LMFDB - Group of Dirichlet characters of modulus 373

Show commands: PariGP / SageMath

sage: H = DirichletGroup(373)

pari: g = idealstar(,373,2)

Character group

sage: G.order() pari: g.no
Order	=	372
sage: H.invariants() pari: g.cyc
Structure	=	$C_{372}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{373}(2,\cdot)$

First 32 of 372 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	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$11$
$\chi_{373}(1,\cdot)$	373.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{373}(2,\cdot)$	373.l	372	yes	$-1$	$1$	$e\left(\frac{1}{372}\right)$	$e\left(\frac{119}{186}\right)$	$e\left(\frac{1}{186}\right)$	$e\left(\frac{169}{372}\right)$	$e\left(\frac{239}{372}\right)$	$e\left(\frac{33}{62}\right)$	$e\left(\frac{1}{124}\right)$	$e\left(\frac{26}{93}\right)$	$e\left(\frac{85}{186}\right)$	$e\left(\frac{245}{372}\right)$
$\chi_{373}(3,\cdot)$	373.k	186	yes	$1$	$1$	$e\left(\frac{119}{186}\right)$	$e\left(\frac{25}{93}\right)$	$e\left(\frac{26}{93}\right)$	$e\left(\frac{23}{186}\right)$	$e\left(\frac{169}{186}\right)$	$e\left(\frac{21}{31}\right)$	$e\left(\frac{57}{62}\right)$	$e\left(\frac{50}{93}\right)$	$e\left(\frac{71}{93}\right)$	$e\left(\frac{139}{186}\right)$
$\chi_{373}(4,\cdot)$	373.k	186	yes	$1$	$1$	$e\left(\frac{1}{186}\right)$	$e\left(\frac{26}{93}\right)$	$e\left(\frac{1}{93}\right)$	$e\left(\frac{169}{186}\right)$	$e\left(\frac{53}{186}\right)$	$e\left(\frac{2}{31}\right)$	$e\left(\frac{1}{62}\right)$	$e\left(\frac{52}{93}\right)$	$e\left(\frac{85}{93}\right)$	$e\left(\frac{59}{186}\right)$
$\chi_{373}(5,\cdot)$	373.l	372	yes	$-1$	$1$	$e\left(\frac{169}{372}\right)$	$e\left(\frac{23}{186}\right)$	$e\left(\frac{169}{186}\right)$	$e\left(\frac{289}{372}\right)$	$e\left(\frac{215}{372}\right)$	$e\left(\frac{59}{62}\right)$	$e\left(\frac{45}{124}\right)$	$e\left(\frac{23}{93}\right)$	$e\left(\frac{43}{186}\right)$	$e\left(\frac{113}{372}\right)$
$\chi_{373}(6,\cdot)$	373.l	372	yes	$-1$	$1$	$e\left(\frac{239}{372}\right)$	$e\left(\frac{169}{186}\right)$	$e\left(\frac{53}{186}\right)$	$e\left(\frac{215}{372}\right)$	$e\left(\frac{205}{372}\right)$	$e\left(\frac{13}{62}\right)$	$e\left(\frac{115}{124}\right)$	$e\left(\frac{76}{93}\right)$	$e\left(\frac{41}{186}\right)$	$e\left(\frac{151}{372}\right)$
$\chi_{373}(7,\cdot)$	373.h	62	yes	$1$	$1$	$e\left(\frac{33}{62}\right)$	$e\left(\frac{21}{31}\right)$	$e\left(\frac{2}{31}\right)$	$e\left(\frac{59}{62}\right)$	$e\left(\frac{13}{62}\right)$	$e\left(\frac{12}{31}\right)$	$e\left(\frac{37}{62}\right)$	$e\left(\frac{11}{31}\right)$	$e\left(\frac{15}{31}\right)$	$e\left(\frac{25}{62}\right)$
$\chi_{373}(8,\cdot)$	373.j	124	yes	$-1$	$1$	$e\left(\frac{1}{124}\right)$	$e\left(\frac{57}{62}\right)$	$e\left(\frac{1}{62}\right)$	$e\left(\frac{45}{124}\right)$	$e\left(\frac{115}{124}\right)$	$e\left(\frac{37}{62}\right)$	$e\left(\frac{3}{124}\right)$	$e\left(\frac{26}{31}\right)$	$e\left(\frac{23}{62}\right)$	$e\left(\frac{121}{124}\right)$
