LMFDB - Group of Dirichlet characters of modulus 223

Show commands: PariGP / SageMath

sage: H = DirichletGroup(223)

pari: g = idealstar(,223,2)

Character group

sage: G.order() pari: g.no
Order	=	222
sage: H.invariants() pari: g.cyc
Structure	=	$C_{222}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{223}(3,\cdot)$

First 32 of 222 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	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$11$
$\chi_{223}(1,\cdot)$	223.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{223}(2,\cdot)$	223.e	37	yes	$1$	$1$	$e\left(\frac{35}{37}\right)$	$e\left(\frac{30}{37}\right)$	$e\left(\frac{33}{37}\right)$	$e\left(\frac{6}{37}\right)$	$e\left(\frac{28}{37}\right)$	$e\left(\frac{10}{37}\right)$	$e\left(\frac{31}{37}\right)$	$e\left(\frac{23}{37}\right)$	$e\left(\frac{4}{37}\right)$	$e\left(\frac{28}{37}\right)$
$\chi_{223}(3,\cdot)$	223.h	222	yes	$-1$	$1$	$e\left(\frac{30}{37}\right)$	$e\left(\frac{1}{222}\right)$	$e\left(\frac{23}{37}\right)$	$e\left(\frac{89}{222}\right)$	$e\left(\frac{181}{222}\right)$	$e\left(\frac{35}{37}\right)$	$e\left(\frac{16}{37}\right)$	$e\left(\frac{1}{111}\right)$	$e\left(\frac{47}{222}\right)$	$e\left(\frac{107}{222}\right)$
$\chi_{223}(4,\cdot)$	223.e	37	yes	$1$	$1$	$e\left(\frac{33}{37}\right)$	$e\left(\frac{23}{37}\right)$	$e\left(\frac{29}{37}\right)$	$e\left(\frac{12}{37}\right)$	$e\left(\frac{19}{37}\right)$	$e\left(\frac{20}{37}\right)$	$e\left(\frac{25}{37}\right)$	$e\left(\frac{9}{37}\right)$	$e\left(\frac{8}{37}\right)$	$e\left(\frac{19}{37}\right)$
$\chi_{223}(5,\cdot)$	223.h	222	yes	$-1$	$1$	$e\left(\frac{6}{37}\right)$	$e\left(\frac{89}{222}\right)$	$e\left(\frac{12}{37}\right)$	$e\left(\frac{151}{222}\right)$	$e\left(\frac{125}{222}\right)$	$e\left(\frac{7}{37}\right)$	$e\left(\frac{18}{37}\right)$	$e\left(\frac{89}{111}\right)$	$e\left(\frac{187}{222}\right)$	$e\left(\frac{199}{222}\right)$
$\chi_{223}(6,\cdot)$	223.h	222	yes	$-1$	$1$	$e\left(\frac{28}{37}\right)$	$e\left(\frac{181}{222}\right)$	$e\left(\frac{19}{37}\right)$	$e\left(\frac{125}{222}\right)$	$e\left(\frac{127}{222}\right)$	$e\left(\frac{8}{37}\right)$	$e\left(\frac{10}{37}\right)$	$e\left(\frac{70}{111}\right)$	$e\left(\frac{71}{222}\right)$	$e\left(\frac{53}{222}\right)$
$\chi_{223}(7,\cdot)$	223.e	37	yes	$1$	$1$	$e\left(\frac{10}{37}\right)$	$e\left(\frac{35}{37}\right)$	$e\left(\frac{20}{37}\right)$	$e\left(\frac{7}{37}\right)$	$e\left(\frac{8}{37}\right)$	$e\left(\frac{24}{37}\right)$	$e\left(\frac{30}{37}\right)$	$e\left(\frac{33}{37}\right)$	$e\left(\frac{17}{37}\right)$	$e\left(\frac{8}{37}\right)$
$\chi_{223}(8,\cdot)$	223.e	37	yes	$1$	$1$	$e\left(\frac{31}{37}\right)$	$e\left(\frac{16}{37}\right)$	$e\left(\frac{25}{37}\right)$	$e\left(\frac{18}{37}\right)$	$e\left(\frac{10}{37}\right)$	$e\left(\frac{30}{37}\right)$	$e\left(\frac{19}{37}\right)$	$e\left(\frac{32}{37}\right)$	$e\left(\frac{12}{37}\right)$	$e\left(\frac{10}{37}\right)$
