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Properties

Modulus 22432243
Structure C2242C_{2242}
Order 22422242

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Show commands: PariGP / SageMath

sage: H = DirichletGroup(2243)
 
pari: g = idealstar(,2243,2)
 

Character group

sage: G.order()
 
pari: g.no
 
Order = 2242
sage: H.invariants()
 
pari: g.cyc
 
Structure = C2242C_{2242}
sage: H.gens()
 
pari: g.gen
 
Generators = χ2243(2,⋅)\chi_{2243}(2,\cdot)

First 32 of 2242 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
χ2243(1,⋅)\chi_{2243}(1,\cdot) 2243.a 1 no 11 11 11 11 11 11 11 11 11 11 11 11
χ2243(2,⋅)\chi_{2243}(2,\cdot) 2243.h 2242 yes −1-1 11 e(12242)e\left(\frac{1}{2242}\right) e(731121)e\left(\frac{73}{1121}\right) e(11121)e\left(\frac{1}{1121}\right) e(13632242)e\left(\frac{1363}{2242}\right) e(1472242)e\left(\frac{147}{2242}\right) e(10701121)e\left(\frac{1070}{1121}\right) e(32242)e\left(\frac{3}{2242}\right) e(1461121)e\left(\frac{146}{1121}\right) e(6821121)e\left(\frac{682}{1121}\right) e(10141121)e\left(\frac{1014}{1121}\right)
χ2243(3,⋅)\chi_{2243}(3,\cdot) 2243.g 1121 yes 11 11 e(731121)e\left(\frac{73}{1121}\right) e(5691121)e\left(\frac{569}{1121}\right) e(1461121)e\left(\frac{146}{1121}\right) e(8511121)e\left(\frac{851}{1121}\right) e(6421121)e\left(\frac{642}{1121}\right) e(4011121)e\left(\frac{401}{1121}\right) e(2191121)e\left(\frac{219}{1121}\right) e(171121)e\left(\frac{17}{1121}\right) e(9241121)e\left(\frac{924}{1121}\right) e(721121)e\left(\frac{72}{1121}\right)
χ2243(4,⋅)\chi_{2243}(4,\cdot) 2243.g 1121 yes 11 11 e(11121)e\left(\frac{1}{1121}\right) e(1461121)e\left(\frac{146}{1121}\right) e(21121)e\left(\frac{2}{1121}\right) e(2421121)e\left(\frac{242}{1121}\right) e(1471121)e\left(\frac{147}{1121}\right) e(10191121)e\left(\frac{1019}{1121}\right) e(31121)e\left(\frac{3}{1121}\right) e(2921121)e\left(\frac{292}{1121}\right) e(2431121)e\left(\frac{243}{1121}\right) e(9071121)e\left(\frac{907}{1121}\right)
χ2243(5,⋅)\chi_{2243}(5,\cdot) 2243.h 2242 yes −1-1 11 e(13632242)e\left(\frac{1363}{2242}\right) e(8511121)e\left(\frac{851}{1121}\right) e(2421121)e\left(\frac{242}{1121}\right) e(13932242)e\left(\frac{1393}{2242}\right) e(8232242)e\left(\frac{823}{2242}\right) e(11101121)e\left(\frac{1110}{1121}\right) e(18472242)e\left(\frac{1847}{2242}\right) e(5811121)e\left(\frac{581}{1121}\right) e(2571121)e\left(\frac{257}{1121}\right) e(10101121)e\left(\frac{1010}{1121}\right)
χ2243(6,⋅)\chi_{2243}(6,\cdot) 2243.h 2242 yes −1-1 11 e(1472242)e\left(\frac{147}{2242}\right) e(6421121)e\left(\frac{642}{1121}\right) e(1471121)e\left(\frac{147}{1121}\right) e(8232242)e\left(\frac{823}{2242}\right) e(14312242)e\left(\frac{1431}{2242}\right) e(3501121)e\left(\frac{350}{1121}\right) e(4412242)e\left(\frac{441}{2242}\right) e(1631121)e\left(\frac{163}{1121}\right) e(4851121)e\left(\frac{485}{1121}\right) e(10861121)e\left(\frac{1086}{1121}\right)
