LMFDB - Group of Dirichlet characters of modulus 167

Show commands: PariGP / SageMath

sage: H = DirichletGroup(167)

pari: g = idealstar(,167,2)

Character group

sage: G.order() pari: g.no
Order	=	166
sage: H.invariants() pari: g.cyc
Structure	=	$C_{166}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{167}(5,\cdot)$

First 32 of 166 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	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$11$
$\chi_{167}(1,\cdot)$	167.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{167}(2,\cdot)$	167.c	83	yes	$1$	$1$	$e\left(\frac{53}{83}\right)$	$e\left(\frac{54}{83}\right)$	$e\left(\frac{23}{83}\right)$	$e\left(\frac{20}{83}\right)$	$e\left(\frac{24}{83}\right)$	$e\left(\frac{36}{83}\right)$	$e\left(\frac{76}{83}\right)$	$e\left(\frac{25}{83}\right)$	$e\left(\frac{73}{83}\right)$	$e\left(\frac{62}{83}\right)$
$\chi_{167}(3,\cdot)$	167.c	83	yes	$1$	$1$	$e\left(\frac{54}{83}\right)$	$e\left(\frac{19}{83}\right)$	$e\left(\frac{25}{83}\right)$	$e\left(\frac{47}{83}\right)$	$e\left(\frac{73}{83}\right)$	$e\left(\frac{68}{83}\right)$	$e\left(\frac{79}{83}\right)$	$e\left(\frac{38}{83}\right)$	$e\left(\frac{18}{83}\right)$	$e\left(\frac{71}{83}\right)$
$\chi_{167}(4,\cdot)$	167.c	83	yes	$1$	$1$	$e\left(\frac{23}{83}\right)$	$e\left(\frac{25}{83}\right)$	$e\left(\frac{46}{83}\right)$	$e\left(\frac{40}{83}\right)$	$e\left(\frac{48}{83}\right)$	$e\left(\frac{72}{83}\right)$	$e\left(\frac{69}{83}\right)$	$e\left(\frac{50}{83}\right)$	$e\left(\frac{63}{83}\right)$	$e\left(\frac{41}{83}\right)$
$\chi_{167}(5,\cdot)$	167.d	166	yes	$-1$	$1$	$e\left(\frac{20}{83}\right)$	$e\left(\frac{47}{83}\right)$	$e\left(\frac{40}{83}\right)$	$e\left(\frac{1}{166}\right)$	$e\left(\frac{67}{83}\right)$	$e\left(\frac{59}{83}\right)$	$e\left(\frac{60}{83}\right)$	$e\left(\frac{11}{83}\right)$	$e\left(\frac{41}{166}\right)$	$e\left(\frac{14}{83}\right)$
$\chi_{167}(6,\cdot)$	167.c	83	yes	$1$	$1$	$e\left(\frac{24}{83}\right)$	$e\left(\frac{73}{83}\right)$	$e\left(\frac{48}{83}\right)$	$e\left(\frac{67}{83}\right)$	$e\left(\frac{14}{83}\right)$	$e\left(\frac{21}{83}\right)$	$e\left(\frac{72}{83}\right)$	$e\left(\frac{63}{83}\right)$	$e\left(\frac{8}{83}\right)$	$e\left(\frac{50}{83}\right)$
$\chi_{167}(7,\cdot)$	167.c	83	yes	$1$	$1$	$e\left(\frac{36}{83}\right)$	$e\left(\frac{68}{83}\right)$	$e\left(\frac{72}{83}\right)$	$e\left(\frac{59}{83}\right)$	$e\left(\frac{21}{83}\right)$	$e\left(\frac{73}{83}\right)$	$e\left(\frac{25}{83}\right)$	$e\left(\frac{53}{83}\right)$	$e\left(\frac{12}{83}\right)$	$e\left(\frac{75}{83}\right)$
$\chi_{167}(8,\cdot)$	167.c	83	yes	$1$	$1$	$e\left(\frac{76}{83}\right)$	$e\left(\frac{79}{83}\right)$	$e\left(\frac{69}{83}\right)$	$e\left(\frac{60}{83}\right)$	$e\left(\frac{72}{83}\right)$	$e\left(\frac{25}{83}\right)$	$e\left(\frac{62}{83}\right)$	$e\left(\frac{75}{83}\right)$	$e\left(\frac{53}{83}\right)$	$e\left(\frac{20}{83}\right)$