$\chi_{223}(9,\cdot)$	223.g	111	yes	$1$	$1$	$e\left(\frac{23}{37}\right)$	$e\left(\frac{1}{111}\right)$	$e\left(\frac{9}{37}\right)$	$e\left(\frac{89}{111}\right)$	$e\left(\frac{70}{111}\right)$	$e\left(\frac{33}{37}\right)$	$e\left(\frac{32}{37}\right)$	$e\left(\frac{2}{111}\right)$	$e\left(\frac{47}{111}\right)$	$e\left(\frac{107}{111}\right)$
$\chi_{223}(10,\cdot)$	223.h	222	yes	$-1$	$1$	$e\left(\frac{4}{37}\right)$	$e\left(\frac{47}{222}\right)$	$e\left(\frac{8}{37}\right)$	$e\left(\frac{187}{222}\right)$	$e\left(\frac{71}{222}\right)$	$e\left(\frac{17}{37}\right)$	$e\left(\frac{12}{37}\right)$	$e\left(\frac{47}{111}\right)$	$e\left(\frac{211}{222}\right)$	$e\left(\frac{145}{222}\right)$
$\chi_{223}(11,\cdot)$	223.h	222	yes	$-1$	$1$	$e\left(\frac{28}{37}\right)$	$e\left(\frac{107}{222}\right)$	$e\left(\frac{19}{37}\right)$	$e\left(\frac{199}{222}\right)$	$e\left(\frac{53}{222}\right)$	$e\left(\frac{8}{37}\right)$	$e\left(\frac{10}{37}\right)$	$e\left(\frac{107}{111}\right)$	$e\left(\frac{145}{222}\right)$	$e\left(\frac{127}{222}\right)$
$\chi_{223}(12,\cdot)$	223.h	222	yes	$-1$	$1$	$e\left(\frac{26}{37}\right)$	$e\left(\frac{139}{222}\right)$	$e\left(\frac{15}{37}\right)$	$e\left(\frac{161}{222}\right)$	$e\left(\frac{73}{222}\right)$	$e\left(\frac{18}{37}\right)$	$e\left(\frac{4}{37}\right)$	$e\left(\frac{28}{111}\right)$	$e\left(\frac{95}{222}\right)$	$e\left(\frac{221}{222}\right)$
$\chi_{223}(13,\cdot)$	223.f	74	yes	$-1$	$1$	$e\left(\frac{7}{37}\right)$	$e\left(\frac{49}{74}\right)$	$e\left(\frac{14}{37}\right)$	$e\left(\frac{69}{74}\right)$	$e\left(\frac{63}{74}\right)$	$e\left(\frac{2}{37}\right)$	$e\left(\frac{21}{37}\right)$	$e\left(\frac{12}{37}\right)$	$e\left(\frac{9}{74}\right)$	$e\left(\frac{63}{74}\right)$
$\chi_{223}(14,\cdot)$	223.e	37	yes	$1$	$1$	$e\left(\frac{8}{37}\right)$	$e\left(\frac{28}{37}\right)$	$e\left(\frac{16}{37}\right)$	$e\left(\frac{13}{37}\right)$	$e\left(\frac{36}{37}\right)$	$e\left(\frac{34}{37}\right)$	$e\left(\frac{24}{37}\right)$	$e\left(\frac{19}{37}\right)$	$e\left(\frac{21}{37}\right)$	$e\left(\frac{36}{37}\right)$
$\chi_{223}(15,\cdot)$	223.e	37	yes	$1$	$1$	$e\left(\frac{36}{37}\right)$	$e\left(\frac{15}{37}\right)$	$e\left(\frac{35}{37}\right)$	$e\left(\frac{3}{37}\right)$	$e\left(\frac{14}{37}\right)$	$e\left(\frac{5}{37}\right)$	$e\left(\frac{34}{37}\right)$	$e\left(\frac{30}{37}\right)$	$e\left(\frac{2}{37}\right)$	$e\left(\frac{14}{37}\right)$
$\chi_{223}(16,\cdot)$	223.e	37	yes	$1$	$1$	$e\left(\frac{29}{37}\right)$	$e\left(\frac{9}{37}\right)$	$e\left(\frac{21}{37}\right)$	$e\left(\frac{24}{37}\right)$	$e\left(\frac{1}{37}\right)$	$e\left(\frac{3}{37}\right)$	$e\left(\frac{13}{37}\right)$	$e\left(\frac{18}{37}\right)$	$e\left(\frac{16}{37}\right)$	$e\left(\frac{1}{37}\right)$
