# Properties

 Modulus $460$ Structure $$C_{44}\times C_{2}\times C_{2}$$ Order $176$

Show commands: Pari/GP / SageMath

sage: H = DirichletGroup(460)

pari: g = idealstar(,460,2)

## Character group

 sage: G.order()  pari: g.no Order = 176 sage: H.invariants()  pari: g.cyc Structure = $$C_{44}\times C_{2}\times C_{2}$$ sage: H.gens()  pari: g.gen Generators = $\chi_{460}(231,\cdot)$, $\chi_{460}(277,\cdot)$, $\chi_{460}(281,\cdot)$

## First 32 of 176 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 $$-1$$ $$1$$ $$3$$ $$7$$ $$9$$ $$11$$ $$13$$ $$17$$ $$19$$ $$21$$ $$27$$ $$29$$
$$\chi_{460}(1,\cdot)$$ 460.a 1 no $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{460}(3,\cdot)$$ 460.w 44 yes $$1$$ $$1$$ $$e\left(\frac{17}{44}\right)$$ $$e\left(\frac{3}{44}\right)$$ $$e\left(\frac{17}{22}\right)$$ $$e\left(\frac{1}{22}\right)$$ $$e\left(\frac{19}{44}\right)$$ $$e\left(\frac{37}{44}\right)$$ $$e\left(\frac{10}{11}\right)$$ $$e\left(\frac{5}{11}\right)$$ $$e\left(\frac{7}{44}\right)$$ $$e\left(\frac{13}{22}\right)$$
$$\chi_{460}(7,\cdot)$$ 460.v 44 yes $$-1$$ $$1$$ $$e\left(\frac{3}{44}\right)$$ $$e\left(\frac{7}{44}\right)$$ $$e\left(\frac{3}{22}\right)$$ $$e\left(\frac{3}{11}\right)$$ $$e\left(\frac{37}{44}\right)$$ $$e\left(\frac{13}{44}\right)$$ $$e\left(\frac{21}{22}\right)$$ $$e\left(\frac{5}{22}\right)$$ $$e\left(\frac{9}{44}\right)$$ $$e\left(\frac{1}{22}\right)$$
$$\chi_{460}(9,\cdot)$$ 460.s 22 no $$1$$ $$1$$ $$e\left(\frac{17}{22}\right)$$ $$e\left(\frac{3}{22}\right)$$ $$e\left(\frac{6}{11}\right)$$ $$e\left(\frac{1}{11}\right)$$ $$e\left(\frac{19}{22}\right)$$ $$e\left(\frac{15}{22}\right)$$ $$e\left(\frac{9}{11}\right)$$ $$e\left(\frac{10}{11}\right)$$ $$e\left(\frac{7}{22}\right)$$ $$e\left(\frac{2}{11}\right)$$
$$\chi_{460}(11,\cdot)$$ 460.q 22 no $$1$$ $$1$$ $$e\left(\frac{1}{22}\right)$$ $$e\left(\frac{3}{11}\right)$$ $$e\left(\frac{1}{11}\right)$$ $$e\left(\frac{2}{11}\right)$$ $$e\left(\frac{8}{11}\right)$$ $$e\left(\frac{19}{22}\right)$$ $$e\left(\frac{7}{11}\right)$$ $$e\left(\frac{7}{22}\right)$$ $$e\left(\frac{3}{22}\right)$$ $$e\left(\frac{4}{11}\right)$$
$$\chi_{460}(13,\cdot)$$ 460.u 44 no $$-1$$ $$1$$ $$e\left(\frac{19}{44}\right)$$ $$e\left(\frac{37}{44}\right)$$ $$e\left(\frac{19}{22}\right)$$ $$e\left(\frac{8}{11}\right)$$ $$e\left(\frac{7}{44}\right)$$ $$e\left(\frac{9}{44}\right)$$ $$e\left(\frac{1}{22}\right)$$ $$e\left(\frac{3}{11}\right)$$ $$e\left(\frac{13}{44}\right)$$ $$e\left(\frac{21}{22}\right)$$
