# Properties

 Modulus $967$ Structure $$C_{966}$$ Order $966$

Show commands: PariGP / SageMath

sage: H = DirichletGroup(967)

pari: g = idealstar(,967,2)

## Character group

 sage: G.order()  pari: g.no Order = 966 sage: H.invariants()  pari: g.cyc Structure = $$C_{966}$$ sage: H.gens()  pari: g.gen Generators = $\chi_{967}(5,\cdot)$

## First 32 of 966 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 $$-1$$ $$1$$ $$2$$ $$3$$ $$4$$ $$5$$ $$6$$ $$7$$ $$8$$ $$9$$ $$10$$ $$11$$
$$\chi_{967}(1,\cdot)$$ 967.a 1 no $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{967}(2,\cdot)$$ 967.o 483 yes $$1$$ $$1$$ $$e\left(\frac{386}{483}\right)$$ $$e\left(\frac{122}{161}\right)$$ $$e\left(\frac{289}{483}\right)$$ $$e\left(\frac{187}{483}\right)$$ $$e\left(\frac{269}{483}\right)$$ $$e\left(\frac{454}{483}\right)$$ $$e\left(\frac{64}{161}\right)$$ $$e\left(\frac{83}{161}\right)$$ $$e\left(\frac{30}{161}\right)$$ $$e\left(\frac{129}{161}\right)$$
$$\chi_{967}(3,\cdot)$$ 967.n 322 yes $$-1$$ $$1$$ $$e\left(\frac{122}{161}\right)$$ $$e\left(\frac{47}{322}\right)$$ $$e\left(\frac{83}{161}\right)$$ $$e\left(\frac{79}{322}\right)$$ $$e\left(\frac{291}{322}\right)$$ $$e\left(\frac{141}{322}\right)$$ $$e\left(\frac{44}{161}\right)$$ $$e\left(\frac{47}{161}\right)$$ $$e\left(\frac{1}{322}\right)$$ $$e\left(\frac{139}{161}\right)$$
$$\chi_{967}(4,\cdot)$$ 967.o 483 yes $$1$$ $$1$$ $$e\left(\frac{289}{483}\right)$$ $$e\left(\frac{83}{161}\right)$$ $$e\left(\frac{95}{483}\right)$$ $$e\left(\frac{374}{483}\right)$$ $$e\left(\frac{55}{483}\right)$$ $$e\left(\frac{425}{483}\right)$$ $$e\left(\frac{128}{161}\right)$$ $$e\left(\frac{5}{161}\right)$$ $$e\left(\frac{60}{161}\right)$$ $$e\left(\frac{97}{161}\right)$$
$$\chi_{967}(5,\cdot)$$ 967.p 966 yes $$-1$$ $$1$$ $$e\left(\frac{187}{483}\right)$$ $$e\left(\frac{79}{322}\right)$$ $$e\left(\frac{374}{483}\right)$$ $$e\left(\frac{1}{966}\right)$$ $$e\left(\frac{611}{966}\right)$$ $$e\left(\frac{67}{966}\right)$$ $$e\left(\frac{26}{161}\right)$$ $$e\left(\frac{79}{161}\right)$$ $$e\left(\frac{125}{322}\right)$$ $$e\left(\frac{148}{161}\right)$$
$$\chi_{967}(6,\cdot)$$ 967.p 966 yes $$-1$$ $$1$$ $$e\left(\frac{269}{483}\right)$$ $$e\left(\frac{291}{322}\right)$$ $$e\left(\frac{55}{483}\right)$$ $$e\left(\frac{611}{966}\right)$$ $$e\left(\frac{445}{966}\right)$$ $$e\left(\frac{365}{966}\right)$$ $$e\left(\frac{108}{161}\right)$$ $$e\left(\frac{130}{161}\right)$$ $$e\left(\frac{61}{322}\right)$$ $$e\left(\frac{107}{161}\right)$$