$\chi_{223}(17,\cdot)$	223.e	37	yes	$1$	$1$	$e\left(\frac{28}{37}\right)$	$e\left(\frac{24}{37}\right)$	$e\left(\frac{19}{37}\right)$	$e\left(\frac{27}{37}\right)$	$e\left(\frac{15}{37}\right)$	$e\left(\frac{8}{37}\right)$	$e\left(\frac{10}{37}\right)$	$e\left(\frac{11}{37}\right)$	$e\left(\frac{18}{37}\right)$	$e\left(\frac{15}{37}\right)$
$\chi_{223}(18,\cdot)$	223.g	111	yes	$1$	$1$	$e\left(\frac{21}{37}\right)$	$e\left(\frac{91}{111}\right)$	$e\left(\frac{5}{37}\right)$	$e\left(\frac{107}{111}\right)$	$e\left(\frac{43}{111}\right)$	$e\left(\frac{6}{37}\right)$	$e\left(\frac{26}{37}\right)$	$e\left(\frac{71}{111}\right)$	$e\left(\frac{59}{111}\right)$	$e\left(\frac{80}{111}\right)$
$\chi_{223}(19,\cdot)$	223.g	111	yes	$1$	$1$	$e\left(\frac{17}{37}\right)$	$e\left(\frac{86}{111}\right)$	$e\left(\frac{34}{37}\right)$	$e\left(\frac{106}{111}\right)$	$e\left(\frac{26}{111}\right)$	$e\left(\frac{26}{37}\right)$	$e\left(\frac{14}{37}\right)$	$e\left(\frac{61}{111}\right)$	$e\left(\frac{46}{111}\right)$	$e\left(\frac{100}{111}\right)$
$\chi_{223}(20,\cdot)$	223.h	222	yes	$-1$	$1$	$e\left(\frac{2}{37}\right)$	$e\left(\frac{5}{222}\right)$	$e\left(\frac{4}{37}\right)$	$e\left(\frac{1}{222}\right)$	$e\left(\frac{17}{222}\right)$	$e\left(\frac{27}{37}\right)$	$e\left(\frac{6}{37}\right)$	$e\left(\frac{5}{111}\right)$	$e\left(\frac{13}{222}\right)$	$e\left(\frac{91}{222}\right)$
$\chi_{223}(21,\cdot)$	223.h	222	yes	$-1$	$1$	$e\left(\frac{3}{37}\right)$	$e\left(\frac{211}{222}\right)$	$e\left(\frac{6}{37}\right)$	$e\left(\frac{131}{222}\right)$	$e\left(\frac{7}{222}\right)$	$e\left(\frac{22}{37}\right)$	$e\left(\frac{9}{37}\right)$	$e\left(\frac{100}{111}\right)$	$e\left(\frac{149}{222}\right)$	$e\left(\frac{155}{222}\right)$
$\chi_{223}(22,\cdot)$	223.h	222	yes	$-1$	$1$	$e\left(\frac{26}{37}\right)$	$e\left(\frac{65}{222}\right)$	$e\left(\frac{15}{37}\right)$	$e\left(\frac{13}{222}\right)$	$e\left(\frac{221}{222}\right)$	$e\left(\frac{18}{37}\right)$	$e\left(\frac{4}{37}\right)$	$e\left(\frac{65}{111}\right)$	$e\left(\frac{169}{222}\right)$	$e\left(\frac{73}{222}\right)$
$\chi_{223}(23,\cdot)$	223.h	222	yes	$-1$	$1$	$e\left(\frac{6}{37}\right)$	$e\left(\frac{163}{222}\right)$	$e\left(\frac{12}{37}\right)$	$e\left(\frac{77}{222}\right)$	$e\left(\frac{199}{222}\right)$	$e\left(\frac{7}{37}\right)$	$e\left(\frac{18}{37}\right)$	$e\left(\frac{52}{111}\right)$	$e\left(\frac{113}{222}\right)$	$e\left(\frac{125}{222}\right)$
$\chi_{223}(24,\cdot)$	223.h	222	yes	$-1$	$1$	$e\left(\frac{24}{37}\right)$	$e\left(\frac{97}{222}\right)$	$e\left(\frac{11}{37}\right)$	$e\left(\frac{197}{222}\right)$	$e\left(\frac{19}{222}\right)$	$e\left(\frac{28}{37}\right)$	$e\left(\frac{35}{37}\right)$	$e\left(\frac{97}{111}\right)$	$e\left(\frac{119}{222}\right)$	$e\left(\frac{167}{222}\right)$
$\chi_{223}(25,\cdot)$	223.g	111	yes	$1$	$1$	$e\left(\frac{12}{37}\right)$	$e\left(\frac{89}{111}\right)$	$e\left(\frac{24}{37}\right)$	$e\left(\frac{40}{111}\right)$	$e\left(\frac{14}{111}\right)$	$e\left(\frac{14}{37}\right)$	$e\left(\frac{36}{37}\right)$	$e\left(\frac{67}{111}\right)$	$e\left(\frac{76}{111}\right)$	$e\left(\frac{88}{111}\right)$