$\chi_{373}(9,\cdot)$	373.i	93	yes	$1$	$1$	$e\left(\frac{26}{93}\right)$	$e\left(\frac{50}{93}\right)$	$e\left(\frac{52}{93}\right)$	$e\left(\frac{23}{93}\right)$	$e\left(\frac{76}{93}\right)$	$e\left(\frac{11}{31}\right)$	$e\left(\frac{26}{31}\right)$	$e\left(\frac{7}{93}\right)$	$e\left(\frac{49}{93}\right)$	$e\left(\frac{46}{93}\right)$
$\chi_{373}(10,\cdot)$	373.k	186	yes	$1$	$1$	$e\left(\frac{85}{186}\right)$	$e\left(\frac{71}{93}\right)$	$e\left(\frac{85}{93}\right)$	$e\left(\frac{43}{186}\right)$	$e\left(\frac{41}{186}\right)$	$e\left(\frac{15}{31}\right)$	$e\left(\frac{23}{62}\right)$	$e\left(\frac{49}{93}\right)$	$e\left(\frac{64}{93}\right)$	$e\left(\frac{179}{186}\right)$
$\chi_{373}(11,\cdot)$	373.l	372	yes	$-1$	$1$	$e\left(\frac{245}{372}\right)$	$e\left(\frac{139}{186}\right)$	$e\left(\frac{59}{186}\right)$	$e\left(\frac{113}{372}\right)$	$e\left(\frac{151}{372}\right)$	$e\left(\frac{25}{62}\right)$	$e\left(\frac{121}{124}\right)$	$e\left(\frac{46}{93}\right)$	$e\left(\frac{179}{186}\right)$	$e\left(\frac{133}{372}\right)$
$\chi_{373}(12,\cdot)$	373.g	31	yes	$1$	$1$	$e\left(\frac{20}{31}\right)$	$e\left(\frac{17}{31}\right)$	$e\left(\frac{9}{31}\right)$	$e\left(\frac{1}{31}\right)$	$e\left(\frac{6}{31}\right)$	$e\left(\frac{23}{31}\right)$	$e\left(\frac{29}{31}\right)$	$e\left(\frac{3}{31}\right)$	$e\left(\frac{21}{31}\right)$	$e\left(\frac{2}{31}\right)$
$\chi_{373}(13,\cdot)$	373.h	62	yes	$1$	$1$	$e\left(\frac{15}{62}\right)$	$e\left(\frac{18}{31}\right)$	$e\left(\frac{15}{31}\right)$	$e\left(\frac{55}{62}\right)$	$e\left(\frac{51}{62}\right)$	$e\left(\frac{28}{31}\right)$	$e\left(\frac{45}{62}\right)$	$e\left(\frac{5}{31}\right)$	$e\left(\frac{4}{31}\right)$	$e\left(\frac{17}{62}\right)$
$\chi_{373}(14,\cdot)$	373.l	372	yes	$-1$	$1$	$e\left(\frac{199}{372}\right)$	$e\left(\frac{59}{186}\right)$	$e\left(\frac{13}{186}\right)$	$e\left(\frac{151}{372}\right)$	$e\left(\frac{317}{372}\right)$	$e\left(\frac{57}{62}\right)$	$e\left(\frac{75}{124}\right)$	$e\left(\frac{59}{93}\right)$	$e\left(\frac{175}{186}\right)$	$e\left(\frac{23}{372}\right)$
$\chi_{373}(15,\cdot)$	373.l	372	yes	$-1$	$1$	$e\left(\frac{35}{372}\right)$	$e\left(\frac{73}{186}\right)$	$e\left(\frac{35}{186}\right)$	$e\left(\frac{335}{372}\right)$	$e\left(\frac{181}{372}\right)$	$e\left(\frac{39}{62}\right)$	$e\left(\frac{35}{124}\right)$	$e\left(\frac{73}{93}\right)$	$e\left(\frac{185}{186}\right)$	$e\left(\frac{19}{372}\right)$
$\chi_{373}(16,\cdot)$	373.i	93	yes	$1$	$1$	$e\left(\frac{1}{93}\right)$	$e\left(\frac{52}{93}\right)$	$e\left(\frac{2}{93}\right)$	$e\left(\frac{76}{93}\right)$	$e\left(\frac{53}{93}\right)$	$e\left(\frac{4}{31}\right)$	$e\left(\frac{1}{31}\right)$	$e\left(\frac{11}{93}\right)$	$e\left(\frac{77}{93}\right)$	$e\left(\frac{59}{93}\right)$