$$\chi_{967}(7,\cdot)$$ 967.p 966 yes $$-1$$ $$1$$ $$e\left(\frac{454}{483}\right)$$ $$e\left(\frac{141}{322}\right)$$ $$e\left(\frac{425}{483}\right)$$ $$e\left(\frac{67}{966}\right)$$ $$e\left(\frac{365}{966}\right)$$ $$e\left(\frac{625}{966}\right)$$ $$e\left(\frac{132}{161}\right)$$ $$e\left(\frac{141}{161}\right)$$ $$e\left(\frac{3}{322}\right)$$ $$e\left(\frac{95}{161}\right)$$
$$\chi_{967}(8,\cdot)$$ 967.m 161 yes $$1$$ $$1$$ $$e\left(\frac{64}{161}\right)$$ $$e\left(\frac{44}{161}\right)$$ $$e\left(\frac{128}{161}\right)$$ $$e\left(\frac{26}{161}\right)$$ $$e\left(\frac{108}{161}\right)$$ $$e\left(\frac{132}{161}\right)$$ $$e\left(\frac{31}{161}\right)$$ $$e\left(\frac{88}{161}\right)$$ $$e\left(\frac{90}{161}\right)$$ $$e\left(\frac{65}{161}\right)$$
$$\chi_{967}(9,\cdot)$$ 967.m 161 yes $$1$$ $$1$$ $$e\left(\frac{83}{161}\right)$$ $$e\left(\frac{47}{161}\right)$$ $$e\left(\frac{5}{161}\right)$$ $$e\left(\frac{79}{161}\right)$$ $$e\left(\frac{130}{161}\right)$$ $$e\left(\frac{141}{161}\right)$$ $$e\left(\frac{88}{161}\right)$$ $$e\left(\frac{94}{161}\right)$$ $$e\left(\frac{1}{161}\right)$$ $$e\left(\frac{117}{161}\right)$$
$$\chi_{967}(10,\cdot)$$ 967.n 322 yes $$-1$$ $$1$$ $$e\left(\frac{30}{161}\right)$$ $$e\left(\frac{1}{322}\right)$$ $$e\left(\frac{60}{161}\right)$$ $$e\left(\frac{125}{322}\right)$$ $$e\left(\frac{61}{322}\right)$$ $$e\left(\frac{3}{322}\right)$$ $$e\left(\frac{90}{161}\right)$$ $$e\left(\frac{1}{161}\right)$$ $$e\left(\frac{185}{322}\right)$$ $$e\left(\frac{116}{161}\right)$$
$$\chi_{967}(11,\cdot)$$ 967.m 161 yes $$1$$ $$1$$ $$e\left(\frac{129}{161}\right)$$ $$e\left(\frac{139}{161}\right)$$ $$e\left(\frac{97}{161}\right)$$ $$e\left(\frac{148}{161}\right)$$ $$e\left(\frac{107}{161}\right)$$ $$e\left(\frac{95}{161}\right)$$ $$e\left(\frac{65}{161}\right)$$ $$e\left(\frac{117}{161}\right)$$ $$e\left(\frac{116}{161}\right)$$ $$e\left(\frac{48}{161}\right)$$
$$\chi_{967}(12,\cdot)$$ 967.p 966 yes $$-1$$ $$1$$ $$e\left(\frac{172}{483}\right)$$ $$e\left(\frac{213}{322}\right)$$ $$e\left(\frac{344}{483}\right)$$ $$e\left(\frac{19}{966}\right)$$ $$e\left(\frac{17}{966}\right)$$ $$e\left(\frac{307}{966}\right)$$ $$e\left(\frac{11}{161}\right)$$ $$e\left(\frac{52}{161}\right)$$ $$e\left(\frac{121}{322}\right)$$ $$e\left(\frac{75}{161}\right)$$
