# Properties

 Modulus $1169$ Structure $$C_{498}\times C_{2}$$ Order $996$

Show commands for: Pari/GP / SageMath

sage: from dirichlet_conrey import DirichletGroup_conrey # requires nonstandard Sage package to be installed

sage: H = DirichletGroup_conrey(1169)

pari: g = idealstar(,1169,2)

## Character group

 sage: G.order()  pari: g.no Order = 996 sage: H.invariants()  pari: g.cyc Structure = $$C_{498}\times C_{2}$$ sage: H.gens()  pari: g.gen Generators = $\chi_{1169}(5,\cdot)$, $\chi_{1169}(834,\cdot)$

## First 32 of 996 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 $$-1$$ $$1$$ $$2$$ $$3$$ $$4$$ $$5$$ $$6$$ $$8$$ $$9$$ $$10$$ $$11$$ $$12$$
$$\chi_{1169}(1,\cdot)$$ 1169.a 1 no $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{1169}(2,\cdot)$$ 1169.m 249 yes $$1$$ $$1$$ $$e\left(\frac{76}{249}\right)$$ $$e\left(\frac{245}{249}\right)$$ $$e\left(\frac{152}{249}\right)$$ $$e\left(\frac{226}{249}\right)$$ $$e\left(\frac{24}{83}\right)$$ $$e\left(\frac{76}{83}\right)$$ $$e\left(\frac{241}{249}\right)$$ $$e\left(\frac{53}{249}\right)$$ $$e\left(\frac{20}{249}\right)$$ $$e\left(\frac{148}{249}\right)$$
$$\chi_{1169}(3,\cdot)$$ 1169.n 498 yes $$-1$$ $$1$$ $$e\left(\frac{245}{249}\right)$$ $$e\left(\frac{197}{498}\right)$$ $$e\left(\frac{241}{249}\right)$$ $$e\left(\frac{199}{498}\right)$$ $$e\left(\frac{63}{166}\right)$$ $$e\left(\frac{79}{83}\right)$$ $$e\left(\frac{197}{249}\right)$$ $$e\left(\frac{191}{498}\right)$$ $$e\left(\frac{130}{249}\right)$$ $$e\left(\frac{181}{498}\right)$$
$$\chi_{1169}(4,\cdot)$$ 1169.m 249 yes $$1$$ $$1$$ $$e\left(\frac{152}{249}\right)$$ $$e\left(\frac{241}{249}\right)$$ $$e\left(\frac{55}{249}\right)$$ $$e\left(\frac{203}{249}\right)$$ $$e\left(\frac{48}{83}\right)$$ $$e\left(\frac{69}{83}\right)$$ $$e\left(\frac{233}{249}\right)$$ $$e\left(\frac{106}{249}\right)$$ $$e\left(\frac{40}{249}\right)$$ $$e\left(\frac{47}{249}\right)$$
$$\chi_{1169}(5,\cdot)$$ 1169.o 498 yes $$1$$ $$1$$ $$e\left(\frac{226}{249}\right)$$ $$e\left(\frac{199}{498}\right)$$ $$e\left(\frac{203}{249}\right)$$ $$e\left(\frac{43}{249}\right)$$ $$e\left(\frac{51}{166}\right)$$ $$e\left(\frac{60}{83}\right)$$ $$e\left(\frac{199}{249}\right)$$ $$e\left(\frac{20}{249}\right)$$ $$e\left(\frac{125}{249}\right)$$ $$e\left(\frac{107}{498}\right)$$
$$\chi_{1169}(6,\cdot)$$ 1169.l 166 yes $$-1$$ $$1$$ $$e\left(\frac{24}{83}\right)$$ $$e\left(\frac{63}{166}\right)$$ $$e\left(\frac{48}{83}\right)$$ $$e\left(\frac{51}{166}\right)$$ $$e\left(\frac{111}{166}\right)$$ $$e\left(\frac{72}{83}\right)$$ $$e\left(\frac{63}{83}\right)$$ $$e\left(\frac{99}{166}\right)$$ $$e\left(\frac{50}{83}\right)$$ $$e\left(\frac{159}{166}\right)$$
