# Properties

 Modulus 1003 Structure $$C_{464}\times C_{2}$$ Order 928

Show commands for: SageMath / Pari/GP

sage: from dirichlet_conrey import DirichletGroup_conrey # requires nonstandard Sage package to be installed

sage: H = DirichletGroup_conrey(1003)

pari: g = idealstar(,1003,2)

## Character group

 sage: G.order()  pari: g.no Order = 928 sage: H.invariants()  pari: g.cyc Structure = $$C_{464}\times C_{2}$$ sage: H.gens()  pari: g.gen Generators = $\chi_{1003}(533,\cdot)$, $\chi_{1003}(1002,\cdot)$

## First 32 of 928 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.

orbit label order primitive -1 1 2 3 4 5 6 7 8 9 10 11
$$\chi_{1003}(1,\cdot)$$ 1003.a 1 No $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{1003}(2,\cdot)$$ 1003.q 232 Yes $$-1$$ $$1$$ $$e\left(\frac{31}{116}\right)$$ $$e\left(\frac{171}{232}\right)$$ $$e\left(\frac{31}{58}\right)$$ $$e\left(\frac{111}{232}\right)$$ $$e\left(\frac{1}{232}\right)$$ $$e\left(\frac{217}{232}\right)$$ $$e\left(\frac{93}{116}\right)$$ $$e\left(\frac{55}{116}\right)$$ $$e\left(\frac{173}{232}\right)$$ $$e\left(\frac{129}{232}\right)$$
$$\chi_{1003}(3,\cdot)$$ 1003.s 464 Yes $$-1$$ $$1$$ $$e\left(\frac{171}{232}\right)$$ $$e\left(\frac{77}{464}\right)$$ $$e\left(\frac{55}{116}\right)$$ $$e\left(\frac{225}{464}\right)$$ $$e\left(\frac{419}{464}\right)$$ $$e\left(\frac{95}{464}\right)$$ $$e\left(\frac{49}{232}\right)$$ $$e\left(\frac{77}{232}\right)$$ $$e\left(\frac{103}{464}\right)$$ $$e\left(\frac{459}{464}\right)$$
$$\chi_{1003}(4,\cdot)$$ 1003.p 116 Yes $$1$$ $$1$$ $$e\left(\frac{31}{58}\right)$$ $$e\left(\frac{55}{116}\right)$$ $$e\left(\frac{2}{29}\right)$$ $$e\left(\frac{111}{116}\right)$$ $$e\left(\frac{1}{116}\right)$$ $$e\left(\frac{101}{116}\right)$$ $$e\left(\frac{35}{58}\right)$$ $$e\left(\frac{55}{58}\right)$$ $$e\left(\frac{57}{116}\right)$$ $$e\left(\frac{13}{116}\right)$$
$$\chi_{1003}(5,\cdot)$$ 1003.s 464 Yes $$-1$$ $$1$$ $$e\left(\frac{111}{232}\right)$$ $$e\left(\frac{225}{464}\right)$$ $$e\left(\frac{111}{116}\right)$$ $$e\left(\frac{85}{464}\right)$$ $$e\left(\frac{447}{464}\right)$$ $$e\left(\frac{139}{464}\right)$$ $$e\left(\frac{101}{232}\right)$$ $$e\left(\frac{225}{232}\right)$$ $$e\left(\frac{307}{464}\right)$$ $$e\left(\frac{359}{464}\right)$$
$$\chi_{1003}(6,\cdot)$$ 1003.t 464 Yes $$1$$ $$1$$ $$e\left(\frac{1}{232}\right)$$ $$e\left(\frac{419}{464}\right)$$ $$e\left(\frac{1}{116}\right)$$ $$e\left(\frac{447}{464}\right)$$ $$e\left(\frac{421}{464}\right)$$ $$e\left(\frac{65}{464}\right)$$ $$e\left(\frac{3}{232}\right)$$ $$e\left(\frac{187}{232}\right)$$ $$e\left(\frac{449}{464}\right)$$ $$e\left(\frac{253}{464}\right)$$