$\chi_{223}(26,\cdot)$	223.f	74	yes	$-1$	$1$	$e\left(\frac{5}{37}\right)$	$e\left(\frac{35}{74}\right)$	$e\left(\frac{10}{37}\right)$	$e\left(\frac{7}{74}\right)$	$e\left(\frac{45}{74}\right)$	$e\left(\frac{12}{37}\right)$	$e\left(\frac{15}{37}\right)$	$e\left(\frac{35}{37}\right)$	$e\left(\frac{17}{74}\right)$	$e\left(\frac{45}{74}\right)$
$\chi_{223}(27,\cdot)$	223.f	74	yes	$-1$	$1$	$e\left(\frac{16}{37}\right)$	$e\left(\frac{1}{74}\right)$	$e\left(\frac{32}{37}\right)$	$e\left(\frac{15}{74}\right)$	$e\left(\frac{33}{74}\right)$	$e\left(\frac{31}{37}\right)$	$e\left(\frac{11}{37}\right)$	$e\left(\frac{1}{37}\right)$	$e\left(\frac{47}{74}\right)$	$e\left(\frac{33}{74}\right)$
$\chi_{223}(28,\cdot)$	223.e	37	yes	$1$	$1$	$e\left(\frac{6}{37}\right)$	$e\left(\frac{21}{37}\right)$	$e\left(\frac{12}{37}\right)$	$e\left(\frac{19}{37}\right)$	$e\left(\frac{27}{37}\right)$	$e\left(\frac{7}{37}\right)$	$e\left(\frac{18}{37}\right)$	$e\left(\frac{5}{37}\right)$	$e\left(\frac{25}{37}\right)$	$e\left(\frac{27}{37}\right)$
$\chi_{223}(29,\cdot)$	223.g	111	yes	$1$	$1$	$e\left(\frac{29}{37}\right)$	$e\left(\frac{64}{111}\right)$	$e\left(\frac{21}{37}\right)$	$e\left(\frac{35}{111}\right)$	$e\left(\frac{40}{111}\right)$	$e\left(\frac{3}{37}\right)$	$e\left(\frac{13}{37}\right)$	$e\left(\frac{17}{111}\right)$	$e\left(\frac{11}{111}\right)$	$e\left(\frac{77}{111}\right)$
$\chi_{223}(30,\cdot)$	223.e	37	yes	$1$	$1$	$e\left(\frac{34}{37}\right)$	$e\left(\frac{8}{37}\right)$	$e\left(\frac{31}{37}\right)$	$e\left(\frac{9}{37}\right)$	$e\left(\frac{5}{37}\right)$	$e\left(\frac{15}{37}\right)$	$e\left(\frac{28}{37}\right)$	$e\left(\frac{16}{37}\right)$	$e\left(\frac{6}{37}\right)$	$e\left(\frac{5}{37}\right)$
$\chi_{223}(31,\cdot)$	223.g	111	yes	$1$	$1$	$e\left(\frac{18}{37}\right)$	$e\left(\frac{41}{111}\right)$	$e\left(\frac{36}{37}\right)$	$e\left(\frac{97}{111}\right)$	$e\left(\frac{95}{111}\right)$	$e\left(\frac{21}{37}\right)$	$e\left(\frac{17}{37}\right)$	$e\left(\frac{82}{111}\right)$	$e\left(\frac{40}{111}\right)$	$e\left(\frac{58}{111}\right)$
$\chi_{223}(32,\cdot)$	223.e	37	yes	$1$	$1$	$e\left(\frac{27}{37}\right)$	$e\left(\frac{2}{37}\right)$	$e\left(\frac{17}{37}\right)$	$e\left(\frac{30}{37}\right)$	$e\left(\frac{29}{37}\right)$	$e\left(\frac{13}{37}\right)$	$e\left(\frac{7}{37}\right)$	$e\left(\frac{4}{37}\right)$	$e\left(\frac{20}{37}\right)$	$e\left(\frac{29}{37}\right)$

Click here to search among the remaining 190 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	$223$
Structure	\(C_{222}\)
Order	$222$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(7\)	\(8\)	\(9\)	\(10\)	\(11\)
