# Properties

 Modulus $277$ Structure $$C_{276}$$ Order $276$

Show commands: PariGP / SageMath

sage: H = DirichletGroup(277)

pari: g = idealstar(,277,2)

## Character group

 sage: G.order()  pari: g.no Order = 276 sage: H.invariants()  pari: g.cyc Structure = $$C_{276}$$ sage: H.gens()  pari: g.gen Generators = $\chi_{277}(5,\cdot)$

## First 32 of 276 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 $$-1$$ $$1$$ $$2$$ $$3$$ $$4$$ $$5$$ $$6$$ $$7$$ $$8$$ $$9$$ $$10$$ $$11$$
$$\chi_{277}(1,\cdot)$$ 277.a 1 no $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{277}(2,\cdot)$$ 277.j 92 yes $$-1$$ $$1$$ $$e\left(\frac{27}{92}\right)$$ $$e\left(\frac{3}{23}\right)$$ $$e\left(\frac{27}{46}\right)$$ $$e\left(\frac{49}{92}\right)$$ $$e\left(\frac{39}{92}\right)$$ $$e\left(\frac{33}{46}\right)$$ $$e\left(\frac{81}{92}\right)$$ $$e\left(\frac{6}{23}\right)$$ $$e\left(\frac{19}{23}\right)$$ $$e\left(\frac{67}{92}\right)$$
$$\chi_{277}(3,\cdot)$$ 277.i 69 yes $$1$$ $$1$$ $$e\left(\frac{3}{23}\right)$$ $$e\left(\frac{4}{69}\right)$$ $$e\left(\frac{6}{23}\right)$$ $$e\left(\frac{47}{69}\right)$$ $$e\left(\frac{13}{69}\right)$$ $$e\left(\frac{68}{69}\right)$$ $$e\left(\frac{9}{23}\right)$$ $$e\left(\frac{8}{69}\right)$$ $$e\left(\frac{56}{69}\right)$$ $$e\left(\frac{53}{69}\right)$$
$$\chi_{277}(4,\cdot)$$ 277.h 46 yes $$1$$ $$1$$ $$e\left(\frac{27}{46}\right)$$ $$e\left(\frac{6}{23}\right)$$ $$e\left(\frac{4}{23}\right)$$ $$e\left(\frac{3}{46}\right)$$ $$e\left(\frac{39}{46}\right)$$ $$e\left(\frac{10}{23}\right)$$ $$e\left(\frac{35}{46}\right)$$ $$e\left(\frac{12}{23}\right)$$ $$e\left(\frac{15}{23}\right)$$ $$e\left(\frac{21}{46}\right)$$
$$\chi_{277}(5,\cdot)$$ 277.l 276 yes $$-1$$ $$1$$ $$e\left(\frac{49}{92}\right)$$ $$e\left(\frac{47}{69}\right)$$ $$e\left(\frac{3}{46}\right)$$ $$e\left(\frac{1}{276}\right)$$ $$e\left(\frac{59}{276}\right)$$ $$e\left(\frac{11}{138}\right)$$ $$e\left(\frac{55}{92}\right)$$ $$e\left(\frac{25}{69}\right)$$ $$e\left(\frac{37}{69}\right)$$ $$e\left(\frac{7}{276}\right)$$
$$\chi_{277}(6,\cdot)$$ 277.l 276 yes $$-1$$ $$1$$ $$e\left(\frac{39}{92}\right)$$ $$e\left(\frac{13}{69}\right)$$ $$e\left(\frac{39}{46}\right)$$ $$e\left(\frac{59}{276}\right)$$ $$e\left(\frac{169}{276}\right)$$ $$e\left(\frac{97}{138}\right)$$ $$e\left(\frac{25}{92}\right)$$ $$e\left(\frac{26}{69}\right)$$ $$e\left(\frac{44}{69}\right)$$ $$e\left(\frac{137}{276}\right)$$
