LMFDB - Group of Dirichlet characters of modulus 4023

Show commands: PariGP / SageMath

sage: H = DirichletGroup(4023)

pari: g = idealstar(,4023,2)

Character group

sage: G.order() pari: g.no
Order	=	2664
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{1332}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{4023}(299,\cdot)$, $\chi_{4023}(3727,\cdot)$

First 32 of 2664 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	$-1$	$1$	$2$	$4$	$5$	$7$	$8$	$10$	$11$	$13$	$14$	$16$
$\chi_{4023}(1,\cdot)$	4023.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{4023}(2,\cdot)$	4023.bi	1332	yes	$1$	$1$	$e\left(\frac{83}{1332}\right)$	$e\left(\frac{83}{666}\right)$	$e\left(\frac{653}{666}\right)$	$e\left(\frac{565}{666}\right)$	$e\left(\frac{83}{444}\right)$	$e\left(\frac{19}{444}\right)$	$e\left(\frac{611}{1332}\right)$	$e\left(\frac{1069}{1332}\right)$	$e\left(\frac{1213}{1332}\right)$	$e\left(\frac{83}{333}\right)$
$\chi_{4023}(4,\cdot)$	4023.bf	666	yes	$1$	$1$	$e\left(\frac{83}{666}\right)$	$e\left(\frac{83}{333}\right)$	$e\left(\frac{320}{333}\right)$	$e\left(\frac{232}{333}\right)$	$e\left(\frac{83}{222}\right)$	$e\left(\frac{19}{222}\right)$	$e\left(\frac{611}{666}\right)$	$e\left(\frac{403}{666}\right)$	$e\left(\frac{547}{666}\right)$	$e\left(\frac{166}{333}\right)$
$\chi_{4023}(5,\cdot)$	4023.bg	666	yes	$-1$	$1$	$e\left(\frac{653}{666}\right)$	$e\left(\frac{320}{333}\right)$	$e\left(\frac{313}{666}\right)$	$e\left(\frac{76}{333}\right)$	$e\left(\frac{209}{222}\right)$	$e\left(\frac{50}{111}\right)$	$e\left(\frac{137}{666}\right)$	$e\left(\frac{155}{333}\right)$	$e\left(\frac{139}{666}\right)$	$e\left(\frac{307}{333}\right)$
$\chi_{4023}(7,\cdot)$	4023.bf	666	yes	$1$	$1$	$e\left(\frac{565}{666}\right)$	$e\left(\frac{232}{333}\right)$	$e\left(\frac{76}{333}\right)$	$e\left(\frac{155}{333}\right)$	$e\left(\frac{121}{222}\right)$	$e\left(\frac{17}{222}\right)$	$e\left(\frac{91}{666}\right)$	$e\left(\frac{641}{666}\right)$	$e\left(\frac{209}{666}\right)$	$e\left(\frac{131}{333}\right)$
$\chi_{4023}(8,\cdot)$	4023.bd	444	no	$1$	$1$	$e\left(\frac{83}{444}\right)$	$e\left(\frac{83}{222}\right)$	$e\left(\frac{209}{222}\right)$	$e\left(\frac{121}{222}\right)$	$e\left(\frac{83}{148}\right)$	$e\left(\frac{19}{148}\right)$	$e\left(\frac{167}{444}\right)$	$e\left(\frac{181}{444}\right)$	$e\left(\frac{325}{444}\right)$	$e\left(\frac{83}{111}\right)$
$\chi_{4023}(10,\cdot)$	4023.be	444	no	$-1$	$1$	$e\left(\frac{19}{444}\right)$	$e\left(\frac{19}{222}\right)$	$e\left(\frac{50}{111}\right)$	$e\left(\frac{17}{222}\right)$	$e\left(\frac{19}{148}\right)$	$e\left(\frac{73}{148}\right)$	$e\left(\frac{295}{444}\right)$	$e\left(\frac{119}{444}\right)$	$e\left(\frac{53}{444}\right)$	$e\left(\frac{19}{111}\right)$
