# Properties

 Modulus $469$ Structure $$C_{66}\times C_{6}$$ Order $396$

Show commands for: Pari/GP / SageMath

sage: H = DirichletGroup(469)

pari: g = idealstar(,469,2)

## Character group

 sage: G.order()  pari: g.no Order = 396 sage: H.invariants()  pari: g.cyc Structure = $$C_{66}\times C_{6}$$ sage: H.gens()  pari: g.gen Generators = $\chi_{469}(269,\cdot)$, $\chi_{469}(337,\cdot)$

## First 32 of 396 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 $$-1$$ $$1$$ $$2$$ $$3$$ $$4$$ $$5$$ $$6$$ $$8$$ $$9$$ $$10$$ $$11$$ $$12$$
$$\chi_{469}(1,\cdot)$$ 469.a 1 no $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{469}(2,\cdot)$$ 469.bm 66 yes $$-1$$ $$1$$ $$e\left(\frac{15}{22}\right)$$ $$e\left(\frac{61}{66}\right)$$ $$e\left(\frac{4}{11}\right)$$ $$e\left(\frac{59}{66}\right)$$ $$e\left(\frac{20}{33}\right)$$ $$e\left(\frac{1}{22}\right)$$ $$e\left(\frac{28}{33}\right)$$ $$e\left(\frac{19}{33}\right)$$ $$e\left(\frac{5}{22}\right)$$ $$e\left(\frac{19}{66}\right)$$
$$\chi_{469}(3,\cdot)$$ 469.bh 66 yes $$1$$ $$1$$ $$e\left(\frac{61}{66}\right)$$ $$e\left(\frac{7}{33}\right)$$ $$e\left(\frac{28}{33}\right)$$ $$e\left(\frac{23}{33}\right)$$ $$e\left(\frac{3}{22}\right)$$ $$e\left(\frac{17}{22}\right)$$ $$e\left(\frac{14}{33}\right)$$ $$e\left(\frac{41}{66}\right)$$ $$e\left(\frac{35}{66}\right)$$ $$e\left(\frac{2}{33}\right)$$
$$\chi_{469}(4,\cdot)$$ 469.y 33 yes $$1$$ $$1$$ $$e\left(\frac{4}{11}\right)$$ $$e\left(\frac{28}{33}\right)$$ $$e\left(\frac{8}{11}\right)$$ $$e\left(\frac{26}{33}\right)$$ $$e\left(\frac{7}{33}\right)$$ $$e\left(\frac{1}{11}\right)$$ $$e\left(\frac{23}{33}\right)$$ $$e\left(\frac{5}{33}\right)$$ $$e\left(\frac{5}{11}\right)$$ $$e\left(\frac{19}{33}\right)$$
$$\chi_{469}(5,\cdot)$$ 469.bh 66 yes $$1$$ $$1$$ $$e\left(\frac{59}{66}\right)$$ $$e\left(\frac{23}{33}\right)$$ $$e\left(\frac{26}{33}\right)$$ $$e\left(\frac{19}{33}\right)$$ $$e\left(\frac{13}{22}\right)$$ $$e\left(\frac{15}{22}\right)$$ $$e\left(\frac{13}{33}\right)$$ $$e\left(\frac{31}{66}\right)$$ $$e\left(\frac{49}{66}\right)$$ $$e\left(\frac{16}{33}\right)$$
$$\chi_{469}(6,\cdot)$$ 469.bl 66 yes $$-1$$ $$1$$ $$e\left(\frac{20}{33}\right)$$ $$e\left(\frac{3}{22}\right)$$ $$e\left(\frac{7}{33}\right)$$ $$e\left(\frac{13}{22}\right)$$ $$e\left(\frac{49}{66}\right)$$ $$e\left(\frac{9}{11}\right)$$ $$e\left(\frac{3}{11}\right)$$ $$e\left(\frac{13}{66}\right)$$ $$e\left(\frac{25}{33}\right)$$ $$e\left(\frac{23}{66}\right)$$