$$\chi_{460}(17,\cdot)$$ 460.x 44 no $$1$$ $$1$$ $$e\left(\frac{37}{44}\right)$$ $$e\left(\frac{13}{44}\right)$$ $$e\left(\frac{15}{22}\right)$$ $$e\left(\frac{19}{22}\right)$$ $$e\left(\frac{9}{44}\right)$$ $$e\left(\frac{21}{44}\right)$$ $$e\left(\frac{3}{11}\right)$$ $$e\left(\frac{3}{22}\right)$$ $$e\left(\frac{23}{44}\right)$$ $$e\left(\frac{5}{22}\right)$$
$$\chi_{460}(19,\cdot)$$ 460.o 22 yes $$1$$ $$1$$ $$e\left(\frac{10}{11}\right)$$ $$e\left(\frac{21}{22}\right)$$ $$e\left(\frac{9}{11}\right)$$ $$e\left(\frac{7}{11}\right)$$ $$e\left(\frac{1}{22}\right)$$ $$e\left(\frac{3}{11}\right)$$ $$e\left(\frac{8}{11}\right)$$ $$e\left(\frac{19}{22}\right)$$ $$e\left(\frac{8}{11}\right)$$ $$e\left(\frac{3}{11}\right)$$
$$\chi_{460}(21,\cdot)$$ 460.p 22 no $$-1$$ $$1$$ $$e\left(\frac{5}{11}\right)$$ $$e\left(\frac{5}{22}\right)$$ $$e\left(\frac{10}{11}\right)$$ $$e\left(\frac{7}{22}\right)$$ $$e\left(\frac{3}{11}\right)$$ $$e\left(\frac{3}{22}\right)$$ $$e\left(\frac{19}{22}\right)$$ $$e\left(\frac{15}{22}\right)$$ $$e\left(\frac{4}{11}\right)$$ $$e\left(\frac{7}{11}\right)$$
$$\chi_{460}(27,\cdot)$$ 460.w 44 yes $$1$$ $$1$$ $$e\left(\frac{7}{44}\right)$$ $$e\left(\frac{9}{44}\right)$$ $$e\left(\frac{7}{22}\right)$$ $$e\left(\frac{3}{22}\right)$$ $$e\left(\frac{13}{44}\right)$$ $$e\left(\frac{23}{44}\right)$$ $$e\left(\frac{8}{11}\right)$$ $$e\left(\frac{4}{11}\right)$$ $$e\left(\frac{21}{44}\right)$$ $$e\left(\frac{17}{22}\right)$$
$$\chi_{460}(29,\cdot)$$ 460.s 22 no $$1$$ $$1$$ $$e\left(\frac{13}{22}\right)$$ $$e\left(\frac{1}{22}\right)$$ $$e\left(\frac{2}{11}\right)$$ $$e\left(\frac{4}{11}\right)$$ $$e\left(\frac{21}{22}\right)$$ $$e\left(\frac{5}{22}\right)$$ $$e\left(\frac{3}{11}\right)$$ $$e\left(\frac{7}{11}\right)$$ $$e\left(\frac{17}{22}\right)$$ $$e\left(\frac{8}{11}\right)$$
$$\chi_{460}(31,\cdot)$$ 460.t 22 no $$-1$$ $$1$$ $$e\left(\frac{19}{22}\right)$$ $$e\left(\frac{15}{22}\right)$$ $$e\left(\frac{8}{11}\right)$$ $$e\left(\frac{21}{22}\right)$$ $$e\left(\frac{9}{11}\right)$$ $$e\left(\frac{10}{11}\right)$$ $$e\left(\frac{13}{22}\right)$$ $$e\left(\frac{6}{11}\right)$$ $$e\left(\frac{13}{22}\right)$$ $$e\left(\frac{10}{11}\right)$$
