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Properties

Modulus 80438043
Structure C2×C2×C1146C_{2}\times C_{2}\times C_{1146}
Order 45844584

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Show commands: PariGP / SageMath

sage: H = DirichletGroup(8043)
 
pari: g = idealstar(,8043,2)
 

Character group

sage: G.order()
 
pari: g.no
 
Order = 4584
sage: H.invariants()
 
pari: g.cyc
 
Structure = C2×C2×C1146C_{2}\times C_{2}\times C_{1146}
sage: H.gens()
 
pari: g.gen
 
Generators = χ8043(5363,⋅)\chi_{8043}(5363,\cdot), χ8043(2299,⋅)\chi_{8043}(2299,\cdot), χ8043(6133,⋅)\chi_{8043}(6133,\cdot)

First 32 of 4584 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 44 55 88 1010 1111 1313 1616 1717 1919
χ8043(1,⋅)\chi_{8043}(1,\cdot) 8043.a 1 no 11 11 11 11 11 11 11 11 11 11 11 11
χ8043(2,⋅)\chi_{8043}(2,\cdot) 8043.z 1146 yes −1-1 11 e(1971146)e\left(\frac{197}{1146}\right) e(197573)e\left(\frac{197}{573}\right) e(5931146)e\left(\frac{593}{1146}\right) e(197382)e\left(\frac{197}{382}\right) e(395573)e\left(\frac{395}{573}\right) e(371146)e\left(\frac{37}{1146}\right) e(26191)e\left(\frac{26}{191}\right) e(394573)e\left(\frac{394}{573}\right) e(6371146)e\left(\frac{637}{1146}\right) e(154573)e\left(\frac{154}{573}\right)
χ8043(4,⋅)\chi_{8043}(4,\cdot) 8043.y 573 no 11 11 e(197573)e\left(\frac{197}{573}\right) e(394573)e\left(\frac{394}{573}\right) e(20573)e\left(\frac{20}{573}\right) e(6191)e\left(\frac{6}{191}\right) e(217573)e\left(\frac{217}{573}\right) e(37573)e\left(\frac{37}{573}\right) e(52191)e\left(\frac{52}{191}\right) e(215573)e\left(\frac{215}{573}\right) e(64573)e\left(\frac{64}{573}\right) e(308573)e\left(\frac{308}{573}\right)
χ8043(5,⋅)\chi_{8043}(5,\cdot) 8043.ba 1146 yes −1-1 11 e(5931146)e\left(\frac{593}{1146}\right) e(20573)e\left(\frac{20}{573}\right) e(7671146)e\left(\frac{767}{1146}\right) e(211382)e\left(\frac{211}{382}\right) e(107573)e\left(\frac{107}{573}\right) e(380573)e\left(\frac{380}{573}\right) e(23191)e\left(\frac{23}{191}\right) e(40573)e\left(\frac{40}{573}\right) e(425573)e\left(\frac{425}{573}\right) e(5811146)e\left(\frac{581}{1146}\right)
χ8043(8,⋅)\chi_{8043}(8,\cdot) 8043.x 382 no −1-1 11 e(197382)e\left(\frac{197}{382}\right) e(6191)e\left(\frac{6}{191}\right) e(211382)e\left(\frac{211}{382}\right) e(209382)e\left(\frac{209}{382}\right) e(13191)e\left(\frac{13}{191}\right) e(37382)e\left(\frac{37}{382}\right) e(78191)e\left(\frac{78}{191}\right) e(12191)e\left(\frac{12}{191}\right) e(255382)e\left(\frac{255}{382}\right) e(154191)e\left(\frac{154}{191}\right)
χ8043(10,⋅)\chi_{8043}(10,\cdot) 8043.bf 1146 no 11 11 e(395573)e\left(\frac{395}{573}\right) e(217573)e\left(\frac{217}{573}\right) e(107573)e\left(\frac{107}{573}\right) e(13191)e\left(\frac{13}{191}\right) e(502573)e\left(\frac{502}{573}\right) e(7971146)e\left(\frac{797}{1146}\right) e(49191)e\left(\frac{49}{191}\right) e(434573)e\left(\frac{434}{573}\right) e(3411146)e\left(\frac{341}{1146}\right) e(8891146)e\left(\frac{889}{1146}\right)
