4+3i}$ ${\displaystyle 5}$	${\displaystyle (2+i)^{2}}$ ${\displaystyle i(2-i)^{2}}$ ${\displaystyle (2+i)(2-i)}$
${\displaystyle 26}$	${\displaystyle 1+5i}$ ${\displaystyle 5+i}$	${\displaystyle (1+i)(3+2i)}$ ${\displaystyle (1+i)(3-2i)}$
${\displaystyle 29}$	${\displaystyle 2+5i}$ ${\displaystyle 5+2i}$	(p) (p)
${\displaystyle 32}$	${\displaystyle 4+4i}$	${\displaystyle -(1+i)^{5}}$
${\displaystyle 34}$	${\displaystyle 3+5i}$ ${\displaystyle 5+3i}$	${\displaystyle (1+i)(4+i)}$ ${\displaystyle (1+i)(4-i)}$
${\displaystyle 36}$	${\displaystyle 6}$	${\displaystyle -i(1+i)^{2}\cdot 3}$
${\displaystyle 37}$	${\displaystyle 1+6i}$ ${\displaystyle 6+i}$	(p) (p)
${\displaystyle 40}$	${\displaystyle 2+6i}$ ${\displaystyle 6+2i}$	${\displaystyle -i(1+i)^{3}(2+i)}$ ${\displaystyle -i(1+i)^{3}(2-i)}$
${\displaystyle 41}$	${\displaystyle 4+5i}$ ${\displaystyle 5+4i}$	(p) (p)
${\displaystyle 45}$	${\displaystyle 3+6i}$ ${\displaystyle 6+3i}$	${\displaystyle i(2-i)\cdot 3}$ ${\displaystyle (2+i)\cdot 3}$
${\displaystyle 49}$	${\displaystyle 7}$	(p)
${\displaystyle 50}$	${\displaystyle 1+7i}$ ${\displaystyle 5+5i}$ ${\displaystyle 7+i}$	${\displaystyle i(1+i)(2-i)^{2}}$ ${\displaystyle (1+i)(2+i)(2-i)}$ ${\displaystyle -i(1+i)(2+i)^{2}}$
${\displaystyle 52}$	${\displaystyle 4+6i}$ ${\displaystyle 6+4i}$	${\displaystyle (1+i)^{2}(3-2i)}$ ${\displaystyle -i(1+i)^{2}(3+2i)}$
${\displaystyle 53}$	${\displaystyle 2+7i}$ ${\displaystyle 7+2i}$	(p) (p)
${\displaystyle 58}$	${\displaystyle 3+7i}$ ${\displaystyle 7+3i}$	${\displaystyle (1+i)(5+2i)}$ ${\displaystyle (1+i)(5-2i)}$
${\displaystyle 61}$	${\displaystyle 5+6i}$ ${\displaystyle 6+5i}$	(p) (p)
${\displaystyle 64}$	${\displaystyle 8}$	${\displaystyle i(1+i)^{6}}$
${\displaystyle 65}$	${\displaystyle 1+8i}$ ${\displaystyle 4+7i}$ ${\displaystyle 7+4i}$ ${\displaystyle 8+i}$	${\displaystyle i(2+i)(3-2i)}$ ${\displaystyle (2+i)(3+2i)}$ ${\displaystyle i(2-i)(3-2i)}$ ${\displaystyle (2-i)(3+2i)}$
${\displaystyle 68}$	${\displaystyle 2+8i}$ ${\displaystyle 8+2i}$	${\displaystyle (1+i)^{2}(4-i)}$ ${\displaystyle -i(1+i)^{2}(4+i)}$
${\displaystyle 72}$	${\displaystyle 6+6i}$	${\displaystyle -i(1+i)^{3}\cdot 3}$
${\displaystyle 73}$	${\displaystyle 3+8i}$ ${\displaystyle 8+3i}$	(p) (p)
${\displaystyle 74}$	${\displaystyle 5+7i}$ ${\displaystyle 7+5i}$	${\displaystyle (1+i)(6+i)}$ ${\displaystyle (1+i)(6-i)}$
${\displaystyle 80}$	${\displaystyle 4+8i}$ ${\displaystyle 8+4i}$	${\displaystyle -i(1+i)^{4}(2-i)}$ ${\displaystyle -(1+i)^{4}(2+i)}$
${\displaystyle 81}$	${\displaystyle 9}$	${\displaystyle 3^{2}}$
${\displaystyle 82}$	${\displaystyle 1+9i}$ ${\displaystyle 9+i}$	${\displaystyle (1+i)(5+4i)}$ ${\displaystyle (1+i)(5-4i)}$
${\displaystyle 85}$	${\displaystyle 2+9i}$ ${\displaystyle 6+7i}$ ${\displaystyle 7+6i}$ ${\displaystyle 9+2i}$	${\displaystyle i(2-i)(4+i)}$ ${\displaystyle i(2-i)(4-i)}$ ${\displaystyle (2+i)(4+i)}$ ${\displaystyle (2+i)(4-i)}$
