# Properties

 Modulus $764$ Structure $$C_{190}\times C_{2}$$ Order $380$

Show commands for: Pari/GP / SageMath

sage: H = DirichletGroup(764)

pari: g = idealstar(,764,2)

## Character group

 sage: G.order()  pari: g.no Order = 380 sage: H.invariants()  pari: g.cyc Structure = $$C_{190}\times C_{2}$$ sage: H.gens()  pari: g.gen Generators = $\chi_{764}(383,\cdot)$, $\chi_{764}(401,\cdot)$

## First 32 of 380 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 $$-1$$ $$1$$ $$3$$ $$5$$ $$7$$ $$9$$ $$11$$ $$13$$ $$15$$ $$17$$ $$19$$ $$21$$
$$\chi_{764}(1,\cdot)$$ 764.a 1 no $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{764}(3,\cdot)$$ 764.o 190 yes $$-1$$ $$1$$ $$e\left(\frac{61}{190}\right)$$ $$e\left(\frac{10}{19}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{61}{95}\right)$$ $$e\left(\frac{15}{38}\right)$$ $$e\left(\frac{36}{95}\right)$$ $$e\left(\frac{161}{190}\right)$$ $$e\left(\frac{79}{95}\right)$$ $$e\left(\frac{21}{190}\right)$$ $$e\left(\frac{21}{95}\right)$$
$$\chi_{764}(5,\cdot)$$ 764.i 19 no $$1$$ $$1$$ $$e\left(\frac{10}{19}\right)$$ $$e\left(\frac{3}{19}\right)$$ $$1$$ $$e\left(\frac{1}{19}\right)$$ $$e\left(\frac{7}{19}\right)$$ $$e\left(\frac{9}{19}\right)$$ $$e\left(\frac{13}{19}\right)$$ $$e\left(\frac{15}{19}\right)$$ $$e\left(\frac{5}{19}\right)$$ $$e\left(\frac{10}{19}\right)$$
$$\chi_{764}(7,\cdot)$$ 764.g 10 yes $$1$$ $$1$$ $$e\left(\frac{9}{10}\right)$$ $$1$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$1$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{3}{10}\right)$$
$$\chi_{764}(9,\cdot)$$ 764.m 95 no $$1$$ $$1$$ $$e\left(\frac{61}{95}\right)$$ $$e\left(\frac{1}{19}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{27}{95}\right)$$ $$e\left(\frac{15}{19}\right)$$ $$e\left(\frac{72}{95}\right)$$ $$e\left(\frac{66}{95}\right)$$ $$e\left(\frac{63}{95}\right)$$ $$e\left(\frac{21}{95}\right)$$ $$e\left(\frac{42}{95}\right)$$
$$\chi_{764}(11,\cdot)$$ 764.l 38 yes $$1$$ $$1$$ $$e\left(\frac{15}{38}\right)$$ $$e\left(\frac{7}{19}\right)$$ $$1$$ $$e\left(\frac{15}{19}\right)$$ $$e\left(\frac{10}{19}\right)$$ $$e\left(\frac{2}{19}\right)$$ $$e\left(\frac{29}{38}\right)$$ $$e\left(\frac{16}{19}\right)$$ $$e\left(\frac{18}{19}\right)$$ $$e\left(\frac{15}{38}\right)$$
$$\chi_{764}(13,\cdot)$$ 764.m 95 no $$1$$ $$1$$ $$e\left(\frac{36}{95}\right)$$ $$e\left(\frac{9}{19}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{72}{95}\right)$$ $$e\left(\frac{2}{19}\right)$$ $$e\left(\frac{2}{95}\right)$$ $$e\left(\frac{81}{95}\right)$$ $$e\left(\frac{73}{95}\right)$$ $$e\left(\frac{56}{95}\right)$$ $$e\left(\frac{17}{95}\right)$$
$$\chi_{764}(15,\cdot)$$ 764.o 190 yes $$-1$$ $$1$$ $$e\left(\frac{161}{190}\right)$$ $$e\left(\frac{13}{19}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{66}{95}\right)$$ $$e\left(\frac{29}{38}\right)$$ $$e\left(\frac{81}{95}\right)$$ $$e\left(\frac{101}{190}\right)$$ $$e\left(\frac{59}{95}\right)$$ $$e\left(\frac{71}{190}\right)$$ $$e\left(\frac{71}{95}\right)$$
