# Properties

 Modulus $1469$ Structure $$C_{4}\times C_{336}$$ Order $1344$

Show commands: PariGP / SageMath

sage: H = DirichletGroup(1469)

pari: g = idealstar(,1469,2)

## Character group

 sage: G.order()  pari: g.no Order = 1344 sage: H.invariants()  pari: g.cyc Structure = $$C_{4}\times C_{336}$$ sage: H.gens()  pari: g.gen Generators = $\chi_{1469}(340,\cdot)$, $\chi_{1469}(794,\cdot)$

## First 32 of 1344 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 $$-1$$ $$1$$ $$2$$ $$3$$ $$4$$ $$5$$ $$6$$ $$7$$ $$8$$ $$9$$ $$10$$ $$11$$
$$\chi_{1469}(1,\cdot)$$ 1469.a 1 no $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{1469}(2,\cdot)$$ 1469.cf 84 yes $$-1$$ $$1$$ $$e\left(\frac{31}{84}\right)$$ $$e\left(\frac{37}{84}\right)$$ $$e\left(\frac{31}{42}\right)$$ $$e\left(\frac{9}{14}\right)$$ $$e\left(\frac{17}{21}\right)$$ $$e\left(\frac{65}{84}\right)$$ $$e\left(\frac{3}{28}\right)$$ $$e\left(\frac{37}{42}\right)$$ $$e\left(\frac{1}{84}\right)$$ $$e\left(\frac{43}{84}\right)$$
$$\chi_{1469}(3,\cdot)$$ 1469.cr 336 yes $$-1$$ $$1$$ $$e\left(\frac{37}{84}\right)$$ $$e\left(\frac{115}{336}\right)$$ $$e\left(\frac{37}{42}\right)$$ $$e\left(\frac{83}{112}\right)$$ $$e\left(\frac{263}{336}\right)$$ $$e\left(\frac{31}{42}\right)$$ $$e\left(\frac{9}{28}\right)$$ $$e\left(\frac{115}{168}\right)$$ $$e\left(\frac{61}{336}\right)$$ $$e\left(\frac{167}{168}\right)$$
$$\chi_{1469}(4,\cdot)$$ 1469.br 42 yes $$1$$ $$1$$ $$e\left(\frac{31}{42}\right)$$ $$e\left(\frac{37}{42}\right)$$ $$e\left(\frac{10}{21}\right)$$ $$e\left(\frac{2}{7}\right)$$ $$e\left(\frac{13}{21}\right)$$ $$e\left(\frac{23}{42}\right)$$ $$e\left(\frac{3}{14}\right)$$ $$e\left(\frac{16}{21}\right)$$ $$e\left(\frac{1}{42}\right)$$ $$e\left(\frac{1}{42}\right)$$
$$\chi_{1469}(5,\cdot)$$ 1469.cl 112 yes $$1$$ $$1$$ $$e\left(\frac{9}{14}\right)$$ $$e\left(\frac{83}{112}\right)$$ $$e\left(\frac{2}{7}\right)$$ $$e\left(\frac{29}{112}\right)$$ $$e\left(\frac{43}{112}\right)$$ $$e\left(\frac{5}{28}\right)$$ $$e\left(\frac{13}{14}\right)$$ $$e\left(\frac{27}{56}\right)$$ $$e\left(\frac{101}{112}\right)$$ $$e\left(\frac{5}{56}\right)$$
$$\chi_{1469}(6,\cdot)$$ 1469.ct 336 yes $$1$$ $$1$$ $$e\left(\frac{17}{21}\right)$$ $$e\left(\frac{263}{336}\right)$$ $$e\left(\frac{13}{21}\right)$$ $$e\left(\frac{43}{112}\right)$$ $$e\left(\frac{199}{336}\right)$$ $$e\left(\frac{43}{84}\right)$$ $$e\left(\frac{3}{7}\right)$$ $$e\left(\frac{95}{168}\right)$$ $$e\left(\frac{65}{336}\right)$$ $$e\left(\frac{85}{168}\right)$$
