# Properties

 Modulus $920$ Structure $$C_{2}\times C_{2}\times C_{2}\times C_{44}$$ Order $352$

Show commands: PariGP / SageMath

sage: H = DirichletGroup(920)

pari: g = idealstar(,920,2)

## Character group

 sage: G.order()  pari: g.no Order = 352 sage: H.invariants()  pari: g.cyc Structure = $$C_{2}\times C_{2}\times C_{2}\times C_{44}$$ sage: H.gens()  pari: g.gen Generators = $\chi_{920}(231,\cdot)$, $\chi_{920}(461,\cdot)$, $\chi_{920}(737,\cdot)$, $\chi_{920}(281,\cdot)$

## First 32 of 352 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 $$-1$$ $$1$$ $$3$$ $$7$$ $$9$$ $$11$$ $$13$$ $$17$$ $$19$$ $$21$$ $$27$$ $$29$$
$$\chi_{920}(1,\cdot)$$ 920.a 1 no $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{920}(3,\cdot)$$ 920.bq 44 yes $$1$$ $$1$$ $$e\left(\frac{39}{44}\right)$$ $$e\left(\frac{3}{44}\right)$$ $$e\left(\frac{17}{22}\right)$$ $$e\left(\frac{6}{11}\right)$$ $$e\left(\frac{41}{44}\right)$$ $$e\left(\frac{37}{44}\right)$$ $$e\left(\frac{9}{22}\right)$$ $$e\left(\frac{21}{22}\right)$$ $$e\left(\frac{29}{44}\right)$$ $$e\left(\frac{1}{11}\right)$$
$$\chi_{920}(7,\cdot)$$ 920.br 44 no $$-1$$ $$1$$ $$e\left(\frac{3}{44}\right)$$ $$e\left(\frac{7}{44}\right)$$ $$e\left(\frac{3}{22}\right)$$ $$e\left(\frac{3}{11}\right)$$ $$e\left(\frac{37}{44}\right)$$ $$e\left(\frac{13}{44}\right)$$ $$e\left(\frac{21}{22}\right)$$ $$e\left(\frac{5}{22}\right)$$ $$e\left(\frac{9}{44}\right)$$ $$e\left(\frac{1}{22}\right)$$
$$\chi_{920}(9,\cdot)$$ 920.bk 22 no $$1$$ $$1$$ $$e\left(\frac{17}{22}\right)$$ $$e\left(\frac{3}{22}\right)$$ $$e\left(\frac{6}{11}\right)$$ $$e\left(\frac{1}{11}\right)$$ $$e\left(\frac{19}{22}\right)$$ $$e\left(\frac{15}{22}\right)$$ $$e\left(\frac{9}{11}\right)$$ $$e\left(\frac{10}{11}\right)$$ $$e\left(\frac{7}{22}\right)$$ $$e\left(\frac{2}{11}\right)$$
$$\chi_{920}(11,\cdot)$$ 920.bb 22 no $$1$$ $$1$$ $$e\left(\frac{6}{11}\right)$$ $$e\left(\frac{3}{11}\right)$$ $$e\left(\frac{1}{11}\right)$$ $$e\left(\frac{15}{22}\right)$$ $$e\left(\frac{5}{22}\right)$$ $$e\left(\frac{19}{22}\right)$$ $$e\left(\frac{3}{22}\right)$$ $$e\left(\frac{9}{11}\right)$$ $$e\left(\frac{7}{11}\right)$$ $$e\left(\frac{19}{22}\right)$$
