Properties

 Modulus $2243$ Structure $$C_{2242}$$ Order $2242$

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 = $$C_{2242}$$ sage: H.gens()  pari: g.gen Generators = $\chi_{2243}(2,\cdot)$

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 $$-1$$ $$1$$ $$2$$ $$3$$ $$4$$ $$5$$ $$6$$ $$7$$ $$8$$ $$9$$ $$10$$ $$11$$
$$\chi_{2243}(1,\cdot)$$ 2243.a 1 no $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{2243}(2,\cdot)$$ 2243.h 2242 yes $$-1$$ $$1$$ $$e\left(\frac{1}{2242}\right)$$ $$e\left(\frac{73}{1121}\right)$$ $$e\left(\frac{1}{1121}\right)$$ $$e\left(\frac{1363}{2242}\right)$$ $$e\left(\frac{147}{2242}\right)$$ $$e\left(\frac{1070}{1121}\right)$$ $$e\left(\frac{3}{2242}\right)$$ $$e\left(\frac{146}{1121}\right)$$ $$e\left(\frac{682}{1121}\right)$$ $$e\left(\frac{1014}{1121}\right)$$
$$\chi_{2243}(3,\cdot)$$ 2243.g 1121 yes $$1$$ $$1$$ $$e\left(\frac{73}{1121}\right)$$ $$e\left(\frac{569}{1121}\right)$$ $$e\left(\frac{146}{1121}\right)$$ $$e\left(\frac{851}{1121}\right)$$ $$e\left(\frac{642}{1121}\right)$$ $$e\left(\frac{401}{1121}\right)$$ $$e\left(\frac{219}{1121}\right)$$ $$e\left(\frac{17}{1121}\right)$$ $$e\left(\frac{924}{1121}\right)$$ $$e\left(\frac{72}{1121}\right)$$
$$\chi_{2243}(4,\cdot)$$ 2243.g 1121 yes $$1$$ $$1$$ $$e\left(\frac{1}{1121}\right)$$ $$e\left(\frac{146}{1121}\right)$$ $$e\left(\frac{2}{1121}\right)$$ $$e\left(\frac{242}{1121}\right)$$ $$e\left(\frac{147}{1121}\right)$$ $$e\left(\frac{1019}{1121}\right)$$ $$e\left(\frac{3}{1121}\right)$$ $$e\left(\frac{292}{1121}\right)$$ $$e\left(\frac{243}{1121}\right)$$ $$e\left(\frac{907}{1121}\right)$$
$$\chi_{2243}(5,\cdot)$$ 2243.h 2242 yes $$-1$$ $$1$$ $$e\left(\frac{1363}{2242}\right)$$ $$e\left(\frac{851}{1121}\right)$$ $$e\left(\frac{242}{1121}\right)$$ $$e\left(\frac{1393}{2242}\right)$$ $$e\left(\frac{823}{2242}\right)$$ $$e\left(\frac{1110}{1121}\right)$$ $$e\left(\frac{1847}{2242}\right)$$ $$e\left(\frac{581}{1121}\right)$$ $$e\left(\frac{257}{1121}\right)$$ $$e\left(\frac{1010}{1121}\right)$$
$$\chi_{2243}(6,\cdot)$$ 2243.h 2242 yes $$-1$$ $$1$$ $$e\left(\frac{147}{2242}\right)$$ $$e\left(\frac{642}{1121}\right)$$ $$e\left(\frac{147}{1121}\right)$$ $$e\left(\frac{823}{2242}\right)$$ $$e\left(\frac{1431}{2242}\right)$$ $$e\left(\frac{350}{1121}\right)$$ $$e\left(\frac{441}{2242}\right)$$ $$e\left(\frac{163}{1121}\right)$$ $$e\left(\frac{485}{1121}\right)$$ $$e\left(\frac{1086}{1121}\right)$$