$$\chi_{469}(8,\cdot)$$ 469.x 22 no $$-1$$ $$1$$ $$e\left(\frac{1}{22}\right)$$ $$e\left(\frac{17}{22}\right)$$ $$e\left(\frac{1}{11}\right)$$ $$e\left(\frac{15}{22}\right)$$ $$e\left(\frac{9}{11}\right)$$ $$e\left(\frac{3}{22}\right)$$ $$e\left(\frac{6}{11}\right)$$ $$e\left(\frac{8}{11}\right)$$ $$e\left(\frac{15}{22}\right)$$ $$e\left(\frac{19}{22}\right)$$
$$\chi_{469}(9,\cdot)$$ 469.ba 33 yes $$1$$ $$1$$ $$e\left(\frac{28}{33}\right)$$ $$e\left(\frac{14}{33}\right)$$ $$e\left(\frac{23}{33}\right)$$ $$e\left(\frac{13}{33}\right)$$ $$e\left(\frac{3}{11}\right)$$ $$e\left(\frac{6}{11}\right)$$ $$e\left(\frac{28}{33}\right)$$ $$e\left(\frac{8}{33}\right)$$ $$e\left(\frac{2}{33}\right)$$ $$e\left(\frac{4}{33}\right)$$
$$\chi_{469}(10,\cdot)$$ 469.bj 66 yes $$-1$$ $$1$$ $$e\left(\frac{19}{33}\right)$$ $$e\left(\frac{41}{66}\right)$$ $$e\left(\frac{5}{33}\right)$$ $$e\left(\frac{31}{66}\right)$$ $$e\left(\frac{13}{66}\right)$$ $$e\left(\frac{8}{11}\right)$$ $$e\left(\frac{8}{33}\right)$$ $$e\left(\frac{1}{22}\right)$$ $$e\left(\frac{32}{33}\right)$$ $$e\left(\frac{17}{22}\right)$$
$$\chi_{469}(11,\cdot)$$ 469.bm 66 yes $$-1$$ $$1$$ $$e\left(\frac{5}{22}\right)$$ $$e\left(\frac{35}{66}\right)$$ $$e\left(\frac{5}{11}\right)$$ $$e\left(\frac{49}{66}\right)$$ $$e\left(\frac{25}{33}\right)$$ $$e\left(\frac{15}{22}\right)$$ $$e\left(\frac{2}{33}\right)$$ $$e\left(\frac{32}{33}\right)$$ $$e\left(\frac{9}{22}\right)$$ $$e\left(\frac{65}{66}\right)$$
$$\chi_{469}(12,\cdot)$$ 469.bg 66 yes $$1$$ $$1$$ $$e\left(\frac{19}{66}\right)$$ $$e\left(\frac{2}{33}\right)$$ $$e\left(\frac{19}{33}\right)$$ $$e\left(\frac{16}{33}\right)$$ $$e\left(\frac{23}{66}\right)$$ $$e\left(\frac{19}{22}\right)$$ $$e\left(\frac{4}{33}\right)$$ $$e\left(\frac{17}{22}\right)$$ $$e\left(\frac{65}{66}\right)$$ $$e\left(\frac{7}{11}\right)$$
$$\chi_{469}(13,\cdot)$$ 469.bd 66 yes $$1$$ $$1$$ $$e\left(\frac{19}{66}\right)$$ $$e\left(\frac{8}{11}\right)$$ $$e\left(\frac{19}{33}\right)$$ $$e\left(\frac{9}{11}\right)$$ $$e\left(\frac{1}{66}\right)$$ $$e\left(\frac{19}{22}\right)$$ $$e\left(\frac{5}{11}\right)$$ $$e\left(\frac{7}{66}\right)$$ $$e\left(\frac{65}{66}\right)$$ $$e\left(\frac{10}{33}\right)$$