$$\chi_{920}(13,\cdot)$$ 920.bu 44 yes $$-1$$ $$1$$ $$e\left(\frac{41}{44}\right)$$ $$e\left(\frac{37}{44}\right)$$ $$e\left(\frac{19}{22}\right)$$ $$e\left(\frac{5}{22}\right)$$ $$e\left(\frac{29}{44}\right)$$ $$e\left(\frac{9}{44}\right)$$ $$e\left(\frac{6}{11}\right)$$ $$e\left(\frac{17}{22}\right)$$ $$e\left(\frac{35}{44}\right)$$ $$e\left(\frac{5}{11}\right)$$
$$\chi_{920}(17,\cdot)$$ 920.bv 44 no $$1$$ $$1$$ $$e\left(\frac{37}{44}\right)$$ $$e\left(\frac{13}{44}\right)$$ $$e\left(\frac{15}{22}\right)$$ $$e\left(\frac{19}{22}\right)$$ $$e\left(\frac{9}{44}\right)$$ $$e\left(\frac{21}{44}\right)$$ $$e\left(\frac{3}{11}\right)$$ $$e\left(\frac{3}{22}\right)$$ $$e\left(\frac{23}{44}\right)$$ $$e\left(\frac{5}{22}\right)$$
$$\chi_{920}(19,\cdot)$$ 920.bn 22 yes $$1$$ $$1$$ $$e\left(\frac{9}{22}\right)$$ $$e\left(\frac{21}{22}\right)$$ $$e\left(\frac{9}{11}\right)$$ $$e\left(\frac{3}{22}\right)$$ $$e\left(\frac{6}{11}\right)$$ $$e\left(\frac{3}{11}\right)$$ $$e\left(\frac{5}{22}\right)$$ $$e\left(\frac{4}{11}\right)$$ $$e\left(\frac{5}{22}\right)$$ $$e\left(\frac{17}{22}\right)$$
$$\chi_{920}(21,\cdot)$$ 920.bl 22 no $$-1$$ $$1$$ $$e\left(\frac{21}{22}\right)$$ $$e\left(\frac{5}{22}\right)$$ $$e\left(\frac{10}{11}\right)$$ $$e\left(\frac{9}{11}\right)$$ $$e\left(\frac{17}{22}\right)$$ $$e\left(\frac{3}{22}\right)$$ $$e\left(\frac{4}{11}\right)$$ $$e\left(\frac{2}{11}\right)$$ $$e\left(\frac{19}{22}\right)$$ $$e\left(\frac{3}{22}\right)$$
$$\chi_{920}(27,\cdot)$$ 920.bq 44 yes $$1$$ $$1$$ $$e\left(\frac{29}{44}\right)$$ $$e\left(\frac{9}{44}\right)$$ $$e\left(\frac{7}{22}\right)$$ $$e\left(\frac{7}{11}\right)$$ $$e\left(\frac{35}{44}\right)$$ $$e\left(\frac{23}{44}\right)$$ $$e\left(\frac{5}{22}\right)$$ $$e\left(\frac{19}{22}\right)$$ $$e\left(\frac{43}{44}\right)$$ $$e\left(\frac{3}{11}\right)$$
$$\chi_{920}(29,\cdot)$$ 920.bf 22 yes $$1$$ $$1$$ $$e\left(\frac{1}{11}\right)$$ $$e\left(\frac{1}{22}\right)$$ $$e\left(\frac{2}{11}\right)$$ $$e\left(\frac{19}{22}\right)$$ $$e\left(\frac{5}{11}\right)$$ $$e\left(\frac{5}{22}\right)$$ $$e\left(\frac{17}{22}\right)$$ $$e\left(\frac{3}{22}\right)$$ $$e\left(\frac{3}{11}\right)$$ $$e\left(\frac{5}{22}\right)$$
$$\chi_{920}(31,\cdot)$$ 920.bm 22 no $$-1$$ $$1$$ $$e\left(\frac{19}{22}\right)$$ $$e\left(\frac{15}{22}\right)$$ $$e\left(\frac{8}{11}\right)$$ $$e\left(\frac{21}{22}\right)$$ $$e\left(\frac{9}{11}\right)$$ $$e\left(\frac{10}{11}\right)$$ $$e\left(\frac{13}{22}\right)$$ $$e\left(\frac{6}{11}\right)$$ $$e\left(\frac{13}{22}\right)$$ $$e\left(\frac{10}{11}\right)$$
