# Properties

 Modulus $966$ Structure $$C_{2}\times C_{2}\times C_{66}$$ Order $264$

Show commands: PariGP / SageMath

sage: H = DirichletGroup(966)

pari: g = idealstar(,966,2)

## Character group

 sage: G.order()  pari: g.no Order = 264 sage: H.invariants()  pari: g.cyc Structure = $$C_{2}\times C_{2}\times C_{66}$$ sage: H.gens()  pari: g.gen Generators = $\chi_{966}(323,\cdot)$, $\chi_{966}(829,\cdot)$, $\chi_{966}(925,\cdot)$

## First 32 of 264 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 $$-1$$ $$1$$ $$5$$ $$11$$ $$13$$ $$17$$ $$19$$ $$25$$ $$29$$ $$31$$ $$37$$ $$41$$
$$\chi_{966}(1,\cdot)$$ 966.a 1 no $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{966}(5,\cdot)$$ 966.bc 66 no $$-1$$ $$1$$ $$e\left(\frac{47}{66}\right)$$ $$e\left(\frac{8}{33}\right)$$ $$e\left(\frac{3}{22}\right)$$ $$e\left(\frac{43}{66}\right)$$ $$e\left(\frac{28}{33}\right)$$ $$e\left(\frac{14}{33}\right)$$ $$e\left(\frac{7}{22}\right)$$ $$e\left(\frac{7}{66}\right)$$ $$e\left(\frac{41}{66}\right)$$ $$e\left(\frac{6}{11}\right)$$
$$\chi_{966}(11,\cdot)$$ 966.bf 66 no $$1$$ $$1$$ $$e\left(\frac{8}{33}\right)$$ $$e\left(\frac{28}{33}\right)$$ $$e\left(\frac{8}{11}\right)$$ $$e\left(\frac{1}{33}\right)$$ $$e\left(\frac{31}{66}\right)$$ $$e\left(\frac{16}{33}\right)$$ $$e\left(\frac{19}{22}\right)$$ $$e\left(\frac{4}{33}\right)$$ $$e\left(\frac{61}{66}\right)$$ $$e\left(\frac{9}{22}\right)$$
$$\chi_{966}(13,\cdot)$$ 966.v 22 no $$-1$$ $$1$$ $$e\left(\frac{3}{22}\right)$$ $$e\left(\frac{8}{11}\right)$$ $$e\left(\frac{9}{22}\right)$$ $$e\left(\frac{21}{22}\right)$$ $$e\left(\frac{1}{22}\right)$$ $$e\left(\frac{3}{11}\right)$$ $$e\left(\frac{5}{11}\right)$$ $$e\left(\frac{7}{22}\right)$$ $$e\left(\frac{4}{11}\right)$$ $$e\left(\frac{3}{22}\right)$$
$$\chi_{966}(17,\cdot)$$ 966.bc 66 no $$-1$$ $$1$$ $$e\left(\frac{43}{66}\right)$$ $$e\left(\frac{1}{33}\right)$$ $$e\left(\frac{21}{22}\right)$$ $$e\left(\frac{59}{66}\right)$$ $$e\left(\frac{20}{33}\right)$$ $$e\left(\frac{10}{33}\right)$$ $$e\left(\frac{5}{22}\right)$$ $$e\left(\frac{5}{66}\right)$$ $$e\left(\frac{1}{66}\right)$$ $$e\left(\frac{9}{11}\right)$$
$$\chi_{966}(19,\cdot)$$ 966.be 66 no $$1$$ $$1$$ $$e\left(\frac{28}{33}\right)$$ $$e\left(\frac{31}{66}\right)$$ $$e\left(\frac{1}{22}\right)$$ $$e\left(\frac{20}{33}\right)$$ $$e\left(\frac{13}{33}\right)$$ $$e\left(\frac{23}{33}\right)$$ $$e\left(\frac{3}{11}\right)$$ $$e\left(\frac{61}{66}\right)$$ $$e\left(\frac{65}{66}\right)$$ $$e\left(\frac{15}{22}\right)$$
