# Properties

 Modulus $322$ Structure $$C_{66}\times C_{2}$$ Order $132$

# Learn more

Show commands: Pari/GP / SageMath

sage: H = DirichletGroup(322)

pari: g = idealstar(,322,2)

## Character group

 sage: G.order()  pari: g.no Order = 132 sage: H.invariants()  pari: g.cyc Structure = $$C_{66}\times C_{2}$$ sage: H.gens()  pari: g.gen Generators = $\chi_{322}(185,\cdot)$, $\chi_{322}(281,\cdot)$

## First 32 of 132 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 $$-1$$ $$1$$ $$3$$ $$5$$ $$9$$ $$11$$ $$13$$ $$15$$ $$17$$ $$19$$ $$25$$ $$27$$
$$\chi_{322}(1,\cdot)$$ 322.a 1 no $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{322}(3,\cdot)$$ 322.n 66 no $$-1$$ $$1$$ $$e\left(\frac{53}{66}\right)$$ $$e\left(\frac{37}{66}\right)$$ $$e\left(\frac{20}{33}\right)$$ $$e\left(\frac{7}{33}\right)$$ $$e\left(\frac{15}{22}\right)$$ $$e\left(\frac{4}{11}\right)$$ $$e\left(\frac{17}{66}\right)$$ $$e\left(\frac{49}{66}\right)$$ $$e\left(\frac{4}{33}\right)$$ $$e\left(\frac{9}{22}\right)$$
$$\chi_{322}(5,\cdot)$$ 322.o 66 no $$1$$ $$1$$ $$e\left(\frac{37}{66}\right)$$ $$e\left(\frac{7}{33}\right)$$ $$e\left(\frac{4}{33}\right)$$ $$e\left(\frac{49}{66}\right)$$ $$e\left(\frac{3}{22}\right)$$ $$e\left(\frac{17}{22}\right)$$ $$e\left(\frac{5}{33}\right)$$ $$e\left(\frac{28}{33}\right)$$ $$e\left(\frac{14}{33}\right)$$ $$e\left(\frac{15}{22}\right)$$
$$\chi_{322}(9,\cdot)$$ 322.m 33 no $$1$$ $$1$$ $$e\left(\frac{20}{33}\right)$$ $$e\left(\frac{4}{33}\right)$$ $$e\left(\frac{7}{33}\right)$$ $$e\left(\frac{14}{33}\right)$$ $$e\left(\frac{4}{11}\right)$$ $$e\left(\frac{8}{11}\right)$$ $$e\left(\frac{17}{33}\right)$$ $$e\left(\frac{16}{33}\right)$$ $$e\left(\frac{8}{33}\right)$$ $$e\left(\frac{9}{11}\right)$$
$$\chi_{322}(11,\cdot)$$ 322.p 66 no $$-1$$ $$1$$ $$e\left(\frac{7}{33}\right)$$ $$e\left(\frac{49}{66}\right)$$ $$e\left(\frac{14}{33}\right)$$ $$e\left(\frac{23}{66}\right)$$ $$e\left(\frac{8}{11}\right)$$ $$e\left(\frac{21}{22}\right)$$ $$e\left(\frac{35}{66}\right)$$ $$e\left(\frac{31}{66}\right)$$ $$e\left(\frac{16}{33}\right)$$ $$e\left(\frac{7}{11}\right)$$
$$\chi_{322}(13,\cdot)$$ 322.l 22 no $$-1$$ $$1$$ $$e\left(\frac{15}{22}\right)$$ $$e\left(\frac{3}{22}\right)$$ $$e\left(\frac{4}{11}\right)$$ $$e\left(\frac{8}{11}\right)$$ $$e\left(\frac{9}{22}\right)$$ $$e\left(\frac{9}{11}\right)$$ $$e\left(\frac{21}{22}\right)$$ $$e\left(\frac{1}{22}\right)$$ $$e\left(\frac{3}{11}\right)$$ $$e\left(\frac{1}{22}\right)$$