$$\chi_{1169}(8,\cdot)$$ 1169.i 83 no $$1$$ $$1$$ $$e\left(\frac{76}{83}\right)$$ $$e\left(\frac{79}{83}\right)$$ $$e\left(\frac{69}{83}\right)$$ $$e\left(\frac{60}{83}\right)$$ $$e\left(\frac{72}{83}\right)$$ $$e\left(\frac{62}{83}\right)$$ $$e\left(\frac{75}{83}\right)$$ $$e\left(\frac{53}{83}\right)$$ $$e\left(\frac{20}{83}\right)$$ $$e\left(\frac{65}{83}\right)$$
$$\chi_{1169}(9,\cdot)$$ 1169.m 249 yes $$1$$ $$1$$ $$e\left(\frac{241}{249}\right)$$ $$e\left(\frac{197}{249}\right)$$ $$e\left(\frac{233}{249}\right)$$ $$e\left(\frac{199}{249}\right)$$ $$e\left(\frac{63}{83}\right)$$ $$e\left(\frac{75}{83}\right)$$ $$e\left(\frac{145}{249}\right)$$ $$e\left(\frac{191}{249}\right)$$ $$e\left(\frac{11}{249}\right)$$ $$e\left(\frac{181}{249}\right)$$
$$\chi_{1169}(10,\cdot)$$ 1169.o 498 yes $$1$$ $$1$$ $$e\left(\frac{53}{249}\right)$$ $$e\left(\frac{191}{498}\right)$$ $$e\left(\frac{106}{249}\right)$$ $$e\left(\frac{20}{249}\right)$$ $$e\left(\frac{99}{166}\right)$$ $$e\left(\frac{53}{83}\right)$$ $$e\left(\frac{191}{249}\right)$$ $$e\left(\frac{73}{249}\right)$$ $$e\left(\frac{145}{249}\right)$$ $$e\left(\frac{403}{498}\right)$$
$$\chi_{1169}(11,\cdot)$$ 1169.m 249 yes $$1$$ $$1$$ $$e\left(\frac{20}{249}\right)$$ $$e\left(\frac{130}{249}\right)$$ $$e\left(\frac{40}{249}\right)$$ $$e\left(\frac{125}{249}\right)$$ $$e\left(\frac{50}{83}\right)$$ $$e\left(\frac{20}{83}\right)$$ $$e\left(\frac{11}{249}\right)$$ $$e\left(\frac{145}{249}\right)$$ $$e\left(\frac{97}{249}\right)$$ $$e\left(\frac{170}{249}\right)$$
$$\chi_{1169}(12,\cdot)$$ 1169.n 498 yes $$-1$$ $$1$$ $$e\left(\frac{148}{249}\right)$$ $$e\left(\frac{181}{498}\right)$$ $$e\left(\frac{47}{249}\right)$$ $$e\left(\frac{107}{498}\right)$$ $$e\left(\frac{159}{166}\right)$$ $$e\left(\frac{65}{83}\right)$$ $$e\left(\frac{181}{249}\right)$$ $$e\left(\frac{403}{498}\right)$$ $$e\left(\frac{170}{249}\right)$$ $$e\left(\frac{275}{498}\right)$$
$$\chi_{1169}(13,\cdot)$$ 1169.k 166 yes $$1$$ $$1$$ $$e\left(\frac{68}{83}\right)$$ $$e\left(\frac{137}{166}\right)$$ $$e\left(\frac{53}{83}\right)$$ $$e\left(\frac{10}{83}\right)$$ $$e\left(\frac{107}{166}\right)$$ $$e\left(\frac{38}{83}\right)$$ $$e\left(\frac{54}{83}\right)$$ $$e\left(\frac{78}{83}\right)$$ $$e\left(\frac{31}{83}\right)$$ $$e\left(\frac{77}{166}\right)$$