$\chi_{4023}(11,\cdot)$	4023.bi	1332	yes	$1$	$1$	$e\left(\frac{611}{1332}\right)$	$e\left(\frac{611}{666}\right)$	$e\left(\frac{137}{666}\right)$	$e\left(\frac{91}{666}\right)$	$e\left(\frac{167}{444}\right)$	$e\left(\frac{295}{444}\right)$	$e\left(\frac{887}{1332}\right)$	$e\left(\frac{1081}{1332}\right)$	$e\left(\frac{793}{1332}\right)$	$e\left(\frac{278}{333}\right)$
$\chi_{4023}(13,\cdot)$	4023.bj	1332	yes	$-1$	$1$	$e\left(\frac{1069}{1332}\right)$	$e\left(\frac{403}{666}\right)$	$e\left(\frac{155}{333}\right)$	$e\left(\frac{641}{666}\right)$	$e\left(\frac{181}{444}\right)$	$e\left(\frac{119}{444}\right)$	$e\left(\frac{1081}{1332}\right)$	$e\left(\frac{713}{1332}\right)$	$e\left(\frac{1019}{1332}\right)$	$e\left(\frac{70}{333}\right)$
$\chi_{4023}(14,\cdot)$	4023.bi	1332	yes	$1$	$1$	$e\left(\frac{1213}{1332}\right)$	$e\left(\frac{547}{666}\right)$	$e\left(\frac{139}{666}\right)$	$e\left(\frac{209}{666}\right)$	$e\left(\frac{325}{444}\right)$	$e\left(\frac{53}{444}\right)$	$e\left(\frac{793}{1332}\right)$	$e\left(\frac{1019}{1332}\right)$	$e\left(\frac{299}{1332}\right)$	$e\left(\frac{214}{333}\right)$
$\chi_{4023}(16,\cdot)$	4023.bc	333	yes	$1$	$1$	$e\left(\frac{83}{333}\right)$	$e\left(\frac{166}{333}\right)$	$e\left(\frac{307}{333}\right)$	$e\left(\frac{131}{333}\right)$	$e\left(\frac{83}{111}\right)$	$e\left(\frac{19}{111}\right)$	$e\left(\frac{278}{333}\right)$	$e\left(\frac{70}{333}\right)$	$e\left(\frac{214}{333}\right)$	$e\left(\frac{332}{333}\right)$
$\chi_{4023}(17,\cdot)$	4023.z	222	no	$-1$	$1$	$e\left(\frac{149}{222}\right)$	$e\left(\frac{38}{111}\right)$	$e\left(\frac{67}{222}\right)$	$e\left(\frac{34}{111}\right)$	$e\left(\frac{1}{74}\right)$	$e\left(\frac{36}{37}\right)$	$e\left(\frac{35}{222}\right)$	$e\left(\frac{8}{111}\right)$	$e\left(\frac{217}{222}\right)$	$e\left(\frac{76}{111}\right)$
$\chi_{4023}(19,\cdot)$	4023.w	111	no	$1$	$1$	$e\left(\frac{26}{111}\right)$	$e\left(\frac{52}{111}\right)$	$e\left(\frac{40}{111}\right)$	$e\left(\frac{29}{111}\right)$	$e\left(\frac{26}{37}\right)$	$e\left(\frac{22}{37}\right)$	$e\left(\frac{59}{111}\right)$	$e\left(\frac{46}{111}\right)$	$e\left(\frac{55}{111}\right)$	$e\left(\frac{104}{111}\right)$
$\chi_{4023}(20,\cdot)$	4023.bh	666	yes	$-1$	$1$	$e\left(\frac{35}{333}\right)$	$e\left(\frac{70}{333}\right)$	$e\left(\frac{287}{666}\right)$	$e\left(\frac{308}{333}\right)$	$e\left(\frac{35}{111}\right)$	$e\left(\frac{119}{222}\right)$	$e\left(\frac{41}{333}\right)$	$e\left(\frac{47}{666}\right)$	$e\left(\frac{10}{333}\right)$	$e\left(\frac{140}{333}\right)$