${\displaystyle 89}$	${\displaystyle 5+8i}$ ${\displaystyle 8+5i}$	(p) (p)
${\displaystyle 90}$	${\displaystyle 3+9i}$ ${\displaystyle 9+3i}$	${\displaystyle (1+i)(2+i)\cdot 3}$ ${\displaystyle (1+i)(2-i)\cdot 3}$
${\displaystyle 97}$	${\displaystyle 4+9i}$ ${\displaystyle 9+4i}$	(p) (p)
${\displaystyle 98}$	${\displaystyle 7+7i}$	${\displaystyle (1+i)\cdot 7}$
${\displaystyle 100}$	${\displaystyle 6+8i}$ ${\displaystyle 8+6i}$ ${\displaystyle 10}$	${\displaystyle -i(1+i)^{2}(2+i)^{2}}$ ${\displaystyle (1+i)^{2}(2-i)^{2}}$ ${\displaystyle -i(1+i)^{2}(2+i)(2-i)}$
${\displaystyle 101}$	${\displaystyle 1+10i}$ ${\displaystyle 10+i}$	(p) (p)
${\displaystyle 104}$	${\displaystyle 2+10i}$ ${\displaystyle 10+2i}$	${\displaystyle -i(1+i)^{3}(3+2i)}$ ${\displaystyle -i(1+i)^{3}(3-2i)}$
${\displaystyle 106}$	${\displaystyle 5+9i}$ ${\displaystyle 9+5i}$	${\displaystyle (1+i)(7+2i)}$ ${\displaystyle (1+i)(7-2i)}$
${\displaystyle 109}$	${\displaystyle 3+10i}$ ${\displaystyle 10+3i}$	(p) (p)
${\displaystyle 113}$	${\displaystyle 7+8i}$ ${\displaystyle 8+7i}$	(p) (p)
${\displaystyle 116}$	${\displaystyle 4+10i}$ ${\displaystyle 10+4i}$	${\displaystyle (1+i)^{2}(5-2i)}$ ${\displaystyle -i(1+i)^{2}(5+2i)}$
${\displaystyle 117}$	${\displaystyle 6+9i}$ ${\displaystyle 9+6i}$	${\displaystyle i\cdot 3\cdot (3-2i)}$ ${\displaystyle 3\cdot (3+2i)}$
${\displaystyle 121}$	${\displaystyle 11}$	(p)
${\displaystyle 122}$	${\displaystyle 1+11i}$ ${\displaystyle 11+i}$	${\displaystyle (1+i)(6+5i)}$ ${\displaystyle (1+i)(6-5i)}$
${\displaystyle 125}$	${\displaystyle 2+11i}$ ${\displaystyle 5+10i}$ ${\displaystyle 10+5i}$ ${\displaystyle 11+2i}$	${\displaystyle (2+i)^{3}}$ ${\displaystyle i(2+i)(2-i)^{2}}$ ${\displaystyle (2+i)^{2}(2-i)}$ ${\displaystyle i(2-i)^{3}}$
${\displaystyle 128}$	${\displaystyle 8+8i}$	${\displaystyle i(1+i)^{7}}$
${\displaystyle 130}$	${\displaystyle 3+11i}$ ${\displaystyle 7+9i}$ ${\displaystyle 9+7i}$ ${\displaystyle 11+3i}$	${\displaystyle i(1+i)(2-i)(3-2i)}$ ${\displaystyle (1+i)(2-i)(3+2i)}$ ${\displaystyle (1+i)(2+i)(3-2i)}$ ${\displaystyle -i(1+i)(2+i)(3+2i)}$
${\displaystyle 136}$	${\displaystyle 6+10i}$ ${\displaystyle 10+6i}$	${\displaystyle -i(1+i)^{3}(4+i)}$ ${\displaystyle -i(1+i)^{3}(4-i)}$
${\displaystyle 137}$	${\displaystyle 4+11i}$ ${\displaystyle 11+4i}$	(p) (p)
${\displaystyle 144}$	${\displaystyle 12}$	${\displaystyle -(1+i)^{4}\cdot 3}$
${\displaystyle 145}$	${\displaystyle 1+12i}$ ${\displaystyle 8+9i}$ ${\displaystyle 9+8i}$ ${\displaystyle 12+i}$	${\displaystyle i(2-i)(5+2i)}$ ${\displaystyle (2+i)(5+2i)}$ ${\displaystyle i(2-i)(5-2i)}$ ${\displaystyle (2+i)(5-2i)}$
${\displaystyle 146}$	${\displaystyle 5+11i}$ ${\displaystyle 11+5i}$	${\displaystyle (1+i)(8+3i)}$ ${\displaystyle (1+i)(8-3i)}$
