# Properties

 Modulus 1033 Structure $$C_{1032}$$ Order 1032

Show commands for: SageMath / Pari/GP

sage: from dirichlet_conrey import DirichletGroup_conrey # requires nonstandard Sage package to be installed
sage: H = DirichletGroup_conrey(1033)
pari: g = idealstar(,1033,2)

## Character group

 sage: G.order() pari: g.no Order = 1032 sage: H.invariants() pari: g.cyc Structure = $$C_{1032}$$ sage: H.gens() pari: g.gen Generators = $\chi_{1033}(5,\cdot)$

## First 32 of 1032 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
$$\chi_{1033}(1,\cdot)$$ 1033.a 1 No $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{1033}(2,\cdot)$$ 1033.m 258 Yes $$1$$ $$1$$ $$e\left(\frac{50}{129}\right)$$ $$e\left(\frac{121}{129}\right)$$ $$e\left(\frac{100}{129}\right)$$ $$e\left(\frac{91}{258}\right)$$ $$e\left(\frac{14}{43}\right)$$ $$e\left(\frac{12}{43}\right)$$ $$e\left(\frac{7}{43}\right)$$ $$e\left(\frac{113}{129}\right)$$ $$e\left(\frac{191}{258}\right)$$ $$e\left(\frac{73}{258}\right)$$
$$\chi_{1033}(3,\cdot)$$ 1033.o 516 Yes $$1$$ $$1$$ $$e\left(\frac{121}{129}\right)$$ $$e\left(\frac{49}{258}\right)$$ $$e\left(\frac{113}{129}\right)$$ $$e\left(\frac{7}{516}\right)$$ $$e\left(\frac{11}{86}\right)$$ $$e\left(\frac{77}{86}\right)$$ $$e\left(\frac{35}{43}\right)$$ $$e\left(\frac{49}{129}\right)$$ $$e\left(\frac{491}{516}\right)$$ $$e\left(\frac{343}{516}\right)$$
$$\chi_{1033}(4,\cdot)$$ 1033.k 129 Yes $$1$$ $$1$$ $$e\left(\frac{100}{129}\right)$$ $$e\left(\frac{113}{129}\right)$$ $$e\left(\frac{71}{129}\right)$$ $$e\left(\frac{91}{129}\right)$$ $$e\left(\frac{28}{43}\right)$$ $$e\left(\frac{24}{43}\right)$$ $$e\left(\frac{14}{43}\right)$$ $$e\left(\frac{97}{129}\right)$$ $$e\left(\frac{62}{129}\right)$$ $$e\left(\frac{73}{129}\right)$$
$$\chi_{1033}(5,\cdot)$$ 1033.p 1032 Yes $$-1$$ $$1$$ $$e\left(\frac{91}{258}\right)$$ $$e\left(\frac{7}{516}\right)$$ $$e\left(\frac{91}{129}\right)$$ $$e\left(\frac{1}{1032}\right)$$ $$e\left(\frac{63}{172}\right)$$ $$e\left(\frac{11}{172}\right)$$ $$e\left(\frac{5}{86}\right)$$ $$e\left(\frac{7}{258}\right)$$ $$e\left(\frac{365}{1032}\right)$$ $$e\left(\frac{565}{1032}\right)$$
$$\chi_{1033}(6,\cdot)$$ 1033.l 172 Yes $$1$$ $$1$$ $$e\left(\frac{14}{43}\right)$$ $$e\left(\frac{11}{86}\right)$$ $$e\left(\frac{28}{43}\right)$$ $$e\left(\frac{63}{172}\right)$$ $$e\left(\frac{39}{86}\right)$$ $$e\left(\frac{15}{86}\right)$$ $$e\left(\frac{42}{43}\right)$$ $$e\left(\frac{11}{43}\right)$$ $$e\left(\frac{119}{172}\right)$$ $$e\left(\frac{163}{172}\right)$$