$\chi_{167}(9,\cdot)$	167.c	83	yes	$1$	$1$	$e\left(\frac{25}{83}\right)$	$e\left(\frac{38}{83}\right)$	$e\left(\frac{50}{83}\right)$	$e\left(\frac{11}{83}\right)$	$e\left(\frac{63}{83}\right)$	$e\left(\frac{53}{83}\right)$	$e\left(\frac{75}{83}\right)$	$e\left(\frac{76}{83}\right)$	$e\left(\frac{36}{83}\right)$	$e\left(\frac{59}{83}\right)$
$\chi_{167}(10,\cdot)$	167.d	166	yes	$-1$	$1$	$e\left(\frac{73}{83}\right)$	$e\left(\frac{18}{83}\right)$	$e\left(\frac{63}{83}\right)$	$e\left(\frac{41}{166}\right)$	$e\left(\frac{8}{83}\right)$	$e\left(\frac{12}{83}\right)$	$e\left(\frac{53}{83}\right)$	$e\left(\frac{36}{83}\right)$	$e\left(\frac{21}{166}\right)$	$e\left(\frac{76}{83}\right)$
$\chi_{167}(11,\cdot)$	167.c	83	yes	$1$	$1$	$e\left(\frac{62}{83}\right)$	$e\left(\frac{71}{83}\right)$	$e\left(\frac{41}{83}\right)$	$e\left(\frac{14}{83}\right)$	$e\left(\frac{50}{83}\right)$	$e\left(\frac{75}{83}\right)$	$e\left(\frac{20}{83}\right)$	$e\left(\frac{59}{83}\right)$	$e\left(\frac{76}{83}\right)$	$e\left(\frac{60}{83}\right)$
$\chi_{167}(12,\cdot)$	167.c	83	yes	$1$	$1$	$e\left(\frac{77}{83}\right)$	$e\left(\frac{44}{83}\right)$	$e\left(\frac{71}{83}\right)$	$e\left(\frac{4}{83}\right)$	$e\left(\frac{38}{83}\right)$	$e\left(\frac{57}{83}\right)$	$e\left(\frac{65}{83}\right)$	$e\left(\frac{5}{83}\right)$	$e\left(\frac{81}{83}\right)$	$e\left(\frac{29}{83}\right)$
$\chi_{167}(13,\cdot)$	167.d	166	yes	$-1$	$1$	$e\left(\frac{68}{83}\right)$	$e\left(\frac{27}{83}\right)$	$e\left(\frac{53}{83}\right)$	$e\left(\frac{103}{166}\right)$	$e\left(\frac{12}{83}\right)$	$e\left(\frac{18}{83}\right)$	$e\left(\frac{38}{83}\right)$	$e\left(\frac{54}{83}\right)$	$e\left(\frac{73}{166}\right)$	$e\left(\frac{31}{83}\right)$
$\chi_{167}(14,\cdot)$	167.c	83	yes	$1$	$1$	$e\left(\frac{6}{83}\right)$	$e\left(\frac{39}{83}\right)$	$e\left(\frac{12}{83}\right)$	$e\left(\frac{79}{83}\right)$	$e\left(\frac{45}{83}\right)$	$e\left(\frac{26}{83}\right)$	$e\left(\frac{18}{83}\right)$	$e\left(\frac{78}{83}\right)$	$e\left(\frac{2}{83}\right)$	$e\left(\frac{54}{83}\right)$
$\chi_{167}(15,\cdot)$	167.d	166	yes	$-1$	$1$	$e\left(\frac{74}{83}\right)$	$e\left(\frac{66}{83}\right)$	$e\left(\frac{65}{83}\right)$	$e\left(\frac{95}{166}\right)$	$e\left(\frac{57}{83}\right)$	$e\left(\frac{44}{83}\right)$	$e\left(\frac{56}{83}\right)$	$e\left(\frac{49}{83}\right)$	$e\left(\frac{77}{166}\right)$	$e\left(\frac{2}{83}\right)$
$\chi_{167}(16,\cdot)$	167.c	83	yes	$1$	$1$	$e\left(\frac{46}{83}\right)$	$e\left(\frac{50}{83}\right)$	$e\left(\frac{9}{83}\right)$	$e\left(\frac{80}{83}\right)$	$e\left(\frac{13}{83}\right)$	$e\left(\frac{61}{83}\right)$	$e\left(\frac{55}{83}\right)$	$e\left(\frac{17}{83}\right)$	$e\left(\frac{43}{83}\right)$	$e\left(\frac{82}{83}\right)$