χ2243(7,⋅)\chi_{2243}(7,\cdot) 2243.g 1121 yes 11 11 e(10701121)e\left(\frac{1070}{1121}\right) e(4011121)e\left(\frac{401}{1121}\right) e(10191121)e\left(\frac{1019}{1121}\right) e(11101121)e\left(\frac{1110}{1121}\right) e(3501121)e\left(\frac{350}{1121}\right) e(7181121)e\left(\frac{718}{1121}\right) e(9681121)e\left(\frac{968}{1121}\right) e(8021121)e\left(\frac{802}{1121}\right) e(10591121)e\left(\frac{1059}{1121}\right) e(8251121)e\left(\frac{825}{1121}\right)
χ2243(8,⋅)\chi_{2243}(8,\cdot) 2243.h 2242 yes −1-1 11 e(32242)e\left(\frac{3}{2242}\right) e(2191121)e\left(\frac{219}{1121}\right) e(31121)e\left(\frac{3}{1121}\right) e(18472242)e\left(\frac{1847}{2242}\right) e(4412242)e\left(\frac{441}{2242}\right) e(9681121)e\left(\frac{968}{1121}\right) e(92242)e\left(\frac{9}{2242}\right) e(4381121)e\left(\frac{438}{1121}\right) e(9251121)e\left(\frac{925}{1121}\right) e(8001121)e\left(\frac{800}{1121}\right)
χ2243(9,⋅)\chi_{2243}(9,\cdot) 2243.g 1121 yes 11 11 e(1461121)e\left(\frac{146}{1121}\right) e(171121)e\left(\frac{17}{1121}\right) e(2921121)e\left(\frac{292}{1121}\right) e(5811121)e\left(\frac{581}{1121}\right) e(1631121)e\left(\frac{163}{1121}\right) e(8021121)e\left(\frac{802}{1121}\right) e(4381121)e\left(\frac{438}{1121}\right) e(341121)e\left(\frac{34}{1121}\right) e(7271121)e\left(\frac{727}{1121}\right) e(1441121)e\left(\frac{144}{1121}\right)
χ2243(10,⋅)\chi_{2243}(10,\cdot) 2243.g 1121 yes 11 11 e(6821121)e\left(\frac{682}{1121}\right) e(9241121)e\left(\frac{924}{1121}\right) e(2431121)e\left(\frac{243}{1121}\right) e(2571121)e\left(\frac{257}{1121}\right) e(4851121)e\left(\frac{485}{1121}\right) e(10591121)e\left(\frac{1059}{1121}\right) e(9251121)e\left(\frac{925}{1121}\right) e(7271121)e\left(\frac{727}{1121}\right) e(9391121)e\left(\frac{939}{1121}\right) e(9031121)e\left(\frac{903}{1121}\right)
χ2243(11,⋅)\chi_{2243}(11,\cdot) 2243.g 1121 yes 11 11 e(10141121)e\left(\frac{1014}{1121}\right) e(721121)e\left(\frac{72}{1121}\right) e(9071121)e\left(\frac{907}{1121}\right) e(10101121)e\left(\frac{1010}{1121}\right) e(10861121)e\left(\frac{1086}{1121}\right) e(8251121)e\left(\frac{825}{1121}\right) e(8001121)e\left(\frac{800}{1121}\right) e(1441121)e\left(\frac{144}{1121}\right) e(9031121)e\left(\frac{903}{1121}\right) e(4781121)e\left(\frac{478}{1121}\right)
χ2243(12,⋅)\chi_{2243}(12,\cdot) 2243.g 1121 yes 11 11 e(741121)e\left(\frac{74}{1121}\right) e(7151121)e\left(\frac{715}{1121}\right) e(1481121)e\left(\frac{148}{1121}\right) e(10931121)e\left(\frac{1093}{1121}\right) e(7891121)e\left(\frac{789}{1121}\right) e(2991121)e\left(\frac{299}{1121}\right) e(2221121)e\left(\frac{222}{1121}\right) e(3091121)e\left(\frac{309}{1121}\right) e(461121)e\left(\frac{46}{1121}\right) e(9791121)e\left(\frac{979}{1121}\right)
χ2243(13,⋅)\chi_{2243}(13,\cdot) 2243.h 2242 yes −1-1 11 e(18652242)e\left(\frac{1865}{2242}\right) e(5041121)e\left(\frac{504}{1121}\right) e(7441121)e\left(\frac{744}{1121}\right) e(18092242)e\left(\frac{1809}{2242}\right) e(6312242)e\left(\frac{631}{2242}\right) e(1701121)e\left(\frac{170}{1121}\right) e(11112242)e\left(\frac{1111}{2242}\right) e(10081121)e\left(\frac{1008}{1121}\right) e(7161121)e\left(\frac{716}{1121}\right) e(11041121)e\left(\frac{1104}{1121}\right)