$$\chi_{1003}(7,\cdot)$$ 1003.s 464 Yes $$-1$$ $$1$$ $$e\left(\frac{217}{232}\right)$$ $$e\left(\frac{95}{464}\right)$$ $$e\left(\frac{101}{116}\right)$$ $$e\left(\frac{139}{464}\right)$$ $$e\left(\frac{65}{464}\right)$$ $$e\left(\frac{69}{464}\right)$$ $$e\left(\frac{187}{232}\right)$$ $$e\left(\frac{95}{232}\right)$$ $$e\left(\frac{109}{464}\right)$$ $$e\left(\frac{265}{464}\right)$$
$$\chi_{1003}(8,\cdot)$$ 1003.q 232 Yes $$-1$$ $$1$$ $$e\left(\frac{93}{116}\right)$$ $$e\left(\frac{49}{232}\right)$$ $$e\left(\frac{35}{58}\right)$$ $$e\left(\frac{101}{232}\right)$$ $$e\left(\frac{3}{232}\right)$$ $$e\left(\frac{187}{232}\right)$$ $$e\left(\frac{47}{116}\right)$$ $$e\left(\frac{49}{116}\right)$$ $$e\left(\frac{55}{232}\right)$$ $$e\left(\frac{155}{232}\right)$$
$$\chi_{1003}(9,\cdot)$$ 1003.r 232 Yes $$1$$ $$1$$ $$e\left(\frac{55}{116}\right)$$ $$e\left(\frac{77}{232}\right)$$ $$e\left(\frac{55}{58}\right)$$ $$e\left(\frac{225}{232}\right)$$ $$e\left(\frac{187}{232}\right)$$ $$e\left(\frac{95}{232}\right)$$ $$e\left(\frac{49}{116}\right)$$ $$e\left(\frac{77}{116}\right)$$ $$e\left(\frac{103}{232}\right)$$ $$e\left(\frac{227}{232}\right)$$
$$\chi_{1003}(10,\cdot)$$ 1003.t 464 Yes $$1$$ $$1$$ $$e\left(\frac{173}{232}\right)$$ $$e\left(\frac{103}{464}\right)$$ $$e\left(\frac{57}{116}\right)$$ $$e\left(\frac{307}{464}\right)$$ $$e\left(\frac{449}{464}\right)$$ $$e\left(\frac{109}{464}\right)$$ $$e\left(\frac{55}{232}\right)$$ $$e\left(\frac{103}{232}\right)$$ $$e\left(\frac{189}{464}\right)$$ $$e\left(\frac{153}{464}\right)$$
$$\chi_{1003}(11,\cdot)$$ 1003.t 464 Yes $$1$$ $$1$$ $$e\left(\frac{129}{232}\right)$$ $$e\left(\frac{459}{464}\right)$$ $$e\left(\frac{13}{116}\right)$$ $$e\left(\frac{359}{464}\right)$$ $$e\left(\frac{253}{464}\right)$$ $$e\left(\frac{265}{464}\right)$$ $$e\left(\frac{155}{232}\right)$$ $$e\left(\frac{227}{232}\right)$$ $$e\left(\frac{153}{464}\right)$$ $$e\left(\frac{389}{464}\right)$$
$$\chi_{1003}(12,\cdot)$$ 1003.s 464 Yes $$-1$$ $$1$$ $$e\left(\frac{63}{232}\right)$$ $$e\left(\frac{297}{464}\right)$$ $$e\left(\frac{63}{116}\right)$$ $$e\left(\frac{205}{464}\right)$$ $$e\left(\frac{423}{464}\right)$$ $$e\left(\frac{35}{464}\right)$$ $$e\left(\frac{189}{232}\right)$$ $$e\left(\frac{65}{232}\right)$$ $$e\left(\frac{331}{464}\right)$$ $$e\left(\frac{47}{464}\right)$$