$$\chi_{920}(33,\cdot)$$ 920.bv 44 no $$1$$ $$1$$ $$e\left(\frac{19}{44}\right)$$ $$e\left(\frac{15}{44}\right)$$ $$e\left(\frac{19}{22}\right)$$ $$e\left(\frac{5}{22}\right)$$ $$e\left(\frac{7}{44}\right)$$ $$e\left(\frac{31}{44}\right)$$ $$e\left(\frac{6}{11}\right)$$ $$e\left(\frac{17}{22}\right)$$ $$e\left(\frac{13}{44}\right)$$ $$e\left(\frac{21}{22}\right)$$
$$\chi_{920}(37,\cdot)$$ 920.bo 44 yes $$1$$ $$1$$ $$e\left(\frac{23}{44}\right)$$ $$e\left(\frac{17}{44}\right)$$ $$e\left(\frac{1}{22}\right)$$ $$e\left(\frac{1}{11}\right)$$ $$e\left(\frac{27}{44}\right)$$ $$e\left(\frac{41}{44}\right)$$ $$e\left(\frac{7}{22}\right)$$ $$e\left(\frac{10}{11}\right)$$ $$e\left(\frac{25}{44}\right)$$ $$e\left(\frac{2}{11}\right)$$
$$\chi_{920}(39,\cdot)$$ 920.ba 22 no $$-1$$ $$1$$ $$e\left(\frac{9}{11}\right)$$ $$e\left(\frac{10}{11}\right)$$ $$e\left(\frac{7}{11}\right)$$ $$e\left(\frac{17}{22}\right)$$ $$e\left(\frac{13}{22}\right)$$ $$e\left(\frac{1}{22}\right)$$ $$e\left(\frac{21}{22}\right)$$ $$e\left(\frac{8}{11}\right)$$ $$e\left(\frac{5}{11}\right)$$ $$e\left(\frac{6}{11}\right)$$
$$\chi_{920}(41,\cdot)$$ 920.y 11 no $$1$$ $$1$$ $$e\left(\frac{8}{11}\right)$$ $$e\left(\frac{4}{11}\right)$$ $$e\left(\frac{5}{11}\right)$$ $$e\left(\frac{10}{11}\right)$$ $$e\left(\frac{7}{11}\right)$$ $$e\left(\frac{9}{11}\right)$$ $$e\left(\frac{2}{11}\right)$$ $$e\left(\frac{1}{11}\right)$$ $$e\left(\frac{2}{11}\right)$$ $$e\left(\frac{9}{11}\right)$$
$$\chi_{920}(43,\cdot)$$ 920.bs 44 yes $$-1$$ $$1$$ $$e\left(\frac{39}{44}\right)$$ $$e\left(\frac{25}{44}\right)$$ $$e\left(\frac{17}{22}\right)$$ $$e\left(\frac{1}{22}\right)$$ $$e\left(\frac{41}{44}\right)$$ $$e\left(\frac{15}{44}\right)$$ $$e\left(\frac{10}{11}\right)$$ $$e\left(\frac{5}{11}\right)$$ $$e\left(\frac{29}{44}\right)$$ $$e\left(\frac{1}{11}\right)$$
$$\chi_{920}(47,\cdot)$$ 920.s 4 no $$1$$ $$1$$ $$i$$ $$-i$$ $$-1$$ $$-1$$ $$-i$$ $$i$$ $$1$$ $$1$$ $$-i$$ $$-1$$
$$\chi_{920}(49,\cdot)$$ 920.bk 22 no $$1$$ $$1$$ $$e\left(\frac{3}{22}\right)$$ $$e\left(\frac{7}{22}\right)$$ $$e\left(\frac{3}{11}\right)$$ $$e\left(\frac{6}{11}\right)$$ $$e\left(\frac{15}{22}\right)$$ $$e\left(\frac{13}{22}\right)$$ $$e\left(\frac{10}{11}\right)$$ $$e\left(\frac{5}{11}\right)$$ $$e\left(\frac{9}{22}\right)$$ $$e\left(\frac{1}{11}\right)$$