$$\chi_{1469}(7,\cdot)$$ 1469.cd 84 yes $$-1$$ $$1$$ $$e\left(\frac{65}{84}\right)$$ $$e\left(\frac{31}{42}\right)$$ $$e\left(\frac{23}{42}\right)$$ $$e\left(\frac{5}{28}\right)$$ $$e\left(\frac{43}{84}\right)$$ $$e\left(\frac{55}{84}\right)$$ $$e\left(\frac{9}{28}\right)$$ $$e\left(\frac{10}{21}\right)$$ $$e\left(\frac{20}{21}\right)$$ $$e\left(\frac{59}{84}\right)$$
$$\chi_{1469}(8,\cdot)$$ 1469.bo 28 yes $$-1$$ $$1$$ $$e\left(\frac{3}{28}\right)$$ $$e\left(\frac{9}{28}\right)$$ $$e\left(\frac{3}{14}\right)$$ $$e\left(\frac{13}{14}\right)$$ $$e\left(\frac{3}{7}\right)$$ $$e\left(\frac{9}{28}\right)$$ $$e\left(\frac{9}{28}\right)$$ $$e\left(\frac{9}{14}\right)$$ $$e\left(\frac{1}{28}\right)$$ $$e\left(\frac{15}{28}\right)$$
$$\chi_{1469}(9,\cdot)$$ 1469.cm 168 yes $$1$$ $$1$$ $$e\left(\frac{37}{42}\right)$$ $$e\left(\frac{115}{168}\right)$$ $$e\left(\frac{16}{21}\right)$$ $$e\left(\frac{27}{56}\right)$$ $$e\left(\frac{95}{168}\right)$$ $$e\left(\frac{10}{21}\right)$$ $$e\left(\frac{9}{14}\right)$$ $$e\left(\frac{31}{84}\right)$$ $$e\left(\frac{61}{168}\right)$$ $$e\left(\frac{83}{84}\right)$$
$$\chi_{1469}(10,\cdot)$$ 1469.cs 336 yes $$-1$$ $$1$$ $$e\left(\frac{1}{84}\right)$$ $$e\left(\frac{61}{336}\right)$$ $$e\left(\frac{1}{42}\right)$$ $$e\left(\frac{101}{112}\right)$$ $$e\left(\frac{65}{336}\right)$$ $$e\left(\frac{20}{21}\right)$$ $$e\left(\frac{1}{28}\right)$$ $$e\left(\frac{61}{168}\right)$$ $$e\left(\frac{307}{336}\right)$$ $$e\left(\frac{101}{168}\right)$$
$$\chi_{1469}(11,\cdot)$$ 1469.cn 168 yes $$-1$$ $$1$$ $$e\left(\frac{43}{84}\right)$$ $$e\left(\frac{167}{168}\right)$$ $$e\left(\frac{1}{42}\right)$$ $$e\left(\frac{5}{56}\right)$$ $$e\left(\frac{85}{168}\right)$$ $$e\left(\frac{59}{84}\right)$$ $$e\left(\frac{15}{28}\right)$$ $$e\left(\frac{83}{84}\right)$$ $$e\left(\frac{101}{168}\right)$$ $$e\left(\frac{41}{42}\right)$$
$$\chi_{1469}(12,\cdot)$$ 1469.cj 112 yes $$-1$$ $$1$$ $$e\left(\frac{5}{28}\right)$$ $$e\left(\frac{25}{112}\right)$$ $$e\left(\frac{5}{14}\right)$$ $$e\left(\frac{3}{112}\right)$$ $$e\left(\frac{45}{112}\right)$$ $$e\left(\frac{2}{7}\right)$$ $$e\left(\frac{15}{28}\right)$$ $$e\left(\frac{25}{56}\right)$$ $$e\left(\frac{23}{112}\right)$$ $$e\left(\frac{1}{56}\right)$$
