Properties

Modulus 967967
Structure C966C_{966}
Order 966966

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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 = C966C_{966}
sage: H.gens()
 
pari: g.gen
 
Generators = χ967(5,)\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 11 22 33 44 55 66 77 88 99 1010 1111
χ967(1,)\chi_{967}(1,\cdot) 967.a 1 no 11 11 11 11 11 11 11 11 11 11 11 11
χ967(2,)\chi_{967}(2,\cdot) 967.o 483 yes 11 11 e(386483)e\left(\frac{386}{483}\right) e(122161)e\left(\frac{122}{161}\right) e(289483)e\left(\frac{289}{483}\right) e(187483)e\left(\frac{187}{483}\right) e(269483)e\left(\frac{269}{483}\right) e(454483)e\left(\frac{454}{483}\right) e(64161)e\left(\frac{64}{161}\right) e(83161)e\left(\frac{83}{161}\right) e(30161)e\left(\frac{30}{161}\right) e(129161)e\left(\frac{129}{161}\right)
χ967(3,)\chi_{967}(3,\cdot) 967.n 322 yes 1-1 11 e(122161)e\left(\frac{122}{161}\right) e(47322)e\left(\frac{47}{322}\right) e(83161)e\left(\frac{83}{161}\right) e(79322)e\left(\frac{79}{322}\right) e(291322)e\left(\frac{291}{322}\right) e(141322)e\left(\frac{141}{322}\right) e(44161)e\left(\frac{44}{161}\right) e(47161)e\left(\frac{47}{161}\right) e(1322)e\left(\frac{1}{322}\right) e(139161)e\left(\frac{139}{161}\right)
χ967(4,)\chi_{967}(4,\cdot) 967.o 483 yes 11 11 e(289483)e\left(\frac{289}{483}\right) e(83161)e\left(\frac{83}{161}\right) e(95483)e\left(\frac{95}{483}\right) e(374483)e\left(\frac{374}{483}\right) e(55483)e\left(\frac{55}{483}\right) e(425483)e\left(\frac{425}{483}\right) e(128161)e\left(\frac{128}{161}\right) e(5161)e\left(\frac{5}{161}\right) e(60161)e\left(\frac{60}{161}\right) e(97161)e\left(\frac{97}{161}\right)
χ967(5,)\chi_{967}(5,\cdot) 967.p 966 yes 1-1 11 e(187483)e\left(\frac{187}{483}\right) e(79322)e\left(\frac{79}{322}\right) e(374483)e\left(\frac{374}{483}\right) e(1966)e\left(\frac{1}{966}\right) e(611966)e\left(\frac{611}{966}\right) e(67966)e\left(\frac{67}{966}\right) e(26161)e\left(\frac{26}{161}\right) e(79161)e\left(\frac{79}{161}\right) e(125322)e\left(\frac{125}{322}\right) e(148161)e\left(\frac{148}{161}\right)
χ967(6,)\chi_{967}(6,\cdot) 967.p 966 yes 1-1 11 e(269483)e\left(\frac{269}{483}\right) e(291322)e\left(\frac{291}{322}\right) e(55483)e\left(\frac{55}{483}\right) e(611966)e\left(\frac{611}{966}\right) e(445966)e\left(\frac{445}{966}\right) e(365966)e\left(\frac{365}{966}\right) e(108161)e\left(\frac{108}{161}\right) e(130161)e\left(\frac{130}{161}\right) e(61322)e\left(\frac{61}{322}\right) e(107161)e\left(\frac{107}{161}\right)