$\chi_{373}(17,\cdot)$	373.h	62	yes	$1$	$1$	$e\left(\frac{21}{62}\right)$	$e\left(\frac{19}{31}\right)$	$e\left(\frac{21}{31}\right)$	$e\left(\frac{15}{62}\right)$	$e\left(\frac{59}{62}\right)$	$e\left(\frac{2}{31}\right)$	$e\left(\frac{1}{62}\right)$	$e\left(\frac{7}{31}\right)$	$e\left(\frac{18}{31}\right)$	$e\left(\frac{61}{62}\right)$
$\chi_{373}(18,\cdot)$	373.j	124	yes	$-1$	$1$	$e\left(\frac{35}{124}\right)$	$e\left(\frac{11}{62}\right)$	$e\left(\frac{35}{62}\right)$	$e\left(\frac{87}{124}\right)$	$e\left(\frac{57}{124}\right)$	$e\left(\frac{55}{62}\right)$	$e\left(\frac{105}{124}\right)$	$e\left(\frac{11}{31}\right)$	$e\left(\frac{61}{62}\right)$	$e\left(\frac{19}{124}\right)$
$\chi_{373}(19,\cdot)$	373.j	124	yes	$-1$	$1$	$e\left(\frac{9}{124}\right)$	$e\left(\frac{17}{62}\right)$	$e\left(\frac{9}{62}\right)$	$e\left(\frac{33}{124}\right)$	$e\left(\frac{43}{124}\right)$	$e\left(\frac{23}{62}\right)$	$e\left(\frac{27}{124}\right)$	$e\left(\frac{17}{31}\right)$	$e\left(\frac{21}{62}\right)$	$e\left(\frac{97}{124}\right)$
$\chi_{373}(20,\cdot)$	373.j	124	yes	$-1$	$1$	$e\left(\frac{57}{124}\right)$	$e\left(\frac{25}{62}\right)$	$e\left(\frac{57}{62}\right)$	$e\left(\frac{85}{124}\right)$	$e\left(\frac{107}{124}\right)$	$e\left(\frac{1}{62}\right)$	$e\left(\frac{47}{124}\right)$	$e\left(\frac{25}{31}\right)$	$e\left(\frac{9}{62}\right)$	$e\left(\frac{77}{124}\right)$
$\chi_{373}(21,\cdot)$	373.i	93	yes	$1$	$1$	$e\left(\frac{16}{93}\right)$	$e\left(\frac{88}{93}\right)$	$e\left(\frac{32}{93}\right)$	$e\left(\frac{7}{93}\right)$	$e\left(\frac{11}{93}\right)$	$e\left(\frac{2}{31}\right)$	$e\left(\frac{16}{31}\right)$	$e\left(\frac{83}{93}\right)$	$e\left(\frac{23}{93}\right)$	$e\left(\frac{14}{93}\right)$
$\chi_{373}(22,\cdot)$	373.h	62	yes	$1$	$1$	$e\left(\frac{41}{62}\right)$	$e\left(\frac{12}{31}\right)$	$e\left(\frac{10}{31}\right)$	$e\left(\frac{47}{62}\right)$	$e\left(\frac{3}{62}\right)$	$e\left(\frac{29}{31}\right)$	$e\left(\frac{61}{62}\right)$	$e\left(\frac{24}{31}\right)$	$e\left(\frac{13}{31}\right)$	$e\left(\frac{1}{62}\right)$
$\chi_{373}(23,\cdot)$	373.j	124	yes	$-1$	$1$	$e\left(\frac{117}{124}\right)$	$e\left(\frac{35}{62}\right)$	$e\left(\frac{55}{62}\right)$	$e\left(\frac{57}{124}\right)$	$e\left(\frac{63}{124}\right)$	$e\left(\frac{51}{62}\right)$	$e\left(\frac{103}{124}\right)$	$e\left(\frac{4}{31}\right)$	$e\left(\frac{25}{62}\right)$	$e\left(\frac{21}{124}\right)$
$\chi_{373}(24,\cdot)$	373.l	372	yes	$-1$	$1$	$e\left(\frac{241}{372}\right)$	$e\left(\frac{35}{186}\right)$	$e\left(\frac{55}{186}\right)$	$e\left(\frac{181}{372}\right)$	$e\left(\frac{311}{372}\right)$	$e\left(\frac{17}{62}\right)$	$e\left(\frac{117}{124}\right)$	$e\left(\frac{35}{93}\right)$	$e\left(\frac{25}{186}\right)$	$e\left(\frac{269}{372}\right)$
$\chi_{373}(25,\cdot)$	373.k	186	yes	$1$	$1$	$e\left(\frac{169}{186}\right)$	$e\left(\frac{23}{93}\right)$	$e\left(\frac{76}{93}\right)$	$e\left(\frac{103}{186}\right)$	$e\left(\frac{29}{186}\right)$	$e\left(\frac{28}{31}\right)$	$e\left(\frac{45}{62}\right)$	$e\left(\frac{46}{93}\right)$	$e\left(\frac{43}{93}\right)$	$e\left(\frac{113}{186}\right)$