\(\chi_{223}(1,\cdot)\)	223.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{223}(2,\cdot)\)	223.e	37	yes	\(1\)	\(1\)	\(e\left(\frac{35}{37}\right)\)	\(e\left(\frac{30}{37}\right)\)	\(e\left(\frac{33}{37}\right)\)	\(e\left(\frac{6}{37}\right)\)	\(e\left(\frac{28}{37}\right)\)	\(e\left(\frac{10}{37}\right)\)	\(e\left(\frac{31}{37}\right)\)	\(e\left(\frac{23}{37}\right)\)	\(e\left(\frac{4}{37}\right)\)	\(e\left(\frac{28}{37}\right)\)
\(\chi_{223}(3,\cdot)\)	223.h	222	yes	\(-1\)	\(1\)	\(e\left(\frac{30}{37}\right)\)	\(e\left(\frac{1}{222}\right)\)	\(e\left(\frac{23}{37}\right)\)	\(e\left(\frac{89}{222}\right)\)	\(e\left(\frac{181}{222}\right)\)	\(e\left(\frac{35}{37}\right)\)	\(e\left(\frac{16}{37}\right)\)	\(e\left(\frac{1}{111}\right)\)	\(e\left(\frac{47}{222}\right)\)	\(e\left(\frac{107}{222}\right)\)
\(\chi_{223}(4,\cdot)\)	223.e	37	yes	\(1\)	\(1\)	\(e\left(\frac{33}{37}\right)\)	\(e\left(\frac{23}{37}\right)\)	\(e\left(\frac{29}{37}\right)\)	\(e\left(\frac{12}{37}\right)\)	\(e\left(\frac{19}{37}\right)\)	\(e\left(\frac{20}{37}\right)\)	\(e\left(\frac{25}{37}\right)\)	\(e\left(\frac{9}{37}\right)\)	\(e\left(\frac{8}{37}\right)\)	\(e\left(\frac{19}{37}\right)\)
\(\chi_{223}(5,\cdot)\)	223.h	222	yes	\(-1\)	\(1\)	\(e\left(\frac{6}{37}\right)\)	\(e\left(\frac{89}{222}\right)\)	\(e\left(\frac{12}{37}\right)\)	\(e\left(\frac{151}{222}\right)\)	\(e\left(\frac{125}{222}\right)\)	\(e\left(\frac{7}{37}\right)\)	\(e\left(\frac{18}{37}\right)\)	\(e\left(\frac{89}{111}\right)\)	\(e\left(\frac{187}{222}\right)\)	\(e\left(\frac{199}{222}\right)\)
\(\chi_{223}(6,\cdot)\)	223.h	222	yes	\(-1\)	\(1\)	\(e\left(\frac{28}{37}\right)\)	\(e\left(\frac{181}{222}\right)\)	\(e\left(\frac{19}{37}\right)\)	\(e\left(\frac{125}{222}\right)\)	\(e\left(\frac{127}{222}\right)\)	\(e\left(\frac{8}{37}\right)\)	\(e\left(\frac{10}{37}\right)\)	\(e\left(\frac{70}{111}\right)\)	\(e\left(\frac{71}{222}\right)\)	\(e\left(\frac{53}{222}\right)\)
\(\chi_{223}(7,\cdot)\)	223.e	37	yes	\(1\)	\(1\)	\(e\left(\frac{10}{37}\right)\)	\(e\left(\frac{35}{37}\right)\)	\(e\left(\frac{20}{37}\right)\)	\(e\left(\frac{7}{37}\right)\)	\(e\left(\frac{8}{37}\right)\)	\(e\left(\frac{24}{37}\right)\)	\(e\left(\frac{30}{37}\right)\)	\(e\left(\frac{33}{37}\right)\)	\(e\left(\frac{17}{37}\right)\)	\(e\left(\frac{8}{37}\right)\)
\(\chi_{223}(8,\cdot)\)	223.e	37	yes	\(1\)	\(1\)	\(e\left(\frac{31}{37}\right)\)	\(e\left(\frac{16}{37}\right)\)	\(e\left(\frac{25}{37}\right)\)	\(e\left(\frac{18}{37}\right)\)	\(e\left(\frac{10}{37}\right)\)	\(e\left(\frac{30}{37}\right)\)	\(e\left(\frac{19}{37}\right)\)	\(e\left(\frac{32}{37}\right)\)	\(e\left(\frac{12}{37}\right)\)	\(e\left(\frac{10}{37}\right)\)
\(\chi_{223}(9,\cdot)\)	223.g	111	yes	\(1\)	\(1\)	\(e\left(\frac{23}{37}\right)\)	\(e\left(\frac{1}{111}\right)\)	\(e\left(\frac{9}{37}\right)\)	\(e\left(\frac{89}{111}\right)\)	\(e\left(\frac{70}{111}\right)\)	\(e\left(\frac{33}{37}\right)\)	\(e\left(\frac{32}{37}\right)\)	\(e\left(\frac{2}{111}\right)\)	\(e\left(\frac{47}{111}\right)\)	\(e\left(\frac{107}{111}\right)\)