$$\chi_{1169}(15,\cdot)$$ 1169.j 166 no $$-1$$ $$1$$ $$e\left(\frac{74}{83}\right)$$ $$e\left(\frac{66}{83}\right)$$ $$e\left(\frac{65}{83}\right)$$ $$e\left(\frac{95}{166}\right)$$ $$e\left(\frac{57}{83}\right)$$ $$e\left(\frac{56}{83}\right)$$ $$e\left(\frac{49}{83}\right)$$ $$e\left(\frac{77}{166}\right)$$ $$e\left(\frac{2}{83}\right)$$ $$e\left(\frac{48}{83}\right)$$
$$\chi_{1169}(16,\cdot)$$ 1169.m 249 yes $$1$$ $$1$$ $$e\left(\frac{55}{249}\right)$$ $$e\left(\frac{233}{249}\right)$$ $$e\left(\frac{110}{249}\right)$$ $$e\left(\frac{157}{249}\right)$$ $$e\left(\frac{13}{83}\right)$$ $$e\left(\frac{55}{83}\right)$$ $$e\left(\frac{217}{249}\right)$$ $$e\left(\frac{212}{249}\right)$$ $$e\left(\frac{80}{249}\right)$$ $$e\left(\frac{94}{249}\right)$$
$$\chi_{1169}(17,\cdot)$$ 1169.o 498 yes $$1$$ $$1$$ $$e\left(\frac{26}{249}\right)$$ $$e\left(\frac{89}{498}\right)$$ $$e\left(\frac{52}{249}\right)$$ $$e\left(\frac{38}{249}\right)$$ $$e\left(\frac{47}{166}\right)$$ $$e\left(\frac{26}{83}\right)$$ $$e\left(\frac{89}{249}\right)$$ $$e\left(\frac{64}{249}\right)$$ $$e\left(\frac{151}{249}\right)$$ $$e\left(\frac{193}{498}\right)$$
$$\chi_{1169}(18,\cdot)$$ 1169.m 249 yes $$1$$ $$1$$ $$e\left(\frac{68}{249}\right)$$ $$e\left(\frac{193}{249}\right)$$ $$e\left(\frac{136}{249}\right)$$ $$e\left(\frac{176}{249}\right)$$ $$e\left(\frac{4}{83}\right)$$ $$e\left(\frac{68}{83}\right)$$ $$e\left(\frac{137}{249}\right)$$ $$e\left(\frac{244}{249}\right)$$ $$e\left(\frac{31}{249}\right)$$ $$e\left(\frac{80}{249}\right)$$
$$\chi_{1169}(19,\cdot)$$ 1169.n 498 yes $$-1$$ $$1$$ $$e\left(\frac{160}{249}\right)$$ $$e\left(\frac{337}{498}\right)$$ $$e\left(\frac{71}{249}\right)$$ $$e\left(\frac{257}{498}\right)$$ $$e\left(\frac{53}{166}\right)$$ $$e\left(\frac{77}{83}\right)$$ $$e\left(\frac{88}{249}\right)$$ $$e\left(\frac{79}{498}\right)$$ $$e\left(\frac{29}{249}\right)$$ $$e\left(\frac{479}{498}\right)$$
$$\chi_{1169}(20,\cdot)$$ 1169.k 166 yes $$1$$ $$1$$ $$e\left(\frac{43}{83}\right)$$ $$e\left(\frac{61}{166}\right)$$ $$e\left(\frac{3}{83}\right)$$ $$e\left(\frac{82}{83}\right)$$ $$e\left(\frac{147}{166}\right)$$ $$e\left(\frac{46}{83}\right)$$ $$e\left(\frac{61}{83}\right)$$ $$e\left(\frac{42}{83}\right)$$ $$e\left(\frac{55}{83}\right)$$ $$e\left(\frac{67}{166}\right)$$
$$\chi_{1169}(22,\cdot)$$ 1169.i 83 no $$1$$ $$1$$ $$e\left(\frac{32}{83}\right)$$ $$e\left(\frac{42}{83}\right)$$ $$e\left(\frac{64}{83}\right)$$ $$e\left(\frac{34}{83}\right)$$ $$e\left(\frac{74}{83}\right)$$ $$e\left(\frac{13}{83}\right)$$ $$e\left(\frac{1}{83}\right)$$ $$e\left(\frac{66}{83}\right)$$ $$e\left(\frac{39}{83}\right)$$ $$e\left(\frac{23}{83}\right)$$
