# Properties

 Modulus $5269$ Structure $$C_{2390}\times C_{2}$$ Order $4780$

Show commands for: Pari/GP / SageMath

sage: H = DirichletGroup(5269)

pari: g = idealstar(,5269,2)

## Character group

 sage: G.order()  pari: g.no Order = 4780 sage: H.invariants()  pari: g.cyc Structure = $$C_{2390}\times C_{2}$$ sage: H.gens()  pari: g.gen Generators = $\chi_{5269}(959,\cdot)$, $\chi_{5269}(4324,\cdot)$

## First 32 of 4780 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 $$-1$$ $$1$$ $$2$$ $$3$$ $$4$$ $$5$$ $$6$$ $$7$$ $$8$$ $$9$$ $$10$$ $$12$$
$$\chi_{5269}(1,\cdot)$$ 5269.a 1 no $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{5269}(2,\cdot)$$ 5269.n 2390 yes $$-1$$ $$1$$ $$e\left(\frac{599}{2390}\right)$$ $$e\left(\frac{676}{1195}\right)$$ $$e\left(\frac{599}{1195}\right)$$ $$e\left(\frac{1053}{1195}\right)$$ $$e\left(\frac{1951}{2390}\right)$$ $$e\left(\frac{1623}{2390}\right)$$ $$e\left(\frac{1797}{2390}\right)$$ $$e\left(\frac{157}{1195}\right)$$ $$e\left(\frac{63}{478}\right)$$ $$e\left(\frac{16}{239}\right)$$
$$\chi_{5269}(3,\cdot)$$ 5269.m 1195 yes $$1$$ $$1$$ $$e\left(\frac{676}{1195}\right)$$ $$e\left(\frac{648}{1195}\right)$$ $$e\left(\frac{157}{1195}\right)$$ $$e\left(\frac{274}{1195}\right)$$ $$e\left(\frac{129}{1195}\right)$$ $$e\left(\frac{92}{1195}\right)$$ $$e\left(\frac{833}{1195}\right)$$ $$e\left(\frac{101}{1195}\right)$$ $$e\left(\frac{190}{239}\right)$$ $$e\left(\frac{161}{239}\right)$$
$$\chi_{5269}(4,\cdot)$$ 5269.m 1195 yes $$1$$ $$1$$ $$e\left(\frac{599}{1195}\right)$$ $$e\left(\frac{157}{1195}\right)$$ $$e\left(\frac{3}{1195}\right)$$ $$e\left(\frac{911}{1195}\right)$$ $$e\left(\frac{756}{1195}\right)$$ $$e\left(\frac{428}{1195}\right)$$ $$e\left(\frac{602}{1195}\right)$$ $$e\left(\frac{314}{1195}\right)$$ $$e\left(\frac{63}{239}\right)$$ $$e\left(\frac{32}{239}\right)$$
$$\chi_{5269}(5,\cdot)$$ 5269.m 1195 yes $$1$$ $$1$$ $$e\left(\frac{1053}{1195}\right)$$ $$e\left(\frac{274}{1195}\right)$$ $$e\left(\frac{911}{1195}\right)$$ $$e\left(\frac{197}{1195}\right)$$ $$e\left(\frac{132}{1195}\right)$$ $$e\left(\frac{511}{1195}\right)$$ $$e\left(\frac{769}{1195}\right)$$ $$e\left(\frac{548}{1195}\right)$$ $$e\left(\frac{11}{239}\right)$$ $$e\left(\frac{237}{239}\right)$$
$$\chi_{5269}(6,\cdot)$$ 5269.n 2390 yes $$-1$$ $$1$$ $$e\left(\frac{1951}{2390}\right)$$ $$e\left(\frac{129}{1195}\right)$$ $$e\left(\frac{756}{1195}\right)$$ $$e\left(\frac{132}{1195}\right)$$ $$e\left(\frac{2209}{2390}\right)$$ $$e\left(\frac{1807}{2390}\right)$$ $$e\left(\frac{1073}{2390}\right)$$ $$e\left(\frac{258}{1195}\right)$$ $$e\left(\frac{443}{478}\right)$$ $$e\left(\frac{177}{239}\right)$$