$$\chi_{1469}(14,\cdot)$$ 1469.bl 28 no $$1$$ $$1$$ $$e\left(\frac{1}{7}\right)$$ $$e\left(\frac{5}{28}\right)$$ $$e\left(\frac{2}{7}\right)$$ $$e\left(\frac{23}{28}\right)$$ $$e\left(\frac{9}{28}\right)$$ $$e\left(\frac{3}{7}\right)$$ $$e\left(\frac{3}{7}\right)$$ $$e\left(\frac{5}{14}\right)$$ $$e\left(\frac{27}{28}\right)$$ $$e\left(\frac{3}{14}\right)$$
$$\chi_{1469}(15,\cdot)$$ 1469.w 12 yes $$-1$$ $$1$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$1$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$i$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{1}{12}\right)$$
$$\chi_{1469}(16,\cdot)$$ 1469.bg 21 yes $$1$$ $$1$$ $$e\left(\frac{10}{21}\right)$$ $$e\left(\frac{16}{21}\right)$$ $$e\left(\frac{20}{21}\right)$$ $$e\left(\frac{4}{7}\right)$$ $$e\left(\frac{5}{21}\right)$$ $$e\left(\frac{2}{21}\right)$$ $$e\left(\frac{3}{7}\right)$$ $$e\left(\frac{11}{21}\right)$$ $$e\left(\frac{1}{21}\right)$$ $$e\left(\frac{1}{21}\right)$$
$$\chi_{1469}(17,\cdot)$$ 1469.cs 336 yes $$-1$$ $$1$$ $$e\left(\frac{59}{84}\right)$$ $$e\left(\frac{239}{336}\right)$$ $$e\left(\frac{17}{42}\right)$$ $$e\left(\frac{23}{112}\right)$$ $$e\left(\frac{139}{336}\right)$$ $$e\left(\frac{4}{21}\right)$$ $$e\left(\frac{3}{28}\right)$$ $$e\left(\frac{71}{168}\right)$$ $$e\left(\frac{305}{336}\right)$$ $$e\left(\frac{79}{168}\right)$$
$$\chi_{1469}(18,\cdot)$$ 1469.q 8 yes $$-1$$ $$1$$ $$i$$ $$e\left(\frac{1}{8}\right)$$ $$-1$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$i$$ $$-i$$ $$i$$ $$e\left(\frac{3}{8}\right)$$ $$-1$$
$$\chi_{1469}(19,\cdot)$$ 1469.cq 336 yes $$1$$ $$1$$ $$e\left(\frac{1}{42}\right)$$ $$e\left(\frac{185}{336}\right)$$ $$e\left(\frac{1}{21}\right)$$ $$e\left(\frac{13}{112}\right)$$ $$e\left(\frac{193}{336}\right)$$ $$e\left(\frac{55}{84}\right)$$ $$e\left(\frac{1}{14}\right)$$ $$e\left(\frac{17}{168}\right)$$ $$e\left(\frac{47}{336}\right)$$ $$e\left(\frac{55}{168}\right)$$
$$\chi_{1469}(20,\cdot)$$ 1469.ct 336 yes $$1$$ $$1$$ $$e\left(\frac{8}{21}\right)$$ $$e\left(\frac{209}{336}\right)$$ $$e\left(\frac{16}{21}\right)$$ $$e\left(\frac{61}{112}\right)$$ $$e\left(\frac{1}{336}\right)$$ $$e\left(\frac{61}{84}\right)$$ $$e\left(\frac{1}{7}\right)$$ $$e\left(\frac{41}{168}\right)$$ $$e\left(\frac{311}{336}\right)$$ $$e\left(\frac{19}{168}\right)$$