${\displaystyle 148}$	${\displaystyle 2+12i}$ ${\displaystyle 12+2i}$	${\displaystyle (1+i)^{2}(6-i)}$ ${\displaystyle -i(1+i)^{2}(6+i)}$
${\displaystyle 149}$	${\displaystyle 7+10i}$ ${\displaystyle 10+7i}$	(p) (p)
${\displaystyle 153}$	${\displaystyle 3+12i}$ ${\displaystyle 12+3i}$	${\displaystyle i\cdot 3\cdot (4-i)}$ ${\displaystyle 3\cdot (4+i)}$
${\displaystyle 157}$	${\displaystyle 6+11i}$ ${\displaystyle 11+6i}$	(p) (p)
${\displaystyle 160}$	${\displaystyle 4+12i}$ ${\displaystyle 12+4i}$	${\displaystyle -(1+i)^{5}(2+i)}$ ${\displaystyle -(1+i)^{5}(2-i)}$
${\displaystyle 162}$	${\displaystyle 9+9i}$	${\displaystyle (1+i)\cdot 3^{2}}$
${\displaystyle 164}$	${\displaystyle 8+10i}$ ${\displaystyle 10+8i}$	${\displaystyle (1+i)^{2}(5-4i)}$ ${\displaystyle -i(1+i)^{2}(5+4i)}$
${\displaystyle 169}$	${\displaystyle 5+12i}$ ${\displaystyle 12+5i}$ ${\displaystyle 13}$	${\displaystyle (3+2i)^{2}}$ ${\displaystyle i(3-2i)^{2}}$ ${\displaystyle (3+2i)(3-2i)}$
${\displaystyle 170}$	${\displaystyle 1+13i}$ ${\displaystyle 7+11i}$ ${\displaystyle 11+7i}$ ${\displaystyle 13+i}$	${\displaystyle (1+i)(2+i)(4+i)}$ ${\displaystyle (1+i)(2+i)(4-i)}$ ${\displaystyle (1+i)(2-i)(4+i)}$ ${\displaystyle (1+i)(2-i)(4-i)}$
${\displaystyle 173}$	${\displaystyle 2+13i}$ ${\displaystyle 13+2i}$	(p) (p)
${\displaystyle 178}$	${\displaystyle 3+13i}$ ${\displaystyle 13+3i}$	${\displaystyle (1+i)(8+5i)}$ ${\displaystyle (1+i)(8-5i)}$
${\displaystyle 180}$	${\displaystyle 6+12i}$ ${\displaystyle 12+6i}$	${\displaystyle (1+i)^{2}(2-i)\cdot 3}$ ${\displaystyle -i(1+i)^{2}(2+i)\cdot 3}$
${\displaystyle 181}$	${\displaystyle 9+10i}$ ${\displaystyle 10+9i}$	(p) (p)
${\displaystyle 185}$	${\displaystyle 4+13i}$ ${\displaystyle 8+11i}$ ${\displaystyle 11+8i}$ ${\displaystyle 13+4i}$	${\displaystyle i(2-i)(6+i)}$ ${\displaystyle i(2-i)(6-i)}$ ${\displaystyle (2+i)(6+i)}$ ${\displaystyle (2+i)(6-i)}$
${\displaystyle 193}$	${\displaystyle 7+12i}$ ${\displaystyle 12+7i}$	(p) (p)
${\displaystyle 194}$	${\displaystyle 5+13i}$ ${\displaystyle 13+5i}$	${\displaystyle (1+i)(9+4i)}$ ${\displaystyle (1+i)(9-4i)}$
${\displaystyle 196}$	${\displaystyle 14}$	${\displaystyle -i(1+i)^{2}\cdot 7}$
${\displaystyle 197}$	${\displaystyle 1+14i}$ ${\displaystyle 14+i}$	(p) (p)
${\displaystyle 200}$	${\displaystyle 2+14i}$ ${\displaystyle 10+10i}$ ${\displaystyle 14+2i}$	${\displaystyle (1+i)^{3}(2-i)^{2}}$ ${\displaystyle -i(1+i)^{3}(2+i)(2-i)}$ ${\displaystyle -(1+i)^{3}(2+i)^{2}}$
${\displaystyle 202}$	${\displaystyle 9+11i}$ ${\displaystyle 11+9i}$	${\displaystyle (1+i)(10+i)}$ ${\displaystyle (1+i)(10-i)}$
${\displaystyle 205}$	${\displaystyle 3+14i}$ ${\displaystyle 6+13i}$ ${\displaystyle 13+6i}$ ${\displaystyle 14+3i}$	${\displaystyle i(2+i)(5-4i)}$ ${\displaystyle (2+i)(5+4i)}$ ${\displaystyle i(2-i)(5-4i)}$ ${\displaystyle (2-i)(5+4i)}$