$$\chi_{1003}(13,\cdot)$$ 1003.o 116 Yes $$-1$$ $$1$$ $$e\left(\frac{8}{29}\right)$$ $$e\left(\frac{5}{116}\right)$$ $$e\left(\frac{16}{29}\right)$$ $$e\left(\frac{105}{116}\right)$$ $$e\left(\frac{37}{116}\right)$$ $$e\left(\frac{83}{116}\right)$$ $$e\left(\frac{24}{29}\right)$$ $$e\left(\frac{5}{58}\right)$$ $$e\left(\frac{21}{116}\right)$$ $$e\left(\frac{17}{116}\right)$$
$$\chi_{1003}(14,\cdot)$$ 1003.t 464 Yes $$1$$ $$1$$ $$e\left(\frac{47}{232}\right)$$ $$e\left(\frac{437}{464}\right)$$ $$e\left(\frac{47}{116}\right)$$ $$e\left(\frac{361}{464}\right)$$ $$e\left(\frac{67}{464}\right)$$ $$e\left(\frac{39}{464}\right)$$ $$e\left(\frac{141}{232}\right)$$ $$e\left(\frac{205}{232}\right)$$ $$e\left(\frac{455}{464}\right)$$ $$e\left(\frac{59}{464}\right)$$
$$\chi_{1003}(15,\cdot)$$ 1003.r 232 Yes $$1$$ $$1$$ $$e\left(\frac{25}{116}\right)$$ $$e\left(\frac{151}{232}\right)$$ $$e\left(\frac{25}{58}\right)$$ $$e\left(\frac{155}{232}\right)$$ $$e\left(\frac{201}{232}\right)$$ $$e\left(\frac{117}{232}\right)$$ $$e\left(\frac{75}{116}\right)$$ $$e\left(\frac{35}{116}\right)$$ $$e\left(\frac{205}{232}\right)$$ $$e\left(\frac{177}{232}\right)$$
$$\chi_{1003}(16,\cdot)$$ 1003.l 58 Yes $$1$$ $$1$$ $$e\left(\frac{2}{29}\right)$$ $$e\left(\frac{55}{58}\right)$$ $$e\left(\frac{4}{29}\right)$$ $$e\left(\frac{53}{58}\right)$$ $$e\left(\frac{1}{58}\right)$$ $$e\left(\frac{43}{58}\right)$$ $$e\left(\frac{6}{29}\right)$$ $$e\left(\frac{26}{29}\right)$$ $$e\left(\frac{57}{58}\right)$$ $$e\left(\frac{13}{58}\right)$$
$$\chi_{1003}(18,\cdot)$$ 1003.m 58 No $$-1$$ $$1$$ $$e\left(\frac{43}{58}\right)$$ $$e\left(\frac{2}{29}\right)$$ $$e\left(\frac{14}{29}\right)$$ $$e\left(\frac{13}{29}\right)$$ $$e\left(\frac{47}{58}\right)$$ $$e\left(\frac{10}{29}\right)$$ $$e\left(\frac{13}{58}\right)$$ $$e\left(\frac{4}{29}\right)$$ $$e\left(\frac{11}{58}\right)$$ $$e\left(\frac{31}{58}\right)$$
$$\chi_{1003}(19,\cdot)$$ 1003.r 232 Yes $$1$$ $$1$$ $$e\left(\frac{105}{116}\right)$$ $$e\left(\frac{147}{232}\right)$$ $$e\left(\frac{47}{58}\right)$$ $$e\left(\frac{71}{232}\right)$$ $$e\left(\frac{125}{232}\right)$$ $$e\left(\frac{97}{232}\right)$$ $$e\left(\frac{83}{116}\right)$$ $$e\left(\frac{31}{116}\right)$$ $$e\left(\frac{49}{232}\right)$$ $$e\left(\frac{117}{232}\right)$$
$$\chi_{1003}(20,\cdot)$$ 1003.s 464 Yes $$-1$$ $$1$$ $$e\left(\frac{3}{232}\right)$$ $$e\left(\frac{445}{464}\right)$$ $$e\left(\frac{3}{116}\right)$$ $$e\left(\frac{65}{464}\right)$$ $$e\left(\frac{451}{464}\right)$$ $$e\left(\frac{79}{464}\right)$$ $$e\left(\frac{9}{232}\right)$$ $$e\left(\frac{213}{232}\right)$$ $$e\left(\frac{71}{464}\right)$$ $$e\left(\frac{411}{464}\right)$$