χ8043(11,⋅)\chi_{8043}(11,\cdot) 8043.bc 1146 yes 11 11 e(371146)e\left(\frac{37}{1146}\right) e(37573)e\left(\frac{37}{573}\right) e(380573)e\left(\frac{380}{573}\right) e(37382)e\left(\frac{37}{382}\right) e(7971146)e\left(\frac{797}{1146}\right) e(130573)e\left(\frac{130}{573}\right) e(257382)e\left(\frac{257}{382}\right) e(74573)e\left(\frac{74}{573}\right) e(7131146)e\left(\frac{713}{1146}\right) e(122573)e\left(\frac{122}{573}\right)
χ8043(13,⋅)\chi_{8043}(13,\cdot) 8043.r 382 no 11 11 e(26191)e\left(\frac{26}{191}\right) e(52191)e\left(\frac{52}{191}\right) e(23191)e\left(\frac{23}{191}\right) e(78191)e\left(\frac{78}{191}\right) e(49191)e\left(\frac{49}{191}\right) e(257382)e\left(\frac{257}{382}\right) e(103191)e\left(\frac{103}{191}\right) e(104191)e\left(\frac{104}{191}\right) e(109382)e\left(\frac{109}{382}\right) e(59382)e\left(\frac{59}{382}\right)
χ8043(16,⋅)\chi_{8043}(16,\cdot) 8043.y 573 no 11 11 e(394573)e\left(\frac{394}{573}\right) e(215573)e\left(\frac{215}{573}\right) e(40573)e\left(\frac{40}{573}\right) e(12191)e\left(\frac{12}{191}\right) e(434573)e\left(\frac{434}{573}\right) e(74573)e\left(\frac{74}{573}\right) e(104191)e\left(\frac{104}{191}\right) e(430573)e\left(\frac{430}{573}\right) e(128573)e\left(\frac{128}{573}\right) e(43573)e\left(\frac{43}{573}\right)
χ8043(17,⋅)\chi_{8043}(17,\cdot) 8043.bb 1146 yes 11 11 e(6371146)e\left(\frac{637}{1146}\right) e(64573)e\left(\frac{64}{573}\right) e(425573)e\left(\frac{425}{573}\right) e(255382)e\left(\frac{255}{382}\right) e(3411146)e\left(\frac{341}{1146}\right) e(7131146)e\left(\frac{713}{1146}\right) e(109382)e\left(\frac{109}{382}\right) e(128573)e\left(\frac{128}{573}\right) e(214573)e\left(\frac{214}{573}\right) e(10571146)e\left(\frac{1057}{1146}\right)
χ8043(19,⋅)\chi_{8043}(19,\cdot) 8043.be 1146 no −1-1 11 e(154573)e\left(\frac{154}{573}\right) e(308573)e\left(\frac{308}{573}\right) e(5811146)e\left(\frac{581}{1146}\right) e(154191)e\left(\frac{154}{191}\right) e(8891146)e\left(\frac{889}{1146}\right) e(122573)e\left(\frac{122}{573}\right) e(59382)e\left(\frac{59}{382}\right) e(43573)e\left(\frac{43}{573}\right) e(10571146)e\left(\frac{1057}{1146}\right) e(4671146)e\left(\frac{467}{1146}\right)
χ8043(20,⋅)\chi_{8043}(20,\cdot) 8043.w 382 yes −1-1 11 e(329382)e\left(\frac{329}{382}\right) e(138191)e\left(\frac{138}{191}\right) e(269382)e\left(\frac{269}{382}\right) e(223382)e\left(\frac{223}{382}\right) e(108191)e\left(\frac{108}{191}\right) e(139191)e\left(\frac{139}{191}\right) e(75191)e\left(\frac{75}{191}\right) e(85191)e\left(\frac{85}{191}\right) e(163191)e\left(\frac{163}{191}\right) e(17382)e\left(\frac{17}{382}\right)