$\chi_{167}(17,\cdot)$	167.d	166	yes	$-1$	$1$	$e\left(\frac{64}{83}\right)$	$e\left(\frac{1}{83}\right)$	$e\left(\frac{45}{83}\right)$	$e\left(\frac{53}{166}\right)$	$e\left(\frac{65}{83}\right)$	$e\left(\frac{56}{83}\right)$	$e\left(\frac{26}{83}\right)$	$e\left(\frac{2}{83}\right)$	$e\left(\frac{15}{166}\right)$	$e\left(\frac{78}{83}\right)$
$\chi_{167}(18,\cdot)$	167.c	83	yes	$1$	$1$	$e\left(\frac{78}{83}\right)$	$e\left(\frac{9}{83}\right)$	$e\left(\frac{73}{83}\right)$	$e\left(\frac{31}{83}\right)$	$e\left(\frac{4}{83}\right)$	$e\left(\frac{6}{83}\right)$	$e\left(\frac{68}{83}\right)$	$e\left(\frac{18}{83}\right)$	$e\left(\frac{26}{83}\right)$	$e\left(\frac{38}{83}\right)$
$\chi_{167}(19,\cdot)$	167.c	83	yes	$1$	$1$	$e\left(\frac{81}{83}\right)$	$e\left(\frac{70}{83}\right)$	$e\left(\frac{79}{83}\right)$	$e\left(\frac{29}{83}\right)$	$e\left(\frac{68}{83}\right)$	$e\left(\frac{19}{83}\right)$	$e\left(\frac{77}{83}\right)$	$e\left(\frac{57}{83}\right)$	$e\left(\frac{27}{83}\right)$	$e\left(\frac{65}{83}\right)$
$\chi_{167}(20,\cdot)$	167.d	166	yes	$-1$	$1$	$e\left(\frac{43}{83}\right)$	$e\left(\frac{72}{83}\right)$	$e\left(\frac{3}{83}\right)$	$e\left(\frac{81}{166}\right)$	$e\left(\frac{32}{83}\right)$	$e\left(\frac{48}{83}\right)$	$e\left(\frac{46}{83}\right)$	$e\left(\frac{61}{83}\right)$	$e\left(\frac{1}{166}\right)$	$e\left(\frac{55}{83}\right)$
$\chi_{167}(21,\cdot)$	167.c	83	yes	$1$	$1$	$e\left(\frac{7}{83}\right)$	$e\left(\frac{4}{83}\right)$	$e\left(\frac{14}{83}\right)$	$e\left(\frac{23}{83}\right)$	$e\left(\frac{11}{83}\right)$	$e\left(\frac{58}{83}\right)$	$e\left(\frac{21}{83}\right)$	$e\left(\frac{8}{83}\right)$	$e\left(\frac{30}{83}\right)$	$e\left(\frac{63}{83}\right)$
$\chi_{167}(22,\cdot)$	167.c	83	yes	$1$	$1$	$e\left(\frac{32}{83}\right)$	$e\left(\frac{42}{83}\right)$	$e\left(\frac{64}{83}\right)$	$e\left(\frac{34}{83}\right)$	$e\left(\frac{74}{83}\right)$	$e\left(\frac{28}{83}\right)$	$e\left(\frac{13}{83}\right)$	$e\left(\frac{1}{83}\right)$	$e\left(\frac{66}{83}\right)$	$e\left(\frac{39}{83}\right)$
$\chi_{167}(23,\cdot)$	167.d	166	yes	$-1$	$1$	$e\left(\frac{71}{83}\right)$	$e\left(\frac{5}{83}\right)$	$e\left(\frac{59}{83}\right)$	$e\left(\frac{99}{166}\right)$	$e\left(\frac{76}{83}\right)$	$e\left(\frac{31}{83}\right)$	$e\left(\frac{47}{83}\right)$	$e\left(\frac{10}{83}\right)$	$e\left(\frac{75}{166}\right)$	$e\left(\frac{58}{83}\right)$
$\chi_{167}(24,\cdot)$	167.c	83	yes	$1$	$1$	$e\left(\frac{47}{83}\right)$	$e\left(\frac{15}{83}\right)$	$e\left(\frac{11}{83}\right)$	$e\left(\frac{24}{83}\right)$	$e\left(\frac{62}{83}\right)$	$e\left(\frac{10}{83}\right)$	$e\left(\frac{58}{83}\right)$	$e\left(\frac{30}{83}\right)$	$e\left(\frac{71}{83}\right)$	$e\left(\frac{8}{83}\right)$
$\chi_{167}(25,\cdot)$	167.c	83	yes	$1$	$1$	$e\left(\frac{40}{83}\right)$	$e\left(\frac{11}{83}\right)$	$e\left(\frac{80}{83}\right)$	$e\left(\frac{1}{83}\right)$	$e\left(\frac{51}{83}\right)$	$e\left(\frac{35}{83}\right)$	$e\left(\frac{37}{83}\right)$	$e\left(\frac{22}{83}\right)$	$e\left(\frac{41}{83}\right)$	$e\left(\frac{28}{83}\right)$