$$\chi_{5269}(7,\cdot)$$ 5269.n 2390 yes $$-1$$ $$1$$ $$e\left(\frac{1623}{2390}\right)$$ $$e\left(\frac{92}{1195}\right)$$ $$e\left(\frac{428}{1195}\right)$$ $$e\left(\frac{511}{1195}\right)$$ $$e\left(\frac{1807}{2390}\right)$$ $$e\left(\frac{631}{2390}\right)$$ $$e\left(\frac{89}{2390}\right)$$ $$e\left(\frac{184}{1195}\right)$$ $$e\left(\frac{51}{478}\right)$$ $$e\left(\frac{104}{239}\right)$$
$$\chi_{5269}(8,\cdot)$$ 5269.n 2390 yes $$-1$$ $$1$$ $$e\left(\frac{1797}{2390}\right)$$ $$e\left(\frac{833}{1195}\right)$$ $$e\left(\frac{602}{1195}\right)$$ $$e\left(\frac{769}{1195}\right)$$ $$e\left(\frac{1073}{2390}\right)$$ $$e\left(\frac{89}{2390}\right)$$ $$e\left(\frac{611}{2390}\right)$$ $$e\left(\frac{471}{1195}\right)$$ $$e\left(\frac{189}{478}\right)$$ $$e\left(\frac{48}{239}\right)$$
$$\chi_{5269}(9,\cdot)$$ 5269.m 1195 yes $$1$$ $$1$$ $$e\left(\frac{157}{1195}\right)$$ $$e\left(\frac{101}{1195}\right)$$ $$e\left(\frac{314}{1195}\right)$$ $$e\left(\frac{548}{1195}\right)$$ $$e\left(\frac{258}{1195}\right)$$ $$e\left(\frac{184}{1195}\right)$$ $$e\left(\frac{471}{1195}\right)$$ $$e\left(\frac{202}{1195}\right)$$ $$e\left(\frac{141}{239}\right)$$ $$e\left(\frac{83}{239}\right)$$
$$\chi_{5269}(10,\cdot)$$ 5269.l 478 yes $$-1$$ $$1$$ $$e\left(\frac{63}{478}\right)$$ $$e\left(\frac{190}{239}\right)$$ $$e\left(\frac{63}{239}\right)$$ $$e\left(\frac{11}{239}\right)$$ $$e\left(\frac{443}{478}\right)$$ $$e\left(\frac{51}{478}\right)$$ $$e\left(\frac{189}{478}\right)$$ $$e\left(\frac{141}{239}\right)$$ $$e\left(\frac{85}{478}\right)$$ $$e\left(\frac{14}{239}\right)$$
$$\chi_{5269}(12,\cdot)$$ 5269.i 239 no $$1$$ $$1$$ $$e\left(\frac{16}{239}\right)$$ $$e\left(\frac{161}{239}\right)$$ $$e\left(\frac{32}{239}\right)$$ $$e\left(\frac{237}{239}\right)$$ $$e\left(\frac{177}{239}\right)$$ $$e\left(\frac{104}{239}\right)$$ $$e\left(\frac{48}{239}\right)$$ $$e\left(\frac{83}{239}\right)$$ $$e\left(\frac{14}{239}\right)$$ $$e\left(\frac{193}{239}\right)$$
$$\chi_{5269}(13,\cdot)$$ 5269.o 2390 yes $$1$$ $$1$$ $$e\left(\frac{2049}{2390}\right)$$ $$e\left(\frac{876}{1195}\right)$$ $$e\left(\frac{854}{1195}\right)$$ $$e\left(\frac{813}{1195}\right)$$ $$e\left(\frac{1411}{2390}\right)$$ $$e\left(\frac{293}{2390}\right)$$ $$e\left(\frac{1367}{2390}\right)$$ $$e\left(\frac{557}{1195}\right)$$ $$e\left(\frac{257}{478}\right)$$ $$e\left(\frac{107}{239}\right)$$