$$\chi_{967}(13,\cdot)$$ 967.p 966 yes $$-1$$ $$1$$ $$e\left(\frac{418}{483}\right)$$ $$e\left(\frac{205}{322}\right)$$ $$e\left(\frac{353}{483}\right)$$ $$e\left(\frac{883}{966}\right)$$ $$e\left(\frac{485}{966}\right)$$ $$e\left(\frac{235}{966}\right)$$ $$e\left(\frac{96}{161}\right)$$ $$e\left(\frac{44}{161}\right)$$ $$e\left(\frac{251}{322}\right)$$ $$e\left(\frac{113}{161}\right)$$
$$\chi_{967}(14,\cdot)$$ 967.j 46 yes $$-1$$ $$1$$ $$e\left(\frac{17}{23}\right)$$ $$e\left(\frac{9}{46}\right)$$ $$e\left(\frac{11}{23}\right)$$ $$e\left(\frac{21}{46}\right)$$ $$e\left(\frac{43}{46}\right)$$ $$e\left(\frac{27}{46}\right)$$ $$e\left(\frac{5}{23}\right)$$ $$e\left(\frac{9}{23}\right)$$ $$e\left(\frac{9}{46}\right)$$ $$e\left(\frac{9}{23}\right)$$
$$\chi_{967}(15,\cdot)$$ 967.k 69 yes $$1$$ $$1$$ $$e\left(\frac{10}{69}\right)$$ $$e\left(\frac{9}{23}\right)$$ $$e\left(\frac{20}{69}\right)$$ $$e\left(\frac{17}{69}\right)$$ $$e\left(\frac{37}{69}\right)$$ $$e\left(\frac{35}{69}\right)$$ $$e\left(\frac{10}{23}\right)$$ $$e\left(\frac{18}{23}\right)$$ $$e\left(\frac{9}{23}\right)$$ $$e\left(\frac{18}{23}\right)$$
$$\chi_{967}(16,\cdot)$$ 967.o 483 yes $$1$$ $$1$$ $$e\left(\frac{95}{483}\right)$$ $$e\left(\frac{5}{161}\right)$$ $$e\left(\frac{190}{483}\right)$$ $$e\left(\frac{265}{483}\right)$$ $$e\left(\frac{110}{483}\right)$$ $$e\left(\frac{367}{483}\right)$$ $$e\left(\frac{95}{161}\right)$$ $$e\left(\frac{10}{161}\right)$$ $$e\left(\frac{120}{161}\right)$$ $$e\left(\frac{33}{161}\right)$$
$$\chi_{967}(17,\cdot)$$ 967.m 161 yes $$1$$ $$1$$ $$e\left(\frac{130}{161}\right)$$ $$e\left(\frac{29}{161}\right)$$ $$e\left(\frac{99}{161}\right)$$ $$e\left(\frac{83}{161}\right)$$ $$e\left(\frac{159}{161}\right)$$ $$e\left(\frac{87}{161}\right)$$ $$e\left(\frac{68}{161}\right)$$ $$e\left(\frac{58}{161}\right)$$ $$e\left(\frac{52}{161}\right)$$ $$e\left(\frac{127}{161}\right)$$
$$\chi_{967}(18,\cdot)$$ 967.o 483 yes $$1$$ $$1$$ $$e\left(\frac{152}{483}\right)$$ $$e\left(\frac{8}{161}\right)$$ $$e\left(\frac{304}{483}\right)$$ $$e\left(\frac{424}{483}\right)$$ $$e\left(\frac{176}{483}\right)$$ $$e\left(\frac{394}{483}\right)$$ $$e\left(\frac{152}{161}\right)$$ $$e\left(\frac{16}{161}\right)$$ $$e\left(\frac{31}{161}\right)$$ $$e\left(\frac{85}{161}\right)$$
$$\chi_{967}(19,\cdot)$$ 967.p 966 yes $$-1$$ $$1$$ $$e\left(\frac{113}{483}\right)$$ $$e\left(\frac{139}{322}\right)$$ $$e\left(\frac{226}{483}\right)$$ $$e\left(\frac{605}{966}\right)$$ $$e\left(\frac{643}{966}\right)$$ $$e\left(\frac{929}{966}\right)$$ $$e\left(\frac{113}{161}\right)$$ $$e\left(\frac{139}{161}\right)$$ $$e\left(\frac{277}{322}\right)$$ $$e\left(\frac{24}{161}\right)$$