χ8043(22,⋅)\chi_{8043}(22,\cdot) 8043.t 382 no −1-1 11 e(39191)e\left(\frac{39}{191}\right) e(78191)e\left(\frac{78}{191}\right) e(69382)e\left(\frac{69}{382}\right) e(117191)e\left(\frac{117}{191}\right) e(147382)e\left(\frac{147}{382}\right) e(99382)e\left(\frac{99}{382}\right) e(309382)e\left(\frac{309}{382}\right) e(156191)e\left(\frac{156}{191}\right) e(34191)e\left(\frac{34}{191}\right) e(92191)e\left(\frac{92}{191}\right)
χ8043(23,⋅)\chi_{8043}(23,\cdot) 8043.z 1146 yes −1-1 11 e(5271146)e\left(\frac{527}{1146}\right) e(527573)e\left(\frac{527}{573}\right) e(9291146)e\left(\frac{929}{1146}\right) e(145382)e\left(\frac{145}{382}\right) e(155573)e\left(\frac{155}{573}\right) e(11171146)e\left(\frac{1117}{1146}\right) e(119191)e\left(\frac{119}{191}\right) e(481573)e\left(\frac{481}{573}\right) e(3371146)e\left(\frac{337}{1146}\right) e(220573)e\left(\frac{220}{573}\right)
χ8043(25,⋅)\chi_{8043}(25,\cdot) 8043.y 573 no 11 11 e(20573)e\left(\frac{20}{573}\right) e(40573)e\left(\frac{40}{573}\right) e(194573)e\left(\frac{194}{573}\right) e(20191)e\left(\frac{20}{191}\right) e(214573)e\left(\frac{214}{573}\right) e(187573)e\left(\frac{187}{573}\right) e(46191)e\left(\frac{46}{191}\right) e(80573)e\left(\frac{80}{573}\right) e(277573)e\left(\frac{277}{573}\right) e(8573)e\left(\frac{8}{573}\right)
χ8043(26,⋅)\chi_{8043}(26,\cdot) 8043.ba 1146 yes −1-1 11 e(3531146)e\left(\frac{353}{1146}\right) e(353573)e\left(\frac{353}{573}\right) e(7311146)e\left(\frac{731}{1146}\right) e(353382)e\left(\frac{353}{382}\right) e(542573)e\left(\frac{542}{573}\right) e(404573)e\left(\frac{404}{573}\right) e(129191)e\left(\frac{129}{191}\right) e(133573)e\left(\frac{133}{573}\right) e(482573)e\left(\frac{482}{573}\right) e(4851146)e\left(\frac{485}{1146}\right)
χ8043(29,⋅)\chi_{8043}(29,\cdot) 8043.x 382 no −1-1 11 e(127382)e\left(\frac{127}{382}\right) e(127191)e\left(\frac{127}{191}\right) e(105382)e\left(\frac{105}{382}\right) e(381382)e\left(\frac{381}{382}\right) e(116191)e\left(\frac{116}{191}\right) e(51382)e\left(\frac{51}{382}\right) e(123191)e\left(\frac{123}{191}\right) e(63191)e\left(\frac{63}{191}\right) e(145382)e\left(\frac{145}{382}\right) e(140191)e\left(\frac{140}{191}\right)
χ8043(31,⋅)\chi_{8043}(31,\cdot) 8043.be 1146 no −1-1 11 e(320573)e\left(\frac{320}{573}\right) e(67573)e\left(\frac{67}{573}\right) e(10511146)e\left(\frac{1051}{1146}\right) e(129191)e\left(\frac{129}{191}\right) e(5451146)e\left(\frac{545}{1146}\right) e(127573)e\left(\frac{127}{573}\right) e(135382)e\left(\frac{135}{382}\right) e(134573)e\left(\frac{134}{573}\right) e(2691146)e\left(\frac{269}{1146}\right) e(8291146)e\left(\frac{829}{1146}\right)
χ8043(32,⋅)\chi_{8043}(32,\cdot) 8043.z 1146 yes −1-1 11 e(9851146)e\left(\frac{985}{1146}\right) e(412573)e\left(\frac{412}{573}\right) e(6731146)e\left(\frac{673}{1146}\right) e(221382)e\left(\frac{221}{382}\right) e(256573)e\left(\frac{256}{573}\right) e(1851146)e\left(\frac{185}{1146}\right) e(130191)e\left(\frac{130}{191}\right) e(251573)e\left(\frac{251}{573}\right) e(8931146)e\left(\frac{893}{1146}\right) e(197573)e\left(\frac{197}{573}\right)