$\chi_{167}(26,\cdot)$	167.d	166	yes	$-1$	$1$	$e\left(\frac{38}{83}\right)$	$e\left(\frac{81}{83}\right)$	$e\left(\frac{76}{83}\right)$	$e\left(\frac{143}{166}\right)$	$e\left(\frac{36}{83}\right)$	$e\left(\frac{54}{83}\right)$	$e\left(\frac{31}{83}\right)$	$e\left(\frac{79}{83}\right)$	$e\left(\frac{53}{166}\right)$	$e\left(\frac{10}{83}\right)$
$\chi_{167}(27,\cdot)$	167.c	83	yes	$1$	$1$	$e\left(\frac{79}{83}\right)$	$e\left(\frac{57}{83}\right)$	$e\left(\frac{75}{83}\right)$	$e\left(\frac{58}{83}\right)$	$e\left(\frac{53}{83}\right)$	$e\left(\frac{38}{83}\right)$	$e\left(\frac{71}{83}\right)$	$e\left(\frac{31}{83}\right)$	$e\left(\frac{54}{83}\right)$	$e\left(\frac{47}{83}\right)$
$\chi_{167}(28,\cdot)$	167.c	83	yes	$1$	$1$	$e\left(\frac{59}{83}\right)$	$e\left(\frac{10}{83}\right)$	$e\left(\frac{35}{83}\right)$	$e\left(\frac{16}{83}\right)$	$e\left(\frac{69}{83}\right)$	$e\left(\frac{62}{83}\right)$	$e\left(\frac{11}{83}\right)$	$e\left(\frac{20}{83}\right)$	$e\left(\frac{75}{83}\right)$	$e\left(\frac{33}{83}\right)$
$\chi_{167}(29,\cdot)$	167.c	83	yes	$1$	$1$	$e\left(\frac{12}{83}\right)$	$e\left(\frac{78}{83}\right)$	$e\left(\frac{24}{83}\right)$	$e\left(\frac{75}{83}\right)$	$e\left(\frac{7}{83}\right)$	$e\left(\frac{52}{83}\right)$	$e\left(\frac{36}{83}\right)$	$e\left(\frac{73}{83}\right)$	$e\left(\frac{4}{83}\right)$	$e\left(\frac{25}{83}\right)$
$\chi_{167}(30,\cdot)$	167.d	166	yes	$-1$	$1$	$e\left(\frac{44}{83}\right)$	$e\left(\frac{37}{83}\right)$	$e\left(\frac{5}{83}\right)$	$e\left(\frac{135}{166}\right)$	$e\left(\frac{81}{83}\right)$	$e\left(\frac{80}{83}\right)$	$e\left(\frac{49}{83}\right)$	$e\left(\frac{74}{83}\right)$	$e\left(\frac{57}{166}\right)$	$e\left(\frac{64}{83}\right)$
$\chi_{167}(31,\cdot)$	167.c	83	yes	$1$	$1$	$e\left(\frac{57}{83}\right)$	$e\left(\frac{80}{83}\right)$	$e\left(\frac{31}{83}\right)$	$e\left(\frac{45}{83}\right)$	$e\left(\frac{54}{83}\right)$	$e\left(\frac{81}{83}\right)$	$e\left(\frac{5}{83}\right)$	$e\left(\frac{77}{83}\right)$	$e\left(\frac{19}{83}\right)$	$e\left(\frac{15}{83}\right)$
$\chi_{167}(32,\cdot)$	167.c	83	yes	$1$	$1$	$e\left(\frac{16}{83}\right)$	$e\left(\frac{21}{83}\right)$	$e\left(\frac{32}{83}\right)$	$e\left(\frac{17}{83}\right)$	$e\left(\frac{37}{83}\right)$	$e\left(\frac{14}{83}\right)$	$e\left(\frac{48}{83}\right)$	$e\left(\frac{42}{83}\right)$	$e\left(\frac{33}{83}\right)$	$e\left(\frac{61}{83}\right)$

Click here to search among the remaining 134 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	$167$
Structure	\(C_{166}\)
Order	$166$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(7\)	\(8\)	\(9\)	\(10\)	\(11\)
