LMFDB - Group of Dirichlet characters of modulus 277

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	$-1$	$1$	$e\left(\frac{43}{92}\right)$	$e\left(\frac{15}{23}\right)$	$e\left(\frac{43}{46}\right)$	$e\left(\frac{61}{92}\right)$	$e\left(\frac{11}{92}\right)$	$e\left(\frac{27}{46}\right)$	$e\left(\frac{37}{92}\right)$	$e\left(\frac{7}{23}\right)$	$e\left(\frac{3}{23}\right)$	$e\left(\frac{59}{92}\right)$

Click here to search among the remaining 244 characters.

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Modulus	$277$
Structure	\(C_{276}\)
Order	$276$

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	\(-1\)	\(1\)	\(e\left(\frac{43}{92}\right)\)	\(e\left(\frac{15}{23}\right)\)	\(e\left(\frac{43}{46}\right)\)	\(e\left(\frac{61}{92}\right)\)	\(e\left(\frac{11}{92}\right)\)	\(e\left(\frac{27}{46}\right)\)	\(e\left(\frac{37}{92}\right)\)	\(e\left(\frac{7}{23}\right)\)	\(e\left(\frac{3}{23}\right)\)	\(e\left(\frac{59}{92}\right)\)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Learn more

Character group

First 32 of 276 characters

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.