$$\chi_{322}(15,\cdot)$$ 322.j 22 no $$-1$$ $$1$$ $$e\left(\frac{4}{11}\right)$$ $$e\left(\frac{17}{22}\right)$$ $$e\left(\frac{8}{11}\right)$$ $$e\left(\frac{21}{22}\right)$$ $$e\left(\frac{9}{11}\right)$$ $$e\left(\frac{3}{22}\right)$$ $$e\left(\frac{9}{22}\right)$$ $$e\left(\frac{13}{22}\right)$$ $$e\left(\frac{6}{11}\right)$$ $$e\left(\frac{1}{11}\right)$$
$$\chi_{322}(17,\cdot)$$ 322.o 66 no $$1$$ $$1$$ $$e\left(\frac{17}{66}\right)$$ $$e\left(\frac{5}{33}\right)$$ $$e\left(\frac{17}{33}\right)$$ $$e\left(\frac{35}{66}\right)$$ $$e\left(\frac{21}{22}\right)$$ $$e\left(\frac{9}{22}\right)$$ $$e\left(\frac{13}{33}\right)$$ $$e\left(\frac{20}{33}\right)$$ $$e\left(\frac{10}{33}\right)$$ $$e\left(\frac{17}{22}\right)$$
$$\chi_{322}(19,\cdot)$$ 322.o 66 no $$1$$ $$1$$ $$e\left(\frac{49}{66}\right)$$ $$e\left(\frac{28}{33}\right)$$ $$e\left(\frac{16}{33}\right)$$ $$e\left(\frac{31}{66}\right)$$ $$e\left(\frac{1}{22}\right)$$ $$e\left(\frac{13}{22}\right)$$ $$e\left(\frac{20}{33}\right)$$ $$e\left(\frac{13}{33}\right)$$ $$e\left(\frac{23}{33}\right)$$ $$e\left(\frac{5}{22}\right)$$
$$\chi_{322}(25,\cdot)$$ 322.m 33 no $$1$$ $$1$$ $$e\left(\frac{4}{33}\right)$$ $$e\left(\frac{14}{33}\right)$$ $$e\left(\frac{8}{33}\right)$$ $$e\left(\frac{16}{33}\right)$$ $$e\left(\frac{3}{11}\right)$$ $$e\left(\frac{6}{11}\right)$$ $$e\left(\frac{10}{33}\right)$$ $$e\left(\frac{23}{33}\right)$$ $$e\left(\frac{28}{33}\right)$$ $$e\left(\frac{4}{11}\right)$$
$$\chi_{322}(27,\cdot)$$ 322.l 22 no $$-1$$ $$1$$ $$e\left(\frac{9}{22}\right)$$ $$e\left(\frac{15}{22}\right)$$ $$e\left(\frac{9}{11}\right)$$ $$e\left(\frac{7}{11}\right)$$ $$e\left(\frac{1}{22}\right)$$ $$e\left(\frac{1}{11}\right)$$ $$e\left(\frac{17}{22}\right)$$ $$e\left(\frac{5}{22}\right)$$ $$e\left(\frac{4}{11}\right)$$ $$e\left(\frac{5}{22}\right)$$
$$\chi_{322}(29,\cdot)$$ 322.i 11 no $$1$$ $$1$$ $$e\left(\frac{1}{11}\right)$$ $$e\left(\frac{9}{11}\right)$$ $$e\left(\frac{2}{11}\right)$$ $$e\left(\frac{4}{11}\right)$$ $$e\left(\frac{5}{11}\right)$$ $$e\left(\frac{10}{11}\right)$$ $$e\left(\frac{8}{11}\right)$$ $$e\left(\frac{3}{11}\right)$$ $$e\left(\frac{7}{11}\right)$$ $$e\left(\frac{3}{11}\right)$$