$$\chi_{469}(15,\cdot)$$ 469.u 11 no $$1$$ $$1$$ $$e\left(\frac{9}{11}\right)$$ $$e\left(\frac{10}{11}\right)$$ $$e\left(\frac{7}{11}\right)$$ $$e\left(\frac{3}{11}\right)$$ $$e\left(\frac{8}{11}\right)$$ $$e\left(\frac{5}{11}\right)$$ $$e\left(\frac{9}{11}\right)$$ $$e\left(\frac{1}{11}\right)$$ $$e\left(\frac{3}{11}\right)$$ $$e\left(\frac{6}{11}\right)$$
$$\chi_{469}(16,\cdot)$$ 469.y 33 yes $$1$$ $$1$$ $$e\left(\frac{8}{11}\right)$$ $$e\left(\frac{23}{33}\right)$$ $$e\left(\frac{5}{11}\right)$$ $$e\left(\frac{19}{33}\right)$$ $$e\left(\frac{14}{33}\right)$$ $$e\left(\frac{2}{11}\right)$$ $$e\left(\frac{13}{33}\right)$$ $$e\left(\frac{10}{33}\right)$$ $$e\left(\frac{10}{11}\right)$$ $$e\left(\frac{5}{33}\right)$$
$$\chi_{469}(17,\cdot)$$ 469.bj 66 yes $$-1$$ $$1$$ $$e\left(\frac{10}{33}\right)$$ $$e\left(\frac{65}{66}\right)$$ $$e\left(\frac{20}{33}\right)$$ $$e\left(\frac{25}{66}\right)$$ $$e\left(\frac{19}{66}\right)$$ $$e\left(\frac{10}{11}\right)$$ $$e\left(\frac{32}{33}\right)$$ $$e\left(\frac{15}{22}\right)$$ $$e\left(\frac{29}{33}\right)$$ $$e\left(\frac{13}{22}\right)$$
$$\chi_{469}(18,\cdot)$$ 469.bf 66 yes $$-1$$ $$1$$ $$e\left(\frac{35}{66}\right)$$ $$e\left(\frac{23}{66}\right)$$ $$e\left(\frac{2}{33}\right)$$ $$e\left(\frac{19}{66}\right)$$ $$e\left(\frac{29}{33}\right)$$ $$e\left(\frac{13}{22}\right)$$ $$e\left(\frac{23}{33}\right)$$ $$e\left(\frac{9}{11}\right)$$ $$e\left(\frac{19}{66}\right)$$ $$e\left(\frac{9}{22}\right)$$
$$\chi_{469}(19,\cdot)$$ 469.bc 66 yes $$-1$$ $$1$$ $$e\left(\frac{9}{11}\right)$$ $$e\left(\frac{49}{66}\right)$$ $$e\left(\frac{7}{11}\right)$$ $$e\left(\frac{29}{66}\right)$$ $$e\left(\frac{37}{66}\right)$$ $$e\left(\frac{5}{11}\right)$$ $$e\left(\frac{16}{33}\right)$$ $$e\left(\frac{17}{66}\right)$$ $$e\left(\frac{3}{11}\right)$$ $$e\left(\frac{25}{66}\right)$$
$$\chi_{469}(20,\cdot)$$ 469.bd 66 yes $$1$$ $$1$$ $$e\left(\frac{17}{66}\right)$$ $$e\left(\frac{6}{11}\right)$$ $$e\left(\frac{17}{33}\right)$$ $$e\left(\frac{4}{11}\right)$$ $$e\left(\frac{53}{66}\right)$$ $$e\left(\frac{17}{22}\right)$$ $$e\left(\frac{1}{11}\right)$$ $$e\left(\frac{41}{66}\right)$$ $$e\left(\frac{13}{66}\right)$$ $$e\left(\frac{2}{33}\right)$$