$\chi_{4023}(22,\cdot)$	4023.bf	666	yes	$1$	$1$	$e\left(\frac{347}{666}\right)$	$e\left(\frac{14}{333}\right)$	$e\left(\frac{62}{333}\right)$	$e\left(\frac{328}{333}\right)$	$e\left(\frac{125}{222}\right)$	$e\left(\frac{157}{222}\right)$	$e\left(\frac{83}{666}\right)$	$e\left(\frac{409}{666}\right)$	$e\left(\frac{337}{666}\right)$	$e\left(\frac{28}{333}\right)$
$\chi_{4023}(23,\cdot)$	4023.bi	1332	yes	$1$	$1$	$e\left(\frac{337}{1332}\right)$	$e\left(\frac{337}{666}\right)$	$e\left(\frac{541}{666}\right)$	$e\left(\frac{617}{666}\right)$	$e\left(\frac{337}{444}\right)$	$e\left(\frac{29}{444}\right)$	$e\left(\frac{1213}{1332}\right)$	$e\left(\frac{1211}{1332}\right)$	$e\left(\frac{239}{1332}\right)$	$e\left(\frac{4}{333}\right)$
$\chi_{4023}(25,\cdot)$	4023.bc	333	yes	$1$	$1$	$e\left(\frac{320}{333}\right)$	$e\left(\frac{307}{333}\right)$	$e\left(\frac{313}{333}\right)$	$e\left(\frac{152}{333}\right)$	$e\left(\frac{98}{111}\right)$	$e\left(\frac{100}{111}\right)$	$e\left(\frac{137}{333}\right)$	$e\left(\frac{310}{333}\right)$	$e\left(\frac{139}{333}\right)$	$e\left(\frac{281}{333}\right)$
$\chi_{4023}(26,\cdot)$	4023.t	74	no	$-1$	$1$	$e\left(\frac{32}{37}\right)$	$e\left(\frac{27}{37}\right)$	$e\left(\frac{33}{74}\right)$	$e\left(\frac{30}{37}\right)$	$e\left(\frac{22}{37}\right)$	$e\left(\frac{23}{74}\right)$	$e\left(\frac{10}{37}\right)$	$e\left(\frac{25}{74}\right)$	$e\left(\frac{25}{37}\right)$	$e\left(\frac{17}{37}\right)$
$\chi_{4023}(28,\cdot)$	4023.s	37	no	$1$	$1$	$e\left(\frac{36}{37}\right)$	$e\left(\frac{35}{37}\right)$	$e\left(\frac{7}{37}\right)$	$e\left(\frac{6}{37}\right)$	$e\left(\frac{34}{37}\right)$	$e\left(\frac{6}{37}\right)$	$e\left(\frac{2}{37}\right)$	$e\left(\frac{21}{37}\right)$	$e\left(\frac{5}{37}\right)$	$e\left(\frac{33}{37}\right)$
$\chi_{4023}(29,\cdot)$	4023.bg	666	yes	$-1$	$1$	$e\left(\frac{577}{666}\right)$	$e\left(\frac{244}{333}\right)$	$e\left(\frac{401}{666}\right)$	$e\left(\frac{8}{333}\right)$	$e\left(\frac{133}{222}\right)$	$e\left(\frac{52}{111}\right)$	$e\left(\frac{67}{666}\right)$	$e\left(\frac{139}{333}\right)$	$e\left(\frac{593}{666}\right)$	$e\left(\frac{155}{333}\right)$
$\chi_{4023}(31,\cdot)$	4023.bc	333	yes	$1$	$1$	$e\left(\frac{1}{333}\right)$	$e\left(\frac{2}{333}\right)$	$e\left(\frac{104}{333}\right)$	$e\left(\frac{142}{333}\right)$	$e\left(\frac{1}{111}\right)$	$e\left(\frac{35}{111}\right)$	$e\left(\frac{220}{333}\right)$	$e\left(\frac{53}{333}\right)$	$e\left(\frac{143}{333}\right)$	$e\left(\frac{4}{333}\right)$