χ967(7,)\chi_{967}(7,\cdot) 967.p 966 yes 1-1 11 e(454483)e\left(\frac{454}{483}\right) e(141322)e\left(\frac{141}{322}\right) e(425483)e\left(\frac{425}{483}\right) e(67966)e\left(\frac{67}{966}\right) e(365966)e\left(\frac{365}{966}\right) e(625966)e\left(\frac{625}{966}\right) e(132161)e\left(\frac{132}{161}\right) e(141161)e\left(\frac{141}{161}\right) e(3322)e\left(\frac{3}{322}\right) e(95161)e\left(\frac{95}{161}\right)
χ967(8,)\chi_{967}(8,\cdot) 967.m 161 yes 11 11 e(64161)e\left(\frac{64}{161}\right) e(44161)e\left(\frac{44}{161}\right) e(128161)e\left(\frac{128}{161}\right) e(26161)e\left(\frac{26}{161}\right) e(108161)e\left(\frac{108}{161}\right) e(132161)e\left(\frac{132}{161}\right) e(31161)e\left(\frac{31}{161}\right) e(88161)e\left(\frac{88}{161}\right) e(90161)e\left(\frac{90}{161}\right) e(65161)e\left(\frac{65}{161}\right)
χ967(9,)\chi_{967}(9,\cdot) 967.m 161 yes 11 11 e(83161)e\left(\frac{83}{161}\right) e(47161)e\left(\frac{47}{161}\right) e(5161)e\left(\frac{5}{161}\right) e(79161)e\left(\frac{79}{161}\right) e(130161)e\left(\frac{130}{161}\right) e(141161)e\left(\frac{141}{161}\right) e(88161)e\left(\frac{88}{161}\right) e(94161)e\left(\frac{94}{161}\right) e(1161)e\left(\frac{1}{161}\right) e(117161)e\left(\frac{117}{161}\right)
χ967(10,)\chi_{967}(10,\cdot) 967.n 322 yes 1-1 11 e(30161)e\left(\frac{30}{161}\right) e(1322)e\left(\frac{1}{322}\right) e(60161)e\left(\frac{60}{161}\right) e(125322)e\left(\frac{125}{322}\right) e(61322)e\left(\frac{61}{322}\right) e(3322)e\left(\frac{3}{322}\right) e(90161)e\left(\frac{90}{161}\right) e(1161)e\left(\frac{1}{161}\right) e(185322)e\left(\frac{185}{322}\right) e(116161)e\left(\frac{116}{161}\right)
χ967(11,)\chi_{967}(11,\cdot) 967.m 161 yes 11 11 e(129161)e\left(\frac{129}{161}\right) e(139161)e\left(\frac{139}{161}\right) e(97161)e\left(\frac{97}{161}\right) e(148161)e\left(\frac{148}{161}\right) e(107161)e\left(\frac{107}{161}\right) e(95161)e\left(\frac{95}{161}\right) e(65161)e\left(\frac{65}{161}\right) e(117161)e\left(\frac{117}{161}\right) e(116161)e\left(\frac{116}{161}\right) e(48161)e\left(\frac{48}{161}\right)
χ967(12,)\chi_{967}(12,\cdot) 967.p 966 yes 1-1 11 e(172483)e\left(\frac{172}{483}\right) e(213322)e\left(\frac{213}{322}\right) e(344483)e\left(\frac{344}{483}\right) e(19966)e\left(\frac{19}{966}\right) e(17966)e\left(\frac{17}{966}\right) e(307966)e\left(\frac{307}{966}\right) e(11161)e\left(\frac{11}{161}\right) e(52161)e\left(\frac{52}{161}\right) e(121322)e\left(\frac{121}{322}\right) e(75161)e\left(\frac{75}{161}\right)
χ967(13,)\chi_{967}(13,\cdot) 967.p 966 yes 1-1 11 e(418483)e\left(\frac{418}{483}\right) e(205322)e\left(\frac{205}{322}\right) e(353483)e\left(\frac{353}{483}\right) e(883966)e\left(\frac{883}{966}\right) e(485966)e\left(\frac{485}{966}\right) e(235966)e\left(\frac{235}{966}\right) e(96161)e\left(\frac{96}{161}\right) e(44161)e\left(\frac{44}{161}\right) e(251322)e\left(\frac{251}{322}\right) e(113161)e\left(\frac{113}{161}\right)