$$\chi_{1033}(7,\cdot)$$ 1033.l 172 Yes $$1$$ $$1$$ $$e\left(\frac{12}{43}\right)$$ $$e\left(\frac{77}{86}\right)$$ $$e\left(\frac{24}{43}\right)$$ $$e\left(\frac{11}{172}\right)$$ $$e\left(\frac{15}{86}\right)$$ $$e\left(\frac{19}{86}\right)$$ $$e\left(\frac{36}{43}\right)$$ $$e\left(\frac{34}{43}\right)$$ $$e\left(\frac{59}{172}\right)$$ $$e\left(\frac{23}{172}\right)$$
$$\chi_{1033}(8,\cdot)$$ 1033.j 86 Yes $$1$$ $$1$$ $$e\left(\frac{7}{43}\right)$$ $$e\left(\frac{35}{43}\right)$$ $$e\left(\frac{14}{43}\right)$$ $$e\left(\frac{5}{86}\right)$$ $$e\left(\frac{42}{43}\right)$$ $$e\left(\frac{36}{43}\right)$$ $$e\left(\frac{21}{43}\right)$$ $$e\left(\frac{27}{43}\right)$$ $$e\left(\frac{19}{86}\right)$$ $$e\left(\frac{73}{86}\right)$$
$$\chi_{1033}(9,\cdot)$$ 1033.m 258 Yes $$1$$ $$1$$ $$e\left(\frac{113}{129}\right)$$ $$e\left(\frac{49}{129}\right)$$ $$e\left(\frac{97}{129}\right)$$ $$e\left(\frac{7}{258}\right)$$ $$e\left(\frac{11}{43}\right)$$ $$e\left(\frac{34}{43}\right)$$ $$e\left(\frac{27}{43}\right)$$ $$e\left(\frac{98}{129}\right)$$ $$e\left(\frac{233}{258}\right)$$ $$e\left(\frac{85}{258}\right)$$
$$\chi_{1033}(10,\cdot)$$ 1033.p 1032 Yes $$-1$$ $$1$$ $$e\left(\frac{191}{258}\right)$$ $$e\left(\frac{491}{516}\right)$$ $$e\left(\frac{62}{129}\right)$$ $$e\left(\frac{365}{1032}\right)$$ $$e\left(\frac{119}{172}\right)$$ $$e\left(\frac{59}{172}\right)$$ $$e\left(\frac{19}{86}\right)$$ $$e\left(\frac{233}{258}\right)$$ $$e\left(\frac{97}{1032}\right)$$ $$e\left(\frac{857}{1032}\right)$$
$$\chi_{1033}(11,\cdot)$$ 1033.p 1032 Yes $$-1$$ $$1$$ $$e\left(\frac{73}{258}\right)$$ $$e\left(\frac{343}{516}\right)$$ $$e\left(\frac{73}{129}\right)$$ $$e\left(\frac{565}{1032}\right)$$ $$e\left(\frac{163}{172}\right)$$ $$e\left(\frac{23}{172}\right)$$ $$e\left(\frac{73}{86}\right)$$ $$e\left(\frac{85}{258}\right)$$ $$e\left(\frac{857}{1032}\right)$$ $$e\left(\frac{337}{1032}\right)$$
$$\chi_{1033}(12,\cdot)$$ 1033.o 516 Yes $$1$$ $$1$$ $$e\left(\frac{92}{129}\right)$$ $$e\left(\frac{17}{258}\right)$$ $$e\left(\frac{55}{129}\right)$$ $$e\left(\frac{371}{516}\right)$$ $$e\left(\frac{67}{86}\right)$$ $$e\left(\frac{39}{86}\right)$$ $$e\left(\frac{6}{43}\right)$$ $$e\left(\frac{17}{129}\right)$$ $$e\left(\frac{223}{516}\right)$$ $$e\left(\frac{119}{516}\right)$$