$$\chi_{460}(33,\cdot)$$ 460.x 44 no $$1$$ $$1$$ $$e\left(\frac{19}{44}\right)$$ $$e\left(\frac{15}{44}\right)$$ $$e\left(\frac{19}{22}\right)$$ $$e\left(\frac{5}{22}\right)$$ $$e\left(\frac{7}{44}\right)$$ $$e\left(\frac{31}{44}\right)$$ $$e\left(\frac{6}{11}\right)$$ $$e\left(\frac{17}{22}\right)$$ $$e\left(\frac{13}{44}\right)$$ $$e\left(\frac{21}{22}\right)$$
$$\chi_{460}(37,\cdot)$$ 460.x 44 no $$1$$ $$1$$ $$e\left(\frac{1}{44}\right)$$ $$e\left(\frac{17}{44}\right)$$ $$e\left(\frac{1}{22}\right)$$ $$e\left(\frac{13}{22}\right)$$ $$e\left(\frac{5}{44}\right)$$ $$e\left(\frac{41}{44}\right)$$ $$e\left(\frac{9}{11}\right)$$ $$e\left(\frac{9}{22}\right)$$ $$e\left(\frac{3}{44}\right)$$ $$e\left(\frac{15}{22}\right)$$
$$\chi_{460}(39,\cdot)$$ 460.n 22 yes $$-1$$ $$1$$ $$e\left(\frac{9}{11}\right)$$ $$e\left(\frac{10}{11}\right)$$ $$e\left(\frac{7}{11}\right)$$ $$e\left(\frac{17}{22}\right)$$ $$e\left(\frac{13}{22}\right)$$ $$e\left(\frac{1}{22}\right)$$ $$e\left(\frac{21}{22}\right)$$ $$e\left(\frac{8}{11}\right)$$ $$e\left(\frac{5}{11}\right)$$ $$e\left(\frac{6}{11}\right)$$
$$\chi_{460}(41,\cdot)$$ 460.m 11 no $$1$$ $$1$$ $$e\left(\frac{8}{11}\right)$$ $$e\left(\frac{4}{11}\right)$$ $$e\left(\frac{5}{11}\right)$$ $$e\left(\frac{10}{11}\right)$$ $$e\left(\frac{7}{11}\right)$$ $$e\left(\frac{9}{11}\right)$$ $$e\left(\frac{2}{11}\right)$$ $$e\left(\frac{1}{11}\right)$$ $$e\left(\frac{2}{11}\right)$$ $$e\left(\frac{9}{11}\right)$$
$$\chi_{460}(43,\cdot)$$ 460.v 44 yes $$-1$$ $$1$$ $$e\left(\frac{17}{44}\right)$$ $$e\left(\frac{25}{44}\right)$$ $$e\left(\frac{17}{22}\right)$$ $$e\left(\frac{6}{11}\right)$$ $$e\left(\frac{19}{44}\right)$$ $$e\left(\frac{15}{44}\right)$$ $$e\left(\frac{9}{22}\right)$$ $$e\left(\frac{21}{22}\right)$$ $$e\left(\frac{7}{44}\right)$$ $$e\left(\frac{13}{22}\right)$$
$$\chi_{460}(47,\cdot)$$ 460.j 4 no $$1$$ $$1$$ $$i$$ $$-i$$ $$-1$$ $$-1$$ $$-i$$ $$i$$ $$1$$ $$1$$ $$-i$$ $$-1$$
$$\chi_{460}(49,\cdot)$$ 460.s 22 no $$1$$ $$1$$ $$e\left(\frac{3}{22}\right)$$ $$e\left(\frac{7}{22}\right)$$ $$e\left(\frac{3}{11}\right)$$ $$e\left(\frac{6}{11}\right)$$ $$e\left(\frac{15}{22}\right)$$ $$e\left(\frac{13}{22}\right)$$ $$e\left(\frac{10}{11}\right)$$ $$e\left(\frac{5}{11}\right)$$ $$e\left(\frac{9}{22}\right)$$ $$e\left(\frac{1}{11}\right)$$