$$\chi_{277}(7,\cdot)$$ 277.k 138 yes $$1$$ $$1$$ $$e\left(\frac{33}{46}\right)$$ $$e\left(\frac{68}{69}\right)$$ $$e\left(\frac{10}{23}\right)$$ $$e\left(\frac{11}{138}\right)$$ $$e\left(\frac{97}{138}\right)$$ $$e\left(\frac{52}{69}\right)$$ $$e\left(\frac{7}{46}\right)$$ $$e\left(\frac{67}{69}\right)$$ $$e\left(\frac{55}{69}\right)$$ $$e\left(\frac{77}{138}\right)$$
$$\chi_{277}(8,\cdot)$$ 277.j 92 yes $$-1$$ $$1$$ $$e\left(\frac{81}{92}\right)$$ $$e\left(\frac{9}{23}\right)$$ $$e\left(\frac{35}{46}\right)$$ $$e\left(\frac{55}{92}\right)$$ $$e\left(\frac{25}{92}\right)$$ $$e\left(\frac{7}{46}\right)$$ $$e\left(\frac{59}{92}\right)$$ $$e\left(\frac{18}{23}\right)$$ $$e\left(\frac{11}{23}\right)$$ $$e\left(\frac{17}{92}\right)$$
$$\chi_{277}(9,\cdot)$$ 277.i 69 yes $$1$$ $$1$$ $$e\left(\frac{6}{23}\right)$$ $$e\left(\frac{8}{69}\right)$$ $$e\left(\frac{12}{23}\right)$$ $$e\left(\frac{25}{69}\right)$$ $$e\left(\frac{26}{69}\right)$$ $$e\left(\frac{67}{69}\right)$$ $$e\left(\frac{18}{23}\right)$$ $$e\left(\frac{16}{69}\right)$$ $$e\left(\frac{43}{69}\right)$$ $$e\left(\frac{37}{69}\right)$$
$$\chi_{277}(10,\cdot)$$ 277.i 69 yes $$1$$ $$1$$ $$e\left(\frac{19}{23}\right)$$ $$e\left(\frac{56}{69}\right)$$ $$e\left(\frac{15}{23}\right)$$ $$e\left(\frac{37}{69}\right)$$ $$e\left(\frac{44}{69}\right)$$ $$e\left(\frac{55}{69}\right)$$ $$e\left(\frac{11}{23}\right)$$ $$e\left(\frac{43}{69}\right)$$ $$e\left(\frac{25}{69}\right)$$ $$e\left(\frac{52}{69}\right)$$
$$\chi_{277}(11,\cdot)$$ 277.l 276 yes $$-1$$ $$1$$ $$e\left(\frac{67}{92}\right)$$ $$e\left(\frac{53}{69}\right)$$ $$e\left(\frac{21}{46}\right)$$ $$e\left(\frac{7}{276}\right)$$ $$e\left(\frac{137}{276}\right)$$ $$e\left(\frac{77}{138}\right)$$ $$e\left(\frac{17}{92}\right)$$ $$e\left(\frac{37}{69}\right)$$ $$e\left(\frac{52}{69}\right)$$ $$e\left(\frac{49}{276}\right)$$
$$\chi_{277}(12,\cdot)$$ 277.k 138 yes $$1$$ $$1$$ $$e\left(\frac{33}{46}\right)$$ $$e\left(\frac{22}{69}\right)$$ $$e\left(\frac{10}{23}\right)$$ $$e\left(\frac{103}{138}\right)$$ $$e\left(\frac{5}{138}\right)$$ $$e\left(\frac{29}{69}\right)$$ $$e\left(\frac{7}{46}\right)$$ $$e\left(\frac{44}{69}\right)$$ $$e\left(\frac{32}{69}\right)$$ $$e\left(\frac{31}{138}\right)$$