$$\chi_{1003}(21,\cdot)$$ 1003.p 116 Yes $$1$$ $$1$$ $$e\left(\frac{39}{58}\right)$$ $$e\left(\frac{43}{116}\right)$$ $$e\left(\frac{10}{29}\right)$$ $$e\left(\frac{91}{116}\right)$$ $$e\left(\frac{5}{116}\right)$$ $$e\left(\frac{41}{116}\right)$$ $$e\left(\frac{1}{58}\right)$$ $$e\left(\frac{43}{58}\right)$$ $$e\left(\frac{53}{116}\right)$$ $$e\left(\frac{65}{116}\right)$$
$$\chi_{1003}(22,\cdot)$$ 1003.s 464 Yes $$-1$$ $$1$$ $$e\left(\frac{191}{232}\right)$$ $$e\left(\frac{337}{464}\right)$$ $$e\left(\frac{75}{116}\right)$$ $$e\left(\frac{117}{464}\right)$$ $$e\left(\frac{255}{464}\right)$$ $$e\left(\frac{235}{464}\right)$$ $$e\left(\frac{109}{232}\right)$$ $$e\left(\frac{105}{232}\right)$$ $$e\left(\frac{35}{464}\right)$$ $$e\left(\frac{183}{464}\right)$$
$$\chi_{1003}(23,\cdot)$$ 1003.t 464 Yes $$1$$ $$1$$ $$e\left(\frac{89}{232}\right)$$ $$e\left(\frac{403}{464}\right)$$ $$e\left(\frac{89}{116}\right)$$ $$e\left(\frac{111}{464}\right)$$ $$e\left(\frac{117}{464}\right)$$ $$e\left(\frac{449}{464}\right)$$ $$e\left(\frac{35}{232}\right)$$ $$e\left(\frac{171}{232}\right)$$ $$e\left(\frac{289}{464}\right)$$ $$e\left(\frac{13}{464}\right)$$
$$\chi_{1003}(24,\cdot)$$ 1003.t 464 Yes $$1$$ $$1$$ $$e\left(\frac{125}{232}\right)$$ $$e\left(\frac{175}{464}\right)$$ $$e\left(\frac{9}{116}\right)$$ $$e\left(\frac{427}{464}\right)$$ $$e\left(\frac{425}{464}\right)$$ $$e\left(\frac{5}{464}\right)$$ $$e\left(\frac{143}{232}\right)$$ $$e\left(\frac{175}{232}\right)$$ $$e\left(\frac{213}{464}\right)$$ $$e\left(\frac{305}{464}\right)$$
$$\chi_{1003}(25,\cdot)$$ 1003.r 232 Yes $$1$$ $$1$$ $$e\left(\frac{111}{116}\right)$$ $$e\left(\frac{225}{232}\right)$$ $$e\left(\frac{53}{58}\right)$$ $$e\left(\frac{85}{232}\right)$$ $$e\left(\frac{215}{232}\right)$$ $$e\left(\frac{139}{232}\right)$$ $$e\left(\frac{101}{116}\right)$$ $$e\left(\frac{109}{116}\right)$$ $$e\left(\frac{75}{232}\right)$$ $$e\left(\frac{127}{232}\right)$$
$$\chi_{1003}(26,\cdot)$$ 1003.r 232 Yes $$1$$ $$1$$ $$e\left(\frac{63}{116}\right)$$ $$e\left(\frac{181}{232}\right)$$ $$e\left(\frac{5}{58}\right)$$ $$e\left(\frac{89}{232}\right)$$ $$e\left(\frac{75}{232}\right)$$ $$e\left(\frac{151}{232}\right)$$ $$e\left(\frac{73}{116}\right)$$ $$e\left(\frac{65}{116}\right)$$ $$e\left(\frac{215}{232}\right)$$ $$e\left(\frac{163}{232}\right)$$