$$\chi_{5269}(14,\cdot)$$ 5269.m 1195 yes $$1$$ $$1$$ $$e\left(\frac{1111}{1195}\right)$$ $$e\left(\frac{768}{1195}\right)$$ $$e\left(\frac{1027}{1195}\right)$$ $$e\left(\frac{369}{1195}\right)$$ $$e\left(\frac{684}{1195}\right)$$ $$e\left(\frac{1127}{1195}\right)$$ $$e\left(\frac{943}{1195}\right)$$ $$e\left(\frac{341}{1195}\right)$$ $$e\left(\frac{57}{239}\right)$$ $$e\left(\frac{120}{239}\right)$$
$$\chi_{5269}(15,\cdot)$$ 5269.m 1195 yes $$1$$ $$1$$ $$e\left(\frac{534}{1195}\right)$$ $$e\left(\frac{922}{1195}\right)$$ $$e\left(\frac{1068}{1195}\right)$$ $$e\left(\frac{471}{1195}\right)$$ $$e\left(\frac{261}{1195}\right)$$ $$e\left(\frac{603}{1195}\right)$$ $$e\left(\frac{407}{1195}\right)$$ $$e\left(\frac{649}{1195}\right)$$ $$e\left(\frac{201}{239}\right)$$ $$e\left(\frac{159}{239}\right)$$
$$\chi_{5269}(16,\cdot)$$ 5269.m 1195 yes $$1$$ $$1$$ $$e\left(\frac{3}{1195}\right)$$ $$e\left(\frac{314}{1195}\right)$$ $$e\left(\frac{6}{1195}\right)$$ $$e\left(\frac{627}{1195}\right)$$ $$e\left(\frac{317}{1195}\right)$$ $$e\left(\frac{856}{1195}\right)$$ $$e\left(\frac{9}{1195}\right)$$ $$e\left(\frac{628}{1195}\right)$$ $$e\left(\frac{126}{239}\right)$$ $$e\left(\frac{64}{239}\right)$$
$$\chi_{5269}(17,\cdot)$$ 5269.o 2390 yes $$1$$ $$1$$ $$e\left(\frac{921}{2390}\right)$$ $$e\left(\frac{399}{1195}\right)$$ $$e\left(\frac{921}{1195}\right)$$ $$e\left(\frac{47}{1195}\right)$$ $$e\left(\frac{1719}{2390}\right)$$ $$e\left(\frac{1087}{2390}\right)$$ $$e\left(\frac{373}{2390}\right)$$ $$e\left(\frac{798}{1195}\right)$$ $$e\left(\frac{203}{478}\right)$$ $$e\left(\frac{25}{239}\right)$$
$$\chi_{5269}(18,\cdot)$$ 5269.n 2390 yes $$-1$$ $$1$$ $$e\left(\frac{913}{2390}\right)$$ $$e\left(\frac{777}{1195}\right)$$ $$e\left(\frac{913}{1195}\right)$$ $$e\left(\frac{406}{1195}\right)$$ $$e\left(\frac{77}{2390}\right)$$ $$e\left(\frac{1991}{2390}\right)$$ $$e\left(\frac{349}{2390}\right)$$ $$e\left(\frac{359}{1195}\right)$$ $$e\left(\frac{345}{478}\right)$$ $$e\left(\frac{99}{239}\right)$$
$$\chi_{5269}(19,\cdot)$$ 5269.o 2390 yes $$1$$ $$1$$ $$e\left(\frac{1527}{2390}\right)$$ $$e\left(\frac{1043}{1195}\right)$$ $$e\left(\frac{332}{1195}\right)$$ $$e\left(\frac{39}{1195}\right)$$ $$e\left(\frac{1223}{2390}\right)$$ $$e\left(\frac{1919}{2390}\right)$$ $$e\left(\frac{2191}{2390}\right)$$ $$e\left(\frac{891}{1195}\right)$$ $$e\left(\frac{321}{478}\right)$$ $$e\left(\frac{36}{239}\right)$$
$$\chi_{5269}(20,\cdot)$$ 5269.m 1195 yes $$1$$ $$1$$ $$e\left(\frac{457}{1195}\right)$$ $$e\left(\frac{431}{1195}\right)$$ $$e\left(\frac{914}{1195}\right)$$ $$e\left(\frac{1108}{1195}\right)$$ $$e\left(\frac{888}{1195}\right)$$ $$e\left(\frac{939}{1195}\right)$$ $$e\left(\frac{176}{1195}\right)$$ $$e\left(\frac{862}{1195}\right)$$ $$e\left(\frac{74}{239}\right)$$ $$e\left(\frac{30}{239}\right)$$