${\displaystyle 208}$	${\displaystyle 8+12i}$ ${\displaystyle 12+8i}$	${\displaystyle -i(1+i)^{4}(3-2i)}$ ${\displaystyle -(1+i)^{4}(3+2i)}$
${\displaystyle 212}$	${\displaystyle 4+14i}$ ${\displaystyle 14+4i}$	${\displaystyle (1+i)^{2}(7-2i)}$ ${\displaystyle -i(1+i)^{2}(7+2i)}$
${\displaystyle 218}$	${\displaystyle 7+13i}$ ${\displaystyle 13+7i}$	${\displaystyle (1+i)(10+3i)}$ ${\displaystyle (1+i)(10-3i)}$
${\displaystyle 221}$	${\displaystyle 5+14i}$ ${\displaystyle 10+11i}$ ${\displaystyle 11+10i}$ ${\displaystyle 14+5i}$	${\displaystyle i(3-2i)(4+i)}$ ${\displaystyle (3+2i)(4+i)}$ ${\displaystyle i(3-2i)(4-i)}$ ${\displaystyle (3+2i)(4-i)}$
${\displaystyle 225}$	${\displaystyle 9+12i}$ ${\displaystyle 12+9i}$ ${\displaystyle 15}$	${\displaystyle (2+i)^{2}\cdot 3}$ ${\displaystyle i(2-i)^{2}\cdot 3}$ ${\displaystyle (2+i)(2-i)\cdot 3}$
${\displaystyle 226}$	${\displaystyle 1+15i}$ ${\displaystyle 15+i}$	${\displaystyle (1+i)(8+7i)}$ ${\displaystyle (1+i)(8-7i)}$
${\displaystyle 229}$	${\displaystyle 2+15i}$ ${\displaystyle 15+2i}$	(p) (p)
${\displaystyle 232}$	${\displaystyle 6+14i}$ ${\displaystyle 14+6i}$	${\displaystyle -i(1+i)^{3}(5+2i)}$ ${\displaystyle -i(1+i)^{3}(5-2i)}$
${\displaystyle 233}$	${\displaystyle 8+13i}$ ${\displaystyle 13+8i}$	(p) (p)
${\displaystyle 234}$	${\displaystyle 3+15i}$ ${\displaystyle 15+3i}$	${\displaystyle (1+i)\cdot 3\cdot (3+2i)}$ ${\displaystyle (1+i)\cdot 3\cdot (3-2i)}$
${\displaystyle 241}$	${\displaystyle 4+15i}$ ${\displaystyle 15+4i}$	(p) (p)
${\displaystyle 242}$	${\displaystyle 11+11i}$	${\displaystyle (1+i)\cdot 11}$
${\displaystyle 244}$	${\displaystyle 10+12i}$ ${\displaystyle 12+10i}$	${\displaystyle (1+i)^{2}(6-5i)}$ ${\displaystyle -i(1+i)^{2}(6+5i)}$
${\displaystyle 245}$	${\displaystyle 7+14i}$ ${\displaystyle 14+7i}$	${\displaystyle i(2-i)\cdot 7}$ ${\displaystyle (2+i)\cdot 7}$
${\displaystyle 250}$	${\displaystyle 5+15i}$ ${\displaystyle 9+13i}$ ${\displaystyle 13+9i}$ ${\displaystyle 15+5i}$	${\displaystyle (1+i)(2+i)^{2}(2-i)}$ ${\displaystyle i(1+i)(2-i)^{3}}$ ${\displaystyle -i(1+i)(2+i)^{3}}$ ${\displaystyle (1+i)(2+i)(2-i)^{2}}$

Norma	Liczba	Czynniki
${\displaystyle 256}$	${\displaystyle 16}$	${\displaystyle (1+i)^{8}}$
${\displaystyle 257}$	${\displaystyle 1+16i}$ ${\displaystyle 16+i}$	(p) (p)
${\displaystyle 260}$	${\displaystyle 2+16i}$ ${\displaystyle 8+14i}$ ${\displaystyle 14+8i}$ ${\displaystyle 16+2i}$	${\displaystyle (1+i)^{2}(2+i)(3-2i)}$ ${\displaystyle -i(1+i)^{2}(2+i)(3+2i)}$ ${\displaystyle (1+i)^{2}(2-i)(3-2i)}$ ${\displaystyle -i(1+i)^{2}(2-i)(3+2i)}$
${\displaystyle 261}$	${\displaystyle 6+15i}$ ${\displaystyle 15+6i}$	${\displaystyle i\cdot 3\cdot (5-2i)}$ ${\displaystyle 3\cdot (5+2i)}$
${\displaystyle 265}$	${\displaystyle 3+16i}$ ${\displaystyle 11+12i}$ ${\displaystyle 12+11i}$ ${\displaystyle 16+3i}$	${\displaystyle i(2-i)(7+2i)}$ ${\displaystyle i(2-i)(7-2i)}$ ${\displaystyle (2+i)(7+2i)}$ ${\displaystyle (2+i)(7-2i)}$