$$\chi_{764}(17,\cdot)$$ 764.m 95 no $$1$$ $$1$$ $$e\left(\frac{79}{95}\right)$$ $$e\left(\frac{15}{19}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{63}{95}\right)$$ $$e\left(\frac{16}{19}\right)$$ $$e\left(\frac{73}{95}\right)$$ $$e\left(\frac{59}{95}\right)$$ $$e\left(\frac{52}{95}\right)$$ $$e\left(\frac{49}{95}\right)$$ $$e\left(\frac{3}{95}\right)$$
$$\chi_{764}(19,\cdot)$$ 764.n 190 yes $$1$$ $$1$$ $$e\left(\frac{21}{190}\right)$$ $$e\left(\frac{5}{19}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{21}{95}\right)$$ $$e\left(\frac{18}{19}\right)$$ $$e\left(\frac{56}{95}\right)$$ $$e\left(\frac{71}{190}\right)$$ $$e\left(\frac{49}{95}\right)$$ $$e\left(\frac{48}{95}\right)$$ $$e\left(\frac{97}{190}\right)$$
$$\chi_{764}(21,\cdot)$$ 764.p 190 no $$-1$$ $$1$$ $$e\left(\frac{21}{95}\right)$$ $$e\left(\frac{10}{19}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{42}{95}\right)$$ $$e\left(\frac{15}{38}\right)$$ $$e\left(\frac{17}{95}\right)$$ $$e\left(\frac{71}{95}\right)$$ $$e\left(\frac{3}{95}\right)$$ $$e\left(\frac{97}{190}\right)$$ $$e\left(\frac{99}{190}\right)$$
$$\chi_{764}(23,\cdot)$$ 764.o 190 yes $$-1$$ $$1$$ $$e\left(\frac{59}{190}\right)$$ $$e\left(\frac{5}{19}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{59}{95}\right)$$ $$e\left(\frac{17}{38}\right)$$ $$e\left(\frac{94}{95}\right)$$ $$e\left(\frac{109}{190}\right)$$ $$e\left(\frac{11}{95}\right)$$ $$e\left(\frac{39}{190}\right)$$ $$e\left(\frac{39}{95}\right)$$
$$\chi_{764}(25,\cdot)$$ 764.i 19 no $$1$$ $$1$$ $$e\left(\frac{1}{19}\right)$$ $$e\left(\frac{6}{19}\right)$$ $$1$$ $$e\left(\frac{2}{19}\right)$$ $$e\left(\frac{14}{19}\right)$$ $$e\left(\frac{18}{19}\right)$$ $$e\left(\frac{7}{19}\right)$$ $$e\left(\frac{11}{19}\right)$$ $$e\left(\frac{10}{19}\right)$$ $$e\left(\frac{1}{19}\right)$$
$$\chi_{764}(27,\cdot)$$ 764.o 190 yes $$-1$$ $$1$$ $$e\left(\frac{183}{190}\right)$$ $$e\left(\frac{11}{19}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{88}{95}\right)$$ $$e\left(\frac{7}{38}\right)$$ $$e\left(\frac{13}{95}\right)$$ $$e\left(\frac{103}{190}\right)$$ $$e\left(\frac{47}{95}\right)$$ $$e\left(\frac{63}{190}\right)$$ $$e\left(\frac{63}{95}\right)$$
$$\chi_{764}(29,\cdot)$$ 764.p 190 no $$-1$$ $$1$$ $$e\left(\frac{14}{95}\right)$$ $$e\left(\frac{13}{19}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{28}{95}\right)$$ $$e\left(\frac{29}{38}\right)$$ $$e\left(\frac{43}{95}\right)$$ $$e\left(\frac{79}{95}\right)$$ $$e\left(\frac{2}{95}\right)$$ $$e\left(\frac{33}{190}\right)$$ $$e\left(\frac{161}{190}\right)$$