$$\chi_{1169}(23,\cdot)$$ 1169.p 498 yes $$-1$$ $$1$$ $$e\left(\frac{130}{249}\right)$$ $$e\left(\frac{98}{249}\right)$$ $$e\left(\frac{11}{249}\right)$$ $$e\left(\frac{131}{498}\right)$$ $$e\left(\frac{76}{83}\right)$$ $$e\left(\frac{47}{83}\right)$$ $$e\left(\frac{196}{249}\right)$$ $$e\left(\frac{391}{498}\right)$$ $$e\left(\frac{8}{249}\right)$$ $$e\left(\frac{109}{249}\right)$$
$$\chi_{1169}(24,\cdot)$$ 1169.n 498 yes $$-1$$ $$1$$ $$e\left(\frac{224}{249}\right)$$ $$e\left(\frac{173}{498}\right)$$ $$e\left(\frac{199}{249}\right)$$ $$e\left(\frac{61}{498}\right)$$ $$e\left(\frac{41}{166}\right)$$ $$e\left(\frac{58}{83}\right)$$ $$e\left(\frac{173}{249}\right)$$ $$e\left(\frac{11}{498}\right)$$ $$e\left(\frac{190}{249}\right)$$ $$e\left(\frac{73}{498}\right)$$
$$\chi_{1169}(25,\cdot)$$ 1169.m 249 yes $$1$$ $$1$$ $$e\left(\frac{203}{249}\right)$$ $$e\left(\frac{199}{249}\right)$$ $$e\left(\frac{157}{249}\right)$$ $$e\left(\frac{86}{249}\right)$$ $$e\left(\frac{51}{83}\right)$$ $$e\left(\frac{37}{83}\right)$$ $$e\left(\frac{149}{249}\right)$$ $$e\left(\frac{40}{249}\right)$$ $$e\left(\frac{1}{249}\right)$$ $$e\left(\frac{107}{249}\right)$$
$$\chi_{1169}(26,\cdot)$$ 1169.o 498 yes $$1$$ $$1$$ $$e\left(\frac{31}{249}\right)$$ $$e\left(\frac{403}{498}\right)$$ $$e\left(\frac{62}{249}\right)$$ $$e\left(\frac{7}{249}\right)$$ $$e\left(\frac{155}{166}\right)$$ $$e\left(\frac{31}{83}\right)$$ $$e\left(\frac{154}{249}\right)$$ $$e\left(\frac{38}{249}\right)$$ $$e\left(\frac{113}{249}\right)$$ $$e\left(\frac{29}{498}\right)$$
$$\chi_{1169}(27,\cdot)$$ 1169.l 166 yes $$-1$$ $$1$$ $$e\left(\frac{79}{83}\right)$$ $$e\left(\frac{31}{166}\right)$$ $$e\left(\frac{75}{83}\right)$$ $$e\left(\frac{33}{166}\right)$$ $$e\left(\frac{23}{166}\right)$$ $$e\left(\frac{71}{83}\right)$$ $$e\left(\frac{31}{83}\right)$$ $$e\left(\frac{25}{166}\right)$$ $$e\left(\frac{47}{83}\right)$$ $$e\left(\frac{15}{166}\right)$$
$$\chi_{1169}(29,\cdot)$$ 1169.i 83 no $$1$$ $$1$$ $$e\left(\frac{12}{83}\right)$$ $$e\left(\frac{78}{83}\right)$$ $$e\left(\frac{24}{83}\right)$$ $$e\left(\frac{75}{83}\right)$$ $$e\left(\frac{7}{83}\right)$$ $$e\left(\frac{36}{83}\right)$$ $$e\left(\frac{73}{83}\right)$$ $$e\left(\frac{4}{83}\right)$$ $$e\left(\frac{25}{83}\right)$$ $$e\left(\frac{19}{83}\right)$$