${\displaystyle 269}$	${\displaystyle 10+13i}$ ${\displaystyle 13+10i}$	(p) (p)
${\displaystyle 272}$	${\displaystyle 4+16i}$ ${\displaystyle 16+4i}$	${\displaystyle -i(1+i)^{4}(4-i)}$ ${\displaystyle -(1+i)^{4}(4+i)}$
${\displaystyle 274}$	${\displaystyle 7+15i}$ ${\displaystyle 15+7i}$	${\displaystyle (1+i)(11+4i)}$ ${\displaystyle (1+i)(11-4i)}$
${\displaystyle 277}$	${\displaystyle 9+14i}$ ${\displaystyle 14+9i}$	(p) (p)
${\displaystyle 281}$	${\displaystyle 5+16i}$ ${\displaystyle 16+5i}$	(p) (p)
${\displaystyle 288}$	${\displaystyle 12+12i}$	${\displaystyle -(1+i)^{5}\cdot 3}$
${\displaystyle 289}$	${\displaystyle 8+15i}$ ${\displaystyle 15+8i}$ ${\displaystyle 17}$	${\displaystyle i(4-i)^{2}}$ ${\displaystyle (4+i)^{2}}$ ${\displaystyle (4+i)(4-i)}$
${\displaystyle 290}$	${\displaystyle 1+17i}$ ${\displaystyle 11+13i}$ ${\displaystyle 13+11i}$ ${\displaystyle 17+i}$	${\displaystyle i(1+i)(2-i)(5-2i)}$ ${\displaystyle (1+i)(2+i)(5-2i)}$ ${\displaystyle (1+i)(2-i)(5+2i)}$ ${\displaystyle -i(1+i)(2+i)(5+2i)}$
${\displaystyle 292}$	${\displaystyle 6+16i}$ ${\displaystyle 16+6i}$	${\displaystyle (1+i)^{2}(8-3i)}$ ${\displaystyle -i(1+i)^{2}(8+3i)}$
${\displaystyle 293}$	${\displaystyle 2+17i}$ ${\displaystyle 17+2i}$	(p) (p)
${\displaystyle 296}$	${\displaystyle 10+14i}$ ${\displaystyle 14+10i}$	${\displaystyle -i(1+i)^{3}(6+i)}$ ${\displaystyle -i(1+i)^{3}(6-i)}$
${\displaystyle 298}$	${\displaystyle 3+17i}$ ${\displaystyle 17+3i}$	${\displaystyle (1+i)(10+7i)}$ ${\displaystyle (1+i)(10-7i)}$
${\displaystyle 305}$	${\displaystyle 4+17i}$ ${\displaystyle 7+16i}$ ${\displaystyle 16+7i}$ ${\displaystyle 17+4i}$	${\displaystyle i(2+i)(6-5i)}$ ${\displaystyle (2+i)(6+5i)}$ ${\displaystyle i(2-i)(6-5i)}$ ${\displaystyle (2-i)(6+5i)}$
${\displaystyle 306}$	${\displaystyle 9+15i}$ ${\displaystyle 15+9i}$	${\displaystyle (1+i)\cdot 3\cdot (4+i)}$ ${\displaystyle (1+i)\cdot 3\cdot (4-i)}$
${\displaystyle 313}$	${\displaystyle 12+13i}$ ${\displaystyle 13+12i}$	(p) (p)
${\displaystyle 314}$	${\displaystyle 5+17i}$ ${\displaystyle 17+5i}$	${\displaystyle (1+i)(11+6i)}$ ${\displaystyle (1+i)(11-6i)}$
${\displaystyle 317}$	${\displaystyle 11+14i}$ ${\displaystyle 14+11i}$	(p) (p)
${\displaystyle 320}$	${\displaystyle 8+16i}$ ${\displaystyle 16+8i}$	${\displaystyle -(1+i)^{6}(2-i)}$ ${\displaystyle i(1+i)^{6}(2+i)}$
${\displaystyle 324}$	${\displaystyle 18}$	${\displaystyle -i(1+i)^{2}\cdot 3^{2}}$
${\displaystyle 325}$	${\displaystyle 1+18i}$ ${\displaystyle 6+17i}$ ${\displaystyle 10+15i}$ ${\displaystyle 15+10i}$ ${\displaystyle 17+6i}$ ${\displaystyle 18+i}$	${\displaystyle (2+i)^{2}(3+2i)}$ ${\displaystyle i(2-i)^{2}(3+2i)}$ ${\displaystyle i(2+i)(2-i)(3-2i)}$ ${\displaystyle (2+i)(2-i)(3+2i)}$ ${\displaystyle (2+i)^{2}(3-2i)}$ ${\displaystyle i(2-i)^{2}(3-2i)}$