$$\chi_{322}(31,\cdot)$$ 322.n 66 no $$-1$$ $$1$$ $$e\left(\frac{35}{66}\right)$$ $$e\left(\frac{7}{66}\right)$$ $$e\left(\frac{2}{33}\right)$$ $$e\left(\frac{4}{33}\right)$$ $$e\left(\frac{7}{22}\right)$$ $$e\left(\frac{7}{11}\right)$$ $$e\left(\frac{5}{66}\right)$$ $$e\left(\frac{61}{66}\right)$$ $$e\left(\frac{7}{33}\right)$$ $$e\left(\frac{13}{22}\right)$$
$$\chi_{322}(33,\cdot)$$ 322.o 66 no $$1$$ $$1$$ $$e\left(\frac{1}{66}\right)$$ $$e\left(\frac{10}{33}\right)$$ $$e\left(\frac{1}{33}\right)$$ $$e\left(\frac{37}{66}\right)$$ $$e\left(\frac{9}{22}\right)$$ $$e\left(\frac{7}{22}\right)$$ $$e\left(\frac{26}{33}\right)$$ $$e\left(\frac{7}{33}\right)$$ $$e\left(\frac{20}{33}\right)$$ $$e\left(\frac{1}{22}\right)$$
$$\chi_{322}(37,\cdot)$$ 322.p 66 no $$-1$$ $$1$$ $$e\left(\frac{20}{33}\right)$$ $$e\left(\frac{41}{66}\right)$$ $$e\left(\frac{7}{33}\right)$$ $$e\left(\frac{61}{66}\right)$$ $$e\left(\frac{4}{11}\right)$$ $$e\left(\frac{5}{22}\right)$$ $$e\left(\frac{1}{66}\right)$$ $$e\left(\frac{65}{66}\right)$$ $$e\left(\frac{8}{33}\right)$$ $$e\left(\frac{9}{11}\right)$$
$$\chi_{322}(39,\cdot)$$ 322.m 33 no $$1$$ $$1$$ $$e\left(\frac{16}{33}\right)$$ $$e\left(\frac{23}{33}\right)$$ $$e\left(\frac{32}{33}\right)$$ $$e\left(\frac{31}{33}\right)$$ $$e\left(\frac{1}{11}\right)$$ $$e\left(\frac{2}{11}\right)$$ $$e\left(\frac{7}{33}\right)$$ $$e\left(\frac{26}{33}\right)$$ $$e\left(\frac{13}{33}\right)$$ $$e\left(\frac{5}{11}\right)$$
$$\chi_{322}(41,\cdot)$$ 322.l 22 no $$-1$$ $$1$$ $$e\left(\frac{5}{22}\right)$$ $$e\left(\frac{1}{22}\right)$$ $$e\left(\frac{5}{11}\right)$$ $$e\left(\frac{10}{11}\right)$$ $$e\left(\frac{3}{22}\right)$$ $$e\left(\frac{3}{11}\right)$$ $$e\left(\frac{7}{22}\right)$$ $$e\left(\frac{15}{22}\right)$$ $$e\left(\frac{1}{11}\right)$$ $$e\left(\frac{15}{22}\right)$$
$$\chi_{322}(43,\cdot)$$ 322.j 22 no $$-1$$ $$1$$ $$e\left(\frac{7}{11}\right)$$ $$e\left(\frac{5}{22}\right)$$ $$e\left(\frac{3}{11}\right)$$ $$e\left(\frac{1}{22}\right)$$ $$e\left(\frac{2}{11}\right)$$ $$e\left(\frac{19}{22}\right)$$ $$e\left(\frac{13}{22}\right)$$ $$e\left(\frac{9}{22}\right)$$ $$e\left(\frac{5}{11}\right)$$ $$e\left(\frac{10}{11}\right)$$
$$\chi_{322}(45,\cdot)$$ 322.g 6 no $$1$$ $$1$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$-1$$ $$-1$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$-1$$