$$\chi_{764}(31,\cdot)$$ 764.l 38 yes $$1$$ $$1$$ $$e\left(\frac{13}{38}\right)$$ $$e\left(\frac{1}{19}\right)$$ $$1$$ $$e\left(\frac{13}{19}\right)$$ $$e\left(\frac{15}{19}\right)$$ $$e\left(\frac{3}{19}\right)$$ $$e\left(\frac{15}{38}\right)$$ $$e\left(\frac{5}{19}\right)$$ $$e\left(\frac{8}{19}\right)$$ $$e\left(\frac{13}{38}\right)$$
$$\chi_{764}(33,\cdot)$$ 764.p 190 no $$-1$$ $$1$$ $$e\left(\frac{68}{95}\right)$$ $$e\left(\frac{17}{19}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{41}{95}\right)$$ $$e\left(\frac{35}{38}\right)$$ $$e\left(\frac{46}{95}\right)$$ $$e\left(\frac{58}{95}\right)$$ $$e\left(\frac{64}{95}\right)$$ $$e\left(\frac{11}{190}\right)$$ $$e\left(\frac{117}{190}\right)$$
$$\chi_{764}(35,\cdot)$$ 764.n 190 yes $$1$$ $$1$$ $$e\left(\frac{81}{190}\right)$$ $$e\left(\frac{3}{19}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{81}{95}\right)$$ $$e\left(\frac{7}{19}\right)$$ $$e\left(\frac{26}{95}\right)$$ $$e\left(\frac{111}{190}\right)$$ $$e\left(\frac{94}{95}\right)$$ $$e\left(\frac{63}{95}\right)$$ $$e\left(\frac{157}{190}\right)$$
$$\chi_{764}(37,\cdot)$$ 764.j 38 no $$-1$$ $$1$$ $$e\left(\frac{3}{19}\right)$$ $$e\left(\frac{18}{19}\right)$$ $$-1$$ $$e\left(\frac{6}{19}\right)$$ $$e\left(\frac{27}{38}\right)$$ $$e\left(\frac{16}{19}\right)$$ $$e\left(\frac{2}{19}\right)$$ $$e\left(\frac{14}{19}\right)$$ $$e\left(\frac{3}{38}\right)$$ $$e\left(\frac{25}{38}\right)$$
$$\chi_{764}(39,\cdot)$$ 764.h 10 yes $$-1$$ $$1$$ $$e\left(\frac{7}{10}\right)$$ $$1$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$-1$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{2}{5}\right)$$
$$\chi_{764}(41,\cdot)$$ 764.j 38 no $$-1$$ $$1$$ $$e\left(\frac{14}{19}\right)$$ $$e\left(\frac{8}{19}\right)$$ $$-1$$ $$e\left(\frac{9}{19}\right)$$ $$e\left(\frac{31}{38}\right)$$ $$e\left(\frac{5}{19}\right)$$ $$e\left(\frac{3}{19}\right)$$ $$e\left(\frac{2}{19}\right)$$ $$e\left(\frac{33}{38}\right)$$ $$e\left(\frac{9}{38}\right)$$
$$\chi_{764}(43,\cdot)$$ 764.o 190 yes $$-1$$ $$1$$ $$e\left(\frac{73}{190}\right)$$ $$e\left(\frac{2}{19}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{73}{95}\right)$$ $$e\left(\frac{3}{38}\right)$$ $$e\left(\frac{68}{95}\right)$$ $$e\left(\frac{93}{190}\right)$$ $$e\left(\frac{12}{95}\right)$$ $$e\left(\frac{103}{190}\right)$$ $$e\left(\frac{8}{95}\right)$$
$$\chi_{764}(45,\cdot)$$ 764.m 95 no $$1$$ $$1$$ $$e\left(\frac{16}{95}\right)$$ $$e\left(\frac{4}{19}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{32}{95}\right)$$ $$e\left(\frac{3}{19}\right)$$ $$e\left(\frac{22}{95}\right)$$ $$e\left(\frac{36}{95}\right)$$ $$e\left(\frac{43}{95}\right)$$ $$e\left(\frac{46}{95}\right)$$ $$e\left(\frac{92}{95}\right)$$
$$\chi_{764}(47,\cdot)$$ 764.n 190 yes $$1$$ $$1$$ $$e\left(\frac{113}{190}\right)$$ $$e\left(\frac{7}{19}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{18}{95}\right)$$ $$e\left(\frac{10}{19}\right)$$ $$e\left(\frac{48}{95}\right)$$ $$e\left(\frac{183}{190}\right)$$ $$e\left(\frac{42}{95}\right)$$ $$e\left(\frac{14}{95}\right)$$ $$e\left(\frac{151}{190}\right)$$
