# Properties

 Modulus $1122$ Structure $$C_{80}\times C_{2}\times C_{2}$$ Order $320$

Show commands for: Pari/GP / SageMath

sage: H = DirichletGroup(1122)

pari: g = idealstar(,1122,2)

## Character group

 sage: G.order()  pari: g.no Order = 320 sage: H.invariants()  pari: g.cyc Structure = $$C_{80}\times C_{2}\times C_{2}$$ sage: H.gens()  pari: g.gen Generators = $\chi_{1122}(749,\cdot)$, $\chi_{1122}(409,\cdot)$, $\chi_{1122}(1057,\cdot)$

## First 32 of 320 characters

Each row describes a character. When available, the columns show the orbit label, order of the character, whether the character is primitive, and several values of the character.

Character Orbit Order Primitive $$-1$$ $$1$$ $$5$$ $$7$$ $$13$$ $$19$$ $$23$$ $$25$$ $$29$$ $$31$$ $$35$$ $$37$$
$$\chi_{1122}(1,\cdot)$$ 1122.a 1 no $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{1122}(5,\cdot)$$ 1122.bn 80 no $$1$$ $$1$$ $$e\left(\frac{53}{80}\right)$$ $$e\left(\frac{19}{80}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{23}{40}\right)$$ $$e\left(\frac{3}{16}\right)$$ $$e\left(\frac{13}{40}\right)$$ $$e\left(\frac{29}{80}\right)$$ $$e\left(\frac{17}{80}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{9}{80}\right)$$
$$\chi_{1122}(7,\cdot)$$ 1122.bm 80 no $$1$$ $$1$$ $$e\left(\frac{19}{80}\right)$$ $$e\left(\frac{37}{80}\right)$$ $$e\left(\frac{9}{20}\right)$$ $$e\left(\frac{29}{40}\right)$$ $$e\left(\frac{5}{16}\right)$$ $$e\left(\frac{19}{40}\right)$$ $$e\left(\frac{67}{80}\right)$$ $$e\left(\frac{31}{80}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{7}{80}\right)$$
$$\chi_{1122}(13,\cdot)$$ 1122.bf 20 no $$-1$$ $$1$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{9}{20}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$-i$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{17}{20}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{9}{20}\right)$$
$$\chi_{1122}(19,\cdot)$$ 1122.bh 40 no $$-1$$ $$1$$ $$e\left(\frac{23}{40}\right)$$ $$e\left(\frac{29}{40}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{3}{20}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{3}{20}\right)$$ $$e\left(\frac{19}{40}\right)$$ $$e\left(\frac{27}{40}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{19}{40}\right)$$
$$\chi_{1122}(23,\cdot)$$ 1122.y 16 no $$1$$ $$1$$ $$e\left(\frac{3}{16}\right)$$ $$e\left(\frac{5}{16}\right)$$ $$-i$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{9}{16}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{11}{16}\right)$$ $$e\left(\frac{7}{16}\right)$$ $$-1$$ $$e\left(\frac{15}{16}\right)$$
$$\chi_{1122}(25,\cdot)$$ 1122.bi 40 no $$1$$ $$1$$ $$e\left(\frac{13}{40}\right)$$ $$e\left(\frac{19}{40}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{3}{20}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{29}{40}\right)$$ $$e\left(\frac{17}{40}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{9}{40}\right)$$
$$\chi_{1122}(29,\cdot)$$ 1122.bl 80 no $$-1$$ $$1$$ $$e\left(\frac{29}{80}\right)$$ $$e\left(\frac{67}{80}\right)$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{19}{40}\right)$$ $$e\left(\frac{11}{16}\right)$$ $$e\left(\frac{29}{40}\right)$$ $$e\left(\frac{77}{80}\right)$$ $$e\left(\frac{41}{80}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{17}{80}\right)$$