${\displaystyle 328}$	${\displaystyle 2+18i}$ ${\displaystyle 18+2i}$	${\displaystyle -i(1+i)^{3}(5+4i)}$ ${\displaystyle -i(1+i)^{3}(5-4i)}$
${\displaystyle 333}$	${\displaystyle 3+18i}$ ${\displaystyle 18+3i}$	${\displaystyle i\cdot 3\cdot (6-i)}$ ${\displaystyle 3\cdot (6+i)}$
${\displaystyle 337}$	${\displaystyle 9+16i}$ ${\displaystyle 16+9i}$	(p) (p)
${\displaystyle 338}$	${\displaystyle 7+17i}$ ${\displaystyle 13+13i}$ ${\displaystyle 17+7i}$	${\displaystyle i(1+i)(3-2i)^{2}}$ ${\displaystyle (1+i)(3+2i)(3-2i)}$ ${\displaystyle -i(1+i)(3+2i)^{2}}$
${\displaystyle 340}$	${\displaystyle 4+18i}$ ${\displaystyle 12+14i}$ ${\displaystyle 14+12i}$ ${\displaystyle 18+4i}$	${\displaystyle (1+i)^{2}(2-i)(4+i)}$ ${\displaystyle (1+i)^{2}(2-i)(4-i)}$ ${\displaystyle -i(1+i)^{2}(2+i)(4+i)}$ ${\displaystyle -i(1+i)^{2}(2+i)(4-i)}$
${\displaystyle 346}$	${\displaystyle 11+15i}$ ${\displaystyle 15+11i}$	${\displaystyle (1+i)(13+2i)}$ ${\displaystyle (1+i)(13-2i)}$
${\displaystyle 349}$	${\displaystyle 5+18i}$ ${\displaystyle 18+5i}$	(p) (p)
${\displaystyle 353}$	${\displaystyle 8+17i}$ ${\displaystyle 17+8i}$	(p) (p)
${\displaystyle 356}$	${\displaystyle 10+16i}$ ${\displaystyle 16+10i}$	${\displaystyle (1+i)^{2}(8-5i)}$ ${\displaystyle -i(1+i)^{2}(8+5i)}$
${\displaystyle 360}$	${\displaystyle 6+18i}$ ${\displaystyle 18+6i}$	${\displaystyle -i(1+i)^{3}(2+i)\cdot 3}$ ${\displaystyle -i(1+i)^{3}(2-i)\cdot 3}$
${\displaystyle 361}$	${\displaystyle 19}$	(p)
${\displaystyle 362}$	${\displaystyle 1+19i}$ ${\displaystyle 19+i}$	${\displaystyle (1+i)(10+9i)}$ ${\displaystyle (1+i)(10-9i)}$
${\displaystyle 365}$	${\displaystyle 2+19i}$ ${\displaystyle 13+14i}$ ${\displaystyle 14+13i}$ ${\displaystyle 19+2i}$	${\displaystyle i(2-i)(8+3i)}$ ${\displaystyle (2+i)(8+3i)}$ ${\displaystyle i(2-i)(8-3i)}$ ${\displaystyle (2+i)(8-3i)}$
${\displaystyle 369}$	${\displaystyle 12+15i}$ ${\displaystyle 15+12i}$	${\displaystyle i\cdot 3\cdot (5-4i)}$ ${\displaystyle 3\cdot (5+4i)}$
${\displaystyle 370}$	${\displaystyle 3+19i}$ ${\displaystyle 9+17i}$ ${\displaystyle 17+9i}$ ${\displaystyle 19+3i}$	${\displaystyle (1+i)(2+i)(6+i)}$ ${\displaystyle (1+i)(2+i)(6-i)}$ ${\displaystyle (1+i)(2-i)(6+i)}$ ${\displaystyle (1+i)(2-i)(6-i)}$
${\displaystyle 373}$	${\displaystyle 7+18i}$ ${\displaystyle 18+7i}$	(p) (p)
${\displaystyle 377}$	${\displaystyle 4+19i}$ ${\displaystyle 11+16i}$ ${\displaystyle 16+11i}$ ${\displaystyle 19+4i}$	${\displaystyle i(3-2i)(5+2i)}$ ${\displaystyle (3+2i)(5+2i)}$ ${\displaystyle i(3-2i)(5-2i)}$ ${\displaystyle (3+2i)(5-2i)}$
${\displaystyle 386}$	${\displaystyle 5+19i}$ ${\displaystyle 19+5i}$	${\displaystyle (1+i)(12+7i)}$ ${\displaystyle (1+i)(12-7i)}$
${\displaystyle 388}$	${\displaystyle 8+18i}$ ${\displaystyle 18+8i}$	${\displaystyle (1+i)^{2}(9-4i)}$ ${\displaystyle -i(1+i)^{2}(9+4i)}$