$\chi_{373}(26,\cdot)$	373.l	372	yes	$-1$	$1$	$e\left(\frac{91}{372}\right)$	$e\left(\frac{41}{186}\right)$	$e\left(\frac{91}{186}\right)$	$e\left(\frac{127}{372}\right)$	$e\left(\frac{173}{372}\right)$	$e\left(\frac{27}{62}\right)$	$e\left(\frac{91}{124}\right)$	$e\left(\frac{41}{93}\right)$	$e\left(\frac{109}{186}\right)$	$e\left(\frac{347}{372}\right)$
$\chi_{373}(27,\cdot)$	373.h	62	yes	$1$	$1$	$e\left(\frac{57}{62}\right)$	$e\left(\frac{25}{31}\right)$	$e\left(\frac{26}{31}\right)$	$e\left(\frac{23}{62}\right)$	$e\left(\frac{45}{62}\right)$	$e\left(\frac{1}{31}\right)$	$e\left(\frac{47}{62}\right)$	$e\left(\frac{19}{31}\right)$	$e\left(\frac{9}{31}\right)$	$e\left(\frac{15}{62}\right)$
$\chi_{373}(28,\cdot)$	373.i	93	yes	$1$	$1$	$e\left(\frac{50}{93}\right)$	$e\left(\frac{89}{93}\right)$	$e\left(\frac{7}{93}\right)$	$e\left(\frac{80}{93}\right)$	$e\left(\frac{46}{93}\right)$	$e\left(\frac{14}{31}\right)$	$e\left(\frac{19}{31}\right)$	$e\left(\frac{85}{93}\right)$	$e\left(\frac{37}{93}\right)$	$e\left(\frac{67}{93}\right)$
$\chi_{373}(29,\cdot)$	373.i	93	yes	$1$	$1$	$e\left(\frac{71}{93}\right)$	$e\left(\frac{65}{93}\right)$	$e\left(\frac{49}{93}\right)$	$e\left(\frac{2}{93}\right)$	$e\left(\frac{43}{93}\right)$	$e\left(\frac{5}{31}\right)$	$e\left(\frac{9}{31}\right)$	$e\left(\frac{37}{93}\right)$	$e\left(\frac{73}{93}\right)$	$e\left(\frac{4}{93}\right)$
$\chi_{373}(30,\cdot)$	373.g	31	yes	$1$	$1$	$e\left(\frac{3}{31}\right)$	$e\left(\frac{1}{31}\right)$	$e\left(\frac{6}{31}\right)$	$e\left(\frac{11}{31}\right)$	$e\left(\frac{4}{31}\right)$	$e\left(\frac{5}{31}\right)$	$e\left(\frac{9}{31}\right)$	$e\left(\frac{2}{31}\right)$	$e\left(\frac{14}{31}\right)$	$e\left(\frac{22}{31}\right)$
$\chi_{373}(31,\cdot)$	373.h	62	yes	$1$	$1$	$e\left(\frac{53}{62}\right)$	$e\left(\frac{14}{31}\right)$	$e\left(\frac{22}{31}\right)$	$e\left(\frac{29}{62}\right)$	$e\left(\frac{19}{62}\right)$	$e\left(\frac{8}{31}\right)$	$e\left(\frac{35}{62}\right)$	$e\left(\frac{28}{31}\right)$	$e\left(\frac{10}{31}\right)$	$e\left(\frac{27}{62}\right)$
$\chi_{373}(32,\cdot)$	373.l	372	yes	$-1$	$1$	$e\left(\frac{5}{372}\right)$	$e\left(\frac{37}{186}\right)$	$e\left(\frac{5}{186}\right)$	$e\left(\frac{101}{372}\right)$	$e\left(\frac{79}{372}\right)$	$e\left(\frac{41}{62}\right)$	$e\left(\frac{5}{124}\right)$	$e\left(\frac{37}{93}\right)$	$e\left(\frac{53}{186}\right)$	$e\left(\frac{109}{372}\right)$

Click here to search among the remaining 340 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	$373$
Structure	\(C_{372}\)
Order	$372$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(7\)	\(8\)	\(9\)	\(10\)	\(11\)