$\chi_{4023}(32,\cdot)$	4023.bi	1332	yes	$1$	$1$	$e\left(\frac{415}{1332}\right)$	$e\left(\frac{415}{666}\right)$	$e\left(\frac{601}{666}\right)$	$e\left(\frac{161}{666}\right)$	$e\left(\frac{415}{444}\right)$	$e\left(\frac{95}{444}\right)$	$e\left(\frac{391}{1332}\right)$	$e\left(\frac{17}{1332}\right)$	$e\left(\frac{737}{1332}\right)$	$e\left(\frac{82}{333}\right)$
$\chi_{4023}(34,\cdot)$	4023.bj	1332	yes	$-1$	$1$	$e\left(\frac{977}{1332}\right)$	$e\left(\frac{311}{666}\right)$	$e\left(\frac{94}{333}\right)$	$e\left(\frac{103}{666}\right)$	$e\left(\frac{89}{444}\right)$	$e\left(\frac{7}{444}\right)$	$e\left(\frac{821}{1332}\right)$	$e\left(\frac{1165}{1332}\right)$	$e\left(\frac{1183}{1332}\right)$	$e\left(\frac{311}{333}\right)$
$\chi_{4023}(35,\cdot)$	4023.bb	222	no	$-1$	$1$	$e\left(\frac{92}{111}\right)$	$e\left(\frac{73}{111}\right)$	$e\left(\frac{155}{222}\right)$	$e\left(\frac{77}{111}\right)$	$e\left(\frac{18}{37}\right)$	$e\left(\frac{39}{74}\right)$	$e\left(\frac{38}{111}\right)$	$e\left(\frac{95}{222}\right)$	$e\left(\frac{58}{111}\right)$	$e\left(\frac{35}{111}\right)$
$\chi_{4023}(37,\cdot)$	4023.w	111	no	$1$	$1$	$e\left(\frac{91}{111}\right)$	$e\left(\frac{71}{111}\right)$	$e\left(\frac{29}{111}\right)$	$e\left(\frac{46}{111}\right)$	$e\left(\frac{17}{37}\right)$	$e\left(\frac{3}{37}\right)$	$e\left(\frac{40}{111}\right)$	$e\left(\frac{50}{111}\right)$	$e\left(\frac{26}{111}\right)$	$e\left(\frac{31}{111}\right)$
$\chi_{4023}(38,\cdot)$	4023.bi	1332	yes	$1$	$1$	$e\left(\frac{395}{1332}\right)$	$e\left(\frac{395}{666}\right)$	$e\left(\frac{227}{666}\right)$	$e\left(\frac{73}{666}\right)$	$e\left(\frac{395}{444}\right)$	$e\left(\frac{283}{444}\right)$	$e\left(\frac{1319}{1332}\right)$	$e\left(\frac{289}{1332}\right)$	$e\left(\frac{541}{1332}\right)$	$e\left(\frac{62}{333}\right)$
$\chi_{4023}(40,\cdot)$	4023.bj	1332	yes	$-1$	$1$	$e\left(\frac{223}{1332}\right)$	$e\left(\frac{223}{666}\right)$	$e\left(\frac{137}{333}\right)$	$e\left(\frac{515}{666}\right)$	$e\left(\frac{223}{444}\right)$	$e\left(\frac{257}{444}\right)$	$e\left(\frac{775}{1332}\right)$	$e\left(\frac{1163}{1332}\right)$	$e\left(\frac{1253}{1332}\right)$	$e\left(\frac{223}{333}\right)$
$\chi_{4023}(41,\cdot)$	4023.bi	1332	yes	$1$	$1$	$e\left(\frac{295}{1332}\right)$	$e\left(\frac{295}{666}\right)$	$e\left(\frac{355}{666}\right)$	$e\left(\frac{299}{666}\right)$	$e\left(\frac{295}{444}\right)$	$e\left(\frac{335}{444}\right)$	$e\left(\frac{631}{1332}\right)$	$e\left(\frac{317}{1332}\right)$	$e\left(\frac{893}{1332}\right)$	$e\left(\frac{295}{333}\right)$
$\chi_{4023}(43,\cdot)$	4023.bj	1332	yes	$-1$	$1$	$e\left(\frac{1133}{1332}\right)$	$e\left(\frac{467}{666}\right)$	$e\left(\frac{154}{333}\right)$	$e\left(\frac{523}{666}\right)$	$e\left(\frac{245}{444}\right)$	$e\left(\frac{139}{444}\right)$	$e\left(\frac{509}{1332}\right)$	$e\left(\frac{109}{1332}\right)$	$e\left(\frac{847}{1332}\right)$	$e\left(\frac{134}{333}\right)$