${\displaystyle 389}$	${\displaystyle 10+17i}$ ${\displaystyle 17+10i}$	(p) (p)
${\displaystyle 392}$	${\displaystyle 14+14i}$	${\displaystyle -i(1+i)^{3}\cdot 7}$
${\displaystyle 394}$	${\displaystyle 13+15i}$ ${\displaystyle 15+13i}$	${\displaystyle (1+i)(14+i)}$ ${\displaystyle (1+i)(14-i)}$
${\displaystyle 397}$	${\displaystyle 6+19i}$ ${\displaystyle 19+6i}$	(p) (p)
${\displaystyle 400}$	${\displaystyle 12+16i}$ ${\displaystyle 16+12i}$ ${\displaystyle 20}$	${\displaystyle -(1+i)^{4}(2+i)^{2}}$ ${\displaystyle -i(1+i)^{4}(2-i)^{2}}$ ${\displaystyle -(1+i)^{4}(2+i)(2-i)}$
${\displaystyle 401}$	${\displaystyle 1+20i}$ ${\displaystyle 20+i}$	(p) (p)
${\displaystyle 404}$	${\displaystyle 2+20i}$ ${\displaystyle 20+2i}$	${\displaystyle (1+i)^{2}(10-i)}$ ${\displaystyle -i(1+i)^{2}(10+i)}$
${\displaystyle 405}$	${\displaystyle 9+18i}$ ${\displaystyle 18+9i}$	${\displaystyle i(2-i)\cdot 3^{2}}$ ${\displaystyle (2+i)\cdot 3^{2}}$
${\displaystyle 409}$	${\displaystyle 3+20i}$ ${\displaystyle 20+3i}$	(p) (p)
${\displaystyle 410}$	${\displaystyle 7+19i}$ ${\displaystyle 11+17i}$ ${\displaystyle 17+11i}$ ${\displaystyle 19+7i}$	${\displaystyle i(1+i)(2-i)(5-4i)}$ ${\displaystyle (1+i)(2-i)(5+4i)}$ ${\displaystyle (1+i)(2+i)(5-4i)}$ ${\displaystyle -i(1+i)(2+i)(5+4i)}$
${\displaystyle 416}$	${\displaystyle 4+20i}$ ${\displaystyle 20+4i}$	${\displaystyle -(1+i)^{5}(3+2i)}$ ${\displaystyle -(1+i)^{5}(3-2i)}$
${\displaystyle 421}$	${\displaystyle 14+15i}$ ${\displaystyle 15+14i}$	(p) (p)
${\displaystyle 424}$	${\displaystyle 10+18i}$ ${\displaystyle 18+10i}$	${\displaystyle -i(1+i)^{3}(7+2i)}$ ${\displaystyle -i(1+i)^{3}(7-2i)}$
${\displaystyle 425}$	${\displaystyle 5+20i}$ ${\displaystyle 8+19i}$ ${\displaystyle 13+16i}$ ${\displaystyle 16+13i}$ ${\displaystyle 19+8i}$ ${\displaystyle 20+5i}$	${\displaystyle i(2+i)(2-i)(4-i)}$ ${\displaystyle (2+i)^{2}(4+i)}$ ${\displaystyle i(2-i)^{2}(4+i)}$ ${\displaystyle (2+i)^{2}(4-i)}$ ${\displaystyle i(2-i)^{2}(4-i)}$ ${\displaystyle (2+i)(2-i)(4+i)}$
${\displaystyle 433}$	${\displaystyle 12+17i}$ ${\displaystyle 17+12i}$	(p) (p)
${\displaystyle 436}$	${\displaystyle 6+20i}$ ${\displaystyle 20+6i}$	${\displaystyle (1+i)^{2}(10-3i)}$ ${\displaystyle -i(1+i)^{2}(10+3i)}$
${\displaystyle 441}$	${\displaystyle 21}$	${\displaystyle 3\cdot 7}$
${\displaystyle 442}$	${\displaystyle 1+21i}$ ${\displaystyle 9+19i}$ ${\displaystyle 19+9i}$ ${\displaystyle 21+i}$	${\displaystyle i(1+i)(3-2i)(4-i)}$ ${\displaystyle (1+i)(3+2i)(4-i)}$ ${\displaystyle (1+i)(3-2i)(4+i)}$ ${\displaystyle -i(1+i)(3+2i)(4+i)}$
${\displaystyle 445}$	${\displaystyle 2+21i}$ ${\displaystyle 11+18i}$ ${\displaystyle 18+11i}$ ${\displaystyle 21+2i}$	${\displaystyle i(2+i)(8-5i)}$ ${\displaystyle (2+i)(8+5i)}$ ${\displaystyle i(2-i)(8-5i)}$ ${\displaystyle (2-i)(8+5i)}$