\(\chi_{223}(10,\cdot)\)	223.h	222	yes	\(-1\)	\(1\)	\(e\left(\frac{4}{37}\right)\)	\(e\left(\frac{47}{222}\right)\)	\(e\left(\frac{8}{37}\right)\)	\(e\left(\frac{187}{222}\right)\)	\(e\left(\frac{71}{222}\right)\)	\(e\left(\frac{17}{37}\right)\)	\(e\left(\frac{12}{37}\right)\)	\(e\left(\frac{47}{111}\right)\)	\(e\left(\frac{211}{222}\right)\)	\(e\left(\frac{145}{222}\right)\)
\(\chi_{223}(11,\cdot)\)	223.h	222	yes	\(-1\)	\(1\)	\(e\left(\frac{28}{37}\right)\)	\(e\left(\frac{107}{222}\right)\)	\(e\left(\frac{19}{37}\right)\)	\(e\left(\frac{199}{222}\right)\)	\(e\left(\frac{53}{222}\right)\)	\(e\left(\frac{8}{37}\right)\)	\(e\left(\frac{10}{37}\right)\)	\(e\left(\frac{107}{111}\right)\)	\(e\left(\frac{145}{222}\right)\)	\(e\left(\frac{127}{222}\right)\)
\(\chi_{223}(12,\cdot)\)	223.h	222	yes	\(-1\)	\(1\)	\(e\left(\frac{26}{37}\right)\)	\(e\left(\frac{139}{222}\right)\)	\(e\left(\frac{15}{37}\right)\)	\(e\left(\frac{161}{222}\right)\)	\(e\left(\frac{73}{222}\right)\)	\(e\left(\frac{18}{37}\right)\)	\(e\left(\frac{4}{37}\right)\)	\(e\left(\frac{28}{111}\right)\)	\(e\left(\frac{95}{222}\right)\)	\(e\left(\frac{221}{222}\right)\)
\(\chi_{223}(13,\cdot)\)	223.f	74	yes	\(-1\)	\(1\)	\(e\left(\frac{7}{37}\right)\)	\(e\left(\frac{49}{74}\right)\)	\(e\left(\frac{14}{37}\right)\)	\(e\left(\frac{69}{74}\right)\)	\(e\left(\frac{63}{74}\right)\)	\(e\left(\frac{2}{37}\right)\)	\(e\left(\frac{21}{37}\right)\)	\(e\left(\frac{12}{37}\right)\)	\(e\left(\frac{9}{74}\right)\)	\(e\left(\frac{63}{74}\right)\)
\(\chi_{223}(14,\cdot)\)	223.e	37	yes	\(1\)	\(1\)	\(e\left(\frac{8}{37}\right)\)	\(e\left(\frac{28}{37}\right)\)	\(e\left(\frac{16}{37}\right)\)	\(e\left(\frac{13}{37}\right)\)	\(e\left(\frac{36}{37}\right)\)	\(e\left(\frac{34}{37}\right)\)	\(e\left(\frac{24}{37}\right)\)	\(e\left(\frac{19}{37}\right)\)	\(e\left(\frac{21}{37}\right)\)	\(e\left(\frac{36}{37}\right)\)
\(\chi_{223}(15,\cdot)\)	223.e	37	yes	\(1\)	\(1\)	\(e\left(\frac{36}{37}\right)\)	\(e\left(\frac{15}{37}\right)\)	\(e\left(\frac{35}{37}\right)\)	\(e\left(\frac{3}{37}\right)\)	\(e\left(\frac{14}{37}\right)\)	\(e\left(\frac{5}{37}\right)\)	\(e\left(\frac{34}{37}\right)\)	\(e\left(\frac{30}{37}\right)\)	\(e\left(\frac{2}{37}\right)\)	\(e\left(\frac{14}{37}\right)\)
\(\chi_{223}(16,\cdot)\)	223.e	37	yes	\(1\)	\(1\)	\(e\left(\frac{29}{37}\right)\)	\(e\left(\frac{9}{37}\right)\)	\(e\left(\frac{21}{37}\right)\)	\(e\left(\frac{24}{37}\right)\)	\(e\left(\frac{1}{37}\right)\)	\(e\left(\frac{3}{37}\right)\)	\(e\left(\frac{13}{37}\right)\)	\(e\left(\frac{18}{37}\right)\)	\(e\left(\frac{16}{37}\right)\)	\(e\left(\frac{1}{37}\right)\)
\(\chi_{223}(17,\cdot)\)	223.e	37	yes	\(1\)	\(1\)	\(e\left(\frac{28}{37}\right)\)	\(e\left(\frac{24}{37}\right)\)	\(e\left(\frac{19}{37}\right)\)	\(e\left(\frac{27}{37}\right)\)	\(e\left(\frac{15}{37}\right)\)	\(e\left(\frac{8}{37}\right)\)	\(e\left(\frac{10}{37}\right)\)	\(e\left(\frac{11}{37}\right)\)	\(e\left(\frac{18}{37}\right)\)	\(e\left(\frac{15}{37}\right)\)