\(\chi_{167}(1,\cdot)\)	167.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{167}(2,\cdot)\)	167.c	83	yes	\(1\)	\(1\)	\(e\left(\frac{53}{83}\right)\)	\(e\left(\frac{54}{83}\right)\)	\(e\left(\frac{23}{83}\right)\)	\(e\left(\frac{20}{83}\right)\)	\(e\left(\frac{24}{83}\right)\)	\(e\left(\frac{36}{83}\right)\)	\(e\left(\frac{76}{83}\right)\)	\(e\left(\frac{25}{83}\right)\)	\(e\left(\frac{73}{83}\right)\)	\(e\left(\frac{62}{83}\right)\)
\(\chi_{167}(3,\cdot)\)	167.c	83	yes	\(1\)	\(1\)	\(e\left(\frac{54}{83}\right)\)	\(e\left(\frac{19}{83}\right)\)	\(e\left(\frac{25}{83}\right)\)	\(e\left(\frac{47}{83}\right)\)	\(e\left(\frac{73}{83}\right)\)	\(e\left(\frac{68}{83}\right)\)	\(e\left(\frac{79}{83}\right)\)	\(e\left(\frac{38}{83}\right)\)	\(e\left(\frac{18}{83}\right)\)	\(e\left(\frac{71}{83}\right)\)
\(\chi_{167}(4,\cdot)\)	167.c	83	yes	\(1\)	\(1\)	\(e\left(\frac{23}{83}\right)\)	\(e\left(\frac{25}{83}\right)\)	\(e\left(\frac{46}{83}\right)\)	\(e\left(\frac{40}{83}\right)\)	\(e\left(\frac{48}{83}\right)\)	\(e\left(\frac{72}{83}\right)\)	\(e\left(\frac{69}{83}\right)\)	\(e\left(\frac{50}{83}\right)\)	\(e\left(\frac{63}{83}\right)\)	\(e\left(\frac{41}{83}\right)\)
\(\chi_{167}(5,\cdot)\)	167.d	166	yes	\(-1\)	\(1\)	\(e\left(\frac{20}{83}\right)\)	\(e\left(\frac{47}{83}\right)\)	\(e\left(\frac{40}{83}\right)\)	\(e\left(\frac{1}{166}\right)\)	\(e\left(\frac{67}{83}\right)\)	\(e\left(\frac{59}{83}\right)\)	\(e\left(\frac{60}{83}\right)\)	\(e\left(\frac{11}{83}\right)\)	\(e\left(\frac{41}{166}\right)\)	\(e\left(\frac{14}{83}\right)\)
\(\chi_{167}(6,\cdot)\)	167.c	83	yes	\(1\)	\(1\)	\(e\left(\frac{24}{83}\right)\)	\(e\left(\frac{73}{83}\right)\)	\(e\left(\frac{48}{83}\right)\)	\(e\left(\frac{67}{83}\right)\)	\(e\left(\frac{14}{83}\right)\)	\(e\left(\frac{21}{83}\right)\)	\(e\left(\frac{72}{83}\right)\)	\(e\left(\frac{63}{83}\right)\)	\(e\left(\frac{8}{83}\right)\)	\(e\left(\frac{50}{83}\right)\)
\(\chi_{167}(7,\cdot)\)	167.c	83	yes	\(1\)	\(1\)	\(e\left(\frac{36}{83}\right)\)	\(e\left(\frac{68}{83}\right)\)	\(e\left(\frac{72}{83}\right)\)	\(e\left(\frac{59}{83}\right)\)	\(e\left(\frac{21}{83}\right)\)	\(e\left(\frac{73}{83}\right)\)	\(e\left(\frac{25}{83}\right)\)	\(e\left(\frac{53}{83}\right)\)	\(e\left(\frac{12}{83}\right)\)	\(e\left(\frac{75}{83}\right)\)
\(\chi_{167}(8,\cdot)\)	167.c	83	yes	\(1\)	\(1\)	\(e\left(\frac{76}{83}\right)\)	\(e\left(\frac{79}{83}\right)\)	\(e\left(\frac{69}{83}\right)\)	\(e\left(\frac{60}{83}\right)\)	\(e\left(\frac{72}{83}\right)\)	\(e\left(\frac{25}{83}\right)\)	\(e\left(\frac{62}{83}\right)\)	\(e\left(\frac{75}{83}\right)\)	\(e\left(\frac{53}{83}\right)\)	\(e\left(\frac{20}{83}\right)\)
\(\chi_{167}(9,\cdot)\)	167.c	83	yes	\(1\)	\(1\)	\(e\left(\frac{25}{83}\right)\)	\(e\left(\frac{38}{83}\right)\)	\(e\left(\frac{50}{83}\right)\)	\(e\left(\frac{11}{83}\right)\)	\(e\left(\frac{63}{83}\right)\)	\(e\left(\frac{53}{83}\right)\)	\(e\left(\frac{75}{83}\right)\)	\(e\left(\frac{76}{83}\right)\)	\(e\left(\frac{36}{83}\right)\)	\(e\left(\frac{59}{83}\right)\)