$$\chi_{1122}(31,\cdot)$$ 1122.bk 80 no $$-1$$ $$1$$ $$e\left(\frac{17}{80}\right)$$ $$e\left(\frac{31}{80}\right)$$ $$e\left(\frac{17}{20}\right)$$ $$e\left(\frac{27}{40}\right)$$ $$e\left(\frac{7}{16}\right)$$ $$e\left(\frac{17}{40}\right)$$ $$e\left(\frac{41}{80}\right)$$ $$e\left(\frac{53}{80}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{61}{80}\right)$$
$$\chi_{1122}(35,\cdot)$$ 1122.x 10 no $$1$$ $$1$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$-1$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{1}{5}\right)$$
$$\chi_{1122}(37,\cdot)$$ 1122.bk 80 no $$-1$$ $$1$$ $$e\left(\frac{9}{80}\right)$$ $$e\left(\frac{7}{80}\right)$$ $$e\left(\frac{9}{20}\right)$$ $$e\left(\frac{19}{40}\right)$$ $$e\left(\frac{15}{16}\right)$$ $$e\left(\frac{9}{40}\right)$$ $$e\left(\frac{17}{80}\right)$$ $$e\left(\frac{61}{80}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{37}{80}\right)$$
$$\chi_{1122}(41,\cdot)$$ 1122.bl 80 no $$-1$$ $$1$$ $$e\left(\frac{11}{80}\right)$$ $$e\left(\frac{53}{80}\right)$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{21}{40}\right)$$ $$e\left(\frac{13}{16}\right)$$ $$e\left(\frac{11}{40}\right)$$ $$e\left(\frac{43}{80}\right)$$ $$e\left(\frac{79}{80}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{23}{80}\right)$$
$$\chi_{1122}(43,\cdot)$$ 1122.p 8 no $$-1$$ $$1$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{7}{8}\right)$$ $$1$$ $$i$$ $$e\left(\frac{7}{8}\right)$$ $$i$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$-1$$ $$e\left(\frac{1}{8}\right)$$
$$\chi_{1122}(47,\cdot)$$ 1122.bd 20 no $$-1$$ $$1$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$i$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{17}{20}\right)$$
$$\chi_{1122}(49,\cdot)$$ 1122.bi 40 no $$1$$ $$1$$ $$e\left(\frac{19}{40}\right)$$ $$e\left(\frac{37}{40}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{9}{20}\right)$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{27}{40}\right)$$ $$e\left(\frac{31}{40}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{7}{40}\right)$$
$$\chi_{1122}(53,\cdot)$$ 1122.bj 40 no $$-1$$ $$1$$ $$e\left(\frac{11}{40}\right)$$ $$e\left(\frac{33}{40}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{3}{40}\right)$$ $$e\left(\frac{19}{40}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{3}{40}\right)$$
$$\chi_{1122}(59,\cdot)$$ 1122.bj 40 no $$-1$$ $$1$$ $$e\left(\frac{17}{40}\right)$$ $$e\left(\frac{11}{40}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{17}{20}\right)$$ $$e\left(\frac{1}{40}\right)$$ $$e\left(\frac{33}{40}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{1}{40}\right)$$
$$\chi_{1122}(61,\cdot)$$ 1122.bm 80 no $$1$$ $$1$$ $$e\left(\frac{43}{80}\right)$$ $$e\left(\frac{29}{80}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{13}{40}\right)$$ $$e\left(\frac{13}{16}\right)$$ $$e\left(\frac{3}{40}\right)$$ $$e\left(\frac{59}{80}\right)$$ $$e\left(\frac{7}{80}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{79}{80}\right)$$
$$\chi_{1122}(65,\cdot)$$ 1122.ba 16 no $$-1$$ $$1$$ $$e\left(\frac{5}{16}\right)$$ $$e\left(\frac{11}{16}\right)$$ $$-i$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{15}{16}\right)$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{5}{16}\right)$$ $$e\left(\frac{1}{16}\right)$$ $$1$$ $$e\left(\frac{9}{16}\right)$$
$$\chi_{1122}(67,\cdot)$$ 1122.c 2 no $$1$$ $$1$$ $$-1$$ $$-1$$ $$1$$ $$1$$ $$-1$$ $$1$$ $$-1$$ $$-1$$ $$1$$ $$-1$$
$$\chi_{1122}(71,\cdot)$$ 1122.bn 80 no $$1$$ $$1$$ $$e\left(\frac{33}{80}\right)$$ $$e\left(\frac{39}{80}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{3}{40}\right)$$ $$e\left(\frac{7}{16}\right)$$ $$e\left(\frac{33}{40}\right)$$ $$e\left(\frac{9}{80}\right)$$ $$e\left(\frac{77}{80}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{69}{80}\right)$$