$$\chi_{5269}(21,\cdot)$$ 5269.l 478 yes $$-1$$ $$1$$ $$e\left(\frac{117}{478}\right)$$ $$e\left(\frac{148}{239}\right)$$ $$e\left(\frac{117}{239}\right)$$ $$e\left(\frac{157}{239}\right)$$ $$e\left(\frac{413}{478}\right)$$ $$e\left(\frac{163}{478}\right)$$ $$e\left(\frac{351}{478}\right)$$ $$e\left(\frac{57}{239}\right)$$ $$e\left(\frac{431}{478}\right)$$ $$e\left(\frac{26}{239}\right)$$
$$\chi_{5269}(23,\cdot)$$ 5269.i 239 no $$1$$ $$1$$ $$e\left(\frac{133}{239}\right)$$ $$e\left(\frac{218}{239}\right)$$ $$e\left(\frac{27}{239}\right)$$ $$e\left(\frac{73}{239}\right)$$ $$e\left(\frac{112}{239}\right)$$ $$e\left(\frac{28}{239}\right)$$ $$e\left(\frac{160}{239}\right)$$ $$e\left(\frac{197}{239}\right)$$ $$e\left(\frac{206}{239}\right)$$ $$e\left(\frac{6}{239}\right)$$
$$\chi_{5269}(24,\cdot)$$ 5269.n 2390 yes $$-1$$ $$1$$ $$e\left(\frac{759}{2390}\right)$$ $$e\left(\frac{286}{1195}\right)$$ $$e\left(\frac{759}{1195}\right)$$ $$e\left(\frac{1043}{1195}\right)$$ $$e\left(\frac{1331}{2390}\right)$$ $$e\left(\frac{273}{2390}\right)$$ $$e\left(\frac{2277}{2390}\right)$$ $$e\left(\frac{572}{1195}\right)$$ $$e\left(\frac{91}{478}\right)$$ $$e\left(\frac{209}{239}\right)$$
$$\chi_{5269}(25,\cdot)$$ 5269.m 1195 yes $$1$$ $$1$$ $$e\left(\frac{911}{1195}\right)$$ $$e\left(\frac{548}{1195}\right)$$ $$e\left(\frac{627}{1195}\right)$$ $$e\left(\frac{394}{1195}\right)$$ $$e\left(\frac{264}{1195}\right)$$ $$e\left(\frac{1022}{1195}\right)$$ $$e\left(\frac{343}{1195}\right)$$ $$e\left(\frac{1096}{1195}\right)$$ $$e\left(\frac{22}{239}\right)$$ $$e\left(\frac{235}{239}\right)$$
$$\chi_{5269}(26,\cdot)$$ 5269.p 2390 yes $$-1$$ $$1$$ $$e\left(\frac{129}{1195}\right)$$ $$e\left(\frac{357}{1195}\right)$$ $$e\left(\frac{258}{1195}\right)$$ $$e\left(\frac{671}{1195}\right)$$ $$e\left(\frac{486}{1195}\right)$$ $$e\left(\frac{958}{1195}\right)$$ $$e\left(\frac{387}{1195}\right)$$ $$e\left(\frac{714}{1195}\right)$$ $$e\left(\frac{160}{239}\right)$$ $$e\left(\frac{123}{239}\right)$$
$$\chi_{5269}(27,\cdot)$$ 5269.m 1195 yes $$1$$ $$1$$ $$e\left(\frac{833}{1195}\right)$$ $$e\left(\frac{749}{1195}\right)$$ $$e\left(\frac{471}{1195}\right)$$ $$e\left(\frac{822}{1195}\right)$$ $$e\left(\frac{387}{1195}\right)$$ $$e\left(\frac{276}{1195}\right)$$ $$e\left(\frac{109}{1195}\right)$$ $$e\left(\frac{303}{1195}\right)$$ $$e\left(\frac{92}{239}\right)$$ $$e\left(\frac{5}{239}\right)$$