\(\chi_{223}(18,\cdot)\)	223.g	111	yes	\(1\)	\(1\)	\(e\left(\frac{21}{37}\right)\)	\(e\left(\frac{91}{111}\right)\)	\(e\left(\frac{5}{37}\right)\)	\(e\left(\frac{107}{111}\right)\)	\(e\left(\frac{43}{111}\right)\)	\(e\left(\frac{6}{37}\right)\)	\(e\left(\frac{26}{37}\right)\)	\(e\left(\frac{71}{111}\right)\)	\(e\left(\frac{59}{111}\right)\)	\(e\left(\frac{80}{111}\right)\)
\(\chi_{223}(19,\cdot)\)	223.g	111	yes	\(1\)	\(1\)	\(e\left(\frac{17}{37}\right)\)	\(e\left(\frac{86}{111}\right)\)	\(e\left(\frac{34}{37}\right)\)	\(e\left(\frac{106}{111}\right)\)	\(e\left(\frac{26}{111}\right)\)	\(e\left(\frac{26}{37}\right)\)	\(e\left(\frac{14}{37}\right)\)	\(e\left(\frac{61}{111}\right)\)	\(e\left(\frac{46}{111}\right)\)	\(e\left(\frac{100}{111}\right)\)
\(\chi_{223}(20,\cdot)\)	223.h	222	yes	\(-1\)	\(1\)	\(e\left(\frac{2}{37}\right)\)	\(e\left(\frac{5}{222}\right)\)	\(e\left(\frac{4}{37}\right)\)	\(e\left(\frac{1}{222}\right)\)	\(e\left(\frac{17}{222}\right)\)	\(e\left(\frac{27}{37}\right)\)	\(e\left(\frac{6}{37}\right)\)	\(e\left(\frac{5}{111}\right)\)	\(e\left(\frac{13}{222}\right)\)	\(e\left(\frac{91}{222}\right)\)
\(\chi_{223}(21,\cdot)\)	223.h	222	yes	\(-1\)	\(1\)	\(e\left(\frac{3}{37}\right)\)	\(e\left(\frac{211}{222}\right)\)	\(e\left(\frac{6}{37}\right)\)	\(e\left(\frac{131}{222}\right)\)	\(e\left(\frac{7}{222}\right)\)	\(e\left(\frac{22}{37}\right)\)	\(e\left(\frac{9}{37}\right)\)	\(e\left(\frac{100}{111}\right)\)	\(e\left(\frac{149}{222}\right)\)	\(e\left(\frac{155}{222}\right)\)
\(\chi_{223}(22,\cdot)\)	223.h	222	yes	\(-1\)	\(1\)	\(e\left(\frac{26}{37}\right)\)	\(e\left(\frac{65}{222}\right)\)	\(e\left(\frac{15}{37}\right)\)	\(e\left(\frac{13}{222}\right)\)	\(e\left(\frac{221}{222}\right)\)	\(e\left(\frac{18}{37}\right)\)	\(e\left(\frac{4}{37}\right)\)	\(e\left(\frac{65}{111}\right)\)	\(e\left(\frac{169}{222}\right)\)	\(e\left(\frac{73}{222}\right)\)
\(\chi_{223}(23,\cdot)\)	223.h	222	yes	\(-1\)	\(1\)	\(e\left(\frac{6}{37}\right)\)	\(e\left(\frac{163}{222}\right)\)	\(e\left(\frac{12}{37}\right)\)	\(e\left(\frac{77}{222}\right)\)	\(e\left(\frac{199}{222}\right)\)	\(e\left(\frac{7}{37}\right)\)	\(e\left(\frac{18}{37}\right)\)	\(e\left(\frac{52}{111}\right)\)	\(e\left(\frac{113}{222}\right)\)	\(e\left(\frac{125}{222}\right)\)
\(\chi_{223}(24,\cdot)\)	223.h	222	yes	\(-1\)	\(1\)	\(e\left(\frac{24}{37}\right)\)	\(e\left(\frac{97}{222}\right)\)	\(e\left(\frac{11}{37}\right)\)	\(e\left(\frac{197}{222}\right)\)	\(e\left(\frac{19}{222}\right)\)	\(e\left(\frac{28}{37}\right)\)	\(e\left(\frac{35}{37}\right)\)	\(e\left(\frac{97}{111}\right)\)	\(e\left(\frac{119}{222}\right)\)	\(e\left(\frac{167}{222}\right)\)
\(\chi_{223}(25,\cdot)\)	223.g	111	yes	\(1\)	\(1\)	\(e\left(\frac{12}{37}\right)\)	\(e\left(\frac{89}{111}\right)\)	\(e\left(\frac{24}{37}\right)\)	\(e\left(\frac{40}{111}\right)\)	\(e\left(\frac{14}{111}\right)\)	\(e\left(\frac{14}{37}\right)\)	\(e\left(\frac{36}{37}\right)\)	\(e\left(\frac{67}{111}\right)\)	\(e\left(\frac{76}{111}\right)\)	\(e\left(\frac{88}{111}\right)\)