$$\chi_{277}(13,\cdot)$$ 277.h 46 yes $$1$$ $$1$$ $$e\left(\frac{11}{46}\right)$$ $$e\left(\frac{5}{23}\right)$$ $$e\left(\frac{11}{23}\right)$$ $$e\left(\frac{37}{46}\right)$$ $$e\left(\frac{21}{46}\right)$$ $$e\left(\frac{16}{23}\right)$$ $$e\left(\frac{33}{46}\right)$$ $$e\left(\frac{10}{23}\right)$$ $$e\left(\frac{1}{23}\right)$$ $$e\left(\frac{29}{46}\right)$$
$$\chi_{277}(14,\cdot)$$ 277.l 276 yes $$-1$$ $$1$$ $$e\left(\frac{1}{92}\right)$$ $$e\left(\frac{8}{69}\right)$$ $$e\left(\frac{1}{46}\right)$$ $$e\left(\frac{169}{276}\right)$$ $$e\left(\frac{35}{276}\right)$$ $$e\left(\frac{65}{138}\right)$$ $$e\left(\frac{3}{92}\right)$$ $$e\left(\frac{16}{69}\right)$$ $$e\left(\frac{43}{69}\right)$$ $$e\left(\frac{79}{276}\right)$$
$$\chi_{277}(15,\cdot)$$ 277.j 92 yes $$-1$$ $$1$$ $$e\left(\frac{61}{92}\right)$$ $$e\left(\frac{17}{23}\right)$$ $$e\left(\frac{15}{46}\right)$$ $$e\left(\frac{63}{92}\right)$$ $$e\left(\frac{37}{92}\right)$$ $$e\left(\frac{3}{46}\right)$$ $$e\left(\frac{91}{92}\right)$$ $$e\left(\frac{11}{23}\right)$$ $$e\left(\frac{8}{23}\right)$$ $$e\left(\frac{73}{92}\right)$$
$$\chi_{277}(16,\cdot)$$ 277.g 23 yes $$1$$ $$1$$ $$e\left(\frac{4}{23}\right)$$ $$e\left(\frac{12}{23}\right)$$ $$e\left(\frac{8}{23}\right)$$ $$e\left(\frac{3}{23}\right)$$ $$e\left(\frac{16}{23}\right)$$ $$e\left(\frac{20}{23}\right)$$ $$e\left(\frac{12}{23}\right)$$ $$e\left(\frac{1}{23}\right)$$ $$e\left(\frac{7}{23}\right)$$ $$e\left(\frac{21}{23}\right)$$
$$\chi_{277}(17,\cdot)$$ 277.l 276 yes $$-1$$ $$1$$ $$e\left(\frac{79}{92}\right)$$ $$e\left(\frac{11}{69}\right)$$ $$e\left(\frac{33}{46}\right)$$ $$e\left(\frac{103}{276}\right)$$ $$e\left(\frac{5}{276}\right)$$ $$e\left(\frac{29}{138}\right)$$ $$e\left(\frac{53}{92}\right)$$ $$e\left(\frac{22}{69}\right)$$ $$e\left(\frac{16}{69}\right)$$ $$e\left(\frac{169}{276}\right)$$
$$\chi_{277}(18,\cdot)$$ 277.l 276 yes $$-1$$ $$1$$ $$e\left(\frac{51}{92}\right)$$ $$e\left(\frac{17}{69}\right)$$ $$e\left(\frac{5}{46}\right)$$ $$e\left(\frac{247}{276}\right)$$ $$e\left(\frac{221}{276}\right)$$ $$e\left(\frac{95}{138}\right)$$ $$e\left(\frac{61}{92}\right)$$ $$e\left(\frac{34}{69}\right)$$ $$e\left(\frac{31}{69}\right)$$ $$e\left(\frac{73}{276}\right)$$
$$\chi_{277}(19,\cdot)$$ 277.g 23 yes $$1$$ $$1$$ $$e\left(\frac{5}{23}\right)$$ $$e\left(\frac{15}{23}\right)$$ $$e\left(\frac{10}{23}\right)$$ $$e\left(\frac{21}{23}\right)$$ $$e\left(\frac{20}{23}\right)$$ $$e\left(\frac{2}{23}\right)$$ $$e\left(\frac{15}{23}\right)$$ $$e\left(\frac{7}{23}\right)$$ $$e\left(\frac{3}{23}\right)$$ $$e\left(\frac{9}{23}\right)$$