χ8043(34,⋅)\chi_{8043}(34,\cdot) 8043.s 382 no −1-1 11 e(139191)e\left(\frac{139}{191}\right) e(87191)e\left(\frac{87}{191}\right) e(99382)e\left(\frac{99}{382}\right) e(35191)e\left(\frac{35}{191}\right) e(377382)e\left(\frac{377}{382}\right) e(125191)e\left(\frac{125}{191}\right) e(161382)e\left(\frac{161}{382}\right) e(174191)e\left(\frac{174}{191}\right) e(355382)e\left(\frac{355}{382}\right) e(73382)e\left(\frac{73}{382}\right)
χ8043(37,⋅)\chi_{8043}(37,\cdot) 8043.bd 1146 no −1-1 11 e(256573)e\left(\frac{256}{573}\right) e(512573)e\left(\frac{512}{573}\right) e(4971146)e\left(\frac{497}{1146}\right) e(65191)e\left(\frac{65}{191}\right) e(10091146)e\left(\frac{1009}{1146}\right) e(5471146)e\left(\frac{547}{1146}\right) e(299382)e\left(\frac{299}{382}\right) e(451573)e\left(\frac{451}{573}\right) e(566573)e\left(\frac{566}{573}\right) e(217573)e\left(\frac{217}{573}\right)
χ8043(38,⋅)\chi_{8043}(38,\cdot) 8043.bb 1146 yes 11 11 e(5051146)e\left(\frac{505}{1146}\right) e(505573)e\left(\frac{505}{573}\right) e(14573)e\left(\frac{14}{573}\right) e(123382)e\left(\frac{123}{382}\right) e(5331146)e\left(\frac{533}{1146}\right) e(2811146)e\left(\frac{281}{1146}\right) e(111382)e\left(\frac{111}{382}\right) e(437573)e\left(\frac{437}{573}\right) e(274573)e\left(\frac{274}{573}\right) e(7751146)e\left(\frac{775}{1146}\right)
χ8043(40,⋅)\chi_{8043}(40,\cdot) 8043.bf 1146 no 11 11 e(19573)e\left(\frac{19}{573}\right) e(38573)e\left(\frac{38}{573}\right) e(127573)e\left(\frac{127}{573}\right) e(19191)e\left(\frac{19}{191}\right) e(146573)e\left(\frac{146}{573}\right) e(8711146)e\left(\frac{871}{1146}\right) e(101191)e\left(\frac{101}{191}\right) e(76573)e\left(\frac{76}{573}\right) e(4691146)e\left(\frac{469}{1146}\right) e(3591146)e\left(\frac{359}{1146}\right)
χ8043(41,⋅)\chi_{8043}(41,\cdot) 8043.w 382 yes −1-1 11 e(13382)e\left(\frac{13}{382}\right) e(13191)e\left(\frac{13}{191}\right) e(107382)e\left(\frac{107}{382}\right) e(39382)e\left(\frac{39}{382}\right) e(60191)e\left(\frac{60}{191}\right) e(56191)e\left(\frac{56}{191}\right) e(169191)e\left(\frac{169}{191}\right) e(26191)e\left(\frac{26}{191}\right) e(133191)e\left(\frac{133}{191}\right) e(349382)e\left(\frac{349}{382}\right)
χ8043(43,⋅)\chi_{8043}(43,\cdot) 8043.q 191 no 11 11 e(16191)e\left(\frac{16}{191}\right) e(32191)e\left(\frac{32}{191}\right) e(117191)e\left(\frac{117}{191}\right) e(48191)e\left(\frac{48}{191}\right) e(133191)e\left(\frac{133}{191}\right) e(35191)e\left(\frac{35}{191}\right) e(34191)e\left(\frac{34}{191}\right) e(64191)e\left(\frac{64}{191}\right) e(107191)e\left(\frac{107}{191}\right) e(121191)e\left(\frac{121}{191}\right)
χ8043(44,⋅)\chi_{8043}(44,\cdot) 8043.bc 1146 yes 11 11 e(4311146)e\left(\frac{431}{1146}\right) e(431573)e\left(\frac{431}{573}\right) e(400573)e\left(\frac{400}{573}\right) e(49382)e\left(\frac{49}{382}\right) e(851146)e\left(\frac{85}{1146}\right) e(167573)e\left(\frac{167}{573}\right) e(361382)e\left(\frac{361}{382}\right) e(289573)e\left(\frac{289}{573}\right) e(8411146)e\left(\frac{841}{1146}\right) e(430573)e\left(\frac{430}{573}\right)