$$\chi_{1033}(13,\cdot)$$ 1033.p 1032 Yes $$-1$$ $$1$$ $$e\left(\frac{97}{258}\right)$$ $$e\left(\frac{67}{516}\right)$$ $$e\left(\frac{97}{129}\right)$$ $$e\left(\frac{673}{1032}\right)$$ $$e\left(\frac{87}{172}\right)$$ $$e\left(\frac{7}{172}\right)$$ $$e\left(\frac{11}{86}\right)$$ $$e\left(\frac{67}{258}\right)$$ $$e\left(\frac{29}{1032}\right)$$ $$e\left(\frac{469}{1032}\right)$$
$$\chi_{1033}(14,\cdot)$$ 1033.g 12 Yes $$1$$ $$1$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$-1$$ $$-1$$ $$1$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{5}{12}\right)$$
$$\chi_{1033}(15,\cdot)$$ 1033.n 344 Yes $$-1$$ $$1$$ $$e\left(\frac{25}{86}\right)$$ $$e\left(\frac{35}{172}\right)$$ $$e\left(\frac{25}{43}\right)$$ $$e\left(\frac{5}{344}\right)$$ $$e\left(\frac{85}{172}\right)$$ $$e\left(\frac{165}{172}\right)$$ $$e\left(\frac{75}{86}\right)$$ $$e\left(\frac{35}{86}\right)$$ $$e\left(\frac{105}{344}\right)$$ $$e\left(\frac{73}{344}\right)$$
$$\chi_{1033}(16,\cdot)$$ 1033.k 129 Yes $$1$$ $$1$$ $$e\left(\frac{71}{129}\right)$$ $$e\left(\frac{97}{129}\right)$$ $$e\left(\frac{13}{129}\right)$$ $$e\left(\frac{53}{129}\right)$$ $$e\left(\frac{13}{43}\right)$$ $$e\left(\frac{5}{43}\right)$$ $$e\left(\frac{28}{43}\right)$$ $$e\left(\frac{65}{129}\right)$$ $$e\left(\frac{124}{129}\right)$$ $$e\left(\frac{17}{129}\right)$$
$$\chi_{1033}(17,\cdot)$$ 1033.o 516 Yes $$1$$ $$1$$ $$e\left(\frac{40}{129}\right)$$ $$e\left(\frac{13}{258}\right)$$ $$e\left(\frac{80}{129}\right)$$ $$e\left(\frac{223}{516}\right)$$ $$e\left(\frac{31}{86}\right)$$ $$e\left(\frac{45}{86}\right)$$ $$e\left(\frac{40}{43}\right)$$ $$e\left(\frac{13}{129}\right)$$ $$e\left(\frac{383}{516}\right)$$ $$e\left(\frac{91}{516}\right)$$
$$\chi_{1033}(18,\cdot)$$ 1033.k 129 Yes $$1$$ $$1$$ $$e\left(\frac{34}{129}\right)$$ $$e\left(\frac{41}{129}\right)$$ $$e\left(\frac{68}{129}\right)$$ $$e\left(\frac{49}{129}\right)$$ $$e\left(\frac{25}{43}\right)$$ $$e\left(\frac{3}{43}\right)$$ $$e\left(\frac{34}{43}\right)$$ $$e\left(\frac{82}{129}\right)$$ $$e\left(\frac{83}{129}\right)$$ $$e\left(\frac{79}{129}\right)$$
$$\chi_{1033}(19,\cdot)$$ 1033.k 129 Yes $$1$$ $$1$$ $$e\left(\frac{10}{129}\right)$$ $$e\left(\frac{50}{129}\right)$$ $$e\left(\frac{20}{129}\right)$$ $$e\left(\frac{22}{129}\right)$$ $$e\left(\frac{20}{43}\right)$$ $$e\left(\frac{11}{43}\right)$$ $$e\left(\frac{10}{43}\right)$$ $$e\left(\frac{100}{129}\right)$$ $$e\left(\frac{32}{129}\right)$$ $$e\left(\frac{46}{129}\right)$$