${\displaystyle 449}$	${\displaystyle 7+20i}$ ${\displaystyle 20+7i}$	(p) (p)
${\displaystyle 450}$	${\displaystyle 3+21i}$ ${\displaystyle 15+15i}$ ${\displaystyle 21+3i}$	${\displaystyle i(1+i)(2-i)^{2}\cdot 3}$ ${\displaystyle (1+i)(2+i)(2-i)\cdot 3}$ ${\displaystyle -i(1+i)(2+i)^{2}\cdot 3}$
${\displaystyle 452}$	${\displaystyle 14+16i}$ ${\displaystyle 16+14i}$	${\displaystyle (1+i)^{2}(8-7i)}$ ${\displaystyle -i(1+i)^{2}(8+7i)}$
${\displaystyle 457}$	${\displaystyle 4+21i}$ ${\displaystyle 21+4i}$	(p) (p)
${\displaystyle 458}$	${\displaystyle 13+17i}$ ${\displaystyle 17+13i}$	${\displaystyle (1+i)(15+2i)}$ ${\displaystyle (1+i)(15-2i)}$
${\displaystyle 461}$	${\displaystyle 10+19i}$ ${\displaystyle 19+10i}$	(p) (p)
${\displaystyle 464}$	${\displaystyle 8+20i}$ ${\displaystyle 20+8i}$	${\displaystyle -i(1+i)^{4}(5-2i)}$ ${\displaystyle -(1+i)^{4}(5+2i)}$
${\displaystyle 466}$	${\displaystyle 5+21i}$ ${\displaystyle 21+5i}$	${\displaystyle (1+i)(13+8i)}$ ${\displaystyle (1+i)(13-8i)}$
${\displaystyle 468}$	${\displaystyle 12+18i}$ ${\displaystyle 18+12i}$	${\displaystyle (1+i)^{2}\cdot 3\cdot (3-2i)}$ ${\displaystyle -i(1+i)^{2}\cdot 3\cdot (3+2i)}$
${\displaystyle 477}$	${\displaystyle 6+21i}$ ${\displaystyle 21+6i}$	${\displaystyle i\cdot 3\cdot (7-2i)}$ ${\displaystyle 3\cdot (7+2i)}$
${\displaystyle 481}$	${\displaystyle 9+20i}$ ${\displaystyle 15+16i}$ ${\displaystyle 16+15i}$ ${\displaystyle 20+9i}$	${\displaystyle i(3-2i)(6+i)}$ ${\displaystyle i(3-2i)(6-i)}$ ${\displaystyle (3+2i)(6+i)}$ ${\displaystyle (3+2i)(6-i)}$
${\displaystyle 482}$	${\displaystyle 11+19i}$ ${\displaystyle 19+11i}$	${\displaystyle (1+i)(15+4i)}$ ${\displaystyle (1+i)(15-4i)}$
${\displaystyle 484}$	${\displaystyle 22}$	${\displaystyle -i(1+i)^{2}\cdot 11}$
${\displaystyle 485}$	${\displaystyle 1+22i}$ ${\displaystyle 14+17i}$ ${\displaystyle 17+14i}$ ${\displaystyle 22+i}$	${\displaystyle i(2-i)(9+4i)}$ ${\displaystyle (2+i)(9+4i)}$ ${\displaystyle i(2-i)(9-4i)}$ ${\displaystyle (2+i)(9-4i)}$
${\displaystyle 488}$	${\displaystyle 2+22i}$ ${\displaystyle 22+2i}$	${\displaystyle -i(1+i)^{3}(6+5i)}$ ${\displaystyle -i(1+i)^{3}(6-5i)}$
${\displaystyle 490}$	${\displaystyle 7+21i}$ ${\displaystyle 21+7i}$	${\displaystyle (1+i)(2+i)\cdot 7}$ ${\displaystyle (1+i)(2-i)\cdot 7}$
${\displaystyle 493}$	${\displaystyle 3+22i}$ ${\displaystyle 13+18i}$ ${\displaystyle 18+13i}$ ${\displaystyle 22+3i}$	${\displaystyle i(4+i)(5-2i)}$ ${\displaystyle i(4-i)(5-2i)}$ ${\displaystyle (4+i)(5+2i)}$ ${\displaystyle (4-i)(5+2i)}$
${\displaystyle 500}$	${\displaystyle 4+22i}$ ${\displaystyle 10+20i}$ ${\displaystyle 20+10i}$ ${\displaystyle 22+4i}$	${\displaystyle -i(1+i)^{2}(2+i)^{3}}$ ${\displaystyle (1+i)^{2}(2+i)(2-i)^{2}}$ ${\displaystyle -i(1+i)^{2}(2+i)^{2}(2-i)}$ ${\displaystyle (1+i)^{2}(2-i)^{3}}$