χ8043(46,⋅)\chi_{8043}(46,\cdot) 8043.y 573 no 11 11 e(362573)e\left(\frac{362}{573}\right) e(151573)e\left(\frac{151}{573}\right) e(188573)e\left(\frac{188}{573}\right) e(171191)e\left(\frac{171}{191}\right) e(550573)e\left(\frac{550}{573}\right) e(4573)e\left(\frac{4}{573}\right) e(145191)e\left(\frac{145}{191}\right) e(302573)e\left(\frac{302}{573}\right) e(487573)e\left(\frac{487}{573}\right) e(374573)e\left(\frac{374}{573}\right)
χ8043(47,⋅)\chi_{8043}(47,\cdot) 8043.ba 1146 yes −1-1 11 e(6951146)e\left(\frac{695}{1146}\right) e(122573)e\left(\frac{122}{573}\right) e(7251146)e\left(\frac{725}{1146}\right) e(313382)e\left(\frac{313}{382}\right) e(137573)e\left(\frac{137}{573}\right) e(26573)e\left(\frac{26}{573}\right) e(83191)e\left(\frac{83}{191}\right) e(244573)e\left(\frac{244}{573}\right) e(14573)e\left(\frac{14}{573}\right) e(8511146)e\left(\frac{851}{1146}\right)
χ8043(50,⋅)\chi_{8043}(50,\cdot) 8043.x 382 no −1-1 11 e(79382)e\left(\frac{79}{382}\right) e(79191)e\left(\frac{79}{191}\right) e(327382)e\left(\frac{327}{382}\right) e(237382)e\left(\frac{237}{382}\right) e(12191)e\left(\frac{12}{191}\right) e(137382)e\left(\frac{137}{382}\right) e(72191)e\left(\frac{72}{191}\right) e(158191)e\left(\frac{158}{191}\right) e(15382)e\left(\frac{15}{382}\right) e(54191)e\left(\frac{54}{191}\right)
χ8043(52,⋅)\chi_{8043}(52,\cdot) 8043.bf 1146 no 11 11 e(275573)e\left(\frac{275}{573}\right) e(550573)e\left(\frac{550}{573}\right) e(89573)e\left(\frac{89}{573}\right) e(84191)e\left(\frac{84}{191}\right) e(364573)e\left(\frac{364}{573}\right) e(8451146)e\left(\frac{845}{1146}\right) e(155191)e\left(\frac{155}{191}\right) e(527573)e\left(\frac{527}{573}\right) e(4551146)e\left(\frac{455}{1146}\right) e(7931146)e\left(\frac{793}{1146}\right)
χ8043(53,⋅)\chi_{8043}(53,\cdot) 8043.bc 1146 yes 11 11 e(4031146)e\left(\frac{403}{1146}\right) e(403573)e\left(\frac{403}{573}\right) e(35573)e\left(\frac{35}{573}\right) e(21382)e\left(\frac{21}{382}\right) e(4731146)e\left(\frac{473}{1146}\right) e(208573)e\left(\frac{208}{573}\right) e(373382)e\left(\frac{373}{382}\right) e(233573)e\left(\frac{233}{573}\right) e(7971146)e\left(\frac{797}{1146}\right) e(539573)e\left(\frac{539}{573}\right)
χ8043(55,⋅)\chi_{8043}(55,\cdot) 8043.s 382 no −1-1 11 e(105191)e\left(\frac{105}{191}\right) e(19191)e\left(\frac{19}{191}\right) e(127382)e\left(\frac{127}{382}\right) e(124191)e\left(\frac{124}{191}\right) e(337382)e\left(\frac{337}{382}\right) e(170191)e\left(\frac{170}{191}\right) e(303382)e\left(\frac{303}{382}\right) e(38191)e\left(\frac{38}{191}\right) e(139382)e\left(\frac{139}{382}\right) e(275382)e\left(\frac{275}{382}\right)
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