χ2243(14,⋅)\chi_{2243}(14,\cdot) 2243.h 2242 yes −1-1 11 e(21412242)e\left(\frac{2141}{2242}\right) e(4741121)e\left(\frac{474}{1121}\right) e(10201121)e\left(\frac{1020}{1121}\right) e(13412242)e\left(\frac{1341}{2242}\right) e(8472242)e\left(\frac{847}{2242}\right) e(6671121)e\left(\frac{667}{1121}\right) e(19392242)e\left(\frac{1939}{2242}\right) e(9481121)e\left(\frac{948}{1121}\right) e(6201121)e\left(\frac{620}{1121}\right) e(7181121)e\left(\frac{718}{1121}\right)
χ2243(15,⋅)\chi_{2243}(15,\cdot) 2243.h 2242 yes −1-1 11 e(15092242)e\left(\frac{1509}{2242}\right) e(2991121)e\left(\frac{299}{1121}\right) e(3881121)e\left(\frac{388}{1121}\right) e(8532242)e\left(\frac{853}{2242}\right) e(21072242)e\left(\frac{2107}{2242}\right) e(3901121)e\left(\frac{390}{1121}\right) e(432242)e\left(\frac{43}{2242}\right) e(5981121)e\left(\frac{598}{1121}\right) e(601121)e\left(\frac{60}{1121}\right) e(10821121)e\left(\frac{1082}{1121}\right)
χ2243(16,⋅)\chi_{2243}(16,\cdot) 2243.g 1121 yes 11 11 e(21121)e\left(\frac{2}{1121}\right) e(2921121)e\left(\frac{292}{1121}\right) e(41121)e\left(\frac{4}{1121}\right) e(4841121)e\left(\frac{484}{1121}\right) e(2941121)e\left(\frac{294}{1121}\right) e(9171121)e\left(\frac{917}{1121}\right) e(61121)e\left(\frac{6}{1121}\right) e(5841121)e\left(\frac{584}{1121}\right) e(4861121)e\left(\frac{486}{1121}\right) e(6931121)e\left(\frac{693}{1121}\right)
χ2243(17,⋅)\chi_{2243}(17,\cdot) 2243.g 1121 yes 11 11 e(331121)e\left(\frac{33}{1121}\right) e(3341121)e\left(\frac{334}{1121}\right) e(661121)e\left(\frac{66}{1121}\right) e(1391121)e\left(\frac{139}{1121}\right) e(3671121)e\left(\frac{367}{1121}\right) e(11181121)e\left(\frac{1118}{1121}\right) e(991121)e\left(\frac{99}{1121}\right) e(6681121)e\left(\frac{668}{1121}\right) e(1721121)e\left(\frac{172}{1121}\right) e(7851121)e\left(\frac{785}{1121}\right)
χ2243(18,⋅)\chi_{2243}(18,\cdot) 2243.h 2242 yes −1-1 11 e(2932242)e\left(\frac{293}{2242}\right) e(901121)e\left(\frac{90}{1121}\right) e(2931121)e\left(\frac{293}{1121}\right) e(2832242)e\left(\frac{283}{2242}\right) e(4732242)e\left(\frac{473}{2242}\right) e(7511121)e\left(\frac{751}{1121}\right) e(8792242)e\left(\frac{879}{2242}\right) e(1801121)e\left(\frac{180}{1121}\right) e(2881121)e\left(\frac{288}{1121}\right) e(371121)e\left(\frac{37}{1121}\right)
χ2243(19,⋅)\chi_{2243}(19,\cdot) 2243.h 2242 yes −1-1 11 e(3292242)e\left(\frac{329}{2242}\right) e(4761121)e\left(\frac{476}{1121}\right) e(3291121)e\left(\frac{329}{1121}\right) e(272242)e\left(\frac{27}{2242}\right) e(12812242)e\left(\frac{1281}{2242}\right) e(361121)e\left(\frac{36}{1121}\right) e(9872242)e\left(\frac{987}{2242}\right) e(9521121)e\left(\frac{952}{1121}\right) e(1781121)e\left(\frac{178}{1121}\right) e(6691121)e\left(\frac{669}{1121}\right)