\(\chi_{373}(1,\cdot)\)	373.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{373}(2,\cdot)\)	373.l	372	yes	\(-1\)	\(1\)	\(e\left(\frac{1}{372}\right)\)	\(e\left(\frac{119}{186}\right)\)	\(e\left(\frac{1}{186}\right)\)	\(e\left(\frac{169}{372}\right)\)	\(e\left(\frac{239}{372}\right)\)	\(e\left(\frac{33}{62}\right)\)	\(e\left(\frac{1}{124}\right)\)	\(e\left(\frac{26}{93}\right)\)	\(e\left(\frac{85}{186}\right)\)	\(e\left(\frac{245}{372}\right)\)
\(\chi_{373}(3,\cdot)\)	373.k	186	yes	\(1\)	\(1\)	\(e\left(\frac{119}{186}\right)\)	\(e\left(\frac{25}{93}\right)\)	\(e\left(\frac{26}{93}\right)\)	\(e\left(\frac{23}{186}\right)\)	\(e\left(\frac{169}{186}\right)\)	\(e\left(\frac{21}{31}\right)\)	\(e\left(\frac{57}{62}\right)\)	\(e\left(\frac{50}{93}\right)\)	\(e\left(\frac{71}{93}\right)\)	\(e\left(\frac{139}{186}\right)\)
\(\chi_{373}(4,\cdot)\)	373.k	186	yes	\(1\)	\(1\)	\(e\left(\frac{1}{186}\right)\)	\(e\left(\frac{26}{93}\right)\)	\(e\left(\frac{1}{93}\right)\)	\(e\left(\frac{169}{186}\right)\)	\(e\left(\frac{53}{186}\right)\)	\(e\left(\frac{2}{31}\right)\)	\(e\left(\frac{1}{62}\right)\)	\(e\left(\frac{52}{93}\right)\)	\(e\left(\frac{85}{93}\right)\)	\(e\left(\frac{59}{186}\right)\)
\(\chi_{373}(5,\cdot)\)	373.l	372	yes	\(-1\)	\(1\)	\(e\left(\frac{169}{372}\right)\)	\(e\left(\frac{23}{186}\right)\)	\(e\left(\frac{169}{186}\right)\)	\(e\left(\frac{289}{372}\right)\)	\(e\left(\frac{215}{372}\right)\)	\(e\left(\frac{59}{62}\right)\)	\(e\left(\frac{45}{124}\right)\)	\(e\left(\frac{23}{93}\right)\)	\(e\left(\frac{43}{186}\right)\)	\(e\left(\frac{113}{372}\right)\)
\(\chi_{373}(6,\cdot)\)	373.l	372	yes	\(-1\)	\(1\)	\(e\left(\frac{239}{372}\right)\)	\(e\left(\frac{169}{186}\right)\)	\(e\left(\frac{53}{186}\right)\)	\(e\left(\frac{215}{372}\right)\)	\(e\left(\frac{205}{372}\right)\)	\(e\left(\frac{13}{62}\right)\)	\(e\left(\frac{115}{124}\right)\)	\(e\left(\frac{76}{93}\right)\)	\(e\left(\frac{41}{186}\right)\)	\(e\left(\frac{151}{372}\right)\)
\(\chi_{373}(7,\cdot)\)	373.h	62	yes	\(1\)	\(1\)	\(e\left(\frac{33}{62}\right)\)	\(e\left(\frac{21}{31}\right)\)	\(e\left(\frac{2}{31}\right)\)	\(e\left(\frac{59}{62}\right)\)	\(e\left(\frac{13}{62}\right)\)	\(e\left(\frac{12}{31}\right)\)	\(e\left(\frac{37}{62}\right)\)	\(e\left(\frac{11}{31}\right)\)	\(e\left(\frac{15}{31}\right)\)	\(e\left(\frac{25}{62}\right)\)
\(\chi_{373}(8,\cdot)\)	373.j	124	yes	\(-1\)	\(1\)	\(e\left(\frac{1}{124}\right)\)	\(e\left(\frac{57}{62}\right)\)	\(e\left(\frac{1}{62}\right)\)	\(e\left(\frac{45}{124}\right)\)	\(e\left(\frac{115}{124}\right)\)	\(e\left(\frac{37}{62}\right)\)	\(e\left(\frac{3}{124}\right)\)	\(e\left(\frac{26}{31}\right)\)	\(e\left(\frac{23}{62}\right)\)	\(e\left(\frac{121}{124}\right)\)
\(\chi_{373}(9,\cdot)\)	373.i	93	yes	\(1\)	\(1\)	\(e\left(\frac{26}{93}\right)\)	\(e\left(\frac{50}{93}\right)\)	\(e\left(\frac{52}{93}\right)\)	\(e\left(\frac{23}{93}\right)\)	\(e\left(\frac{76}{93}\right)\)	\(e\left(\frac{11}{31}\right)\)	\(e\left(\frac{26}{31}\right)\)	\(e\left(\frac{7}{93}\right)\)	\(e\left(\frac{49}{93}\right)\)	\(e\left(\frac{46}{93}\right)\)