$$\chi_{966}(25,\cdot)$$ 966.y 33 no $$1$$ $$1$$ $$e\left(\frac{14}{33}\right)$$ $$e\left(\frac{16}{33}\right)$$ $$e\left(\frac{3}{11}\right)$$ $$e\left(\frac{10}{33}\right)$$ $$e\left(\frac{23}{33}\right)$$ $$e\left(\frac{28}{33}\right)$$ $$e\left(\frac{7}{11}\right)$$ $$e\left(\frac{7}{33}\right)$$ $$e\left(\frac{8}{33}\right)$$ $$e\left(\frac{1}{11}\right)$$
$$\chi_{966}(29,\cdot)$$ 966.w 22 no $$-1$$ $$1$$ $$e\left(\frac{7}{22}\right)$$ $$e\left(\frac{19}{22}\right)$$ $$e\left(\frac{5}{11}\right)$$ $$e\left(\frac{5}{22}\right)$$ $$e\left(\frac{3}{11}\right)$$ $$e\left(\frac{7}{11}\right)$$ $$e\left(\frac{5}{22}\right)$$ $$e\left(\frac{10}{11}\right)$$ $$e\left(\frac{2}{11}\right)$$ $$e\left(\frac{7}{22}\right)$$
$$\chi_{966}(31,\cdot)$$ 966.bb 66 no $$-1$$ $$1$$ $$e\left(\frac{7}{66}\right)$$ $$e\left(\frac{4}{33}\right)$$ $$e\left(\frac{7}{22}\right)$$ $$e\left(\frac{5}{66}\right)$$ $$e\left(\frac{61}{66}\right)$$ $$e\left(\frac{7}{33}\right)$$ $$e\left(\frac{10}{11}\right)$$ $$e\left(\frac{53}{66}\right)$$ $$e\left(\frac{2}{33}\right)$$ $$e\left(\frac{17}{22}\right)$$
$$\chi_{966}(37,\cdot)$$ 966.z 66 no $$-1$$ $$1$$ $$e\left(\frac{41}{66}\right)$$ $$e\left(\frac{61}{66}\right)$$ $$e\left(\frac{4}{11}\right)$$ $$e\left(\frac{1}{66}\right)$$ $$e\left(\frac{65}{66}\right)$$ $$e\left(\frac{8}{33}\right)$$ $$e\left(\frac{2}{11}\right)$$ $$e\left(\frac{2}{33}\right)$$ $$e\left(\frac{47}{66}\right)$$ $$e\left(\frac{5}{11}\right)$$
$$\chi_{966}(41,\cdot)$$ 966.t 22 no $$1$$ $$1$$ $$e\left(\frac{6}{11}\right)$$ $$e\left(\frac{9}{22}\right)$$ $$e\left(\frac{3}{22}\right)$$ $$e\left(\frac{9}{11}\right)$$ $$e\left(\frac{15}{22}\right)$$ $$e\left(\frac{1}{11}\right)$$ $$e\left(\frac{7}{22}\right)$$ $$e\left(\frac{17}{22}\right)$$ $$e\left(\frac{5}{11}\right)$$ $$e\left(\frac{6}{11}\right)$$
$$\chi_{966}(43,\cdot)$$ 966.x 22 no $$-1$$ $$1$$ $$e\left(\frac{5}{22}\right)$$ $$e\left(\frac{1}{22}\right)$$ $$e\left(\frac{2}{11}\right)$$ $$e\left(\frac{13}{22}\right)$$ $$e\left(\frac{9}{22}\right)$$ $$e\left(\frac{5}{11}\right)$$ $$e\left(\frac{1}{11}\right)$$ $$e\left(\frac{4}{11}\right)$$ $$e\left(\frac{17}{22}\right)$$ $$e\left(\frac{8}{11}\right)$$