$$\chi_{460}(51,\cdot)$$ 460.q 22 no $$1$$ $$1$$ $$e\left(\frac{5}{22}\right)$$ $$e\left(\frac{4}{11}\right)$$ $$e\left(\frac{5}{11}\right)$$ $$e\left(\frac{10}{11}\right)$$ $$e\left(\frac{7}{11}\right)$$ $$e\left(\frac{7}{22}\right)$$ $$e\left(\frac{2}{11}\right)$$ $$e\left(\frac{13}{22}\right)$$ $$e\left(\frac{15}{22}\right)$$ $$e\left(\frac{9}{11}\right)$$
$$\chi_{460}(53,\cdot)$$ 460.x 44 no $$1$$ $$1$$ $$e\left(\frac{3}{44}\right)$$ $$e\left(\frac{7}{44}\right)$$ $$e\left(\frac{3}{22}\right)$$ $$e\left(\frac{17}{22}\right)$$ $$e\left(\frac{15}{44}\right)$$ $$e\left(\frac{35}{44}\right)$$ $$e\left(\frac{5}{11}\right)$$ $$e\left(\frac{5}{22}\right)$$ $$e\left(\frac{9}{44}\right)$$ $$e\left(\frac{1}{22}\right)$$
$$\chi_{460}(57,\cdot)$$ 460.x 44 no $$1$$ $$1$$ $$e\left(\frac{13}{44}\right)$$ $$e\left(\frac{1}{44}\right)$$ $$e\left(\frac{13}{22}\right)$$ $$e\left(\frac{15}{22}\right)$$ $$e\left(\frac{21}{44}\right)$$ $$e\left(\frac{5}{44}\right)$$ $$e\left(\frac{7}{11}\right)$$ $$e\left(\frac{7}{22}\right)$$ $$e\left(\frac{39}{44}\right)$$ $$e\left(\frac{19}{22}\right)$$
$$\chi_{460}(59,\cdot)$$ 460.n 22 yes $$-1$$ $$1$$ $$e\left(\frac{2}{11}\right)$$ $$e\left(\frac{1}{11}\right)$$ $$e\left(\frac{4}{11}\right)$$ $$e\left(\frac{5}{22}\right)$$ $$e\left(\frac{9}{22}\right)$$ $$e\left(\frac{21}{22}\right)$$ $$e\left(\frac{1}{22}\right)$$ $$e\left(\frac{3}{11}\right)$$ $$e\left(\frac{6}{11}\right)$$ $$e\left(\frac{5}{11}\right)$$
$$\chi_{460}(61,\cdot)$$ 460.p 22 no $$-1$$ $$1$$ $$e\left(\frac{4}{11}\right)$$ $$e\left(\frac{15}{22}\right)$$ $$e\left(\frac{8}{11}\right)$$ $$e\left(\frac{21}{22}\right)$$ $$e\left(\frac{9}{11}\right)$$ $$e\left(\frac{9}{22}\right)$$ $$e\left(\frac{13}{22}\right)$$ $$e\left(\frac{1}{22}\right)$$ $$e\left(\frac{1}{11}\right)$$ $$e\left(\frac{10}{11}\right)$$
$$\chi_{460}(63,\cdot)$$ 460.v 44 yes $$-1$$ $$1$$ $$e\left(\frac{37}{44}\right)$$ $$e\left(\frac{13}{44}\right)$$ $$e\left(\frac{15}{22}\right)$$ $$e\left(\frac{4}{11}\right)$$ $$e\left(\frac{31}{44}\right)$$ $$e\left(\frac{43}{44}\right)$$ $$e\left(\frac{17}{22}\right)$$ $$e\left(\frac{3}{22}\right)$$ $$e\left(\frac{23}{44}\right)$$ $$e\left(\frac{5}{22}\right)$$
$$\chi_{460}(67,\cdot)$$ 460.v 44 yes $$-1$$ $$1$$ $$e\left(\frac{31}{44}\right)$$ $$e\left(\frac{43}{44}\right)$$ $$e\left(\frac{9}{22}\right)$$ $$e\left(\frac{9}{11}\right)$$ $$e\left(\frac{1}{44}\right)$$ $$e\left(\frac{17}{44}\right)$$ $$e\left(\frac{19}{22}\right)$$ $$e\left(\frac{15}{22}\right)$$ $$e\left(\frac{5}{44}\right)$$ $$e\left(\frac{3}{22}\right)$$