$$\chi_{469}(22,\cdot)$$ 469.u 11 no $$1$$ $$1$$ $$e\left(\frac{10}{11}\right)$$ $$e\left(\frac{5}{11}\right)$$ $$e\left(\frac{9}{11}\right)$$ $$e\left(\frac{7}{11}\right)$$ $$e\left(\frac{4}{11}\right)$$ $$e\left(\frac{8}{11}\right)$$ $$e\left(\frac{10}{11}\right)$$ $$e\left(\frac{6}{11}\right)$$ $$e\left(\frac{7}{11}\right)$$ $$e\left(\frac{3}{11}\right)$$
$$\chi_{469}(23,\cdot)$$ 469.y 33 yes $$1$$ $$1$$ $$e\left(\frac{1}{11}\right)$$ $$e\left(\frac{29}{33}\right)$$ $$e\left(\frac{2}{11}\right)$$ $$e\left(\frac{1}{33}\right)$$ $$e\left(\frac{32}{33}\right)$$ $$e\left(\frac{3}{11}\right)$$ $$e\left(\frac{25}{33}\right)$$ $$e\left(\frac{4}{33}\right)$$ $$e\left(\frac{4}{11}\right)$$ $$e\left(\frac{2}{33}\right)$$
$$\chi_{469}(24,\cdot)$$ 469.bk 66 yes $$-1$$ $$1$$ $$e\left(\frac{32}{33}\right)$$ $$e\left(\frac{65}{66}\right)$$ $$e\left(\frac{31}{33}\right)$$ $$e\left(\frac{25}{66}\right)$$ $$e\left(\frac{21}{22}\right)$$ $$e\left(\frac{10}{11}\right)$$ $$e\left(\frac{32}{33}\right)$$ $$e\left(\frac{23}{66}\right)$$ $$e\left(\frac{7}{33}\right)$$ $$e\left(\frac{61}{66}\right)$$
$$\chi_{469}(25,\cdot)$$ 469.ba 33 yes $$1$$ $$1$$ $$e\left(\frac{26}{33}\right)$$ $$e\left(\frac{13}{33}\right)$$ $$e\left(\frac{19}{33}\right)$$ $$e\left(\frac{5}{33}\right)$$ $$e\left(\frac{2}{11}\right)$$ $$e\left(\frac{4}{11}\right)$$ $$e\left(\frac{26}{33}\right)$$ $$e\left(\frac{31}{33}\right)$$ $$e\left(\frac{16}{33}\right)$$ $$e\left(\frac{32}{33}\right)$$
$$\chi_{469}(26,\cdot)$$ 469.bj 66 yes $$-1$$ $$1$$ $$e\left(\frac{32}{33}\right)$$ $$e\left(\frac{43}{66}\right)$$ $$e\left(\frac{31}{33}\right)$$ $$e\left(\frac{47}{66}\right)$$ $$e\left(\frac{41}{66}\right)$$ $$e\left(\frac{10}{11}\right)$$ $$e\left(\frac{10}{33}\right)$$ $$e\left(\frac{15}{22}\right)$$ $$e\left(\frac{7}{33}\right)$$ $$e\left(\frac{13}{22}\right)$$
$$\chi_{469}(27,\cdot)$$ 469.w 22 yes $$1$$ $$1$$ $$e\left(\frac{17}{22}\right)$$ $$e\left(\frac{7}{11}\right)$$ $$e\left(\frac{6}{11}\right)$$ $$e\left(\frac{1}{11}\right)$$ $$e\left(\frac{9}{22}\right)$$ $$e\left(\frac{7}{22}\right)$$ $$e\left(\frac{3}{11}\right)$$ $$e\left(\frac{19}{22}\right)$$ $$e\left(\frac{13}{22}\right)$$ $$e\left(\frac{2}{11}\right)$$
$$\chi_{469}(29,\cdot)$$ 469.g 3 no $$1$$ $$1$$ $$e\left(\frac{2}{3}\right)$$ $$1$$ $$e\left(\frac{1}{3}\right)$$ $$1$$ $$e\left(\frac{2}{3}\right)$$ $$1$$ $$1$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{3}\right)$$
