# Properties

 Modulus $916$ Structure $$C_{228}\times C_{2}$$ Order $456$

Show commands for: Pari/GP / SageMath

sage: H = DirichletGroup(916)

pari: g = idealstar(,916,2)

## Character group

 sage: G.order()  pari: g.no Order = 456 sage: H.invariants()  pari: g.cyc Structure = $$C_{228}\times C_{2}$$ sage: H.gens()  pari: g.gen Generators = $\chi_{916}(459,\cdot)$, $\chi_{916}(693,\cdot)$

## First 32 of 456 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 $$-1$$ $$1$$ $$3$$ $$5$$ $$7$$ $$9$$ $$11$$ $$13$$ $$15$$ $$17$$ $$19$$ $$21$$
$$\chi_{916}(1,\cdot)$$ 916.a 1 no $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{916}(3,\cdot)$$ 916.t 114 yes $$-1$$ $$1$$ $$e\left(\frac{29}{114}\right)$$ $$e\left(\frac{23}{57}\right)$$ $$e\left(\frac{13}{114}\right)$$ $$e\left(\frac{29}{57}\right)$$ $$e\left(\frac{11}{38}\right)$$ $$e\left(\frac{14}{19}\right)$$ $$e\left(\frac{25}{38}\right)$$ $$e\left(\frac{14}{19}\right)$$ $$e\left(\frac{49}{114}\right)$$ $$e\left(\frac{7}{19}\right)$$
$$\chi_{916}(5,\cdot)$$ 916.v 114 no $$1$$ $$1$$ $$e\left(\frac{23}{57}\right)$$ $$e\left(\frac{7}{57}\right)$$ $$e\left(\frac{113}{114}\right)$$ $$e\left(\frac{46}{57}\right)$$ $$e\left(\frac{12}{19}\right)$$ $$e\left(\frac{11}{38}\right)$$ $$e\left(\frac{10}{19}\right)$$ $$e\left(\frac{15}{19}\right)$$ $$e\left(\frac{31}{57}\right)$$ $$e\left(\frac{15}{38}\right)$$
$$\chi_{916}(7,\cdot)$$ 916.w 228 yes $$1$$ $$1$$ $$e\left(\frac{13}{114}\right)$$ $$e\left(\frac{113}{114}\right)$$ $$e\left(\frac{163}{228}\right)$$ $$e\left(\frac{13}{57}\right)$$ $$e\left(\frac{10}{19}\right)$$ $$e\left(\frac{69}{76}\right)$$ $$e\left(\frac{2}{19}\right)$$ $$e\left(\frac{3}{19}\right)$$ $$e\left(\frac{77}{114}\right)$$ $$e\left(\frac{63}{76}\right)$$
$$\chi_{916}(9,\cdot)$$ 916.q 57 no $$1$$ $$1$$ $$e\left(\frac{29}{57}\right)$$ $$e\left(\frac{46}{57}\right)$$ $$e\left(\frac{13}{57}\right)$$ $$e\left(\frac{1}{57}\right)$$ $$e\left(\frac{11}{19}\right)$$ $$e\left(\frac{9}{19}\right)$$ $$e\left(\frac{6}{19}\right)$$ $$e\left(\frac{9}{19}\right)$$ $$e\left(\frac{49}{57}\right)$$ $$e\left(\frac{14}{19}\right)$$
$$\chi_{916}(11,\cdot)$$ 916.o 38 yes $$-1$$ $$1$$ $$e\left(\frac{11}{38}\right)$$ $$e\left(\frac{12}{19}\right)$$ $$e\left(\frac{10}{19}\right)$$ $$e\left(\frac{11}{19}\right)$$ $$e\left(\frac{23}{38}\right)$$ $$e\left(\frac{5}{38}\right)$$ $$e\left(\frac{35}{38}\right)$$ $$e\left(\frac{12}{19}\right)$$ $$e\left(\frac{33}{38}\right)$$ $$e\left(\frac{31}{38}\right)$$