$$\chi_{1033}(20,\cdot)$$ 1033.n 344 Yes $$-1$$ $$1$$ $$e\left(\frac{11}{86}\right)$$ $$e\left(\frac{153}{172}\right)$$ $$e\left(\frac{11}{43}\right)$$ $$e\left(\frac{243}{344}\right)$$ $$e\left(\frac{3}{172}\right)$$ $$e\left(\frac{107}{172}\right)$$ $$e\left(\frac{33}{86}\right)$$ $$e\left(\frac{67}{86}\right)$$ $$e\left(\frac{287}{344}\right)$$ $$e\left(\frac{39}{344}\right)$$
$$\chi_{1033}(21,\cdot)$$ 1033.k 129 Yes $$1$$ $$1$$ $$e\left(\frac{28}{129}\right)$$ $$e\left(\frac{11}{129}\right)$$ $$e\left(\frac{56}{129}\right)$$ $$e\left(\frac{10}{129}\right)$$ $$e\left(\frac{13}{43}\right)$$ $$e\left(\frac{5}{43}\right)$$ $$e\left(\frac{28}{43}\right)$$ $$e\left(\frac{22}{129}\right)$$ $$e\left(\frac{38}{129}\right)$$ $$e\left(\frac{103}{129}\right)$$
$$\chi_{1033}(22,\cdot)$$ 1033.p 1032 Yes $$-1$$ $$1$$ $$e\left(\frac{173}{258}\right)$$ $$e\left(\frac{311}{516}\right)$$ $$e\left(\frac{44}{129}\right)$$ $$e\left(\frac{929}{1032}\right)$$ $$e\left(\frac{47}{172}\right)$$ $$e\left(\frac{71}{172}\right)$$ $$e\left(\frac{1}{86}\right)$$ $$e\left(\frac{53}{258}\right)$$ $$e\left(\frac{589}{1032}\right)$$ $$e\left(\frac{629}{1032}\right)$$
$$\chi_{1033}(23,\cdot)$$ 1033.p 1032 Yes $$-1$$ $$1$$ $$e\left(\frac{41}{258}\right)$$ $$e\left(\frac{281}{516}\right)$$ $$e\left(\frac{41}{129}\right)$$ $$e\left(\frac{335}{1032}\right)$$ $$e\left(\frac{121}{172}\right)$$ $$e\left(\frac{73}{172}\right)$$ $$e\left(\frac{41}{86}\right)$$ $$e\left(\frac{23}{258}\right)$$ $$e\left(\frac{499}{1032}\right)$$ $$e\left(\frac{419}{1032}\right)$$
$$\chi_{1033}(24,\cdot)$$ 1033.o 516 Yes $$1$$ $$1$$ $$e\left(\frac{13}{129}\right)$$ $$e\left(\frac{1}{258}\right)$$ $$e\left(\frac{26}{129}\right)$$ $$e\left(\frac{37}{516}\right)$$ $$e\left(\frac{9}{86}\right)$$ $$e\left(\frac{63}{86}\right)$$ $$e\left(\frac{13}{43}\right)$$ $$e\left(\frac{1}{129}\right)$$ $$e\left(\frac{89}{516}\right)$$ $$e\left(\frac{265}{516}\right)$$
$$\chi_{1033}(25,\cdot)$$ 1033.o 516 Yes $$1$$ $$1$$ $$e\left(\frac{91}{129}\right)$$ $$e\left(\frac{7}{258}\right)$$ $$e\left(\frac{53}{129}\right)$$ $$e\left(\frac{1}{516}\right)$$ $$e\left(\frac{63}{86}\right)$$ $$e\left(\frac{11}{86}\right)$$ $$e\left(\frac{5}{43}\right)$$ $$e\left(\frac{7}{129}\right)$$ $$e\left(\frac{365}{516}\right)$$ $$e\left(\frac{49}{516}\right)$$
$$\chi_{1033}(26,\cdot)$$ 1033.p 1032 Yes $$-1$$ $$1$$ $$e\left(\frac{197}{258}\right)$$ $$e\left(\frac{35}{516}\right)$$ $$e\left(\frac{68}{129}\right)$$ $$e\left(\frac{5}{1032}\right)$$ $$e\left(\frac{143}{172}\right)$$ $$e\left(\frac{55}{172}\right)$$ $$e\left(\frac{25}{86}\right)$$ $$e\left(\frac{35}{258}\right)$$ $$e\left(\frac{793}{1032}\right)$$ $$e\left(\frac{761}{1032}\right)$$