\(\chi_{223}(26,\cdot)\)	223.f	74	yes	\(-1\)	\(1\)	\(e\left(\frac{5}{37}\right)\)	\(e\left(\frac{35}{74}\right)\)	\(e\left(\frac{10}{37}\right)\)	\(e\left(\frac{7}{74}\right)\)	\(e\left(\frac{45}{74}\right)\)	\(e\left(\frac{12}{37}\right)\)	\(e\left(\frac{15}{37}\right)\)	\(e\left(\frac{35}{37}\right)\)	\(e\left(\frac{17}{74}\right)\)	\(e\left(\frac{45}{74}\right)\)
\(\chi_{223}(27,\cdot)\)	223.f	74	yes	\(-1\)	\(1\)	\(e\left(\frac{16}{37}\right)\)	\(e\left(\frac{1}{74}\right)\)	\(e\left(\frac{32}{37}\right)\)	\(e\left(\frac{15}{74}\right)\)	\(e\left(\frac{33}{74}\right)\)	\(e\left(\frac{31}{37}\right)\)	\(e\left(\frac{11}{37}\right)\)	\(e\left(\frac{1}{37}\right)\)	\(e\left(\frac{47}{74}\right)\)	\(e\left(\frac{33}{74}\right)\)
\(\chi_{223}(28,\cdot)\)	223.e	37	yes	\(1\)	\(1\)	\(e\left(\frac{6}{37}\right)\)	\(e\left(\frac{21}{37}\right)\)	\(e\left(\frac{12}{37}\right)\)	\(e\left(\frac{19}{37}\right)\)	\(e\left(\frac{27}{37}\right)\)	\(e\left(\frac{7}{37}\right)\)	\(e\left(\frac{18}{37}\right)\)	\(e\left(\frac{5}{37}\right)\)	\(e\left(\frac{25}{37}\right)\)	\(e\left(\frac{27}{37}\right)\)
\(\chi_{223}(29,\cdot)\)	223.g	111	yes	\(1\)	\(1\)	\(e\left(\frac{29}{37}\right)\)	\(e\left(\frac{64}{111}\right)\)	\(e\left(\frac{21}{37}\right)\)	\(e\left(\frac{35}{111}\right)\)	\(e\left(\frac{40}{111}\right)\)	\(e\left(\frac{3}{37}\right)\)	\(e\left(\frac{13}{37}\right)\)	\(e\left(\frac{17}{111}\right)\)	\(e\left(\frac{11}{111}\right)\)	\(e\left(\frac{77}{111}\right)\)
\(\chi_{223}(30,\cdot)\)	223.e	37	yes	\(1\)	\(1\)	\(e\left(\frac{34}{37}\right)\)	\(e\left(\frac{8}{37}\right)\)	\(e\left(\frac{31}{37}\right)\)	\(e\left(\frac{9}{37}\right)\)	\(e\left(\frac{5}{37}\right)\)	\(e\left(\frac{15}{37}\right)\)	\(e\left(\frac{28}{37}\right)\)	\(e\left(\frac{16}{37}\right)\)	\(e\left(\frac{6}{37}\right)\)	\(e\left(\frac{5}{37}\right)\)
\(\chi_{223}(31,\cdot)\)	223.g	111	yes	\(1\)	\(1\)	\(e\left(\frac{18}{37}\right)\)	\(e\left(\frac{41}{111}\right)\)	\(e\left(\frac{36}{37}\right)\)	\(e\left(\frac{97}{111}\right)\)	\(e\left(\frac{95}{111}\right)\)	\(e\left(\frac{21}{37}\right)\)	\(e\left(\frac{17}{37}\right)\)	\(e\left(\frac{82}{111}\right)\)	\(e\left(\frac{40}{111}\right)\)	\(e\left(\frac{58}{111}\right)\)
\(\chi_{223}(32,\cdot)\)	223.e	37	yes	\(1\)	\(1\)	\(e\left(\frac{27}{37}\right)\)	\(e\left(\frac{2}{37}\right)\)	\(e\left(\frac{17}{37}\right)\)	\(e\left(\frac{30}{37}\right)\)	\(e\left(\frac{29}{37}\right)\)	\(e\left(\frac{13}{37}\right)\)	\(e\left(\frac{7}{37}\right)\)	\(e\left(\frac{4}{37}\right)\)	\(e\left(\frac{20}{37}\right)\)	\(e\left(\frac{29}{37}\right)\)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Learn more

Character group

First 32 of 222 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.