$$\chi_{322}(47,\cdot)$$ 322.h 6 no $$-1$$ $$1$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$-1$$ $$1$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$-1$$
$$\chi_{322}(51,\cdot)$$ 322.p 66 no $$-1$$ $$1$$ $$e\left(\frac{2}{33}\right)$$ $$e\left(\frac{47}{66}\right)$$ $$e\left(\frac{4}{33}\right)$$ $$e\left(\frac{49}{66}\right)$$ $$e\left(\frac{7}{11}\right)$$ $$e\left(\frac{17}{22}\right)$$ $$e\left(\frac{43}{66}\right)$$ $$e\left(\frac{23}{66}\right)$$ $$e\left(\frac{14}{33}\right)$$ $$e\left(\frac{2}{11}\right)$$
$$\chi_{322}(53,\cdot)$$ 322.p 66 no $$-1$$ $$1$$ $$e\left(\frac{16}{33}\right)$$ $$e\left(\frac{13}{66}\right)$$ $$e\left(\frac{32}{33}\right)$$ $$e\left(\frac{29}{66}\right)$$ $$e\left(\frac{1}{11}\right)$$ $$e\left(\frac{15}{22}\right)$$ $$e\left(\frac{47}{66}\right)$$ $$e\left(\frac{19}{66}\right)$$ $$e\left(\frac{13}{33}\right)$$ $$e\left(\frac{5}{11}\right)$$
$$\chi_{322}(55,\cdot)$$ 322.l 22 no $$-1$$ $$1$$ $$e\left(\frac{17}{22}\right)$$ $$e\left(\frac{21}{22}\right)$$ $$e\left(\frac{6}{11}\right)$$ $$e\left(\frac{1}{11}\right)$$ $$e\left(\frac{19}{22}\right)$$ $$e\left(\frac{8}{11}\right)$$ $$e\left(\frac{15}{22}\right)$$ $$e\left(\frac{7}{22}\right)$$ $$e\left(\frac{10}{11}\right)$$ $$e\left(\frac{7}{22}\right)$$
$$\chi_{322}(57,\cdot)$$ 322.j 22 no $$-1$$ $$1$$ $$e\left(\frac{6}{11}\right)$$ $$e\left(\frac{9}{22}\right)$$ $$e\left(\frac{1}{11}\right)$$ $$e\left(\frac{15}{22}\right)$$ $$e\left(\frac{8}{11}\right)$$ $$e\left(\frac{21}{22}\right)$$ $$e\left(\frac{19}{22}\right)$$ $$e\left(\frac{3}{22}\right)$$ $$e\left(\frac{9}{11}\right)$$ $$e\left(\frac{7}{11}\right)$$
$$\chi_{322}(59,\cdot)$$ 322.n 66 no $$-1$$ $$1$$ $$e\left(\frac{23}{66}\right)$$ $$e\left(\frac{31}{66}\right)$$ $$e\left(\frac{23}{33}\right)$$ $$e\left(\frac{13}{33}\right)$$ $$e\left(\frac{9}{22}\right)$$ $$e\left(\frac{9}{11}\right)$$ $$e\left(\frac{41}{66}\right)$$ $$e\left(\frac{25}{66}\right)$$ $$e\left(\frac{31}{33}\right)$$ $$e\left(\frac{1}{22}\right)$$
$$\chi_{322}(61,\cdot)$$ 322.o 66 no $$1$$ $$1$$ $$e\left(\frac{13}{66}\right)$$ $$e\left(\frac{31}{33}\right)$$ $$e\left(\frac{13}{33}\right)$$ $$e\left(\frac{19}{66}\right)$$ $$e\left(\frac{7}{22}\right)$$ $$e\left(\frac{3}{22}\right)$$ $$e\left(\frac{8}{33}\right)$$ $$e\left(\frac{25}{33}\right)$$ $$e\left(\frac{29}{33}\right)$$ $$e\left(\frac{13}{22}\right)$$