$$\chi_{916}(13,\cdot)$$ 916.r 76 no $$-1$$ $$1$$ $$e\left(\frac{14}{19}\right)$$ $$e\left(\frac{11}{38}\right)$$ $$e\left(\frac{69}{76}\right)$$ $$e\left(\frac{9}{19}\right)$$ $$e\left(\frac{5}{38}\right)$$ $$e\left(\frac{3}{76}\right)$$ $$e\left(\frac{1}{38}\right)$$ $$e\left(\frac{15}{19}\right)$$ $$e\left(\frac{4}{19}\right)$$ $$e\left(\frac{49}{76}\right)$$
$$\chi_{916}(15,\cdot)$$ 916.o 38 yes $$-1$$ $$1$$ $$e\left(\frac{25}{38}\right)$$ $$e\left(\frac{10}{19}\right)$$ $$e\left(\frac{2}{19}\right)$$ $$e\left(\frac{6}{19}\right)$$ $$e\left(\frac{35}{38}\right)$$ $$e\left(\frac{1}{38}\right)$$ $$e\left(\frac{7}{38}\right)$$ $$e\left(\frac{10}{19}\right)$$ $$e\left(\frac{37}{38}\right)$$ $$e\left(\frac{29}{38}\right)$$
$$\chi_{916}(17,\cdot)$$ 916.m 19 no $$1$$ $$1$$ $$e\left(\frac{14}{19}\right)$$ $$e\left(\frac{15}{19}\right)$$ $$e\left(\frac{3}{19}\right)$$ $$e\left(\frac{9}{19}\right)$$ $$e\left(\frac{12}{19}\right)$$ $$e\left(\frac{15}{19}\right)$$ $$e\left(\frac{10}{19}\right)$$ $$e\left(\frac{15}{19}\right)$$ $$e\left(\frac{4}{19}\right)$$ $$e\left(\frac{17}{19}\right)$$
$$\chi_{916}(19,\cdot)$$ 916.t 114 yes $$-1$$ $$1$$ $$e\left(\frac{49}{114}\right)$$ $$e\left(\frac{31}{57}\right)$$ $$e\left(\frac{77}{114}\right)$$ $$e\left(\frac{49}{57}\right)$$ $$e\left(\frac{33}{38}\right)$$ $$e\left(\frac{4}{19}\right)$$ $$e\left(\frac{37}{38}\right)$$ $$e\left(\frac{4}{19}\right)$$ $$e\left(\frac{71}{114}\right)$$ $$e\left(\frac{2}{19}\right)$$
$$\chi_{916}(21,\cdot)$$ 916.r 76 no $$-1$$ $$1$$ $$e\left(\frac{7}{19}\right)$$ $$e\left(\frac{15}{38}\right)$$ $$e\left(\frac{63}{76}\right)$$ $$e\left(\frac{14}{19}\right)$$ $$e\left(\frac{31}{38}\right)$$ $$e\left(\frac{49}{76}\right)$$ $$e\left(\frac{29}{38}\right)$$ $$e\left(\frac{17}{19}\right)$$ $$e\left(\frac{2}{19}\right)$$ $$e\left(\frac{15}{76}\right)$$
$$\chi_{916}(23,\cdot)$$ 916.w 228 yes $$1$$ $$1$$ $$e\left(\frac{107}{114}\right)$$ $$e\left(\frac{97}{114}\right)$$ $$e\left(\frac{149}{228}\right)$$ $$e\left(\frac{50}{57}\right)$$ $$e\left(\frac{18}{19}\right)$$ $$e\left(\frac{71}{76}\right)$$ $$e\left(\frac{15}{19}\right)$$ $$e\left(\frac{13}{19}\right)$$ $$e\left(\frac{55}{114}\right)$$ $$e\left(\frac{45}{76}\right)$$