$$\chi_{277}(20,\cdot)$$ 277.l 276 yes $$-1$$ $$1$$ $$e\left(\frac{11}{92}\right)$$ $$e\left(\frac{65}{69}\right)$$ $$e\left(\frac{11}{46}\right)$$ $$e\left(\frac{19}{276}\right)$$ $$e\left(\frac{17}{276}\right)$$ $$e\left(\frac{71}{138}\right)$$ $$e\left(\frac{33}{92}\right)$$ $$e\left(\frac{61}{69}\right)$$ $$e\left(\frac{13}{69}\right)$$ $$e\left(\frac{133}{276}\right)$$
$$\chi_{277}(21,\cdot)$$ 277.h 46 yes $$1$$ $$1$$ $$e\left(\frac{39}{46}\right)$$ $$e\left(\frac{1}{23}\right)$$ $$e\left(\frac{16}{23}\right)$$ $$e\left(\frac{35}{46}\right)$$ $$e\left(\frac{41}{46}\right)$$ $$e\left(\frac{17}{23}\right)$$ $$e\left(\frac{25}{46}\right)$$ $$e\left(\frac{2}{23}\right)$$ $$e\left(\frac{14}{23}\right)$$ $$e\left(\frac{15}{46}\right)$$
$$\chi_{277}(22,\cdot)$$ 277.k 138 yes $$1$$ $$1$$ $$e\left(\frac{1}{46}\right)$$ $$e\left(\frac{62}{69}\right)$$ $$e\left(\frac{1}{23}\right)$$ $$e\left(\frac{77}{138}\right)$$ $$e\left(\frac{127}{138}\right)$$ $$e\left(\frac{19}{69}\right)$$ $$e\left(\frac{3}{46}\right)$$ $$e\left(\frac{55}{69}\right)$$ $$e\left(\frac{40}{69}\right)$$ $$e\left(\frac{125}{138}\right)$$
$$\chi_{277}(23,\cdot)$$ 277.i 69 yes $$1$$ $$1$$ $$e\left(\frac{18}{23}\right)$$ $$e\left(\frac{47}{69}\right)$$ $$e\left(\frac{13}{23}\right)$$ $$e\left(\frac{52}{69}\right)$$ $$e\left(\frac{32}{69}\right)$$ $$e\left(\frac{40}{69}\right)$$ $$e\left(\frac{8}{23}\right)$$ $$e\left(\frac{25}{69}\right)$$ $$e\left(\frac{37}{69}\right)$$ $$e\left(\frac{19}{69}\right)$$
$$\chi_{277}(24,\cdot)$$ 277.l 276 yes $$-1$$ $$1$$ $$e\left(\frac{1}{92}\right)$$ $$e\left(\frac{31}{69}\right)$$ $$e\left(\frac{1}{46}\right)$$ $$e\left(\frac{77}{276}\right)$$ $$e\left(\frac{127}{276}\right)$$ $$e\left(\frac{19}{138}\right)$$ $$e\left(\frac{3}{92}\right)$$ $$e\left(\frac{62}{69}\right)$$ $$e\left(\frac{20}{69}\right)$$ $$e\left(\frac{263}{276}\right)$$
$$\chi_{277}(25,\cdot)$$ 277.k 138 yes $$1$$ $$1$$ $$e\left(\frac{3}{46}\right)$$ $$e\left(\frac{25}{69}\right)$$ $$e\left(\frac{3}{23}\right)$$ $$e\left(\frac{1}{138}\right)$$ $$e\left(\frac{59}{138}\right)$$ $$e\left(\frac{11}{69}\right)$$ $$e\left(\frac{9}{46}\right)$$ $$e\left(\frac{50}{69}\right)$$ $$e\left(\frac{5}{69}\right)$$ $$e\left(\frac{7}{138}\right)$$