χ2243(20,⋅)\chi_{2243}(20,\cdot) 2243.h 2242 yes −1-1 11 e(13652242)e\left(\frac{1365}{2242}\right) e(9971121)e\left(\frac{997}{1121}\right) e(2441121)e\left(\frac{244}{1121}\right) e(18772242)e\left(\frac{1877}{2242}\right) e(11172242)e\left(\frac{1117}{2242}\right) e(10081121)e\left(\frac{1008}{1121}\right) e(18532242)e\left(\frac{1853}{2242}\right) e(8731121)e\left(\frac{873}{1121}\right) e(5001121)e\left(\frac{500}{1121}\right) e(7961121)e\left(\frac{796}{1121}\right)
χ2243(21,⋅)\chi_{2243}(21,\cdot) 2243.g 1121 yes 11 11 e(221121)e\left(\frac{22}{1121}\right) e(9701121)e\left(\frac{970}{1121}\right) e(441121)e\left(\frac{44}{1121}\right) e(8401121)e\left(\frac{840}{1121}\right) e(9921121)e\left(\frac{992}{1121}\right) e(11191121)e\left(\frac{1119}{1121}\right) e(661121)e\left(\frac{66}{1121}\right) e(8191121)e\left(\frac{819}{1121}\right) e(8621121)e\left(\frac{862}{1121}\right) e(8971121)e\left(\frac{897}{1121}\right)
χ2243(22,⋅)\chi_{2243}(22,\cdot) 2243.h 2242 yes −1-1 11 e(20292242)e\left(\frac{2029}{2242}\right) e(1451121)e\left(\frac{145}{1121}\right) e(9081121)e\left(\frac{908}{1121}\right) e(11412242)e\left(\frac{1141}{2242}\right) e(772242)e\left(\frac{77}{2242}\right) e(7741121)e\left(\frac{774}{1121}\right) e(16032242)e\left(\frac{1603}{2242}\right) e(2901121)e\left(\frac{290}{1121}\right) e(4641121)e\left(\frac{464}{1121}\right) e(3711121)e\left(\frac{371}{1121}\right)
χ2243(23,⋅)\chi_{2243}(23,\cdot) 2243.h 2242 yes −1-1 11 e(22312242)e\left(\frac{2231}{2242}\right) e(3181121)e\left(\frac{318}{1121}\right) e(11101121)e\left(\frac{1110}{1121}\right) e(7012242)e\left(\frac{701}{2242}\right) e(6252242)e\left(\frac{625}{2242}\right) e(5611121)e\left(\frac{561}{1121}\right) e(22092242)e\left(\frac{2209}{2242}\right) e(6361121)e\left(\frac{636}{1121}\right) e(3451121)e\left(\frac{345}{1121}\right) e(561121)e\left(\frac{56}{1121}\right)
χ2243(24,⋅)\chi_{2243}(24,\cdot) 2243.h 2242 yes −1-1 11 e(1492242)e\left(\frac{149}{2242}\right) e(7881121)e\left(\frac{788}{1121}\right) e(1491121)e\left(\frac{149}{1121}\right) e(13072242)e\left(\frac{1307}{2242}\right) e(17252242)e\left(\frac{1725}{2242}\right) e(2481121)e\left(\frac{248}{1121}\right) e(4472242)e\left(\frac{447}{2242}\right) e(4551121)e\left(\frac{455}{1121}\right) e(7281121)e\left(\frac{728}{1121}\right) e(8721121)e\left(\frac{872}{1121}\right)
χ2243(25,⋅)\chi_{2243}(25,\cdot) 2243.g 1121 yes 11 11 e(2421121)e\left(\frac{242}{1121}\right) e(5811121)e\left(\frac{581}{1121}\right) e(4841121)e\left(\frac{484}{1121}\right) e(2721121)e\left(\frac{272}{1121}\right) e(8231121)e\left(\frac{823}{1121}\right) e(10991121)e\left(\frac{1099}{1121}\right) e(7261121)e\left(\frac{726}{1121}\right) e(411121)e\left(\frac{41}{1121}\right) e(5141121)e\left(\frac{514}{1121}\right) e(8991121)e\left(\frac{899}{1121}\right)
χ2243(26,⋅)\chi_{2243}(26,\cdot) 2243.g 1121 yes 11 11 e(9331121)e\left(\frac{933}{1121}\right) e(5771121)e\left(\frac{577}{1121}\right) e(7451121)e\left(\frac{745}{1121}\right) e(4651121)e\left(\frac{465}{1121}\right) e(3891121)e\left(\frac{389}{1121}\right) e(1191121)e\left(\frac{119}{1121}\right) e(5571121)e\left(\frac{557}{1121}\right) e(331121)e\left(\frac{33}{1121}\right) e(2771121)e\left(\frac{277}{1121}\right) e(9971121)e\left(\frac{997}{1121}\right)