χ967(14,)\chi_{967}(14,\cdot) 967.j 46 yes 1-1 11 e(1723)e\left(\frac{17}{23}\right) e(946)e\left(\frac{9}{46}\right) e(1123)e\left(\frac{11}{23}\right) e(2146)e\left(\frac{21}{46}\right) e(4346)e\left(\frac{43}{46}\right) e(2746)e\left(\frac{27}{46}\right) e(523)e\left(\frac{5}{23}\right) e(923)e\left(\frac{9}{23}\right) e(946)e\left(\frac{9}{46}\right) e(923)e\left(\frac{9}{23}\right)
χ967(15,)\chi_{967}(15,\cdot) 967.k 69 yes 11 11 e(1069)e\left(\frac{10}{69}\right) e(923)e\left(\frac{9}{23}\right) e(2069)e\left(\frac{20}{69}\right) e(1769)e\left(\frac{17}{69}\right) e(3769)e\left(\frac{37}{69}\right) e(3569)e\left(\frac{35}{69}\right) e(1023)e\left(\frac{10}{23}\right) e(1823)e\left(\frac{18}{23}\right) e(923)e\left(\frac{9}{23}\right) e(1823)e\left(\frac{18}{23}\right)
χ967(16,)\chi_{967}(16,\cdot) 967.o 483 yes 11 11 e(95483)e\left(\frac{95}{483}\right) e(5161)e\left(\frac{5}{161}\right) e(190483)e\left(\frac{190}{483}\right) e(265483)e\left(\frac{265}{483}\right) e(110483)e\left(\frac{110}{483}\right) e(367483)e\left(\frac{367}{483}\right) e(95161)e\left(\frac{95}{161}\right) e(10161)e\left(\frac{10}{161}\right) e(120161)e\left(\frac{120}{161}\right) e(33161)e\left(\frac{33}{161}\right)
χ967(17,)\chi_{967}(17,\cdot) 967.m 161 yes 11 11 e(130161)e\left(\frac{130}{161}\right) e(29161)e\left(\frac{29}{161}\right) e(99161)e\left(\frac{99}{161}\right) e(83161)e\left(\frac{83}{161}\right) e(159161)e\left(\frac{159}{161}\right) e(87161)e\left(\frac{87}{161}\right) e(68161)e\left(\frac{68}{161}\right) e(58161)e\left(\frac{58}{161}\right) e(52161)e\left(\frac{52}{161}\right) e(127161)e\left(\frac{127}{161}\right)
χ967(18,)\chi_{967}(18,\cdot) 967.o 483 yes 11 11 e(152483)e\left(\frac{152}{483}\right) e(8161)e\left(\frac{8}{161}\right) e(304483)e\left(\frac{304}{483}\right) e(424483)e\left(\frac{424}{483}\right) e(176483)e\left(\frac{176}{483}\right) e(394483)e\left(\frac{394}{483}\right) e(152161)e\left(\frac{152}{161}\right) e(16161)e\left(\frac{16}{161}\right) e(31161)e\left(\frac{31}{161}\right) e(85161)e\left(\frac{85}{161}\right)
χ967(19,)\chi_{967}(19,\cdot) 967.p 966 yes 1-1 11 e(113483)e\left(\frac{113}{483}\right) e(139322)e\left(\frac{139}{322}\right) e(226483)e\left(\frac{226}{483}\right) e(605966)e\left(\frac{605}{966}\right) e(643966)e\left(\frac{643}{966}\right) e(929966)e\left(\frac{929}{966}\right) e(113161)e\left(\frac{113}{161}\right) e(139161)e\left(\frac{139}{161}\right) e(277322)e\left(\frac{277}{322}\right) e(24161)e\left(\frac{24}{161}\right)