$$\chi_{460}(71,\cdot)$$ 460.t 22 no $$-1$$ $$1$$ $$e\left(\frac{21}{22}\right)$$ $$e\left(\frac{5}{22}\right)$$ $$e\left(\frac{10}{11}\right)$$ $$e\left(\frac{7}{22}\right)$$ $$e\left(\frac{3}{11}\right)$$ $$e\left(\frac{7}{11}\right)$$ $$e\left(\frac{19}{22}\right)$$ $$e\left(\frac{2}{11}\right)$$ $$e\left(\frac{19}{22}\right)$$ $$e\left(\frac{7}{11}\right)$$
$$\chi_{460}(73,\cdot)$$ 460.u 44 no $$-1$$ $$1$$ $$e\left(\frac{7}{44}\right)$$ $$e\left(\frac{9}{44}\right)$$ $$e\left(\frac{7}{22}\right)$$ $$e\left(\frac{7}{11}\right)$$ $$e\left(\frac{35}{44}\right)$$ $$e\left(\frac{1}{44}\right)$$ $$e\left(\frac{5}{22}\right)$$ $$e\left(\frac{4}{11}\right)$$ $$e\left(\frac{21}{44}\right)$$ $$e\left(\frac{17}{22}\right)$$
$$\chi_{460}(77,\cdot)$$ 460.u 44 no $$-1$$ $$1$$ $$e\left(\frac{5}{44}\right)$$ $$e\left(\frac{19}{44}\right)$$ $$e\left(\frac{5}{22}\right)$$ $$e\left(\frac{5}{11}\right)$$ $$e\left(\frac{25}{44}\right)$$ $$e\left(\frac{7}{44}\right)$$ $$e\left(\frac{13}{22}\right)$$ $$e\left(\frac{6}{11}\right)$$ $$e\left(\frac{15}{44}\right)$$ $$e\left(\frac{9}{22}\right)$$
$$\chi_{460}(79,\cdot)$$ 460.o 22 yes $$1$$ $$1$$ $$e\left(\frac{2}{11}\right)$$ $$e\left(\frac{13}{22}\right)$$ $$e\left(\frac{4}{11}\right)$$ $$e\left(\frac{8}{11}\right)$$ $$e\left(\frac{9}{22}\right)$$ $$e\left(\frac{5}{11}\right)$$ $$e\left(\frac{6}{11}\right)$$ $$e\left(\frac{17}{22}\right)$$ $$e\left(\frac{6}{11}\right)$$ $$e\left(\frac{5}{11}\right)$$
$$\chi_{460}(81,\cdot)$$ 460.m 11 no $$1$$ $$1$$ $$e\left(\frac{6}{11}\right)$$ $$e\left(\frac{3}{11}\right)$$ $$e\left(\frac{1}{11}\right)$$ $$e\left(\frac{2}{11}\right)$$ $$e\left(\frac{8}{11}\right)$$ $$e\left(\frac{4}{11}\right)$$ $$e\left(\frac{7}{11}\right)$$ $$e\left(\frac{9}{11}\right)$$ $$e\left(\frac{7}{11}\right)$$ $$e\left(\frac{4}{11}\right)$$
$$\chi_{460}(83,\cdot)$$ 460.v 44 yes $$-1$$ $$1$$ $$e\left(\frac{1}{44}\right)$$ $$e\left(\frac{17}{44}\right)$$ $$e\left(\frac{1}{22}\right)$$ $$e\left(\frac{1}{11}\right)$$ $$e\left(\frac{27}{44}\right)$$ $$e\left(\frac{19}{44}\right)$$ $$e\left(\frac{7}{22}\right)$$ $$e\left(\frac{9}{22}\right)$$ $$e\left(\frac{3}{44}\right)$$ $$e\left(\frac{15}{22}\right)$$