$$\chi_{1169}(30,\cdot)$$ 1169.p 498 yes $$-1$$ $$1$$ $$e\left(\frac{49}{249}\right)$$ $$e\left(\frac{194}{249}\right)$$ $$e\left(\frac{98}{249}\right)$$ $$e\left(\frac{239}{498}\right)$$ $$e\left(\frac{81}{83}\right)$$ $$e\left(\frac{49}{83}\right)$$ $$e\left(\frac{139}{249}\right)$$ $$e\left(\frac{337}{498}\right)$$ $$e\left(\frac{26}{249}\right)$$ $$e\left(\frac{43}{249}\right)$$
$$\chi_{1169}(31,\cdot)$$ 1169.n 498 yes $$-1$$ $$1$$ $$e\left(\frac{5}{249}\right)$$ $$e\left(\frac{65}{498}\right)$$ $$e\left(\frac{10}{249}\right)$$ $$e\left(\frac{187}{498}\right)$$ $$e\left(\frac{25}{166}\right)$$ $$e\left(\frac{5}{83}\right)$$ $$e\left(\frac{65}{249}\right)$$ $$e\left(\frac{197}{498}\right)$$ $$e\left(\frac{211}{249}\right)$$ $$e\left(\frac{85}{498}\right)$$
$$\chi_{1169}(32,\cdot)$$ 1169.m 249 yes $$1$$ $$1$$ $$e\left(\frac{131}{249}\right)$$ $$e\left(\frac{229}{249}\right)$$ $$e\left(\frac{13}{249}\right)$$ $$e\left(\frac{134}{249}\right)$$ $$e\left(\frac{37}{83}\right)$$ $$e\left(\frac{48}{83}\right)$$ $$e\left(\frac{209}{249}\right)$$ $$e\left(\frac{16}{249}\right)$$ $$e\left(\frac{100}{249}\right)$$ $$e\left(\frac{242}{249}\right)$$
$$\chi_{1169}(33,\cdot)$$ 1169.n 498 yes $$-1$$ $$1$$ $$e\left(\frac{16}{249}\right)$$ $$e\left(\frac{457}{498}\right)$$ $$e\left(\frac{32}{249}\right)$$ $$e\left(\frac{449}{498}\right)$$ $$e\left(\frac{163}{166}\right)$$ $$e\left(\frac{16}{83}\right)$$ $$e\left(\frac{208}{249}\right)$$ $$e\left(\frac{481}{498}\right)$$ $$e\left(\frac{227}{249}\right)$$ $$e\left(\frac{23}{498}\right)$$
$$\chi_{1169}(34,\cdot)$$ 1169.k 166 yes $$1$$ $$1$$ $$e\left(\frac{34}{83}\right)$$ $$e\left(\frac{27}{166}\right)$$ $$e\left(\frac{68}{83}\right)$$ $$e\left(\frac{5}{83}\right)$$ $$e\left(\frac{95}{166}\right)$$ $$e\left(\frac{19}{83}\right)$$ $$e\left(\frac{27}{83}\right)$$ $$e\left(\frac{39}{83}\right)$$ $$e\left(\frac{57}{83}\right)$$ $$e\left(\frac{163}{166}\right)$$
$$\chi_{1169}(36,\cdot)$$ 1169.i 83 no $$1$$ $$1$$ $$e\left(\frac{48}{83}\right)$$ $$e\left(\frac{63}{83}\right)$$ $$e\left(\frac{13}{83}\right)$$ $$e\left(\frac{51}{83}\right)$$ $$e\left(\frac{28}{83}\right)$$ $$e\left(\frac{61}{83}\right)$$ $$e\left(\frac{43}{83}\right)$$ $$e\left(\frac{16}{83}\right)$$ $$e\left(\frac{17}{83}\right)$$ $$e\left(\frac{76}{83}\right)$$
$$\chi_{1169}(37,\cdot)$$ 1169.p 498 yes $$-1$$ $$1$$ $$e\left(\frac{91}{249}\right)$$ $$e\left(\frac{218}{249}\right)$$ $$e\left(\frac{182}{249}\right)$$ $$e\left(\frac{17}{498}\right)$$ $$e\left(\frac{20}{83}\right)$$ $$e\left(\frac{8}{83}\right)$$ $$e\left(\frac{187}{249}\right)$$ $$e\left(\frac{199}{498}\right)$$ $$e\left(\frac{155}{249}\right)$$ $$e\left(\frac{151}{249}\right)$$