χ967(20,)\chi_{967}(20,\cdot) 967.l 138 yes 1-1 11 e(6869)e\left(\frac{68}{69}\right) e(3546)e\left(\frac{35}{46}\right) e(6769)e\left(\frac{67}{69}\right) e(107138)e\left(\frac{107}{138}\right) e(103138)e\left(\frac{103}{138}\right) e(131138)e\left(\frac{131}{138}\right) e(2223)e\left(\frac{22}{23}\right) e(1223)e\left(\frac{12}{23}\right) e(3546)e\left(\frac{35}{46}\right) e(1223)e\left(\frac{12}{23}\right)
χ967(21,)\chi_{967}(21,\cdot) 967.o 483 yes 11 11 e(337483)e\left(\frac{337}{483}\right) e(94161)e\left(\frac{94}{161}\right) e(191483)e\left(\frac{191}{483}\right) e(152483)e\left(\frac{152}{483}\right) e(136483)e\left(\frac{136}{483}\right) e(41483)e\left(\frac{41}{483}\right) e(15161)e\left(\frac{15}{161}\right) e(27161)e\left(\frac{27}{161}\right) e(2161)e\left(\frac{2}{161}\right) e(73161)e\left(\frac{73}{161}\right)
χ967(22,)\chi_{967}(22,\cdot) 967.o 483 yes 11 11 e(290483)e\left(\frac{290}{483}\right) e(100161)e\left(\frac{100}{161}\right) e(97483)e\left(\frac{97}{483}\right) e(148483)e\left(\frac{148}{483}\right) e(107483)e\left(\frac{107}{483}\right) e(256483)e\left(\frac{256}{483}\right) e(129161)e\left(\frac{129}{161}\right) e(39161)e\left(\frac{39}{161}\right) e(146161)e\left(\frac{146}{161}\right) e(16161)e\left(\frac{16}{161}\right)
χ967(23,)\chi_{967}(23,\cdot) 967.n 322 yes 1-1 11 e(81161)e\left(\frac{81}{161}\right) e(51322)e\left(\frac{51}{322}\right) e(1161)e\left(\frac{1}{161}\right) e(257322)e\left(\frac{257}{322}\right) e(213322)e\left(\frac{213}{322}\right) e(153322)e\left(\frac{153}{322}\right) e(82161)e\left(\frac{82}{161}\right) e(51161)e\left(\frac{51}{161}\right) e(97322)e\left(\frac{97}{322}\right) e(120161)e\left(\frac{120}{161}\right)
χ967(24,)\chi_{967}(24,\cdot) 967.n 322 yes 1-1 11 e(25161)e\left(\frac{25}{161}\right) e(135322)e\left(\frac{135}{322}\right) e(50161)e\left(\frac{50}{161}\right) e(131322)e\left(\frac{131}{322}\right) e(185322)e\left(\frac{185}{322}\right) e(83322)e\left(\frac{83}{322}\right) e(75161)e\left(\frac{75}{161}\right) e(135161)e\left(\frac{135}{161}\right) e(181322)e\left(\frac{181}{322}\right) e(43161)e\left(\frac{43}{161}\right)
χ967(25,)\chi_{967}(25,\cdot) 967.o 483 yes 11 11 e(374483)e\left(\frac{374}{483}\right) e(79161)e\left(\frac{79}{161}\right) e(265483)e\left(\frac{265}{483}\right) e(1483)e\left(\frac{1}{483}\right) e(128483)e\left(\frac{128}{483}\right) e(67483)e\left(\frac{67}{483}\right) e(52161)e\left(\frac{52}{161}\right) e(158161)e\left(\frac{158}{161}\right) e(125161)e\left(\frac{125}{161}\right) e(135161)e\left(\frac{135}{161}\right)
χ967(26,)\chi_{967}(26,\cdot) 967.n 322 yes 1-1 11 e(107161)e\left(\frac{107}{161}\right) e(127322)e\left(\frac{127}{322}\right) e(53161)e\left(\frac{53}{161}\right) e(97322)e\left(\frac{97}{322}\right) e(19322)e\left(\frac{19}{322}\right) e(59322)e\left(\frac{59}{322}\right) e(160161)e\left(\frac{160}{161}\right) e(127161)e\left(\frac{127}{161}\right) e(311322)e\left(\frac{311}{322}\right) e(81161)e\left(\frac{81}{161}\right)