$$\chi_{916}(25,\cdot)$$ 916.q 57 no $$1$$ $$1$$ $$e\left(\frac{46}{57}\right)$$ $$e\left(\frac{14}{57}\right)$$ $$e\left(\frac{56}{57}\right)$$ $$e\left(\frac{35}{57}\right)$$ $$e\left(\frac{5}{19}\right)$$ $$e\left(\frac{11}{19}\right)$$ $$e\left(\frac{1}{19}\right)$$ $$e\left(\frac{11}{19}\right)$$ $$e\left(\frac{5}{57}\right)$$ $$e\left(\frac{15}{19}\right)$$
$$\chi_{916}(27,\cdot)$$ 916.p 38 yes $$-1$$ $$1$$ $$e\left(\frac{29}{38}\right)$$ $$e\left(\frac{4}{19}\right)$$ $$e\left(\frac{13}{38}\right)$$ $$e\left(\frac{10}{19}\right)$$ $$e\left(\frac{33}{38}\right)$$ $$e\left(\frac{4}{19}\right)$$ $$e\left(\frac{37}{38}\right)$$ $$e\left(\frac{4}{19}\right)$$ $$e\left(\frac{11}{38}\right)$$ $$e\left(\frac{2}{19}\right)$$
$$\chi_{916}(29,\cdot)$$ 916.x 228 no $$-1$$ $$1$$ $$e\left(\frac{16}{57}\right)$$ $$e\left(\frac{37}{114}\right)$$ $$e\left(\frac{11}{228}\right)$$ $$e\left(\frac{32}{57}\right)$$ $$e\left(\frac{1}{38}\right)$$ $$e\left(\frac{31}{76}\right)$$ $$e\left(\frac{23}{38}\right)$$ $$e\left(\frac{3}{19}\right)$$ $$e\left(\frac{29}{57}\right)$$ $$e\left(\frac{25}{76}\right)$$
$$\chi_{916}(31,\cdot)$$ 916.w 228 yes $$1$$ $$1$$ $$e\left(\frac{109}{114}\right)$$ $$e\left(\frac{53}{114}\right)$$ $$e\left(\frac{25}{228}\right)$$ $$e\left(\frac{52}{57}\right)$$ $$e\left(\frac{2}{19}\right)$$ $$e\left(\frac{67}{76}\right)$$ $$e\left(\frac{8}{19}\right)$$ $$e\left(\frac{12}{19}\right)$$ $$e\left(\frac{23}{114}\right)$$ $$e\left(\frac{5}{76}\right)$$
$$\chi_{916}(33,\cdot)$$ 916.v 114 no $$1$$ $$1$$ $$e\left(\frac{31}{57}\right)$$ $$e\left(\frac{2}{57}\right)$$ $$e\left(\frac{73}{114}\right)$$ $$e\left(\frac{5}{57}\right)$$ $$e\left(\frac{17}{19}\right)$$ $$e\left(\frac{33}{38}\right)$$ $$e\left(\frac{11}{19}\right)$$ $$e\left(\frac{7}{19}\right)$$ $$e\left(\frac{17}{57}\right)$$ $$e\left(\frac{7}{38}\right)$$
$$\chi_{916}(35,\cdot)$$ 916.w 228 yes $$1$$ $$1$$ $$e\left(\frac{59}{114}\right)$$ $$e\left(\frac{13}{114}\right)$$ $$e\left(\frac{161}{228}\right)$$ $$e\left(\frac{2}{57}\right)$$ $$e\left(\frac{3}{19}\right)$$ $$e\left(\frac{15}{76}\right)$$ $$e\left(\frac{12}{19}\right)$$ $$e\left(\frac{18}{19}\right)$$ $$e\left(\frac{25}{114}\right)$$ $$e\left(\frac{17}{76}\right)$$
$$\chi_{916}(37,\cdot)$$ 916.q 57 no $$1$$ $$1$$ $$e\left(\frac{40}{57}\right)$$ $$e\left(\frac{32}{57}\right)$$ $$e\left(\frac{14}{57}\right)$$ $$e\left(\frac{23}{57}\right)$$ $$e\left(\frac{6}{19}\right)$$ $$e\left(\frac{17}{19}\right)$$ $$e\left(\frac{5}{19}\right)$$ $$e\left(\frac{17}{19}\right)$$ $$e\left(\frac{44}{57}\right)$$ $$e\left(\frac{18}{19}\right)$$