$$\chi_{920}(51,\cdot)$$ 920.bb 22 no $$1$$ $$1$$ $$e\left(\frac{8}{11}\right)$$ $$e\left(\frac{4}{11}\right)$$ $$e\left(\frac{5}{11}\right)$$ $$e\left(\frac{9}{22}\right)$$ $$e\left(\frac{3}{22}\right)$$ $$e\left(\frac{7}{22}\right)$$ $$e\left(\frac{15}{22}\right)$$ $$e\left(\frac{1}{11}\right)$$ $$e\left(\frac{2}{11}\right)$$ $$e\left(\frac{7}{22}\right)$$
$$\chi_{920}(53,\cdot)$$ 920.bo 44 yes $$1$$ $$1$$ $$e\left(\frac{25}{44}\right)$$ $$e\left(\frac{7}{44}\right)$$ $$e\left(\frac{3}{22}\right)$$ $$e\left(\frac{3}{11}\right)$$ $$e\left(\frac{37}{44}\right)$$ $$e\left(\frac{35}{44}\right)$$ $$e\left(\frac{21}{22}\right)$$ $$e\left(\frac{8}{11}\right)$$ $$e\left(\frac{31}{44}\right)$$ $$e\left(\frac{6}{11}\right)$$
$$\chi_{920}(57,\cdot)$$ 920.bv 44 no $$1$$ $$1$$ $$e\left(\frac{13}{44}\right)$$ $$e\left(\frac{1}{44}\right)$$ $$e\left(\frac{13}{22}\right)$$ $$e\left(\frac{15}{22}\right)$$ $$e\left(\frac{21}{44}\right)$$ $$e\left(\frac{5}{44}\right)$$ $$e\left(\frac{7}{11}\right)$$ $$e\left(\frac{7}{22}\right)$$ $$e\left(\frac{39}{44}\right)$$ $$e\left(\frac{19}{22}\right)$$
$$\chi_{920}(59,\cdot)$$ 920.bh 22 yes $$-1$$ $$1$$ $$e\left(\frac{15}{22}\right)$$ $$e\left(\frac{1}{11}\right)$$ $$e\left(\frac{4}{11}\right)$$ $$e\left(\frac{8}{11}\right)$$ $$e\left(\frac{10}{11}\right)$$ $$e\left(\frac{21}{22}\right)$$ $$e\left(\frac{6}{11}\right)$$ $$e\left(\frac{17}{22}\right)$$ $$e\left(\frac{1}{22}\right)$$ $$e\left(\frac{21}{22}\right)$$
$$\chi_{920}(61,\cdot)$$ 920.bl 22 no $$-1$$ $$1$$ $$e\left(\frac{19}{22}\right)$$ $$e\left(\frac{15}{22}\right)$$ $$e\left(\frac{8}{11}\right)$$ $$e\left(\frac{5}{11}\right)$$ $$e\left(\frac{7}{22}\right)$$ $$e\left(\frac{9}{22}\right)$$ $$e\left(\frac{1}{11}\right)$$ $$e\left(\frac{6}{11}\right)$$ $$e\left(\frac{13}{22}\right)$$ $$e\left(\frac{9}{22}\right)$$
$$\chi_{920}(63,\cdot)$$ 920.br 44 no $$-1$$ $$1$$ $$e\left(\frac{37}{44}\right)$$ $$e\left(\frac{13}{44}\right)$$ $$e\left(\frac{15}{22}\right)$$ $$e\left(\frac{4}{11}\right)$$ $$e\left(\frac{31}{44}\right)$$ $$e\left(\frac{43}{44}\right)$$ $$e\left(\frac{17}{22}\right)$$ $$e\left(\frac{3}{22}\right)$$ $$e\left(\frac{23}{44}\right)$$ $$e\left(\frac{5}{22}\right)$$
$$\chi_{920}(67,\cdot)$$ 920.bs 44 yes $$-1$$ $$1$$ $$e\left(\frac{9}{44}\right)$$ $$e\left(\frac{43}{44}\right)$$ $$e\left(\frac{9}{22}\right)$$ $$e\left(\frac{7}{22}\right)$$ $$e\left(\frac{23}{44}\right)$$ $$e\left(\frac{17}{44}\right)$$ $$e\left(\frac{4}{11}\right)$$ $$e\left(\frac{2}{11}\right)$$ $$e\left(\frac{27}{44}\right)$$ $$e\left(\frac{7}{11}\right)$$