\(\chi_{167}(10,\cdot)\)	167.d	166	yes	\(-1\)	\(1\)	\(e\left(\frac{73}{83}\right)\)	\(e\left(\frac{18}{83}\right)\)	\(e\left(\frac{63}{83}\right)\)	\(e\left(\frac{41}{166}\right)\)	\(e\left(\frac{8}{83}\right)\)	\(e\left(\frac{12}{83}\right)\)	\(e\left(\frac{53}{83}\right)\)	\(e\left(\frac{36}{83}\right)\)	\(e\left(\frac{21}{166}\right)\)	\(e\left(\frac{76}{83}\right)\)
\(\chi_{167}(11,\cdot)\)	167.c	83	yes	\(1\)	\(1\)	\(e\left(\frac{62}{83}\right)\)	\(e\left(\frac{71}{83}\right)\)	\(e\left(\frac{41}{83}\right)\)	\(e\left(\frac{14}{83}\right)\)	\(e\left(\frac{50}{83}\right)\)	\(e\left(\frac{75}{83}\right)\)	\(e\left(\frac{20}{83}\right)\)	\(e\left(\frac{59}{83}\right)\)	\(e\left(\frac{76}{83}\right)\)	\(e\left(\frac{60}{83}\right)\)
\(\chi_{167}(12,\cdot)\)	167.c	83	yes	\(1\)	\(1\)	\(e\left(\frac{77}{83}\right)\)	\(e\left(\frac{44}{83}\right)\)	\(e\left(\frac{71}{83}\right)\)	\(e\left(\frac{4}{83}\right)\)	\(e\left(\frac{38}{83}\right)\)	\(e\left(\frac{57}{83}\right)\)	\(e\left(\frac{65}{83}\right)\)	\(e\left(\frac{5}{83}\right)\)	\(e\left(\frac{81}{83}\right)\)	\(e\left(\frac{29}{83}\right)\)
\(\chi_{167}(13,\cdot)\)	167.d	166	yes	\(-1\)	\(1\)	\(e\left(\frac{68}{83}\right)\)	\(e\left(\frac{27}{83}\right)\)	\(e\left(\frac{53}{83}\right)\)	\(e\left(\frac{103}{166}\right)\)	\(e\left(\frac{12}{83}\right)\)	\(e\left(\frac{18}{83}\right)\)	\(e\left(\frac{38}{83}\right)\)	\(e\left(\frac{54}{83}\right)\)	\(e\left(\frac{73}{166}\right)\)	\(e\left(\frac{31}{83}\right)\)
\(\chi_{167}(14,\cdot)\)	167.c	83	yes	\(1\)	\(1\)	\(e\left(\frac{6}{83}\right)\)	\(e\left(\frac{39}{83}\right)\)	\(e\left(\frac{12}{83}\right)\)	\(e\left(\frac{79}{83}\right)\)	\(e\left(\frac{45}{83}\right)\)	\(e\left(\frac{26}{83}\right)\)	\(e\left(\frac{18}{83}\right)\)	\(e\left(\frac{78}{83}\right)\)	\(e\left(\frac{2}{83}\right)\)	\(e\left(\frac{54}{83}\right)\)
\(\chi_{167}(15,\cdot)\)	167.d	166	yes	\(-1\)	\(1\)	\(e\left(\frac{74}{83}\right)\)	\(e\left(\frac{66}{83}\right)\)	\(e\left(\frac{65}{83}\right)\)	\(e\left(\frac{95}{166}\right)\)	\(e\left(\frac{57}{83}\right)\)	\(e\left(\frac{44}{83}\right)\)	\(e\left(\frac{56}{83}\right)\)	\(e\left(\frac{49}{83}\right)\)	\(e\left(\frac{77}{166}\right)\)	\(e\left(\frac{2}{83}\right)\)
\(\chi_{167}(16,\cdot)\)	167.c	83	yes	\(1\)	\(1\)	\(e\left(\frac{46}{83}\right)\)	\(e\left(\frac{50}{83}\right)\)	\(e\left(\frac{9}{83}\right)\)	\(e\left(\frac{80}{83}\right)\)	\(e\left(\frac{13}{83}\right)\)	\(e\left(\frac{61}{83}\right)\)	\(e\left(\frac{55}{83}\right)\)	\(e\left(\frac{17}{83}\right)\)	\(e\left(\frac{43}{83}\right)\)	\(e\left(\frac{82}{83}\right)\)
\(\chi_{167}(17,\cdot)\)	167.d	166	yes	\(-1\)	\(1\)	\(e\left(\frac{64}{83}\right)\)	\(e\left(\frac{1}{83}\right)\)	\(e\left(\frac{45}{83}\right)\)	\(e\left(\frac{53}{166}\right)\)	\(e\left(\frac{65}{83}\right)\)	\(e\left(\frac{56}{83}\right)\)	\(e\left(\frac{26}{83}\right)\)	\(e\left(\frac{2}{83}\right)\)	\(e\left(\frac{15}{166}\right)\)	\(e\left(\frac{78}{83}\right)\)