$$\chi_{916}(39,\cdot)$$ 916.w 228 yes $$1$$ $$1$$ $$e\left(\frac{113}{114}\right)$$ $$e\left(\frac{79}{114}\right)$$ $$e\left(\frac{5}{228}\right)$$ $$e\left(\frac{56}{57}\right)$$ $$e\left(\frac{8}{19}\right)$$ $$e\left(\frac{59}{76}\right)$$ $$e\left(\frac{13}{19}\right)$$ $$e\left(\frac{10}{19}\right)$$ $$e\left(\frac{73}{114}\right)$$ $$e\left(\frac{1}{76}\right)$$
$$\chi_{916}(41,\cdot)$$ 916.x 228 no $$-1$$ $$1$$ $$e\left(\frac{47}{57}\right)$$ $$e\left(\frac{41}{114}\right)$$ $$e\left(\frac{157}{228}\right)$$ $$e\left(\frac{37}{57}\right)$$ $$e\left(\frac{35}{38}\right)$$ $$e\left(\frac{21}{76}\right)$$ $$e\left(\frac{7}{38}\right)$$ $$e\left(\frac{10}{19}\right)$$ $$e\left(\frac{46}{57}\right)$$ $$e\left(\frac{39}{76}\right)$$
$$\chi_{916}(43,\cdot)$$ 916.p 38 yes $$-1$$ $$1$$ $$e\left(\frac{33}{38}\right)$$ $$e\left(\frac{17}{19}\right)$$ $$e\left(\frac{3}{38}\right)$$ $$e\left(\frac{14}{19}\right)$$ $$e\left(\frac{31}{38}\right)$$ $$e\left(\frac{17}{19}\right)$$ $$e\left(\frac{29}{38}\right)$$ $$e\left(\frac{17}{19}\right)$$ $$e\left(\frac{23}{38}\right)$$ $$e\left(\frac{18}{19}\right)$$
$$\chi_{916}(45,\cdot)$$ 916.v 114 no $$1$$ $$1$$ $$e\left(\frac{52}{57}\right)$$ $$e\left(\frac{53}{57}\right)$$ $$e\left(\frac{25}{114}\right)$$ $$e\left(\frac{47}{57}\right)$$ $$e\left(\frac{4}{19}\right)$$ $$e\left(\frac{29}{38}\right)$$ $$e\left(\frac{16}{19}\right)$$ $$e\left(\frac{5}{19}\right)$$ $$e\left(\frac{23}{57}\right)$$ $$e\left(\frac{5}{38}\right)$$
$$\chi_{916}(47,\cdot)$$ 916.w 228 yes $$1$$ $$1$$ $$e\left(\frac{1}{114}\right)$$ $$e\left(\frac{35}{114}\right)$$ $$e\left(\frac{223}{228}\right)$$ $$e\left(\frac{1}{57}\right)$$ $$e\left(\frac{11}{19}\right)$$ $$e\left(\frac{17}{76}\right)$$ $$e\left(\frac{6}{19}\right)$$ $$e\left(\frac{9}{19}\right)$$ $$e\left(\frac{41}{114}\right)$$ $$e\left(\frac{75}{76}\right)$$
$$\chi_{916}(49,\cdot)$$ 916.v 114 no $$1$$ $$1$$ $$e\left(\frac{13}{57}\right)$$ $$e\left(\frac{56}{57}\right)$$ $$e\left(\frac{49}{114}\right)$$ $$e\left(\frac{26}{57}\right)$$ $$e\left(\frac{1}{19}\right)$$ $$e\left(\frac{31}{38}\right)$$ $$e\left(\frac{4}{19}\right)$$ $$e\left(\frac{6}{19}\right)$$ $$e\left(\frac{20}{57}\right)$$ $$e\left(\frac{25}{38}\right)$$