$$\chi_{920}(71,\cdot)$$ 920.bm 22 no $$-1$$ $$1$$ $$e\left(\frac{21}{22}\right)$$ $$e\left(\frac{5}{22}\right)$$ $$e\left(\frac{10}{11}\right)$$ $$e\left(\frac{7}{22}\right)$$ $$e\left(\frac{3}{11}\right)$$ $$e\left(\frac{7}{11}\right)$$ $$e\left(\frac{19}{22}\right)$$ $$e\left(\frac{2}{11}\right)$$ $$e\left(\frac{19}{22}\right)$$ $$e\left(\frac{7}{11}\right)$$
$$\chi_{920}(73,\cdot)$$ 920.bp 44 no $$-1$$ $$1$$ $$e\left(\frac{7}{44}\right)$$ $$e\left(\frac{9}{44}\right)$$ $$e\left(\frac{7}{22}\right)$$ $$e\left(\frac{7}{11}\right)$$ $$e\left(\frac{35}{44}\right)$$ $$e\left(\frac{1}{44}\right)$$ $$e\left(\frac{5}{22}\right)$$ $$e\left(\frac{4}{11}\right)$$ $$e\left(\frac{21}{44}\right)$$ $$e\left(\frac{17}{22}\right)$$
$$\chi_{920}(77,\cdot)$$ 920.bu 44 yes $$-1$$ $$1$$ $$e\left(\frac{27}{44}\right)$$ $$e\left(\frac{19}{44}\right)$$ $$e\left(\frac{5}{22}\right)$$ $$e\left(\frac{21}{22}\right)$$ $$e\left(\frac{3}{44}\right)$$ $$e\left(\frac{7}{44}\right)$$ $$e\left(\frac{1}{11}\right)$$ $$e\left(\frac{1}{22}\right)$$ $$e\left(\frac{37}{44}\right)$$ $$e\left(\frac{10}{11}\right)$$
$$\chi_{920}(79,\cdot)$$ 920.bc 22 no $$1$$ $$1$$ $$e\left(\frac{2}{11}\right)$$ $$e\left(\frac{13}{22}\right)$$ $$e\left(\frac{4}{11}\right)$$ $$e\left(\frac{8}{11}\right)$$ $$e\left(\frac{9}{22}\right)$$ $$e\left(\frac{5}{11}\right)$$ $$e\left(\frac{6}{11}\right)$$ $$e\left(\frac{17}{22}\right)$$ $$e\left(\frac{6}{11}\right)$$ $$e\left(\frac{5}{11}\right)$$
$$\chi_{920}(81,\cdot)$$ 920.y 11 no $$1$$ $$1$$ $$e\left(\frac{6}{11}\right)$$ $$e\left(\frac{3}{11}\right)$$ $$e\left(\frac{1}{11}\right)$$ $$e\left(\frac{2}{11}\right)$$ $$e\left(\frac{8}{11}\right)$$ $$e\left(\frac{4}{11}\right)$$ $$e\left(\frac{7}{11}\right)$$ $$e\left(\frac{9}{11}\right)$$ $$e\left(\frac{7}{11}\right)$$ $$e\left(\frac{4}{11}\right)$$
$$\chi_{920}(83,\cdot)$$ 920.bs 44 yes $$-1$$ $$1$$ $$e\left(\frac{23}{44}\right)$$ $$e\left(\frac{17}{44}\right)$$ $$e\left(\frac{1}{22}\right)$$ $$e\left(\frac{13}{22}\right)$$ $$e\left(\frac{5}{44}\right)$$ $$e\left(\frac{19}{44}\right)$$ $$e\left(\frac{9}{11}\right)$$ $$e\left(\frac{10}{11}\right)$$ $$e\left(\frac{25}{44}\right)$$ $$e\left(\frac{2}{11}\right)$$