$\chi_{4023}(44,\cdot)$	4023.m	12	no	$1$	$1$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$	$-i$	$-i$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{4023}(46,\cdot)$	4023.w	111	no	$1$	$1$	$e\left(\frac{35}{111}\right)$	$e\left(\frac{70}{111}\right)$	$e\left(\frac{88}{111}\right)$	$e\left(\frac{86}{111}\right)$	$e\left(\frac{35}{37}\right)$	$e\left(\frac{4}{37}\right)$	$e\left(\frac{41}{111}\right)$	$e\left(\frac{79}{111}\right)$	$e\left(\frac{10}{111}\right)$	$e\left(\frac{29}{111}\right)$
$\chi_{4023}(47,\cdot)$	4023.bh	666	yes	$-1$	$1$	$e\left(\frac{107}{333}\right)$	$e\left(\frac{214}{333}\right)$	$e\left(\frac{611}{666}\right)$	$e\left(\frac{209}{333}\right)$	$e\left(\frac{107}{111}\right)$	$e\left(\frac{53}{222}\right)$	$e\left(\frac{230}{333}\right)$	$e\left(\frac{353}{666}\right)$	$e\left(\frac{316}{333}\right)$	$e\left(\frac{95}{333}\right)$

Click here to search among the remaining 2632 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	$4023$
Structure	\(C_{2}\times C_{1332}\)
Order	$2664$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(4\)	\(5\)	\(7\)	\(8\)	\(10\)	\(11\)	\(13\)	\(14\)	\(16\)
\(\chi_{4023}(1,\cdot)\)	4023.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{4023}(2,\cdot)\)	4023.bi	1332	yes	\(1\)	\(1\)	\(e\left(\frac{83}{1332}\right)\)	\(e\left(\frac{83}{666}\right)\)	\(e\left(\frac{653}{666}\right)\)	\(e\left(\frac{565}{666}\right)\)	\(e\left(\frac{83}{444}\right)\)	\(e\left(\frac{19}{444}\right)\)	\(e\left(\frac{611}{1332}\right)\)	\(e\left(\frac{1069}{1332}\right)\)	\(e\left(\frac{1213}{1332}\right)\)	\(e\left(\frac{83}{333}\right)\)
\(\chi_{4023}(4,\cdot)\)	4023.bf	666	yes	\(1\)	\(1\)	\(e\left(\frac{83}{666}\right)\)	\(e\left(\frac{83}{333}\right)\)	\(e\left(\frac{320}{333}\right)\)	\(e\left(\frac{232}{333}\right)\)	\(e\left(\frac{83}{222}\right)\)	\(e\left(\frac{19}{222}\right)\)	\(e\left(\frac{611}{666}\right)\)	\(e\left(\frac{403}{666}\right)\)	\(e\left(\frac{547}{666}\right)\)	\(e\left(\frac{166}{333}\right)\)
\(\chi_{4023}(5,\cdot)\)	4023.bg	666	yes	\(-1\)	\(1\)	\(e\left(\frac{653}{666}\right)\)	\(e\left(\frac{320}{333}\right)\)	\(e\left(\frac{313}{666}\right)\)	\(e\left(\frac{76}{333}\right)\)	\(e\left(\frac{209}{222}\right)\)	\(e\left(\frac{50}{111}\right)\)	\(e\left(\frac{137}{666}\right)\)	\(e\left(\frac{155}{333}\right)\)	\(e\left(\frac{139}{666}\right)\)	\(e\left(\frac{307}{333}\right)\)