$$\chi_{916}(51,\cdot)$$ 916.t 114 yes $$-1$$ $$1$$ $$e\left(\frac{113}{114}\right)$$ $$e\left(\frac{11}{57}\right)$$ $$e\left(\frac{31}{114}\right)$$ $$e\left(\frac{56}{57}\right)$$ $$e\left(\frac{35}{38}\right)$$ $$e\left(\frac{10}{19}\right)$$ $$e\left(\frac{7}{38}\right)$$ $$e\left(\frac{10}{19}\right)$$ $$e\left(\frac{73}{114}\right)$$ $$e\left(\frac{5}{19}\right)$$
$$\chi_{916}(53,\cdot)$$ 916.m 19 no $$1$$ $$1$$ $$e\left(\frac{8}{19}\right)$$ $$e\left(\frac{14}{19}\right)$$ $$e\left(\frac{18}{19}\right)$$ $$e\left(\frac{16}{19}\right)$$ $$e\left(\frac{15}{19}\right)$$ $$e\left(\frac{14}{19}\right)$$ $$e\left(\frac{3}{19}\right)$$ $$e\left(\frac{14}{19}\right)$$ $$e\left(\frac{5}{19}\right)$$ $$e\left(\frac{7}{19}\right)$$
$$\chi_{916}(55,\cdot)$$ 916.t 114 yes $$-1$$ $$1$$ $$e\left(\frac{79}{114}\right)$$ $$e\left(\frac{43}{57}\right)$$ $$e\left(\frac{59}{114}\right)$$ $$e\left(\frac{22}{57}\right)$$ $$e\left(\frac{9}{38}\right)$$ $$e\left(\frac{8}{19}\right)$$ $$e\left(\frac{17}{38}\right)$$ $$e\left(\frac{8}{19}\right)$$ $$e\left(\frac{47}{114}\right)$$ $$e\left(\frac{4}{19}\right)$$
$$\chi_{916}(57,\cdot)$$ 916.m 19 no $$1$$ $$1$$ $$e\left(\frac{13}{19}\right)$$ $$e\left(\frac{18}{19}\right)$$ $$e\left(\frac{15}{19}\right)$$ $$e\left(\frac{7}{19}\right)$$ $$e\left(\frac{3}{19}\right)$$ $$e\left(\frac{18}{19}\right)$$ $$e\left(\frac{12}{19}\right)$$ $$e\left(\frac{18}{19}\right)$$ $$e\left(\frac{1}{19}\right)$$ $$e\left(\frac{9}{19}\right)$$
$$\chi_{916}(59,\cdot)$$ 916.w 228 yes $$1$$ $$1$$ $$e\left(\frac{91}{114}\right)$$ $$e\left(\frac{107}{114}\right)$$ $$e\left(\frac{1}{228}\right)$$ $$e\left(\frac{34}{57}\right)$$ $$e\left(\frac{13}{19}\right)$$ $$e\left(\frac{27}{76}\right)$$ $$e\left(\frac{14}{19}\right)$$ $$e\left(\frac{2}{19}\right)$$ $$e\left(\frac{83}{114}\right)$$ $$e\left(\frac{61}{76}\right)$$
$$\chi_{916}(61,\cdot)$$ 916.m 19 no $$1$$ $$1$$ $$e\left(\frac{16}{19}\right)$$ $$e\left(\frac{9}{19}\right)$$ $$e\left(\frac{17}{19}\right)$$ $$e\left(\frac{13}{19}\right)$$ $$e\left(\frac{11}{19}\right)$$ $$e\left(\frac{9}{19}\right)$$ $$e\left(\frac{6}{19}\right)$$ $$e\left(\frac{9}{19}\right)$$ $$e\left(\frac{10}{19}\right)$$ $$e\left(\frac{14}{19}\right)$$
$$\chi_{916}(63,\cdot)$$ 916.w 228 yes $$1$$ $$1$$ $$e\left(\frac{71}{114}\right)$$ $$e\left(\frac{91}{114}\right)$$ $$e\left(\frac{215}{228}\right)$$ $$e\left(\frac{14}{57}\right)$$ $$e\left(\frac{2}{19}\right)$$ $$e\left(\frac{29}{76}\right)$$ $$e\left(\frac{8}{19}\right)$$ $$e\left(\frac{12}{19}\right)$$ $$e\left(\frac{61}{114}\right)$$ $$e\left(\frac{43}{76}\right)$$