$$\chi_{967}(20,\cdot)$$ 967.l 138 yes $$-1$$ $$1$$ $$e\left(\frac{68}{69}\right)$$ $$e\left(\frac{35}{46}\right)$$ $$e\left(\frac{67}{69}\right)$$ $$e\left(\frac{107}{138}\right)$$ $$e\left(\frac{103}{138}\right)$$ $$e\left(\frac{131}{138}\right)$$ $$e\left(\frac{22}{23}\right)$$ $$e\left(\frac{12}{23}\right)$$ $$e\left(\frac{35}{46}\right)$$ $$e\left(\frac{12}{23}\right)$$
$$\chi_{967}(21,\cdot)$$ 967.o 483 yes $$1$$ $$1$$ $$e\left(\frac{337}{483}\right)$$ $$e\left(\frac{94}{161}\right)$$ $$e\left(\frac{191}{483}\right)$$ $$e\left(\frac{152}{483}\right)$$ $$e\left(\frac{136}{483}\right)$$ $$e\left(\frac{41}{483}\right)$$ $$e\left(\frac{15}{161}\right)$$ $$e\left(\frac{27}{161}\right)$$ $$e\left(\frac{2}{161}\right)$$ $$e\left(\frac{73}{161}\right)$$
$$\chi_{967}(22,\cdot)$$ 967.o 483 yes $$1$$ $$1$$ $$e\left(\frac{290}{483}\right)$$ $$e\left(\frac{100}{161}\right)$$ $$e\left(\frac{97}{483}\right)$$ $$e\left(\frac{148}{483}\right)$$ $$e\left(\frac{107}{483}\right)$$ $$e\left(\frac{256}{483}\right)$$ $$e\left(\frac{129}{161}\right)$$ $$e\left(\frac{39}{161}\right)$$ $$e\left(\frac{146}{161}\right)$$ $$e\left(\frac{16}{161}\right)$$
$$\chi_{967}(23,\cdot)$$ 967.n 322 yes $$-1$$ $$1$$ $$e\left(\frac{81}{161}\right)$$ $$e\left(\frac{51}{322}\right)$$ $$e\left(\frac{1}{161}\right)$$ $$e\left(\frac{257}{322}\right)$$ $$e\left(\frac{213}{322}\right)$$ $$e\left(\frac{153}{322}\right)$$ $$e\left(\frac{82}{161}\right)$$ $$e\left(\frac{51}{161}\right)$$ $$e\left(\frac{97}{322}\right)$$ $$e\left(\frac{120}{161}\right)$$
$$\chi_{967}(24,\cdot)$$ 967.n 322 yes $$-1$$ $$1$$ $$e\left(\frac{25}{161}\right)$$ $$e\left(\frac{135}{322}\right)$$ $$e\left(\frac{50}{161}\right)$$ $$e\left(\frac{131}{322}\right)$$ $$e\left(\frac{185}{322}\right)$$ $$e\left(\frac{83}{322}\right)$$ $$e\left(\frac{75}{161}\right)$$ $$e\left(\frac{135}{161}\right)$$ $$e\left(\frac{181}{322}\right)$$ $$e\left(\frac{43}{161}\right)$$
$$\chi_{967}(25,\cdot)$$ 967.o 483 yes $$1$$ $$1$$ $$e\left(\frac{374}{483}\right)$$ $$e\left(\frac{79}{161}\right)$$ $$e\left(\frac{265}{483}\right)$$ $$e\left(\frac{1}{483}\right)$$ $$e\left(\frac{128}{483}\right)$$ $$e\left(\frac{67}{483}\right)$$ $$e\left(\frac{52}{161}\right)$$ $$e\left(\frac{158}{161}\right)$$ $$e\left(\frac{125}{161}\right)$$ $$e\left(\frac{135}{161}\right)$$
$$\chi_{967}(26,\cdot)$$ 967.n 322 yes $$-1$$ $$1$$ $$e\left(\frac{107}{161}\right)$$ $$e\left(\frac{127}{322}\right)$$ $$e\left(\frac{53}{161}\right)$$ $$e\left(\frac{97}{322}\right)$$ $$e\left(\frac{19}{322}\right)$$ $$e\left(\frac{59}{322}\right)$$ $$e\left(\frac{160}{161}\right)$$ $$e\left(\frac{127}{161}\right)$$ $$e\left(\frac{311}{322}\right)$$ $$e\left(\frac{81}{161}\right)$$