$$\chi_{966}(47,\cdot)$$ 966.l 6 no $$1$$ $$1$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$-1$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$-1$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$1$$
$$\chi_{966}(53,\cdot)$$ 966.bf 66 no $$1$$ $$1$$ $$e\left(\frac{23}{33}\right)$$ $$e\left(\frac{31}{33}\right)$$ $$e\left(\frac{1}{11}\right)$$ $$e\left(\frac{7}{33}\right)$$ $$e\left(\frac{19}{66}\right)$$ $$e\left(\frac{13}{33}\right)$$ $$e\left(\frac{1}{22}\right)$$ $$e\left(\frac{28}{33}\right)$$ $$e\left(\frac{31}{66}\right)$$ $$e\left(\frac{19}{22}\right)$$
$$\chi_{966}(55,\cdot)$$ 966.v 22 no $$-1$$ $$1$$ $$e\left(\frac{21}{22}\right)$$ $$e\left(\frac{1}{11}\right)$$ $$e\left(\frac{19}{22}\right)$$ $$e\left(\frac{15}{22}\right)$$ $$e\left(\frac{7}{22}\right)$$ $$e\left(\frac{10}{11}\right)$$ $$e\left(\frac{2}{11}\right)$$ $$e\left(\frac{5}{22}\right)$$ $$e\left(\frac{6}{11}\right)$$ $$e\left(\frac{21}{22}\right)$$
$$\chi_{966}(59,\cdot)$$ 966.bd 66 no $$1$$ $$1$$ $$e\left(\frac{32}{33}\right)$$ $$e\left(\frac{59}{66}\right)$$ $$e\left(\frac{9}{22}\right)$$ $$e\left(\frac{4}{33}\right)$$ $$e\left(\frac{25}{66}\right)$$ $$e\left(\frac{31}{33}\right)$$ $$e\left(\frac{21}{22}\right)$$ $$e\left(\frac{65}{66}\right)$$ $$e\left(\frac{23}{33}\right)$$ $$e\left(\frac{7}{11}\right)$$
$$\chi_{966}(61,\cdot)$$ 966.be 66 no $$1$$ $$1$$ $$e\left(\frac{31}{33}\right)$$ $$e\left(\frac{19}{66}\right)$$ $$e\left(\frac{7}{22}\right)$$ $$e\left(\frac{8}{33}\right)$$ $$e\left(\frac{25}{33}\right)$$ $$e\left(\frac{29}{33}\right)$$ $$e\left(\frac{10}{11}\right)$$ $$e\left(\frac{31}{66}\right)$$ $$e\left(\frac{59}{66}\right)$$ $$e\left(\frac{17}{22}\right)$$
$$\chi_{966}(65,\cdot)$$ 966.bf 66 no $$1$$ $$1$$ $$e\left(\frac{28}{33}\right)$$ $$e\left(\frac{32}{33}\right)$$ $$e\left(\frac{6}{11}\right)$$ $$e\left(\frac{20}{33}\right)$$ $$e\left(\frac{59}{66}\right)$$ $$e\left(\frac{23}{33}\right)$$ $$e\left(\frac{17}{22}\right)$$ $$e\left(\frac{14}{33}\right)$$ $$e\left(\frac{65}{66}\right)$$ $$e\left(\frac{15}{22}\right)$$
$$\chi_{966}(67,\cdot)$$ 966.z 66 no $$-1$$ $$1$$ $$e\left(\frac{61}{66}\right)$$ $$e\left(\frac{65}{66}\right)$$ $$e\left(\frac{3}{11}\right)$$ $$e\left(\frac{53}{66}\right)$$ $$e\left(\frac{13}{66}\right)$$ $$e\left(\frac{28}{33}\right)$$ $$e\left(\frac{7}{11}\right)$$ $$e\left(\frac{7}{33}\right)$$ $$e\left(\frac{49}{66}\right)$$ $$e\left(\frac{1}{11}\right)$$