\(\chi_{167}(18,\cdot)\)	167.c	83	yes	\(1\)	\(1\)	\(e\left(\frac{78}{83}\right)\)	\(e\left(\frac{9}{83}\right)\)	\(e\left(\frac{73}{83}\right)\)	\(e\left(\frac{31}{83}\right)\)	\(e\left(\frac{4}{83}\right)\)	\(e\left(\frac{6}{83}\right)\)	\(e\left(\frac{68}{83}\right)\)	\(e\left(\frac{18}{83}\right)\)	\(e\left(\frac{26}{83}\right)\)	\(e\left(\frac{38}{83}\right)\)
\(\chi_{167}(19,\cdot)\)	167.c	83	yes	\(1\)	\(1\)	\(e\left(\frac{81}{83}\right)\)	\(e\left(\frac{70}{83}\right)\)	\(e\left(\frac{79}{83}\right)\)	\(e\left(\frac{29}{83}\right)\)	\(e\left(\frac{68}{83}\right)\)	\(e\left(\frac{19}{83}\right)\)	\(e\left(\frac{77}{83}\right)\)	\(e\left(\frac{57}{83}\right)\)	\(e\left(\frac{27}{83}\right)\)	\(e\left(\frac{65}{83}\right)\)
\(\chi_{167}(20,\cdot)\)	167.d	166	yes	\(-1\)	\(1\)	\(e\left(\frac{43}{83}\right)\)	\(e\left(\frac{72}{83}\right)\)	\(e\left(\frac{3}{83}\right)\)	\(e\left(\frac{81}{166}\right)\)	\(e\left(\frac{32}{83}\right)\)	\(e\left(\frac{48}{83}\right)\)	\(e\left(\frac{46}{83}\right)\)	\(e\left(\frac{61}{83}\right)\)	\(e\left(\frac{1}{166}\right)\)	\(e\left(\frac{55}{83}\right)\)
\(\chi_{167}(21,\cdot)\)	167.c	83	yes	\(1\)	\(1\)	\(e\left(\frac{7}{83}\right)\)	\(e\left(\frac{4}{83}\right)\)	\(e\left(\frac{14}{83}\right)\)	\(e\left(\frac{23}{83}\right)\)	\(e\left(\frac{11}{83}\right)\)	\(e\left(\frac{58}{83}\right)\)	\(e\left(\frac{21}{83}\right)\)	\(e\left(\frac{8}{83}\right)\)	\(e\left(\frac{30}{83}\right)\)	\(e\left(\frac{63}{83}\right)\)
\(\chi_{167}(22,\cdot)\)	167.c	83	yes	\(1\)	\(1\)	\(e\left(\frac{32}{83}\right)\)	\(e\left(\frac{42}{83}\right)\)	\(e\left(\frac{64}{83}\right)\)	\(e\left(\frac{34}{83}\right)\)	\(e\left(\frac{74}{83}\right)\)	\(e\left(\frac{28}{83}\right)\)	\(e\left(\frac{13}{83}\right)\)	\(e\left(\frac{1}{83}\right)\)	\(e\left(\frac{66}{83}\right)\)	\(e\left(\frac{39}{83}\right)\)
\(\chi_{167}(23,\cdot)\)	167.d	166	yes	\(-1\)	\(1\)	\(e\left(\frac{71}{83}\right)\)	\(e\left(\frac{5}{83}\right)\)	\(e\left(\frac{59}{83}\right)\)	\(e\left(\frac{99}{166}\right)\)	\(e\left(\frac{76}{83}\right)\)	\(e\left(\frac{31}{83}\right)\)	\(e\left(\frac{47}{83}\right)\)	\(e\left(\frac{10}{83}\right)\)	\(e\left(\frac{75}{166}\right)\)	\(e\left(\frac{58}{83}\right)\)
\(\chi_{167}(24,\cdot)\)	167.c	83	yes	\(1\)	\(1\)	\(e\left(\frac{47}{83}\right)\)	\(e\left(\frac{15}{83}\right)\)	\(e\left(\frac{11}{83}\right)\)	\(e\left(\frac{24}{83}\right)\)	\(e\left(\frac{62}{83}\right)\)	\(e\left(\frac{10}{83}\right)\)	\(e\left(\frac{58}{83}\right)\)	\(e\left(\frac{30}{83}\right)\)	\(e\left(\frac{71}{83}\right)\)	\(e\left(\frac{8}{83}\right)\)
\(\chi_{167}(25,\cdot)\)	167.c	83	yes	\(1\)	\(1\)	\(e\left(\frac{40}{83}\right)\)	\(e\left(\frac{11}{83}\right)\)	\(e\left(\frac{80}{83}\right)\)	\(e\left(\frac{1}{83}\right)\)	\(e\left(\frac{51}{83}\right)\)	\(e\left(\frac{35}{83}\right)\)	\(e\left(\frac{37}{83}\right)\)	\(e\left(\frac{22}{83}\right)\)	\(e\left(\frac{41}{83}\right)\)	\(e\left(\frac{28}{83}\right)\)