\(\chi_{4023}(7,\cdot)\)	4023.bf	666	yes	\(1\)	\(1\)	\(e\left(\frac{565}{666}\right)\)	\(e\left(\frac{232}{333}\right)\)	\(e\left(\frac{76}{333}\right)\)	\(e\left(\frac{155}{333}\right)\)	\(e\left(\frac{121}{222}\right)\)	\(e\left(\frac{17}{222}\right)\)	\(e\left(\frac{91}{666}\right)\)	\(e\left(\frac{641}{666}\right)\)	\(e\left(\frac{209}{666}\right)\)	\(e\left(\frac{131}{333}\right)\)
\(\chi_{4023}(8,\cdot)\)	4023.bd	444	no	\(1\)	\(1\)	\(e\left(\frac{83}{444}\right)\)	\(e\left(\frac{83}{222}\right)\)	\(e\left(\frac{209}{222}\right)\)	\(e\left(\frac{121}{222}\right)\)	\(e\left(\frac{83}{148}\right)\)	\(e\left(\frac{19}{148}\right)\)	\(e\left(\frac{167}{444}\right)\)	\(e\left(\frac{181}{444}\right)\)	\(e\left(\frac{325}{444}\right)\)	\(e\left(\frac{83}{111}\right)\)
\(\chi_{4023}(10,\cdot)\)	4023.be	444	no	\(-1\)	\(1\)	\(e\left(\frac{19}{444}\right)\)	\(e\left(\frac{19}{222}\right)\)	\(e\left(\frac{50}{111}\right)\)	\(e\left(\frac{17}{222}\right)\)	\(e\left(\frac{19}{148}\right)\)	\(e\left(\frac{73}{148}\right)\)	\(e\left(\frac{295}{444}\right)\)	\(e\left(\frac{119}{444}\right)\)	\(e\left(\frac{53}{444}\right)\)	\(e\left(\frac{19}{111}\right)\)
\(\chi_{4023}(11,\cdot)\)	4023.bi	1332	yes	\(1\)	\(1\)	\(e\left(\frac{611}{1332}\right)\)	\(e\left(\frac{611}{666}\right)\)	\(e\left(\frac{137}{666}\right)\)	\(e\left(\frac{91}{666}\right)\)	\(e\left(\frac{167}{444}\right)\)	\(e\left(\frac{295}{444}\right)\)	\(e\left(\frac{887}{1332}\right)\)	\(e\left(\frac{1081}{1332}\right)\)	\(e\left(\frac{793}{1332}\right)\)	\(e\left(\frac{278}{333}\right)\)
\(\chi_{4023}(13,\cdot)\)	4023.bj	1332	yes	\(-1\)	\(1\)	\(e\left(\frac{1069}{1332}\right)\)	\(e\left(\frac{403}{666}\right)\)	\(e\left(\frac{155}{333}\right)\)	\(e\left(\frac{641}{666}\right)\)	\(e\left(\frac{181}{444}\right)\)	\(e\left(\frac{119}{444}\right)\)	\(e\left(\frac{1081}{1332}\right)\)	\(e\left(\frac{713}{1332}\right)\)	\(e\left(\frac{1019}{1332}\right)\)	\(e\left(\frac{70}{333}\right)\)
\(\chi_{4023}(14,\cdot)\)	4023.bi	1332	yes	\(1\)	\(1\)	\(e\left(\frac{1213}{1332}\right)\)	\(e\left(\frac{547}{666}\right)\)	\(e\left(\frac{139}{666}\right)\)	\(e\left(\frac{209}{666}\right)\)	\(e\left(\frac{325}{444}\right)\)	\(e\left(\frac{53}{444}\right)\)	\(e\left(\frac{793}{1332}\right)\)	\(e\left(\frac{1019}{1332}\right)\)	\(e\left(\frac{299}{1332}\right)\)	\(e\left(\frac{214}{333}\right)\)
\(\chi_{4023}(16,\cdot)\)	4023.bc	333	yes	\(1\)	\(1\)	\(e\left(\frac{83}{333}\right)\)	\(e\left(\frac{166}{333}\right)\)	\(e\left(\frac{307}{333}\right)\)	\(e\left(\frac{131}{333}\right)\)	\(e\left(\frac{83}{111}\right)\)	\(e\left(\frac{19}{111}\right)\)	\(e\left(\frac{278}{333}\right)\)	\(e\left(\frac{70}{333}\right)\)	\(e\left(\frac{214}{333}\right)\)	\(e\left(\frac{332}{333}\right)\)