$$\chi_{1469}(21,\cdot)$$ 1469.cl 112 yes $$1$$ $$1$$ $$e\left(\frac{3}{14}\right)$$ $$e\left(\frac{9}{112}\right)$$ $$e\left(\frac{3}{7}\right)$$ $$e\left(\frac{103}{112}\right)$$ $$e\left(\frac{33}{112}\right)$$ $$e\left(\frac{11}{28}\right)$$ $$e\left(\frac{9}{14}\right)$$ $$e\left(\frac{9}{56}\right)$$ $$e\left(\frac{15}{112}\right)$$ $$e\left(\frac{39}{56}\right)$$
$$\chi_{1469}(22,\cdot)$$ 1469.cm 168 yes $$1$$ $$1$$ $$e\left(\frac{37}{42}\right)$$ $$e\left(\frac{73}{168}\right)$$ $$e\left(\frac{16}{21}\right)$$ $$e\left(\frac{41}{56}\right)$$ $$e\left(\frac{53}{168}\right)$$ $$e\left(\frac{10}{21}\right)$$ $$e\left(\frac{9}{14}\right)$$ $$e\left(\frac{73}{84}\right)$$ $$e\left(\frac{103}{168}\right)$$ $$e\left(\frac{41}{84}\right)$$
$$\chi_{1469}(23,\cdot)$$ 1469.cs 336 yes $$-1$$ $$1$$ $$e\left(\frac{19}{84}\right)$$ $$e\left(\frac{235}{336}\right)$$ $$e\left(\frac{19}{42}\right)$$ $$e\left(\frac{99}{112}\right)$$ $$e\left(\frac{311}{336}\right)$$ $$e\left(\frac{2}{21}\right)$$ $$e\left(\frac{19}{28}\right)$$ $$e\left(\frac{67}{168}\right)$$ $$e\left(\frac{37}{336}\right)$$ $$e\left(\frac{155}{168}\right)$$
$$\chi_{1469}(24,\cdot)$$ 1469.cq 336 yes $$1$$ $$1$$ $$e\left(\frac{23}{42}\right)$$ $$e\left(\frac{223}{336}\right)$$ $$e\left(\frac{2}{21}\right)$$ $$e\left(\frac{75}{112}\right)$$ $$e\left(\frac{71}{336}\right)$$ $$e\left(\frac{5}{84}\right)$$ $$e\left(\frac{9}{14}\right)$$ $$e\left(\frac{55}{168}\right)$$ $$e\left(\frac{73}{336}\right)$$ $$e\left(\frac{89}{168}\right)$$
$$\chi_{1469}(25,\cdot)$$ 1469.by 56 yes $$1$$ $$1$$ $$e\left(\frac{2}{7}\right)$$ $$e\left(\frac{27}{56}\right)$$ $$e\left(\frac{4}{7}\right)$$ $$e\left(\frac{29}{56}\right)$$ $$e\left(\frac{43}{56}\right)$$ $$e\left(\frac{5}{14}\right)$$ $$e\left(\frac{6}{7}\right)$$ $$e\left(\frac{27}{28}\right)$$ $$e\left(\frac{45}{56}\right)$$ $$e\left(\frac{5}{28}\right)$$
$$\chi_{1469}(27,\cdot)$$ 1469.ck 112 no $$-1$$ $$1$$ $$e\left(\frac{9}{28}\right)$$ $$e\left(\frac{3}{112}\right)$$ $$e\left(\frac{9}{14}\right)$$ $$e\left(\frac{25}{112}\right)$$ $$e\left(\frac{39}{112}\right)$$ $$e\left(\frac{3}{14}\right)$$ $$e\left(\frac{27}{28}\right)$$ $$e\left(\frac{3}{56}\right)$$ $$e\left(\frac{61}{112}\right)$$ $$e\left(\frac{55}{56}\right)$$
$$\chi_{1469}(28,\cdot)$$ 1469.cg 84 yes $$-1$$ $$1$$ $$e\left(\frac{43}{84}\right)$$ $$e\left(\frac{13}{21}\right)$$ $$e\left(\frac{1}{42}\right)$$ $$e\left(\frac{13}{28}\right)$$ $$e\left(\frac{11}{84}\right)$$ $$e\left(\frac{17}{84}\right)$$ $$e\left(\frac{15}{28}\right)$$ $$e\left(\frac{5}{21}\right)$$ $$e\left(\frac{41}{42}\right)$$ $$e\left(\frac{61}{84}\right)$$