\(\chi_{167}(26,\cdot)\)	167.d	166	yes	\(-1\)	\(1\)	\(e\left(\frac{38}{83}\right)\)	\(e\left(\frac{81}{83}\right)\)	\(e\left(\frac{76}{83}\right)\)	\(e\left(\frac{143}{166}\right)\)	\(e\left(\frac{36}{83}\right)\)	\(e\left(\frac{54}{83}\right)\)	\(e\left(\frac{31}{83}\right)\)	\(e\left(\frac{79}{83}\right)\)	\(e\left(\frac{53}{166}\right)\)	\(e\left(\frac{10}{83}\right)\)
\(\chi_{167}(27,\cdot)\)	167.c	83	yes	\(1\)	\(1\)	\(e\left(\frac{79}{83}\right)\)	\(e\left(\frac{57}{83}\right)\)	\(e\left(\frac{75}{83}\right)\)	\(e\left(\frac{58}{83}\right)\)	\(e\left(\frac{53}{83}\right)\)	\(e\left(\frac{38}{83}\right)\)	\(e\left(\frac{71}{83}\right)\)	\(e\left(\frac{31}{83}\right)\)	\(e\left(\frac{54}{83}\right)\)	\(e\left(\frac{47}{83}\right)\)
\(\chi_{167}(28,\cdot)\)	167.c	83	yes	\(1\)	\(1\)	\(e\left(\frac{59}{83}\right)\)	\(e\left(\frac{10}{83}\right)\)	\(e\left(\frac{35}{83}\right)\)	\(e\left(\frac{16}{83}\right)\)	\(e\left(\frac{69}{83}\right)\)	\(e\left(\frac{62}{83}\right)\)	\(e\left(\frac{11}{83}\right)\)	\(e\left(\frac{20}{83}\right)\)	\(e\left(\frac{75}{83}\right)\)	\(e\left(\frac{33}{83}\right)\)
\(\chi_{167}(29,\cdot)\)	167.c	83	yes	\(1\)	\(1\)	\(e\left(\frac{12}{83}\right)\)	\(e\left(\frac{78}{83}\right)\)	\(e\left(\frac{24}{83}\right)\)	\(e\left(\frac{75}{83}\right)\)	\(e\left(\frac{7}{83}\right)\)	\(e\left(\frac{52}{83}\right)\)	\(e\left(\frac{36}{83}\right)\)	\(e\left(\frac{73}{83}\right)\)	\(e\left(\frac{4}{83}\right)\)	\(e\left(\frac{25}{83}\right)\)
\(\chi_{167}(30,\cdot)\)	167.d	166	yes	\(-1\)	\(1\)	\(e\left(\frac{44}{83}\right)\)	\(e\left(\frac{37}{83}\right)\)	\(e\left(\frac{5}{83}\right)\)	\(e\left(\frac{135}{166}\right)\)	\(e\left(\frac{81}{83}\right)\)	\(e\left(\frac{80}{83}\right)\)	\(e\left(\frac{49}{83}\right)\)	\(e\left(\frac{74}{83}\right)\)	\(e\left(\frac{57}{166}\right)\)	\(e\left(\frac{64}{83}\right)\)
\(\chi_{167}(31,\cdot)\)	167.c	83	yes	\(1\)	\(1\)	\(e\left(\frac{57}{83}\right)\)	\(e\left(\frac{80}{83}\right)\)	\(e\left(\frac{31}{83}\right)\)	\(e\left(\frac{45}{83}\right)\)	\(e\left(\frac{54}{83}\right)\)	\(e\left(\frac{81}{83}\right)\)	\(e\left(\frac{5}{83}\right)\)	\(e\left(\frac{77}{83}\right)\)	\(e\left(\frac{19}{83}\right)\)	\(e\left(\frac{15}{83}\right)\)
\(\chi_{167}(32,\cdot)\)	167.c	83	yes	\(1\)	\(1\)	\(e\left(\frac{16}{83}\right)\)	\(e\left(\frac{21}{83}\right)\)	\(e\left(\frac{32}{83}\right)\)	\(e\left(\frac{17}{83}\right)\)	\(e\left(\frac{37}{83}\right)\)	\(e\left(\frac{14}{83}\right)\)	\(e\left(\frac{48}{83}\right)\)	\(e\left(\frac{42}{83}\right)\)	\(e\left(\frac{33}{83}\right)\)	\(e\left(\frac{61}{83}\right)\)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Learn more

Character group

First 32 of 166 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.