\(\chi_{373}(10,\cdot)\)	373.k	186	yes	\(1\)	\(1\)	\(e\left(\frac{85}{186}\right)\)	\(e\left(\frac{71}{93}\right)\)	\(e\left(\frac{85}{93}\right)\)	\(e\left(\frac{43}{186}\right)\)	\(e\left(\frac{41}{186}\right)\)	\(e\left(\frac{15}{31}\right)\)	\(e\left(\frac{23}{62}\right)\)	\(e\left(\frac{49}{93}\right)\)	\(e\left(\frac{64}{93}\right)\)	\(e\left(\frac{179}{186}\right)\)
\(\chi_{373}(11,\cdot)\)	373.l	372	yes	\(-1\)	\(1\)	\(e\left(\frac{245}{372}\right)\)	\(e\left(\frac{139}{186}\right)\)	\(e\left(\frac{59}{186}\right)\)	\(e\left(\frac{113}{372}\right)\)	\(e\left(\frac{151}{372}\right)\)	\(e\left(\frac{25}{62}\right)\)	\(e\left(\frac{121}{124}\right)\)	\(e\left(\frac{46}{93}\right)\)	\(e\left(\frac{179}{186}\right)\)	\(e\left(\frac{133}{372}\right)\)
\(\chi_{373}(12,\cdot)\)	373.g	31	yes	\(1\)	\(1\)	\(e\left(\frac{20}{31}\right)\)	\(e\left(\frac{17}{31}\right)\)	\(e\left(\frac{9}{31}\right)\)	\(e\left(\frac{1}{31}\right)\)	\(e\left(\frac{6}{31}\right)\)	\(e\left(\frac{23}{31}\right)\)	\(e\left(\frac{29}{31}\right)\)	\(e\left(\frac{3}{31}\right)\)	\(e\left(\frac{21}{31}\right)\)	\(e\left(\frac{2}{31}\right)\)
\(\chi_{373}(13,\cdot)\)	373.h	62	yes	\(1\)	\(1\)	\(e\left(\frac{15}{62}\right)\)	\(e\left(\frac{18}{31}\right)\)	\(e\left(\frac{15}{31}\right)\)	\(e\left(\frac{55}{62}\right)\)	\(e\left(\frac{51}{62}\right)\)	\(e\left(\frac{28}{31}\right)\)	\(e\left(\frac{45}{62}\right)\)	\(e\left(\frac{5}{31}\right)\)	\(e\left(\frac{4}{31}\right)\)	\(e\left(\frac{17}{62}\right)\)
\(\chi_{373}(14,\cdot)\)	373.l	372	yes	\(-1\)	\(1\)	\(e\left(\frac{199}{372}\right)\)	\(e\left(\frac{59}{186}\right)\)	\(e\left(\frac{13}{186}\right)\)	\(e\left(\frac{151}{372}\right)\)	\(e\left(\frac{317}{372}\right)\)	\(e\left(\frac{57}{62}\right)\)	\(e\left(\frac{75}{124}\right)\)	\(e\left(\frac{59}{93}\right)\)	\(e\left(\frac{175}{186}\right)\)	\(e\left(\frac{23}{372}\right)\)
\(\chi_{373}(15,\cdot)\)	373.l	372	yes	\(-1\)	\(1\)	\(e\left(\frac{35}{372}\right)\)	\(e\left(\frac{73}{186}\right)\)	\(e\left(\frac{35}{186}\right)\)	\(e\left(\frac{335}{372}\right)\)	\(e\left(\frac{181}{372}\right)\)	\(e\left(\frac{39}{62}\right)\)	\(e\left(\frac{35}{124}\right)\)	\(e\left(\frac{73}{93}\right)\)	\(e\left(\frac{185}{186}\right)\)	\(e\left(\frac{19}{372}\right)\)
\(\chi_{373}(16,\cdot)\)	373.i	93	yes	\(1\)	\(1\)	\(e\left(\frac{1}{93}\right)\)	\(e\left(\frac{52}{93}\right)\)	\(e\left(\frac{2}{93}\right)\)	\(e\left(\frac{76}{93}\right)\)	\(e\left(\frac{53}{93}\right)\)	\(e\left(\frac{4}{31}\right)\)	\(e\left(\frac{1}{31}\right)\)	\(e\left(\frac{11}{93}\right)\)	\(e\left(\frac{77}{93}\right)\)	\(e\left(\frac{59}{93}\right)\)
\(\chi_{373}(17,\cdot)\)	373.h	62	yes	\(1\)	\(1\)	\(e\left(\frac{21}{62}\right)\)	\(e\left(\frac{19}{31}\right)\)	\(e\left(\frac{21}{31}\right)\)	\(e\left(\frac{15}{62}\right)\)	\(e\left(\frac{59}{62}\right)\)	\(e\left(\frac{2}{31}\right)\)	\(e\left(\frac{1}{62}\right)\)	\(e\left(\frac{7}{31}\right)\)	\(e\left(\frac{18}{31}\right)\)	\(e\left(\frac{61}{62}\right)\)