$$\chi_{277}(26,\cdot)$$ 277.j 92 yes $$-1$$ $$1$$ $$e\left(\frac{49}{92}\right)$$ $$e\left(\frac{8}{23}\right)$$ $$e\left(\frac{3}{46}\right)$$ $$e\left(\frac{31}{92}\right)$$ $$e\left(\frac{81}{92}\right)$$ $$e\left(\frac{19}{46}\right)$$ $$e\left(\frac{55}{92}\right)$$ $$e\left(\frac{16}{23}\right)$$ $$e\left(\frac{20}{23}\right)$$ $$e\left(\frac{33}{92}\right)$$
$$\chi_{277}(27,\cdot)$$ 277.g 23 yes $$1$$ $$1$$ $$e\left(\frac{9}{23}\right)$$ $$e\left(\frac{4}{23}\right)$$ $$e\left(\frac{18}{23}\right)$$ $$e\left(\frac{1}{23}\right)$$ $$e\left(\frac{13}{23}\right)$$ $$e\left(\frac{22}{23}\right)$$ $$e\left(\frac{4}{23}\right)$$ $$e\left(\frac{8}{23}\right)$$ $$e\left(\frac{10}{23}\right)$$ $$e\left(\frac{7}{23}\right)$$
$$\chi_{277}(28,\cdot)$$ 277.i 69 yes $$1$$ $$1$$ $$e\left(\frac{7}{23}\right)$$ $$e\left(\frac{17}{69}\right)$$ $$e\left(\frac{14}{23}\right)$$ $$e\left(\frac{10}{69}\right)$$ $$e\left(\frac{38}{69}\right)$$ $$e\left(\frac{13}{69}\right)$$ $$e\left(\frac{21}{23}\right)$$ $$e\left(\frac{34}{69}\right)$$ $$e\left(\frac{31}{69}\right)$$ $$e\left(\frac{1}{69}\right)$$
$$\chi_{277}(29,\cdot)$$ 277.k 138 yes $$1$$ $$1$$ $$e\left(\frac{19}{46}\right)$$ $$e\left(\frac{28}{69}\right)$$ $$e\left(\frac{19}{23}\right)$$ $$e\left(\frac{37}{138}\right)$$ $$e\left(\frac{113}{138}\right)$$ $$e\left(\frac{62}{69}\right)$$ $$e\left(\frac{11}{46}\right)$$ $$e\left(\frac{56}{69}\right)$$ $$e\left(\frac{47}{69}\right)$$ $$e\left(\frac{121}{138}\right)$$
$$\chi_{277}(30,\cdot)$$ 277.g 23 yes $$1$$ $$1$$ $$e\left(\frac{22}{23}\right)$$ $$e\left(\frac{20}{23}\right)$$ $$e\left(\frac{21}{23}\right)$$ $$e\left(\frac{5}{23}\right)$$ $$e\left(\frac{19}{23}\right)$$ $$e\left(\frac{18}{23}\right)$$ $$e\left(\frac{20}{23}\right)$$ $$e\left(\frac{17}{23}\right)$$ $$e\left(\frac{4}{23}\right)$$ $$e\left(\frac{12}{23}\right)$$
$$\chi_{277}(31,\cdot)$$ 277.l 276 yes $$-1$$ $$1$$ $$e\left(\frac{3}{92}\right)$$ $$e\left(\frac{1}{69}\right)$$ $$e\left(\frac{3}{46}\right)$$ $$e\left(\frac{47}{276}\right)$$ $$e\left(\frac{13}{276}\right)$$ $$e\left(\frac{103}{138}\right)$$ $$e\left(\frac{9}{92}\right)$$ $$e\left(\frac{2}{69}\right)$$ $$e\left(\frac{14}{69}\right)$$ $$e\left(\frac{53}{276}\right)$$
$$\chi_{277}(32,\cdot)$$ 277.j 92 yes $$-1$$ $$1$$ $$e\left(\frac{43}{92}\right)$$ $$e\left(\frac{15}{23}\right)$$ $$e\left(\frac{43}{46}\right)$$ $$e\left(\frac{61}{92}\right)$$ $$e\left(\frac{11}{92}\right)$$ $$e\left(\frac{27}{46}\right)$$ $$e\left(\frac{37}{92}\right)$$ $$e\left(\frac{7}{23}\right)$$ $$e\left(\frac{3}{23}\right)$$ $$e\left(\frac{59}{92}\right)$$