$$\chi_{1469}(29,\cdot)$$ 1469.cr 336 yes $$-1$$ $$1$$ $$e\left(\frac{73}{84}\right)$$ $$e\left(\frac{43}{336}\right)$$ $$e\left(\frac{31}{42}\right)$$ $$e\left(\frac{107}{112}\right)$$ $$e\left(\frac{335}{336}\right)$$ $$e\left(\frac{1}{42}\right)$$ $$e\left(\frac{17}{28}\right)$$ $$e\left(\frac{43}{168}\right)$$ $$e\left(\frac{277}{336}\right)$$ $$e\left(\frac{23}{168}\right)$$
$$\chi_{1469}(30,\cdot)$$ 1469.bs 42 yes $$1$$ $$1$$ $$e\left(\frac{19}{42}\right)$$ $$e\left(\frac{11}{21}\right)$$ $$e\left(\frac{19}{21}\right)$$ $$e\left(\frac{9}{14}\right)$$ $$e\left(\frac{41}{42}\right)$$ $$e\left(\frac{29}{42}\right)$$ $$e\left(\frac{5}{14}\right)$$ $$e\left(\frac{1}{21}\right)$$ $$e\left(\frac{2}{21}\right)$$ $$e\left(\frac{25}{42}\right)$$
$$\chi_{1469}(31,\cdot)$$ 1469.bz 56 yes $$-1$$ $$1$$ $$e\left(\frac{3}{28}\right)$$ $$e\left(\frac{25}{56}\right)$$ $$e\left(\frac{3}{14}\right)$$ $$e\left(\frac{45}{56}\right)$$ $$e\left(\frac{31}{56}\right)$$ $$e\left(\frac{23}{28}\right)$$ $$e\left(\frac{9}{28}\right)$$ $$e\left(\frac{25}{28}\right)$$ $$e\left(\frac{51}{56}\right)$$ $$e\left(\frac{2}{7}\right)$$
$$\chi_{1469}(32,\cdot)$$ 1469.cf 84 yes $$-1$$ $$1$$ $$e\left(\frac{71}{84}\right)$$ $$e\left(\frac{17}{84}\right)$$ $$e\left(\frac{29}{42}\right)$$ $$e\left(\frac{3}{14}\right)$$ $$e\left(\frac{1}{21}\right)$$ $$e\left(\frac{73}{84}\right)$$ $$e\left(\frac{15}{28}\right)$$ $$e\left(\frac{17}{42}\right)$$ $$e\left(\frac{5}{84}\right)$$ $$e\left(\frac{47}{84}\right)$$
$$\chi_{1469}(33,\cdot)$$ 1469.ct 336 yes $$1$$ $$1$$ $$e\left(\frac{20}{21}\right)$$ $$e\left(\frac{113}{336}\right)$$ $$e\left(\frac{19}{21}\right)$$ $$e\left(\frac{93}{112}\right)$$ $$e\left(\frac{97}{336}\right)$$ $$e\left(\frac{37}{84}\right)$$ $$e\left(\frac{6}{7}\right)$$ $$e\left(\frac{113}{168}\right)$$ $$e\left(\frac{263}{336}\right)$$ $$e\left(\frac{163}{168}\right)$$
$$\chi_{1469}(34,\cdot)$$ 1469.cl 112 yes $$1$$ $$1$$ $$e\left(\frac{1}{14}\right)$$ $$e\left(\frac{17}{112}\right)$$ $$e\left(\frac{1}{7}\right)$$ $$e\left(\frac{95}{112}\right)$$ $$e\left(\frac{25}{112}\right)$$ $$e\left(\frac{27}{28}\right)$$ $$e\left(\frac{3}{14}\right)$$ $$e\left(\frac{17}{56}\right)$$ $$e\left(\frac{103}{112}\right)$$ $$e\left(\frac{55}{56}\right)$$