$$\chi_{1033}(27,\cdot)$$ 1033.l 172 Yes $$1$$ $$1$$ $$e\left(\frac{35}{43}\right)$$ $$e\left(\frac{49}{86}\right)$$ $$e\left(\frac{27}{43}\right)$$ $$e\left(\frac{7}{172}\right)$$ $$e\left(\frac{33}{86}\right)$$ $$e\left(\frac{59}{86}\right)$$ $$e\left(\frac{19}{43}\right)$$ $$e\left(\frac{6}{43}\right)$$ $$e\left(\frac{147}{172}\right)$$ $$e\left(\frac{171}{172}\right)$$
$$\chi_{1033}(28,\cdot)$$ 1033.o 516 Yes $$1$$ $$1$$ $$e\left(\frac{7}{129}\right)$$ $$e\left(\frac{199}{258}\right)$$ $$e\left(\frac{14}{129}\right)$$ $$e\left(\frac{397}{516}\right)$$ $$e\left(\frac{71}{86}\right)$$ $$e\left(\frac{67}{86}\right)$$ $$e\left(\frac{7}{43}\right)$$ $$e\left(\frac{70}{129}\right)$$ $$e\left(\frac{425}{516}\right)$$ $$e\left(\frac{361}{516}\right)$$
$$\chi_{1033}(29,\cdot)$$ 1033.p 1032 Yes $$-1$$ $$1$$ $$e\left(\frac{163}{258}\right)$$ $$e\left(\frac{211}{516}\right)$$ $$e\left(\frac{34}{129}\right)$$ $$e\left(\frac{841}{1032}\right)$$ $$e\left(\frac{7}{172}\right)$$ $$e\left(\frac{135}{172}\right)$$ $$e\left(\frac{77}{86}\right)$$ $$e\left(\frac{211}{258}\right)$$ $$e\left(\frac{461}{1032}\right)$$ $$e\left(\frac{445}{1032}\right)$$
$$\chi_{1033}(30,\cdot)$$ 1033.p 1032 Yes $$-1$$ $$1$$ $$e\left(\frac{175}{258}\right)$$ $$e\left(\frac{73}{516}\right)$$ $$e\left(\frac{46}{129}\right)$$ $$e\left(\frac{379}{1032}\right)$$ $$e\left(\frac{141}{172}\right)$$ $$e\left(\frac{41}{172}\right)$$ $$e\left(\frac{3}{86}\right)$$ $$e\left(\frac{73}{258}\right)$$ $$e\left(\frac{47}{1032}\right)$$ $$e\left(\frac{511}{1032}\right)$$
$$\chi_{1033}(31,\cdot)$$ 1033.o 516 Yes $$1$$ $$1$$ $$e\left(\frac{67}{129}\right)$$ $$e\left(\frac{25}{258}\right)$$ $$e\left(\frac{5}{129}\right)$$ $$e\left(\frac{151}{516}\right)$$ $$e\left(\frac{53}{86}\right)$$ $$e\left(\frac{27}{86}\right)$$ $$e\left(\frac{24}{43}\right)$$ $$e\left(\frac{25}{129}\right)$$ $$e\left(\frac{419}{516}\right)$$ $$e\left(\frac{175}{516}\right)$$
$$\chi_{1033}(32,\cdot)$$ 1033.m 258 Yes $$1$$ $$1$$ $$e\left(\frac{121}{129}\right)$$ $$e\left(\frac{89}{129}\right)$$ $$e\left(\frac{113}{129}\right)$$ $$e\left(\frac{197}{258}\right)$$ $$e\left(\frac{27}{43}\right)$$ $$e\left(\frac{17}{43}\right)$$ $$e\left(\frac{35}{43}\right)$$ $$e\left(\frac{49}{129}\right)$$ $$e\left(\frac{181}{258}\right)$$ $$e\left(\frac{107}{258}\right)$$