$$\chi_{764}(49,\cdot)$$ 764.e 5 no $$1$$ $$1$$ $$e\left(\frac{4}{5}\right)$$ $$1$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$1$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{3}{5}\right)$$
$$\chi_{764}(51,\cdot)$$ 764.o 190 yes $$-1$$ $$1$$ $$e\left(\frac{29}{190}\right)$$ $$e\left(\frac{6}{19}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{29}{95}\right)$$ $$e\left(\frac{9}{38}\right)$$ $$e\left(\frac{14}{95}\right)$$ $$e\left(\frac{89}{190}\right)$$ $$e\left(\frac{36}{95}\right)$$ $$e\left(\frac{119}{190}\right)$$ $$e\left(\frac{24}{95}\right)$$
$$\chi_{764}(53,\cdot)$$ 764.p 190 no $$-1$$ $$1$$ $$e\left(\frac{47}{95}\right)$$ $$e\left(\frac{7}{19}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{94}{95}\right)$$ $$e\left(\frac{1}{38}\right)$$ $$e\left(\frac{29}{95}\right)$$ $$e\left(\frac{82}{95}\right)$$ $$e\left(\frac{61}{95}\right)$$ $$e\left(\frac{9}{190}\right)$$ $$e\left(\frac{113}{190}\right)$$
$$\chi_{764}(55,\cdot)$$ 764.l 38 yes $$1$$ $$1$$ $$e\left(\frac{35}{38}\right)$$ $$e\left(\frac{10}{19}\right)$$ $$1$$ $$e\left(\frac{16}{19}\right)$$ $$e\left(\frac{17}{19}\right)$$ $$e\left(\frac{11}{19}\right)$$ $$e\left(\frac{17}{38}\right)$$ $$e\left(\frac{12}{19}\right)$$ $$e\left(\frac{4}{19}\right)$$ $$e\left(\frac{35}{38}\right)$$
$$\chi_{764}(57,\cdot)$$ 764.p 190 no $$-1$$ $$1$$ $$e\left(\frac{41}{95}\right)$$ $$e\left(\frac{15}{19}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{82}{95}\right)$$ $$e\left(\frac{13}{38}\right)$$ $$e\left(\frac{92}{95}\right)$$ $$e\left(\frac{21}{95}\right)$$ $$e\left(\frac{33}{95}\right)$$ $$e\left(\frac{117}{190}\right)$$ $$e\left(\frac{139}{190}\right)$$
$$\chi_{764}(59,\cdot)$$ 764.o 190 yes $$-1$$ $$1$$ $$e\left(\frac{179}{190}\right)$$ $$e\left(\frac{1}{19}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{84}{95}\right)$$ $$e\left(\frac{11}{38}\right)$$ $$e\left(\frac{34}{95}\right)$$ $$e\left(\frac{189}{190}\right)$$ $$e\left(\frac{6}{95}\right)$$ $$e\left(\frac{99}{190}\right)$$ $$e\left(\frac{4}{95}\right)$$
$$\chi_{764}(61,\cdot)$$ 764.p 190 no $$-1$$ $$1$$ $$e\left(\frac{73}{95}\right)$$ $$e\left(\frac{4}{19}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{51}{95}\right)$$ $$e\left(\frac{25}{38}\right)$$ $$e\left(\frac{41}{95}\right)$$ $$e\left(\frac{93}{95}\right)$$ $$e\left(\frac{24}{95}\right)$$ $$e\left(\frac{111}{190}\right)$$ $$e\left(\frac{127}{190}\right)$$
$$\chi_{764}(63,\cdot)$$ 764.n 190 yes $$1$$ $$1$$ $$e\left(\frac{103}{190}\right)$$ $$e\left(\frac{1}{19}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{8}{95}\right)$$ $$e\left(\frac{15}{19}\right)$$ $$e\left(\frac{53}{95}\right)$$ $$e\left(\frac{113}{190}\right)$$ $$e\left(\frac{82}{95}\right)$$ $$e\left(\frac{59}{95}\right)$$ $$e\left(\frac{141}{190}\right)$$