$$\chi_{966}(71,\cdot)$$ 966.w 22 no $$-1$$ $$1$$ $$e\left(\frac{13}{22}\right)$$ $$e\left(\frac{7}{22}\right)$$ $$e\left(\frac{3}{11}\right)$$ $$e\left(\frac{3}{22}\right)$$ $$e\left(\frac{4}{11}\right)$$ $$e\left(\frac{2}{11}\right)$$ $$e\left(\frac{3}{22}\right)$$ $$e\left(\frac{6}{11}\right)$$ $$e\left(\frac{10}{11}\right)$$ $$e\left(\frac{13}{22}\right)$$
$$\chi_{966}(73,\cdot)$$ 966.bb 66 no $$-1$$ $$1$$ $$e\left(\frac{1}{66}\right)$$ $$e\left(\frac{10}{33}\right)$$ $$e\left(\frac{1}{22}\right)$$ $$e\left(\frac{29}{66}\right)$$ $$e\left(\frac{37}{66}\right)$$ $$e\left(\frac{1}{33}\right)$$ $$e\left(\frac{3}{11}\right)$$ $$e\left(\frac{17}{66}\right)$$ $$e\left(\frac{5}{33}\right)$$ $$e\left(\frac{15}{22}\right)$$
$$\chi_{966}(79,\cdot)$$ 966.z 66 no $$-1$$ $$1$$ $$e\left(\frac{53}{66}\right)$$ $$e\left(\frac{37}{66}\right)$$ $$e\left(\frac{10}{11}\right)$$ $$e\left(\frac{19}{66}\right)$$ $$e\left(\frac{47}{66}\right)$$ $$e\left(\frac{20}{33}\right)$$ $$e\left(\frac{5}{11}\right)$$ $$e\left(\frac{5}{33}\right)$$ $$e\left(\frac{35}{66}\right)$$ $$e\left(\frac{7}{11}\right)$$
$$\chi_{966}(83,\cdot)$$ 966.u 22 no $$-1$$ $$1$$ $$e\left(\frac{21}{22}\right)$$ $$e\left(\frac{1}{11}\right)$$ $$e\left(\frac{19}{22}\right)$$ $$e\left(\frac{15}{22}\right)$$ $$e\left(\frac{9}{11}\right)$$ $$e\left(\frac{10}{11}\right)$$ $$e\left(\frac{15}{22}\right)$$ $$e\left(\frac{5}{22}\right)$$ $$e\left(\frac{1}{22}\right)$$ $$e\left(\frac{5}{11}\right)$$
$$\chi_{966}(85,\cdot)$$ 966.q 11 no $$1$$ $$1$$ $$e\left(\frac{4}{11}\right)$$ $$e\left(\frac{3}{11}\right)$$ $$e\left(\frac{1}{11}\right)$$ $$e\left(\frac{6}{11}\right)$$ $$e\left(\frac{5}{11}\right)$$ $$e\left(\frac{8}{11}\right)$$ $$e\left(\frac{6}{11}\right)$$ $$e\left(\frac{2}{11}\right)$$ $$e\left(\frac{7}{11}\right)$$ $$e\left(\frac{4}{11}\right)$$
$$\chi_{966}(89,\cdot)$$ 966.bc 66 no $$-1$$ $$1$$ $$e\left(\frac{59}{66}\right)$$ $$e\left(\frac{29}{33}\right)$$ $$e\left(\frac{15}{22}\right)$$ $$e\left(\frac{61}{66}\right)$$ $$e\left(\frac{19}{33}\right)$$ $$e\left(\frac{26}{33}\right)$$ $$e\left(\frac{13}{22}\right)$$ $$e\left(\frac{13}{66}\right)$$ $$e\left(\frac{29}{66}\right)$$ $$e\left(\frac{8}{11}\right)$$
$$\chi_{966}(95,\cdot)$$ 966.ba 66 no $$-1$$ $$1$$ $$e\left(\frac{37}{66}\right)$$ $$e\left(\frac{47}{66}\right)$$ $$e\left(\frac{2}{11}\right)$$ $$e\left(\frac{17}{66}\right)$$ $$e\left(\frac{8}{33}\right)$$ $$e\left(\frac{4}{33}\right)$$ $$e\left(\frac{13}{22}\right)$$ $$e\left(\frac{1}{33}\right)$$ $$e\left(\frac{20}{33}\right)$$ $$e\left(\frac{5}{22}\right)$$