\(\chi_{373}(18,\cdot)\)	373.j	124	yes	\(-1\)	\(1\)	\(e\left(\frac{35}{124}\right)\)	\(e\left(\frac{11}{62}\right)\)	\(e\left(\frac{35}{62}\right)\)	\(e\left(\frac{87}{124}\right)\)	\(e\left(\frac{57}{124}\right)\)	\(e\left(\frac{55}{62}\right)\)	\(e\left(\frac{105}{124}\right)\)	\(e\left(\frac{11}{31}\right)\)	\(e\left(\frac{61}{62}\right)\)	\(e\left(\frac{19}{124}\right)\)
\(\chi_{373}(19,\cdot)\)	373.j	124	yes	\(-1\)	\(1\)	\(e\left(\frac{9}{124}\right)\)	\(e\left(\frac{17}{62}\right)\)	\(e\left(\frac{9}{62}\right)\)	\(e\left(\frac{33}{124}\right)\)	\(e\left(\frac{43}{124}\right)\)	\(e\left(\frac{23}{62}\right)\)	\(e\left(\frac{27}{124}\right)\)	\(e\left(\frac{17}{31}\right)\)	\(e\left(\frac{21}{62}\right)\)	\(e\left(\frac{97}{124}\right)\)
\(\chi_{373}(20,\cdot)\)	373.j	124	yes	\(-1\)	\(1\)	\(e\left(\frac{57}{124}\right)\)	\(e\left(\frac{25}{62}\right)\)	\(e\left(\frac{57}{62}\right)\)	\(e\left(\frac{85}{124}\right)\)	\(e\left(\frac{107}{124}\right)\)	\(e\left(\frac{1}{62}\right)\)	\(e\left(\frac{47}{124}\right)\)	\(e\left(\frac{25}{31}\right)\)	\(e\left(\frac{9}{62}\right)\)	\(e\left(\frac{77}{124}\right)\)
\(\chi_{373}(21,\cdot)\)	373.i	93	yes	\(1\)	\(1\)	\(e\left(\frac{16}{93}\right)\)	\(e\left(\frac{88}{93}\right)\)	\(e\left(\frac{32}{93}\right)\)	\(e\left(\frac{7}{93}\right)\)	\(e\left(\frac{11}{93}\right)\)	\(e\left(\frac{2}{31}\right)\)	\(e\left(\frac{16}{31}\right)\)	\(e\left(\frac{83}{93}\right)\)	\(e\left(\frac{23}{93}\right)\)	\(e\left(\frac{14}{93}\right)\)
\(\chi_{373}(22,\cdot)\)	373.h	62	yes	\(1\)	\(1\)	\(e\left(\frac{41}{62}\right)\)	\(e\left(\frac{12}{31}\right)\)	\(e\left(\frac{10}{31}\right)\)	\(e\left(\frac{47}{62}\right)\)	\(e\left(\frac{3}{62}\right)\)	\(e\left(\frac{29}{31}\right)\)	\(e\left(\frac{61}{62}\right)\)	\(e\left(\frac{24}{31}\right)\)	\(e\left(\frac{13}{31}\right)\)	\(e\left(\frac{1}{62}\right)\)
\(\chi_{373}(23,\cdot)\)	373.j	124	yes	\(-1\)	\(1\)	\(e\left(\frac{117}{124}\right)\)	\(e\left(\frac{35}{62}\right)\)	\(e\left(\frac{55}{62}\right)\)	\(e\left(\frac{57}{124}\right)\)	\(e\left(\frac{63}{124}\right)\)	\(e\left(\frac{51}{62}\right)\)	\(e\left(\frac{103}{124}\right)\)	\(e\left(\frac{4}{31}\right)\)	\(e\left(\frac{25}{62}\right)\)	\(e\left(\frac{21}{124}\right)\)
\(\chi_{373}(24,\cdot)\)	373.l	372	yes	\(-1\)	\(1\)	\(e\left(\frac{241}{372}\right)\)	\(e\left(\frac{35}{186}\right)\)	\(e\left(\frac{55}{186}\right)\)	\(e\left(\frac{181}{372}\right)\)	\(e\left(\frac{311}{372}\right)\)	\(e\left(\frac{17}{62}\right)\)	\(e\left(\frac{117}{124}\right)\)	\(e\left(\frac{35}{93}\right)\)	\(e\left(\frac{25}{186}\right)\)	\(e\left(\frac{269}{372}\right)\)
\(\chi_{373}(25,\cdot)\)	373.k	186	yes	\(1\)	\(1\)	\(e\left(\frac{169}{186}\right)\)	\(e\left(\frac{23}{93}\right)\)	\(e\left(\frac{76}{93}\right)\)	\(e\left(\frac{103}{186}\right)\)	\(e\left(\frac{29}{186}\right)\)	\(e\left(\frac{28}{31}\right)\)	\(e\left(\frac{45}{62}\right)\)	\(e\left(\frac{46}{93}\right)\)	\(e\left(\frac{43}{93}\right)\)	\(e\left(\frac{113}{186}\right)\)