$$\chi_{2243}(7,\cdot)$$ 2243.g 1121 yes $$1$$ $$1$$ $$e\left(\frac{1070}{1121}\right)$$ $$e\left(\frac{401}{1121}\right)$$ $$e\left(\frac{1019}{1121}\right)$$ $$e\left(\frac{1110}{1121}\right)$$ $$e\left(\frac{350}{1121}\right)$$ $$e\left(\frac{718}{1121}\right)$$ $$e\left(\frac{968}{1121}\right)$$ $$e\left(\frac{802}{1121}\right)$$ $$e\left(\frac{1059}{1121}\right)$$ $$e\left(\frac{825}{1121}\right)$$
$$\chi_{2243}(8,\cdot)$$ 2243.h 2242 yes $$-1$$ $$1$$ $$e\left(\frac{3}{2242}\right)$$ $$e\left(\frac{219}{1121}\right)$$ $$e\left(\frac{3}{1121}\right)$$ $$e\left(\frac{1847}{2242}\right)$$ $$e\left(\frac{441}{2242}\right)$$ $$e\left(\frac{968}{1121}\right)$$ $$e\left(\frac{9}{2242}\right)$$ $$e\left(\frac{438}{1121}\right)$$ $$e\left(\frac{925}{1121}\right)$$ $$e\left(\frac{800}{1121}\right)$$
$$\chi_{2243}(9,\cdot)$$ 2243.g 1121 yes $$1$$ $$1$$ $$e\left(\frac{146}{1121}\right)$$ $$e\left(\frac{17}{1121}\right)$$ $$e\left(\frac{292}{1121}\right)$$ $$e\left(\frac{581}{1121}\right)$$ $$e\left(\frac{163}{1121}\right)$$ $$e\left(\frac{802}{1121}\right)$$ $$e\left(\frac{438}{1121}\right)$$ $$e\left(\frac{34}{1121}\right)$$ $$e\left(\frac{727}{1121}\right)$$ $$e\left(\frac{144}{1121}\right)$$
$$\chi_{2243}(10,\cdot)$$ 2243.g 1121 yes $$1$$ $$1$$ $$e\left(\frac{682}{1121}\right)$$ $$e\left(\frac{924}{1121}\right)$$ $$e\left(\frac{243}{1121}\right)$$ $$e\left(\frac{257}{1121}\right)$$ $$e\left(\frac{485}{1121}\right)$$ $$e\left(\frac{1059}{1121}\right)$$ $$e\left(\frac{925}{1121}\right)$$ $$e\left(\frac{727}{1121}\right)$$ $$e\left(\frac{939}{1121}\right)$$ $$e\left(\frac{903}{1121}\right)$$
$$\chi_{2243}(11,\cdot)$$ 2243.g 1121 yes $$1$$ $$1$$ $$e\left(\frac{1014}{1121}\right)$$ $$e\left(\frac{72}{1121}\right)$$ $$e\left(\frac{907}{1121}\right)$$ $$e\left(\frac{1010}{1121}\right)$$ $$e\left(\frac{1086}{1121}\right)$$ $$e\left(\frac{825}{1121}\right)$$ $$e\left(\frac{800}{1121}\right)$$ $$e\left(\frac{144}{1121}\right)$$ $$e\left(\frac{903}{1121}\right)$$ $$e\left(\frac{478}{1121}\right)$$
$$\chi_{2243}(12,\cdot)$$ 2243.g 1121 yes $$1$$ $$1$$ $$e\left(\frac{74}{1121}\right)$$ $$e\left(\frac{715}{1121}\right)$$ $$e\left(\frac{148}{1121}\right)$$ $$e\left(\frac{1093}{1121}\right)$$ $$e\left(\frac{789}{1121}\right)$$ $$e\left(\frac{299}{1121}\right)$$ $$e\left(\frac{222}{1121}\right)$$ $$e\left(\frac{309}{1121}\right)$$ $$e\left(\frac{46}{1121}\right)$$ $$e\left(\frac{979}{1121}\right)$$
$$\chi_{2243}(13,\cdot)$$ 2243.h 2242 yes $$-1$$ $$1$$ $$e\left(\frac{1865}{2242}\right)$$ $$e\left(\frac{504}{1121}\right)$$ $$e\left(\frac{744}{1121}\right)$$ $$e\left(\frac{1809}{2242}\right)$$ $$e\left(\frac{631}{2242}\right)$$ $$e\left(\frac{170}{1121}\right)$$ $$e\left(\frac{1111}{2242}\right)$$ $$e\left(\frac{1008}{1121}\right)$$ $$e\left(\frac{716}{1121}\right)$$ $$e\left(\frac{1104}{1121}\right)$$