\(\chi_{4023}(17,\cdot)\)	4023.z	222	no	\(-1\)	\(1\)	\(e\left(\frac{149}{222}\right)\)	\(e\left(\frac{38}{111}\right)\)	\(e\left(\frac{67}{222}\right)\)	\(e\left(\frac{34}{111}\right)\)	\(e\left(\frac{1}{74}\right)\)	\(e\left(\frac{36}{37}\right)\)	\(e\left(\frac{35}{222}\right)\)	\(e\left(\frac{8}{111}\right)\)	\(e\left(\frac{217}{222}\right)\)	\(e\left(\frac{76}{111}\right)\)
\(\chi_{4023}(19,\cdot)\)	4023.w	111	no	\(1\)	\(1\)	\(e\left(\frac{26}{111}\right)\)	\(e\left(\frac{52}{111}\right)\)	\(e\left(\frac{40}{111}\right)\)	\(e\left(\frac{29}{111}\right)\)	\(e\left(\frac{26}{37}\right)\)	\(e\left(\frac{22}{37}\right)\)	\(e\left(\frac{59}{111}\right)\)	\(e\left(\frac{46}{111}\right)\)	\(e\left(\frac{55}{111}\right)\)	\(e\left(\frac{104}{111}\right)\)
\(\chi_{4023}(20,\cdot)\)	4023.bh	666	yes	\(-1\)	\(1\)	\(e\left(\frac{35}{333}\right)\)	\(e\left(\frac{70}{333}\right)\)	\(e\left(\frac{287}{666}\right)\)	\(e\left(\frac{308}{333}\right)\)	\(e\left(\frac{35}{111}\right)\)	\(e\left(\frac{119}{222}\right)\)	\(e\left(\frac{41}{333}\right)\)	\(e\left(\frac{47}{666}\right)\)	\(e\left(\frac{10}{333}\right)\)	\(e\left(\frac{140}{333}\right)\)
\(\chi_{4023}(22,\cdot)\)	4023.bf	666	yes	\(1\)	\(1\)	\(e\left(\frac{347}{666}\right)\)	\(e\left(\frac{14}{333}\right)\)	\(e\left(\frac{62}{333}\right)\)	\(e\left(\frac{328}{333}\right)\)	\(e\left(\frac{125}{222}\right)\)	\(e\left(\frac{157}{222}\right)\)	\(e\left(\frac{83}{666}\right)\)	\(e\left(\frac{409}{666}\right)\)	\(e\left(\frac{337}{666}\right)\)	\(e\left(\frac{28}{333}\right)\)
\(\chi_{4023}(23,\cdot)\)	4023.bi	1332	yes	\(1\)	\(1\)	\(e\left(\frac{337}{1332}\right)\)	\(e\left(\frac{337}{666}\right)\)	\(e\left(\frac{541}{666}\right)\)	\(e\left(\frac{617}{666}\right)\)	\(e\left(\frac{337}{444}\right)\)	\(e\left(\frac{29}{444}\right)\)	\(e\left(\frac{1213}{1332}\right)\)	\(e\left(\frac{1211}{1332}\right)\)	\(e\left(\frac{239}{1332}\right)\)	\(e\left(\frac{4}{333}\right)\)
\(\chi_{4023}(25,\cdot)\)	4023.bc	333	yes	\(1\)	\(1\)	\(e\left(\frac{320}{333}\right)\)	\(e\left(\frac{307}{333}\right)\)	\(e\left(\frac{313}{333}\right)\)	\(e\left(\frac{152}{333}\right)\)	\(e\left(\frac{98}{111}\right)\)	\(e\left(\frac{100}{111}\right)\)	\(e\left(\frac{137}{333}\right)\)	\(e\left(\frac{310}{333}\right)\)	\(e\left(\frac{139}{333}\right)\)	\(e\left(\frac{281}{333}\right)\)
\(\chi_{4023}(26,\cdot)\)	4023.t	74	no	\(-1\)	\(1\)	\(e\left(\frac{32}{37}\right)\)	\(e\left(\frac{27}{37}\right)\)	\(e\left(\frac{33}{74}\right)\)	\(e\left(\frac{30}{37}\right)\)	\(e\left(\frac{22}{37}\right)\)	\(e\left(\frac{23}{74}\right)\)	\(e\left(\frac{10}{37}\right)\)	\(e\left(\frac{25}{74}\right)\)	\(e\left(\frac{25}{37}\right)\)	\(e\left(\frac{17}{37}\right)\)