$$\chi_{322}(65,\cdot)$$ 322.p 66 no $$-1$$ $$1$$ $$e\left(\frac{8}{33}\right)$$ $$e\left(\frac{23}{66}\right)$$ $$e\left(\frac{16}{33}\right)$$ $$e\left(\frac{31}{66}\right)$$ $$e\left(\frac{6}{11}\right)$$ $$e\left(\frac{13}{22}\right)$$ $$e\left(\frac{7}{66}\right)$$ $$e\left(\frac{59}{66}\right)$$ $$e\left(\frac{23}{33}\right)$$ $$e\left(\frac{8}{11}\right)$$
$$\chi_{322}(67,\cdot)$$ 322.p 66 no $$-1$$ $$1$$ $$e\left(\frac{4}{33}\right)$$ $$e\left(\frac{61}{66}\right)$$ $$e\left(\frac{8}{33}\right)$$ $$e\left(\frac{65}{66}\right)$$ $$e\left(\frac{3}{11}\right)$$ $$e\left(\frac{1}{22}\right)$$ $$e\left(\frac{53}{66}\right)$$ $$e\left(\frac{13}{66}\right)$$ $$e\left(\frac{28}{33}\right)$$ $$e\left(\frac{4}{11}\right)$$
$$\chi_{322}(71,\cdot)$$ 322.i 11 no $$1$$ $$1$$ $$e\left(\frac{5}{11}\right)$$ $$e\left(\frac{1}{11}\right)$$ $$e\left(\frac{10}{11}\right)$$ $$e\left(\frac{9}{11}\right)$$ $$e\left(\frac{3}{11}\right)$$ $$e\left(\frac{6}{11}\right)$$ $$e\left(\frac{7}{11}\right)$$ $$e\left(\frac{4}{11}\right)$$ $$e\left(\frac{2}{11}\right)$$ $$e\left(\frac{4}{11}\right)$$
$$\chi_{322}(73,\cdot)$$ 322.n 66 no $$-1$$ $$1$$ $$e\left(\frac{5}{66}\right)$$ $$e\left(\frac{1}{66}\right)$$ $$e\left(\frac{5}{33}\right)$$ $$e\left(\frac{10}{33}\right)$$ $$e\left(\frac{1}{22}\right)$$ $$e\left(\frac{1}{11}\right)$$ $$e\left(\frac{29}{66}\right)$$ $$e\left(\frac{37}{66}\right)$$ $$e\left(\frac{1}{33}\right)$$ $$e\left(\frac{5}{22}\right)$$
$$\chi_{322}(75,\cdot)$$ 322.n 66 no $$-1$$ $$1$$ $$e\left(\frac{61}{66}\right)$$ $$e\left(\frac{65}{66}\right)$$ $$e\left(\frac{28}{33}\right)$$ $$e\left(\frac{23}{33}\right)$$ $$e\left(\frac{21}{22}\right)$$ $$e\left(\frac{10}{11}\right)$$ $$e\left(\frac{37}{66}\right)$$ $$e\left(\frac{29}{66}\right)$$ $$e\left(\frac{32}{33}\right)$$ $$e\left(\frac{17}{22}\right)$$
$$\chi_{322}(79,\cdot)$$ 322.p 66 no $$-1$$ $$1$$ $$e\left(\frac{17}{33}\right)$$ $$e\left(\frac{53}{66}\right)$$ $$e\left(\frac{1}{33}\right)$$ $$e\left(\frac{37}{66}\right)$$ $$e\left(\frac{10}{11}\right)$$ $$e\left(\frac{7}{22}\right)$$ $$e\left(\frac{19}{66}\right)$$ $$e\left(\frac{47}{66}\right)$$ $$e\left(\frac{20}{33}\right)$$ $$e\left(\frac{6}{11}\right)$$