$$\chi_{2243}(14,\cdot)$$ 2243.h 2242 yes $$-1$$ $$1$$ $$e\left(\frac{2141}{2242}\right)$$ $$e\left(\frac{474}{1121}\right)$$ $$e\left(\frac{1020}{1121}\right)$$ $$e\left(\frac{1341}{2242}\right)$$ $$e\left(\frac{847}{2242}\right)$$ $$e\left(\frac{667}{1121}\right)$$ $$e\left(\frac{1939}{2242}\right)$$ $$e\left(\frac{948}{1121}\right)$$ $$e\left(\frac{620}{1121}\right)$$ $$e\left(\frac{718}{1121}\right)$$
$$\chi_{2243}(15,\cdot)$$ 2243.h 2242 yes $$-1$$ $$1$$ $$e\left(\frac{1509}{2242}\right)$$ $$e\left(\frac{299}{1121}\right)$$ $$e\left(\frac{388}{1121}\right)$$ $$e\left(\frac{853}{2242}\right)$$ $$e\left(\frac{2107}{2242}\right)$$ $$e\left(\frac{390}{1121}\right)$$ $$e\left(\frac{43}{2242}\right)$$ $$e\left(\frac{598}{1121}\right)$$ $$e\left(\frac{60}{1121}\right)$$ $$e\left(\frac{1082}{1121}\right)$$
$$\chi_{2243}(16,\cdot)$$ 2243.g 1121 yes $$1$$ $$1$$ $$e\left(\frac{2}{1121}\right)$$ $$e\left(\frac{292}{1121}\right)$$ $$e\left(\frac{4}{1121}\right)$$ $$e\left(\frac{484}{1121}\right)$$ $$e\left(\frac{294}{1121}\right)$$ $$e\left(\frac{917}{1121}\right)$$ $$e\left(\frac{6}{1121}\right)$$ $$e\left(\frac{584}{1121}\right)$$ $$e\left(\frac{486}{1121}\right)$$ $$e\left(\frac{693}{1121}\right)$$
$$\chi_{2243}(17,\cdot)$$ 2243.g 1121 yes $$1$$ $$1$$ $$e\left(\frac{33}{1121}\right)$$ $$e\left(\frac{334}{1121}\right)$$ $$e\left(\frac{66}{1121}\right)$$ $$e\left(\frac{139}{1121}\right)$$ $$e\left(\frac{367}{1121}\right)$$ $$e\left(\frac{1118}{1121}\right)$$ $$e\left(\frac{99}{1121}\right)$$ $$e\left(\frac{668}{1121}\right)$$ $$e\left(\frac{172}{1121}\right)$$ $$e\left(\frac{785}{1121}\right)$$
$$\chi_{2243}(18,\cdot)$$ 2243.h 2242 yes $$-1$$ $$1$$ $$e\left(\frac{293}{2242}\right)$$ $$e\left(\frac{90}{1121}\right)$$ $$e\left(\frac{293}{1121}\right)$$ $$e\left(\frac{283}{2242}\right)$$ $$e\left(\frac{473}{2242}\right)$$ $$e\left(\frac{751}{1121}\right)$$ $$e\left(\frac{879}{2242}\right)$$ $$e\left(\frac{180}{1121}\right)$$ $$e\left(\frac{288}{1121}\right)$$ $$e\left(\frac{37}{1121}\right)$$
$$\chi_{2243}(19,\cdot)$$ 2243.h 2242 yes $$-1$$ $$1$$ $$e\left(\frac{329}{2242}\right)$$ $$e\left(\frac{476}{1121}\right)$$ $$e\left(\frac{329}{1121}\right)$$ $$e\left(\frac{27}{2242}\right)$$ $$e\left(\frac{1281}{2242}\right)$$ $$e\left(\frac{36}{1121}\right)$$ $$e\left(\frac{987}{2242}\right)$$ $$e\left(\frac{952}{1121}\right)$$ $$e\left(\frac{178}{1121}\right)$$ $$e\left(\frac{669}{1121}\right)$$