χ967(27,)\chi_{967}(27,\cdot) 967.n 322 yes 1-1 11 e(44161)e\left(\frac{44}{161}\right) e(141322)e\left(\frac{141}{322}\right) e(88161)e\left(\frac{88}{161}\right) e(237322)e\left(\frac{237}{322}\right) e(229322)e\left(\frac{229}{322}\right) e(101322)e\left(\frac{101}{322}\right) e(132161)e\left(\frac{132}{161}\right) e(141161)e\left(\frac{141}{161}\right) e(3322)e\left(\frac{3}{322}\right) e(95161)e\left(\frac{95}{161}\right)
χ967(28,)\chi_{967}(28,\cdot) 967.p 966 yes 1-1 11 e(260483)e\left(\frac{260}{483}\right) e(307322)e\left(\frac{307}{322}\right) e(37483)e\left(\frac{37}{483}\right) e(815966)e\left(\frac{815}{966}\right) e(475966)e\left(\frac{475}{966}\right) e(509966)e\left(\frac{509}{966}\right) e(99161)e\left(\frac{99}{161}\right) e(146161)e\left(\frac{146}{161}\right) e(123322)e\left(\frac{123}{322}\right) e(31161)e\left(\frac{31}{161}\right)
χ967(29,)\chi_{967}(29,\cdot) 967.n 322 yes 1-1 11 e(101161)e\left(\frac{101}{161}\right) e(159322)e\left(\frac{159}{322}\right) e(41161)e\left(\frac{41}{161}\right) e(233322)e\left(\frac{233}{322}\right) e(39322)e\left(\frac{39}{322}\right) e(155322)e\left(\frac{155}{322}\right) e(142161)e\left(\frac{142}{161}\right) e(159161)e\left(\frac{159}{161}\right) e(113322)e\left(\frac{113}{322}\right) e(90161)e\left(\frac{90}{161}\right)
χ967(30,)\chi_{967}(30,\cdot) 967.m 161 yes 11 11 e(152161)e\left(\frac{152}{161}\right) e(24161)e\left(\frac{24}{161}\right) e(143161)e\left(\frac{143}{161}\right) e(102161)e\left(\frac{102}{161}\right) e(15161)e\left(\frac{15}{161}\right) e(72161)e\left(\frac{72}{161}\right) e(134161)e\left(\frac{134}{161}\right) e(48161)e\left(\frac{48}{161}\right) e(93161)e\left(\frac{93}{161}\right) e(94161)e\left(\frac{94}{161}\right)
χ967(31,)\chi_{967}(31,\cdot) 967.o 483 yes 11 11 e(376483)e\left(\frac{376}{483}\right) e(113161)e\left(\frac{113}{161}\right) e(269483)e\left(\frac{269}{483}\right) e(32483)e\left(\frac{32}{483}\right) e(232483)e\left(\frac{232}{483}\right) e(212483)e\left(\frac{212}{483}\right) e(54161)e\left(\frac{54}{161}\right) e(65161)e\left(\frac{65}{161}\right) e(136161)e\left(\frac{136}{161}\right) e(134161)e\left(\frac{134}{161}\right)
χ967(32,)\chi_{967}(32,\cdot) 967.o 483 yes 11 11 e(481483)e\left(\frac{481}{483}\right) e(127161)e\left(\frac{127}{161}\right) e(479483)e\left(\frac{479}{483}\right) e(452483)e\left(\frac{452}{483}\right) e(379483)e\left(\frac{379}{483}\right) e(338483)e\left(\frac{338}{483}\right) e(159161)e\left(\frac{159}{161}\right) e(93161)e\left(\frac{93}{161}\right) e(150161)e\left(\frac{150}{161}\right) e(1161)e\left(\frac{1}{161}\right)
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