$$\chi_{469}(30,\cdot)$$ 469.j 6 yes $$-1$$ $$1$$ $$-1$$ $$e\left(\frac{5}{6}\right)$$ $$1$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$-1$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$-1$$ $$e\left(\frac{5}{6}\right)$$
$$\chi_{469}(31,\cdot)$$ 469.bn 66 yes $$1$$ $$1$$ $$e\left(\frac{1}{22}\right)$$ $$e\left(\frac{31}{33}\right)$$ $$e\left(\frac{1}{11}\right)$$ $$e\left(\frac{17}{33}\right)$$ $$e\left(\frac{65}{66}\right)$$ $$e\left(\frac{3}{22}\right)$$ $$e\left(\frac{29}{33}\right)$$ $$e\left(\frac{37}{66}\right)$$ $$e\left(\frac{15}{22}\right)$$ $$e\left(\frac{1}{33}\right)$$
$$\chi_{469}(32,\cdot)$$ 469.bm 66 yes $$-1$$ $$1$$ $$e\left(\frac{9}{22}\right)$$ $$e\left(\frac{41}{66}\right)$$ $$e\left(\frac{9}{11}\right)$$ $$e\left(\frac{31}{66}\right)$$ $$e\left(\frac{1}{33}\right)$$ $$e\left(\frac{5}{22}\right)$$ $$e\left(\frac{8}{33}\right)$$ $$e\left(\frac{29}{33}\right)$$ $$e\left(\frac{3}{22}\right)$$ $$e\left(\frac{29}{66}\right)$$
$$\chi_{469}(33,\cdot)$$ 469.bj 66 yes $$-1$$ $$1$$ $$e\left(\frac{5}{33}\right)$$ $$e\left(\frac{49}{66}\right)$$ $$e\left(\frac{10}{33}\right)$$ $$e\left(\frac{29}{66}\right)$$ $$e\left(\frac{59}{66}\right)$$ $$e\left(\frac{5}{11}\right)$$ $$e\left(\frac{16}{33}\right)$$ $$e\left(\frac{13}{22}\right)$$ $$e\left(\frac{31}{33}\right)$$ $$e\left(\frac{1}{22}\right)$$
$$\chi_{469}(34,\cdot)$$ 469.bd 66 yes $$1$$ $$1$$ $$e\left(\frac{65}{66}\right)$$ $$e\left(\frac{10}{11}\right)$$ $$e\left(\frac{32}{33}\right)$$ $$e\left(\frac{3}{11}\right)$$ $$e\left(\frac{59}{66}\right)$$ $$e\left(\frac{21}{22}\right)$$ $$e\left(\frac{9}{11}\right)$$ $$e\left(\frac{17}{66}\right)$$ $$e\left(\frac{7}{66}\right)$$ $$e\left(\frac{29}{33}\right)$$
$$\chi_{469}(36,\cdot)$$ 469.z 33 no $$1$$ $$1$$ $$e\left(\frac{7}{33}\right)$$ $$e\left(\frac{3}{11}\right)$$ $$e\left(\frac{14}{33}\right)$$ $$e\left(\frac{2}{11}\right)$$ $$e\left(\frac{16}{33}\right)$$ $$e\left(\frac{7}{11}\right)$$ $$e\left(\frac{6}{11}\right)$$ $$e\left(\frac{13}{33}\right)$$ $$e\left(\frac{17}{33}\right)$$ $$e\left(\frac{23}{33}\right)$$
$$\chi_{469}(37,\cdot)$$ 469.h 3 yes $$1$$ $$1$$ $$1$$ $$e\left(\frac{1}{3}\right)$$ $$1$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$1$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$1$$ $$e\left(\frac{1}{3}\right)$$