$$\chi_{2243}(20,\cdot)$$ 2243.h 2242 yes $$-1$$ $$1$$ $$e\left(\frac{1365}{2242}\right)$$ $$e\left(\frac{997}{1121}\right)$$ $$e\left(\frac{244}{1121}\right)$$ $$e\left(\frac{1877}{2242}\right)$$ $$e\left(\frac{1117}{2242}\right)$$ $$e\left(\frac{1008}{1121}\right)$$ $$e\left(\frac{1853}{2242}\right)$$ $$e\left(\frac{873}{1121}\right)$$ $$e\left(\frac{500}{1121}\right)$$ $$e\left(\frac{796}{1121}\right)$$
$$\chi_{2243}(21,\cdot)$$ 2243.g 1121 yes $$1$$ $$1$$ $$e\left(\frac{22}{1121}\right)$$ $$e\left(\frac{970}{1121}\right)$$ $$e\left(\frac{44}{1121}\right)$$ $$e\left(\frac{840}{1121}\right)$$ $$e\left(\frac{992}{1121}\right)$$ $$e\left(\frac{1119}{1121}\right)$$ $$e\left(\frac{66}{1121}\right)$$ $$e\left(\frac{819}{1121}\right)$$ $$e\left(\frac{862}{1121}\right)$$ $$e\left(\frac{897}{1121}\right)$$
$$\chi_{2243}(22,\cdot)$$ 2243.h 2242 yes $$-1$$ $$1$$ $$e\left(\frac{2029}{2242}\right)$$ $$e\left(\frac{145}{1121}\right)$$ $$e\left(\frac{908}{1121}\right)$$ $$e\left(\frac{1141}{2242}\right)$$ $$e\left(\frac{77}{2242}\right)$$ $$e\left(\frac{774}{1121}\right)$$ $$e\left(\frac{1603}{2242}\right)$$ $$e\left(\frac{290}{1121}\right)$$ $$e\left(\frac{464}{1121}\right)$$ $$e\left(\frac{371}{1121}\right)$$
$$\chi_{2243}(23,\cdot)$$ 2243.h 2242 yes $$-1$$ $$1$$ $$e\left(\frac{2231}{2242}\right)$$ $$e\left(\frac{318}{1121}\right)$$ $$e\left(\frac{1110}{1121}\right)$$ $$e\left(\frac{701}{2242}\right)$$ $$e\left(\frac{625}{2242}\right)$$ $$e\left(\frac{561}{1121}\right)$$ $$e\left(\frac{2209}{2242}\right)$$ $$e\left(\frac{636}{1121}\right)$$ $$e\left(\frac{345}{1121}\right)$$ $$e\left(\frac{56}{1121}\right)$$
$$\chi_{2243}(24,\cdot)$$ 2243.h 2242 yes $$-1$$ $$1$$ $$e\left(\frac{149}{2242}\right)$$ $$e\left(\frac{788}{1121}\right)$$ $$e\left(\frac{149}{1121}\right)$$ $$e\left(\frac{1307}{2242}\right)$$ $$e\left(\frac{1725}{2242}\right)$$ $$e\left(\frac{248}{1121}\right)$$ $$e\left(\frac{447}{2242}\right)$$ $$e\left(\frac{455}{1121}\right)$$ $$e\left(\frac{728}{1121}\right)$$ $$e\left(\frac{872}{1121}\right)$$
$$\chi_{2243}(25,\cdot)$$ 2243.g 1121 yes $$1$$ $$1$$ $$e\left(\frac{242}{1121}\right)$$ $$e\left(\frac{581}{1121}\right)$$ $$e\left(\frac{484}{1121}\right)$$ $$e\left(\frac{272}{1121}\right)$$ $$e\left(\frac{823}{1121}\right)$$ $$e\left(\frac{1099}{1121}\right)$$ $$e\left(\frac{726}{1121}\right)$$ $$e\left(\frac{41}{1121}\right)$$ $$e\left(\frac{514}{1121}\right)$$ $$e\left(\frac{899}{1121}\right)$$
$$\chi_{2243}(26,\cdot)$$ 2243.g 1121 yes $$1$$ $$1$$ $$e\left(\frac{933}{1121}\right)$$ $$e\left(\frac{577}{1121}\right)$$ $$e\left(\frac{745}{1121}\right)$$ $$e\left(\frac{465}{1121}\right)$$ $$e\left(\frac{389}{1121}\right)$$ $$e\left(\frac{119}{1121}\right)$$ $$e\left(\frac{557}{1121}\right)$$ $$e\left(\frac{33}{1121}\right)$$ $$e\left(\frac{277}{1121}\right)$$ $$e\left(\frac{997}{1121}\right)$$