$$\chi_{5269}(28,\cdot)$$ 5269.n 2390 yes $$-1$$ $$1$$ $$e\left(\frac{431}{2390}\right)$$ $$e\left(\frac{249}{1195}\right)$$ $$e\left(\frac{431}{1195}\right)$$ $$e\left(\frac{227}{1195}\right)$$ $$e\left(\frac{929}{2390}\right)$$ $$e\left(\frac{1487}{2390}\right)$$ $$e\left(\frac{1293}{2390}\right)$$ $$e\left(\frac{498}{1195}\right)$$ $$e\left(\frac{177}{478}\right)$$ $$e\left(\frac{136}{239}\right)$$
$$\chi_{5269}(29,\cdot)$$ 5269.o 2390 yes $$1$$ $$1$$ $$e\left(\frac{823}{2390}\right)$$ $$e\left(\frac{847}{1195}\right)$$ $$e\left(\frac{823}{1195}\right)$$ $$e\left(\frac{561}{1195}\right)$$ $$e\left(\frac{127}{2390}\right)$$ $$e\left(\frac{211}{2390}\right)$$ $$e\left(\frac{79}{2390}\right)$$ $$e\left(\frac{499}{1195}\right)$$ $$e\left(\frac{389}{478}\right)$$ $$e\left(\frac{95}{239}\right)$$
$$\chi_{5269}(30,\cdot)$$ 5269.n 2390 yes $$-1$$ $$1$$ $$e\left(\frac{1667}{2390}\right)$$ $$e\left(\frac{403}{1195}\right)$$ $$e\left(\frac{472}{1195}\right)$$ $$e\left(\frac{329}{1195}\right)$$ $$e\left(\frac{83}{2390}\right)$$ $$e\left(\frac{439}{2390}\right)$$ $$e\left(\frac{221}{2390}\right)$$ $$e\left(\frac{806}{1195}\right)$$ $$e\left(\frac{465}{478}\right)$$ $$e\left(\frac{175}{239}\right)$$
$$\chi_{5269}(31,\cdot)$$ 5269.p 2390 yes $$-1$$ $$1$$ $$e\left(\frac{577}{1195}\right)$$ $$e\left(\frac{1041}{1195}\right)$$ $$e\left(\frac{1154}{1195}\right)$$ $$e\left(\frac{1093}{1195}\right)$$ $$e\left(\frac{423}{1195}\right)$$ $$e\left(\frac{524}{1195}\right)$$ $$e\left(\frac{536}{1195}\right)$$ $$e\left(\frac{887}{1195}\right)$$ $$e\left(\frac{95}{239}\right)$$ $$e\left(\frac{200}{239}\right)$$
$$\chi_{5269}(32,\cdot)$$ 5269.l 478 yes $$-1$$ $$1$$ $$e\left(\frac{121}{478}\right)$$ $$e\left(\frac{198}{239}\right)$$ $$e\left(\frac{121}{239}\right)$$ $$e\left(\frac{97}{239}\right)$$ $$e\left(\frac{39}{478}\right)$$ $$e\left(\frac{189}{478}\right)$$ $$e\left(\frac{363}{478}\right)$$ $$e\left(\frac{157}{239}\right)$$ $$e\left(\frac{315}{478}\right)$$ $$e\left(\frac{80}{239}\right)$$
$$\chi_{5269}(34,\cdot)$$ 5269.j 478 no $$-1$$ $$1$$ $$e\left(\frac{152}{239}\right)$$ $$e\left(\frac{215}{239}\right)$$ $$e\left(\frac{65}{239}\right)$$ $$e\left(\frac{220}{239}\right)$$ $$e\left(\frac{128}{239}\right)$$ $$e\left(\frac{32}{239}\right)$$ $$e\left(\frac{217}{239}\right)$$ $$e\left(\frac{191}{239}\right)$$ $$e\left(\frac{133}{239}\right)$$ $$e\left(\frac{41}{239}\right)$$
$$\chi_{5269}(35,\cdot)$$ 5269.n 2390 yes $$-1$$ $$1$$ $$e\left(\frac{1339}{2390}\right)$$ $$e\left(\frac{366}{1195}\right)$$ $$e\left(\frac{144}{1195}\right)$$ $$e\left(\frac{708}{1195}\right)$$ $$e\left(\frac{2071}{2390}\right)$$ $$e\left(\frac{1653}{2390}\right)$$ $$e\left(\frac{1627}{2390}\right)$$ $$e\left(\frac{732}{1195}\right)$$ $$e\left(\frac{73}{478}\right)$$ $$e\left(\frac{102}{239}\right)$$