$$\chi_{1122}(73,\cdot)$$ 1122.bm 80 no $$1$$ $$1$$ $$e\left(\frac{29}{80}\right)$$ $$e\left(\frac{27}{80}\right)$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{19}{40}\right)$$ $$e\left(\frac{11}{16}\right)$$ $$e\left(\frac{29}{40}\right)$$ $$e\left(\frac{77}{80}\right)$$ $$e\left(\frac{1}{80}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{57}{80}\right)$$
$$\chi_{1122}(79,\cdot)$$ 1122.bm 80 no $$1$$ $$1$$ $$e\left(\frac{47}{80}\right)$$ $$e\left(\frac{41}{80}\right)$$ $$e\left(\frac{17}{20}\right)$$ $$e\left(\frac{17}{40}\right)$$ $$e\left(\frac{9}{16}\right)$$ $$e\left(\frac{7}{40}\right)$$ $$e\left(\frac{31}{80}\right)$$ $$e\left(\frac{43}{80}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{51}{80}\right)$$
$$\chi_{1122}(83,\cdot)$$ 1122.bg 40 no $$1$$ $$1$$ $$e\left(\frac{39}{40}\right)$$ $$e\left(\frac{17}{40}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{27}{40}\right)$$ $$e\left(\frac{31}{40}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{7}{40}\right)$$
$$\chi_{1122}(89,\cdot)$$ 1122.k 4 no $$-1$$ $$1$$ $$i$$ $$i$$ $$1$$ $$-1$$ $$-i$$ $$-1$$ $$i$$ $$-i$$ $$-1$$ $$-i$$
$$\chi_{1122}(91,\cdot)$$ 1122.bk 80 no $$-1$$ $$1$$ $$e\left(\frac{71}{80}\right)$$ $$e\left(\frac{73}{80}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{21}{40}\right)$$ $$e\left(\frac{1}{16}\right)$$ $$e\left(\frac{31}{40}\right)$$ $$e\left(\frac{63}{80}\right)$$ $$e\left(\frac{19}{80}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{43}{80}\right)$$
$$\chi_{1122}(95,\cdot)$$ 1122.bl 80 no $$-1$$ $$1$$ $$e\left(\frac{19}{80}\right)$$ $$e\left(\frac{77}{80}\right)$$ $$e\left(\frac{9}{20}\right)$$ $$e\left(\frac{29}{40}\right)$$ $$e\left(\frac{5}{16}\right)$$ $$e\left(\frac{19}{40}\right)$$ $$e\left(\frac{67}{80}\right)$$ $$e\left(\frac{71}{80}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{47}{80}\right)$$
$$\chi_{1122}(97,\cdot)$$ 1122.bk 80 no $$-1$$ $$1$$ $$e\left(\frac{37}{80}\right)$$ $$e\left(\frac{11}{80}\right)$$ $$e\left(\frac{17}{20}\right)$$ $$e\left(\frac{7}{40}\right)$$ $$e\left(\frac{3}{16}\right)$$ $$e\left(\frac{37}{40}\right)$$ $$e\left(\frac{61}{80}\right)$$ $$e\left(\frac{73}{80}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{1}{80}\right)$$
$$\chi_{1122}(101,\cdot)$$ 1122.r 10 no $$1$$ $$1$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$1$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{7}{10}\right)$$
$$\chi_{1122}(103,\cdot)$$ 1122.m 5 no $$1$$ $$1$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$1$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{2}{5}\right)$$
$$\chi_{1122}(107,\cdot)$$ 1122.bl 80 no $$-1$$ $$1$$ $$e\left(\frac{21}{80}\right)$$ $$e\left(\frac{43}{80}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{11}{40}\right)$$ $$e\left(\frac{3}{16}\right)$$ $$e\left(\frac{21}{40}\right)$$ $$e\left(\frac{53}{80}\right)$$ $$e\left(\frac{49}{80}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{73}{80}\right)$$
$$\chi_{1122}(109,\cdot)$$ 1122.z 16 no $$1$$ $$1$$ $$e\left(\frac{7}{16}\right)$$ $$e\left(\frac{1}{16}\right)$$ $$i$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{5}{16}\right)$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{7}{16}\right)$$ $$e\left(\frac{3}{16}\right)$$ $$-1$$ $$e\left(\frac{11}{16}\right)$$