$$\chi_{967}(27,\cdot)$$ 967.n 322 yes $$-1$$ $$1$$ $$e\left(\frac{44}{161}\right)$$ $$e\left(\frac{141}{322}\right)$$ $$e\left(\frac{88}{161}\right)$$ $$e\left(\frac{237}{322}\right)$$ $$e\left(\frac{229}{322}\right)$$ $$e\left(\frac{101}{322}\right)$$ $$e\left(\frac{132}{161}\right)$$ $$e\left(\frac{141}{161}\right)$$ $$e\left(\frac{3}{322}\right)$$ $$e\left(\frac{95}{161}\right)$$
$$\chi_{967}(28,\cdot)$$ 967.p 966 yes $$-1$$ $$1$$ $$e\left(\frac{260}{483}\right)$$ $$e\left(\frac{307}{322}\right)$$ $$e\left(\frac{37}{483}\right)$$ $$e\left(\frac{815}{966}\right)$$ $$e\left(\frac{475}{966}\right)$$ $$e\left(\frac{509}{966}\right)$$ $$e\left(\frac{99}{161}\right)$$ $$e\left(\frac{146}{161}\right)$$ $$e\left(\frac{123}{322}\right)$$ $$e\left(\frac{31}{161}\right)$$
$$\chi_{967}(29,\cdot)$$ 967.n 322 yes $$-1$$ $$1$$ $$e\left(\frac{101}{161}\right)$$ $$e\left(\frac{159}{322}\right)$$ $$e\left(\frac{41}{161}\right)$$ $$e\left(\frac{233}{322}\right)$$ $$e\left(\frac{39}{322}\right)$$ $$e\left(\frac{155}{322}\right)$$ $$e\left(\frac{142}{161}\right)$$ $$e\left(\frac{159}{161}\right)$$ $$e\left(\frac{113}{322}\right)$$ $$e\left(\frac{90}{161}\right)$$
$$\chi_{967}(30,\cdot)$$ 967.m 161 yes $$1$$ $$1$$ $$e\left(\frac{152}{161}\right)$$ $$e\left(\frac{24}{161}\right)$$ $$e\left(\frac{143}{161}\right)$$ $$e\left(\frac{102}{161}\right)$$ $$e\left(\frac{15}{161}\right)$$ $$e\left(\frac{72}{161}\right)$$ $$e\left(\frac{134}{161}\right)$$ $$e\left(\frac{48}{161}\right)$$ $$e\left(\frac{93}{161}\right)$$ $$e\left(\frac{94}{161}\right)$$
$$\chi_{967}(31,\cdot)$$ 967.o 483 yes $$1$$ $$1$$ $$e\left(\frac{376}{483}\right)$$ $$e\left(\frac{113}{161}\right)$$ $$e\left(\frac{269}{483}\right)$$ $$e\left(\frac{32}{483}\right)$$ $$e\left(\frac{232}{483}\right)$$ $$e\left(\frac{212}{483}\right)$$ $$e\left(\frac{54}{161}\right)$$ $$e\left(\frac{65}{161}\right)$$ $$e\left(\frac{136}{161}\right)$$ $$e\left(\frac{134}{161}\right)$$
$$\chi_{967}(32,\cdot)$$ 967.o 483 yes $$1$$ $$1$$ $$e\left(\frac{481}{483}\right)$$ $$e\left(\frac{127}{161}\right)$$ $$e\left(\frac{479}{483}\right)$$ $$e\left(\frac{452}{483}\right)$$ $$e\left(\frac{379}{483}\right)$$ $$e\left(\frac{338}{483}\right)$$ $$e\left(\frac{159}{161}\right)$$ $$e\left(\frac{93}{161}\right)$$ $$e\left(\frac{150}{161}\right)$$ $$e\left(\frac{1}{161}\right)$$