$$\chi_{2243}(27,\cdot)$$ 2243.g 1121 yes $$1$$ $$1$$ $$e\left(\frac{219}{1121}\right)$$ $$e\left(\frac{586}{1121}\right)$$ $$e\left(\frac{438}{1121}\right)$$ $$e\left(\frac{311}{1121}\right)$$ $$e\left(\frac{805}{1121}\right)$$ $$e\left(\frac{82}{1121}\right)$$ $$e\left(\frac{657}{1121}\right)$$ $$e\left(\frac{51}{1121}\right)$$ $$e\left(\frac{530}{1121}\right)$$ $$e\left(\frac{216}{1121}\right)$$
$$\chi_{2243}(28,\cdot)$$ 2243.g 1121 yes $$1$$ $$1$$ $$e\left(\frac{1071}{1121}\right)$$ $$e\left(\frac{547}{1121}\right)$$ $$e\left(\frac{1021}{1121}\right)$$ $$e\left(\frac{231}{1121}\right)$$ $$e\left(\frac{497}{1121}\right)$$ $$e\left(\frac{616}{1121}\right)$$ $$e\left(\frac{971}{1121}\right)$$ $$e\left(\frac{1094}{1121}\right)$$ $$e\left(\frac{181}{1121}\right)$$ $$e\left(\frac{611}{1121}\right)$$
$$\chi_{2243}(29,\cdot)$$ 2243.h 2242 yes $$-1$$ $$1$$ $$e\left(\frac{559}{2242}\right)$$ $$e\left(\frac{451}{1121}\right)$$ $$e\left(\frac{559}{1121}\right)$$ $$e\left(\frac{1879}{2242}\right)$$ $$e\left(\frac{1461}{2242}\right)$$ $$e\left(\frac{637}{1121}\right)$$ $$e\left(\frac{1677}{2242}\right)$$ $$e\left(\frac{902}{1121}\right)$$ $$e\left(\frac{98}{1121}\right)$$ $$e\left(\frac{721}{1121}\right)$$
$$\chi_{2243}(30,\cdot)$$ 2243.g 1121 yes $$1$$ $$1$$ $$e\left(\frac{755}{1121}\right)$$ $$e\left(\frac{372}{1121}\right)$$ $$e\left(\frac{389}{1121}\right)$$ $$e\left(\frac{1108}{1121}\right)$$ $$e\left(\frac{6}{1121}\right)$$ $$e\left(\frac{339}{1121}\right)$$ $$e\left(\frac{23}{1121}\right)$$ $$e\left(\frac{744}{1121}\right)$$ $$e\left(\frac{742}{1121}\right)$$ $$e\left(\frac{975}{1121}\right)$$
$$\chi_{2243}(31,\cdot)$$ 2243.g 1121 yes $$1$$ $$1$$ $$e\left(\frac{306}{1121}\right)$$ $$e\left(\frac{957}{1121}\right)$$ $$e\left(\frac{612}{1121}\right)$$ $$e\left(\frac{66}{1121}\right)$$ $$e\left(\frac{142}{1121}\right)$$ $$e\left(\frac{176}{1121}\right)$$ $$e\left(\frac{918}{1121}\right)$$ $$e\left(\frac{793}{1121}\right)$$ $$e\left(\frac{372}{1121}\right)$$ $$e\left(\frac{655}{1121}\right)$$
$$\chi_{2243}(32,\cdot)$$ 2243.h 2242 yes $$-1$$ $$1$$ $$e\left(\frac{5}{2242}\right)$$ $$e\left(\frac{365}{1121}\right)$$ $$e\left(\frac{5}{1121}\right)$$ $$e\left(\frac{89}{2242}\right)$$ $$e\left(\frac{735}{2242}\right)$$ $$e\left(\frac{866}{1121}\right)$$ $$e\left(\frac{15}{2242}\right)$$ $$e\left(\frac{730}{1121}\right)$$ $$e\left(\frac{47}{1121}\right)$$ $$e\left(\frac{586}{1121}\right)$$