$$\chi_{1003}(27,\cdot)$$ 1003.s 464 Yes $$-1$$ $$1$$ $$e\left(\frac{49}{232}\right)$$ $$e\left(\frac{231}{464}\right)$$ $$e\left(\frac{49}{116}\right)$$ $$e\left(\frac{211}{464}\right)$$ $$e\left(\frac{329}{464}\right)$$ $$e\left(\frac{285}{464}\right)$$ $$e\left(\frac{147}{232}\right)$$ $$e\left(\frac{231}{232}\right)$$ $$e\left(\frac{309}{464}\right)$$ $$e\left(\frac{449}{464}\right)$$
$$\chi_{1003}(28,\cdot)$$ 1003.s 464 Yes $$-1$$ $$1$$ $$e\left(\frac{109}{232}\right)$$ $$e\left(\frac{315}{464}\right)$$ $$e\left(\frac{109}{116}\right)$$ $$e\left(\frac{119}{464}\right)$$ $$e\left(\frac{69}{464}\right)$$ $$e\left(\frac{9}{464}\right)$$ $$e\left(\frac{95}{232}\right)$$ $$e\left(\frac{83}{232}\right)$$ $$e\left(\frac{337}{464}\right)$$ $$e\left(\frac{317}{464}\right)$$
$$\chi_{1003}(29,\cdot)$$ 1003.s 464 Yes $$-1$$ $$1$$ $$e\left(\frac{199}{232}\right)$$ $$e\left(\frac{441}{464}\right)$$ $$e\left(\frac{83}{116}\right)$$ $$e\left(\frac{445}{464}\right)$$ $$e\left(\frac{375}{464}\right)$$ $$e\left(\frac{291}{464}\right)$$ $$e\left(\frac{133}{232}\right)$$ $$e\left(\frac{209}{232}\right)$$ $$e\left(\frac{379}{464}\right)$$ $$e\left(\frac{351}{464}\right)$$
$$\chi_{1003}(30,\cdot)$$ 1003.o 116 Yes $$-1$$ $$1$$ $$e\left(\frac{14}{29}\right)$$ $$e\left(\frac{45}{116}\right)$$ $$e\left(\frac{28}{29}\right)$$ $$e\left(\frac{17}{116}\right)$$ $$e\left(\frac{101}{116}\right)$$ $$e\left(\frac{51}{116}\right)$$ $$e\left(\frac{13}{29}\right)$$ $$e\left(\frac{45}{58}\right)$$ $$e\left(\frac{73}{116}\right)$$ $$e\left(\frac{37}{116}\right)$$
$$\chi_{1003}(31,\cdot)$$ 1003.t 464 Yes $$1$$ $$1$$ $$e\left(\frac{167}{232}\right)$$ $$e\left(\frac{373}{464}\right)$$ $$e\left(\frac{51}{116}\right)$$ $$e\left(\frac{409}{464}\right)$$ $$e\left(\frac{243}{464}\right)$$ $$e\left(\frac{183}{464}\right)$$ $$e\left(\frac{37}{232}\right)$$ $$e\left(\frac{141}{232}\right)$$ $$e\left(\frac{279}{464}\right)$$ $$e\left(\frac{27}{464}\right)$$
$$\chi_{1003}(32,\cdot)$$ 1003.q 232 Yes $$-1$$ $$1$$ $$e\left(\frac{39}{116}\right)$$ $$e\left(\frac{159}{232}\right)$$ $$e\left(\frac{39}{58}\right)$$ $$e\left(\frac{91}{232}\right)$$ $$e\left(\frac{5}{232}\right)$$ $$e\left(\frac{157}{232}\right)$$ $$e\left(\frac{1}{116}\right)$$ $$e\left(\frac{43}{116}\right)$$ $$e\left(\frac{169}{232}\right)$$ $$e\left(\frac{181}{232}\right)$$
$$\chi_{1003}(33,\cdot)$$ 1003.n 58 Yes $$-1$$ $$1$$ $$e\left(\frac{17}{58}\right)$$ $$e\left(\frac{9}{58}\right)$$ $$e\left(\frac{17}{29}\right)$$ $$e\left(\frac{15}{58}\right)$$ $$e\left(\frac{13}{29}\right)$$ $$e\left(\frac{45}{58}\right)$$ $$e\left(\frac{51}{58}\right)$$ $$e\left(\frac{9}{29}\right)$$ $$e\left(\frac{16}{29}\right)$$ $$e\left(\frac{24}{29}\right)$$