\(\chi_{373}(26,\cdot)\)	373.l	372	yes	\(-1\)	\(1\)	\(e\left(\frac{91}{372}\right)\)	\(e\left(\frac{41}{186}\right)\)	\(e\left(\frac{91}{186}\right)\)	\(e\left(\frac{127}{372}\right)\)	\(e\left(\frac{173}{372}\right)\)	\(e\left(\frac{27}{62}\right)\)	\(e\left(\frac{91}{124}\right)\)	\(e\left(\frac{41}{93}\right)\)	\(e\left(\frac{109}{186}\right)\)	\(e\left(\frac{347}{372}\right)\)
\(\chi_{373}(27,\cdot)\)	373.h	62	yes	\(1\)	\(1\)	\(e\left(\frac{57}{62}\right)\)	\(e\left(\frac{25}{31}\right)\)	\(e\left(\frac{26}{31}\right)\)	\(e\left(\frac{23}{62}\right)\)	\(e\left(\frac{45}{62}\right)\)	\(e\left(\frac{1}{31}\right)\)	\(e\left(\frac{47}{62}\right)\)	\(e\left(\frac{19}{31}\right)\)	\(e\left(\frac{9}{31}\right)\)	\(e\left(\frac{15}{62}\right)\)
\(\chi_{373}(28,\cdot)\)	373.i	93	yes	\(1\)	\(1\)	\(e\left(\frac{50}{93}\right)\)	\(e\left(\frac{89}{93}\right)\)	\(e\left(\frac{7}{93}\right)\)	\(e\left(\frac{80}{93}\right)\)	\(e\left(\frac{46}{93}\right)\)	\(e\left(\frac{14}{31}\right)\)	\(e\left(\frac{19}{31}\right)\)	\(e\left(\frac{85}{93}\right)\)	\(e\left(\frac{37}{93}\right)\)	\(e\left(\frac{67}{93}\right)\)
\(\chi_{373}(29,\cdot)\)	373.i	93	yes	\(1\)	\(1\)	\(e\left(\frac{71}{93}\right)\)	\(e\left(\frac{65}{93}\right)\)	\(e\left(\frac{49}{93}\right)\)	\(e\left(\frac{2}{93}\right)\)	\(e\left(\frac{43}{93}\right)\)	\(e\left(\frac{5}{31}\right)\)	\(e\left(\frac{9}{31}\right)\)	\(e\left(\frac{37}{93}\right)\)	\(e\left(\frac{73}{93}\right)\)	\(e\left(\frac{4}{93}\right)\)
\(\chi_{373}(30,\cdot)\)	373.g	31	yes	\(1\)	\(1\)	\(e\left(\frac{3}{31}\right)\)	\(e\left(\frac{1}{31}\right)\)	\(e\left(\frac{6}{31}\right)\)	\(e\left(\frac{11}{31}\right)\)	\(e\left(\frac{4}{31}\right)\)	\(e\left(\frac{5}{31}\right)\)	\(e\left(\frac{9}{31}\right)\)	\(e\left(\frac{2}{31}\right)\)	\(e\left(\frac{14}{31}\right)\)	\(e\left(\frac{22}{31}\right)\)
\(\chi_{373}(31,\cdot)\)	373.h	62	yes	\(1\)	\(1\)	\(e\left(\frac{53}{62}\right)\)	\(e\left(\frac{14}{31}\right)\)	\(e\left(\frac{22}{31}\right)\)	\(e\left(\frac{29}{62}\right)\)	\(e\left(\frac{19}{62}\right)\)	\(e\left(\frac{8}{31}\right)\)	\(e\left(\frac{35}{62}\right)\)	\(e\left(\frac{28}{31}\right)\)	\(e\left(\frac{10}{31}\right)\)	\(e\left(\frac{27}{62}\right)\)
\(\chi_{373}(32,\cdot)\)	373.l	372	yes	\(-1\)	\(1\)	\(e\left(\frac{5}{372}\right)\)	\(e\left(\frac{37}{186}\right)\)	\(e\left(\frac{5}{186}\right)\)	\(e\left(\frac{101}{372}\right)\)	\(e\left(\frac{79}{372}\right)\)	\(e\left(\frac{41}{62}\right)\)	\(e\left(\frac{5}{124}\right)\)	\(e\left(\frac{37}{93}\right)\)	\(e\left(\frac{53}{186}\right)\)	\(e\left(\frac{109}{372}\right)\)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Learn more

Character group

First 32 of 372 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.