$$\chi_{966}(97,\cdot)$$ 966.s 22 no $$1$$ $$1$$ $$e\left(\frac{6}{11}\right)$$ $$e\left(\frac{9}{22}\right)$$ $$e\left(\frac{3}{22}\right)$$ $$e\left(\frac{9}{11}\right)$$ $$e\left(\frac{2}{11}\right)$$ $$e\left(\frac{1}{11}\right)$$ $$e\left(\frac{9}{11}\right)$$ $$e\left(\frac{17}{22}\right)$$ $$e\left(\frac{21}{22}\right)$$ $$e\left(\frac{1}{22}\right)$$
$$\chi_{966}(101,\cdot)$$ 966.bd 66 no $$1$$ $$1$$ $$e\left(\frac{26}{33}\right)$$ $$e\left(\frac{17}{66}\right)$$ $$e\left(\frac{19}{22}\right)$$ $$e\left(\frac{28}{33}\right)$$ $$e\left(\frac{43}{66}\right)$$ $$e\left(\frac{19}{33}\right)$$ $$e\left(\frac{15}{22}\right)$$ $$e\left(\frac{59}{66}\right)$$ $$e\left(\frac{29}{33}\right)$$ $$e\left(\frac{5}{11}\right)$$
$$\chi_{966}(103,\cdot)$$ 966.be 66 no $$1$$ $$1$$ $$e\left(\frac{19}{33}\right)$$ $$e\left(\frac{1}{66}\right)$$ $$e\left(\frac{5}{22}\right)$$ $$e\left(\frac{23}{33}\right)$$ $$e\left(\frac{10}{33}\right)$$ $$e\left(\frac{5}{33}\right)$$ $$e\left(\frac{4}{11}\right)$$ $$e\left(\frac{19}{66}\right)$$ $$e\left(\frac{17}{66}\right)$$ $$e\left(\frac{9}{22}\right)$$
$$\chi_{966}(107,\cdot)$$ 966.bf 66 no $$1$$ $$1$$ $$e\left(\frac{31}{33}\right)$$ $$e\left(\frac{26}{33}\right)$$ $$e\left(\frac{9}{11}\right)$$ $$e\left(\frac{8}{33}\right)$$ $$e\left(\frac{17}{66}\right)$$ $$e\left(\frac{29}{33}\right)$$ $$e\left(\frac{9}{22}\right)$$ $$e\left(\frac{32}{33}\right)$$ $$e\left(\frac{59}{66}\right)$$ $$e\left(\frac{17}{22}\right)$$
$$\chi_{966}(109,\cdot)$$ 966.z 66 no $$-1$$ $$1$$ $$e\left(\frac{43}{66}\right)$$ $$e\left(\frac{35}{66}\right)$$ $$e\left(\frac{5}{11}\right)$$ $$e\left(\frac{59}{66}\right)$$ $$e\left(\frac{7}{66}\right)$$ $$e\left(\frac{10}{33}\right)$$ $$e\left(\frac{8}{11}\right)$$ $$e\left(\frac{19}{33}\right)$$ $$e\left(\frac{1}{66}\right)$$ $$e\left(\frac{9}{11}\right)$$
$$\chi_{966}(113,\cdot)$$ 966.r 22 no $$1$$ $$1$$ $$e\left(\frac{1}{11}\right)$$ $$e\left(\frac{9}{11}\right)$$ $$e\left(\frac{3}{11}\right)$$ $$e\left(\frac{7}{11}\right)$$ $$e\left(\frac{19}{22}\right)$$ $$e\left(\frac{2}{11}\right)$$ $$e\left(\frac{3}{22}\right)$$ $$e\left(\frac{6}{11}\right)$$ $$e\left(\frac{9}{22}\right)$$ $$e\left(\frac{13}{22}\right)$$
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