χ2243(27,⋅)\chi_{2243}(27,\cdot) 2243.g 1121 yes 11 11 e(2191121)e\left(\frac{219}{1121}\right) e(5861121)e\left(\frac{586}{1121}\right) e(4381121)e\left(\frac{438}{1121}\right) e(3111121)e\left(\frac{311}{1121}\right) e(8051121)e\left(\frac{805}{1121}\right) e(821121)e\left(\frac{82}{1121}\right) e(6571121)e\left(\frac{657}{1121}\right) e(511121)e\left(\frac{51}{1121}\right) e(5301121)e\left(\frac{530}{1121}\right) e(2161121)e\left(\frac{216}{1121}\right)
χ2243(28,⋅)\chi_{2243}(28,\cdot) 2243.g 1121 yes 11 11 e(10711121)e\left(\frac{1071}{1121}\right) e(5471121)e\left(\frac{547}{1121}\right) e(10211121)e\left(\frac{1021}{1121}\right) e(2311121)e\left(\frac{231}{1121}\right) e(4971121)e\left(\frac{497}{1121}\right) e(6161121)e\left(\frac{616}{1121}\right) e(9711121)e\left(\frac{971}{1121}\right) e(10941121)e\left(\frac{1094}{1121}\right) e(1811121)e\left(\frac{181}{1121}\right) e(6111121)e\left(\frac{611}{1121}\right)
χ2243(29,⋅)\chi_{2243}(29,\cdot) 2243.h 2242 yes −1-1 11 e(5592242)e\left(\frac{559}{2242}\right) e(4511121)e\left(\frac{451}{1121}\right) e(5591121)e\left(\frac{559}{1121}\right) e(18792242)e\left(\frac{1879}{2242}\right) e(14612242)e\left(\frac{1461}{2242}\right) e(6371121)e\left(\frac{637}{1121}\right) e(16772242)e\left(\frac{1677}{2242}\right) e(9021121)e\left(\frac{902}{1121}\right) e(981121)e\left(\frac{98}{1121}\right) e(7211121)e\left(\frac{721}{1121}\right)
χ2243(30,⋅)\chi_{2243}(30,\cdot) 2243.g 1121 yes 11 11 e(7551121)e\left(\frac{755}{1121}\right) e(3721121)e\left(\frac{372}{1121}\right) e(3891121)e\left(\frac{389}{1121}\right) e(11081121)e\left(\frac{1108}{1121}\right) e(61121)e\left(\frac{6}{1121}\right) e(3391121)e\left(\frac{339}{1121}\right) e(231121)e\left(\frac{23}{1121}\right) e(7441121)e\left(\frac{744}{1121}\right) e(7421121)e\left(\frac{742}{1121}\right) e(9751121)e\left(\frac{975}{1121}\right)
χ2243(31,⋅)\chi_{2243}(31,\cdot) 2243.g 1121 yes 11 11 e(3061121)e\left(\frac{306}{1121}\right) e(9571121)e\left(\frac{957}{1121}\right) e(6121121)e\left(\frac{612}{1121}\right) e(661121)e\left(\frac{66}{1121}\right) e(1421121)e\left(\frac{142}{1121}\right) e(1761121)e\left(\frac{176}{1121}\right) e(9181121)e\left(\frac{918}{1121}\right) e(7931121)e\left(\frac{793}{1121}\right) e(3721121)e\left(\frac{372}{1121}\right) e(6551121)e\left(\frac{655}{1121}\right)
χ2243(32,⋅)\chi_{2243}(32,\cdot) 2243.h 2242 yes −1-1 11 e(52242)e\left(\frac{5}{2242}\right) e(3651121)e\left(\frac{365}{1121}\right) e(51121)e\left(\frac{5}{1121}\right) e(892242)e\left(\frac{89}{2242}\right) e(7352242)e\left(\frac{735}{2242}\right) e(8661121)e\left(\frac{866}{1121}\right) e(152242)e\left(\frac{15}{2242}\right) e(7301121)e\left(\frac{730}{1121}\right) e(471121)e\left(\frac{47}{1121}\right) e(5861121)e\left(\frac{586}{1121}\right)
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