\(\chi_{4023}(28,\cdot)\)	4023.s	37	no	\(1\)	\(1\)	\(e\left(\frac{36}{37}\right)\)	\(e\left(\frac{35}{37}\right)\)	\(e\left(\frac{7}{37}\right)\)	\(e\left(\frac{6}{37}\right)\)	\(e\left(\frac{34}{37}\right)\)	\(e\left(\frac{6}{37}\right)\)	\(e\left(\frac{2}{37}\right)\)	\(e\left(\frac{21}{37}\right)\)	\(e\left(\frac{5}{37}\right)\)	\(e\left(\frac{33}{37}\right)\)
\(\chi_{4023}(29,\cdot)\)	4023.bg	666	yes	\(-1\)	\(1\)	\(e\left(\frac{577}{666}\right)\)	\(e\left(\frac{244}{333}\right)\)	\(e\left(\frac{401}{666}\right)\)	\(e\left(\frac{8}{333}\right)\)	\(e\left(\frac{133}{222}\right)\)	\(e\left(\frac{52}{111}\right)\)	\(e\left(\frac{67}{666}\right)\)	\(e\left(\frac{139}{333}\right)\)	\(e\left(\frac{593}{666}\right)\)	\(e\left(\frac{155}{333}\right)\)
\(\chi_{4023}(31,\cdot)\)	4023.bc	333	yes	\(1\)	\(1\)	\(e\left(\frac{1}{333}\right)\)	\(e\left(\frac{2}{333}\right)\)	\(e\left(\frac{104}{333}\right)\)	\(e\left(\frac{142}{333}\right)\)	\(e\left(\frac{1}{111}\right)\)	\(e\left(\frac{35}{111}\right)\)	\(e\left(\frac{220}{333}\right)\)	\(e\left(\frac{53}{333}\right)\)	\(e\left(\frac{143}{333}\right)\)	\(e\left(\frac{4}{333}\right)\)
\(\chi_{4023}(32,\cdot)\)	4023.bi	1332	yes	\(1\)	\(1\)	\(e\left(\frac{415}{1332}\right)\)	\(e\left(\frac{415}{666}\right)\)	\(e\left(\frac{601}{666}\right)\)	\(e\left(\frac{161}{666}\right)\)	\(e\left(\frac{415}{444}\right)\)	\(e\left(\frac{95}{444}\right)\)	\(e\left(\frac{391}{1332}\right)\)	\(e\left(\frac{17}{1332}\right)\)	\(e\left(\frac{737}{1332}\right)\)	\(e\left(\frac{82}{333}\right)\)
\(\chi_{4023}(34,\cdot)\)	4023.bj	1332	yes	\(-1\)	\(1\)	\(e\left(\frac{977}{1332}\right)\)	\(e\left(\frac{311}{666}\right)\)	\(e\left(\frac{94}{333}\right)\)	\(e\left(\frac{103}{666}\right)\)	\(e\left(\frac{89}{444}\right)\)	\(e\left(\frac{7}{444}\right)\)	\(e\left(\frac{821}{1332}\right)\)	\(e\left(\frac{1165}{1332}\right)\)	\(e\left(\frac{1183}{1332}\right)\)	\(e\left(\frac{311}{333}\right)\)
\(\chi_{4023}(35,\cdot)\)	4023.bb	222	no	\(-1\)	\(1\)	\(e\left(\frac{92}{111}\right)\)	\(e\left(\frac{73}{111}\right)\)	\(e\left(\frac{155}{222}\right)\)	\(e\left(\frac{77}{111}\right)\)	\(e\left(\frac{18}{37}\right)\)	\(e\left(\frac{39}{74}\right)\)	\(e\left(\frac{38}{111}\right)\)	\(e\left(\frac{95}{222}\right)\)	\(e\left(\frac{58}{111}\right)\)	\(e\left(\frac{35}{111}\right)\)
\(\chi_{4023}(37,\cdot)\)	4023.w	111	no	\(1\)	\(1\)	\(e\left(\frac{91}{111}\right)\)	\(e\left(\frac{71}{111}\right)\)	\(e\left(\frac{29}{111}\right)\)	\(e\left(\frac{46}{111}\right)\)	\(e\left(\frac{17}{37}\right)\)	\(e\left(\frac{3}{37}\right)\)	\(e\left(\frac{40}{111}\right)\)	\(e\left(\frac{50}{111}\right)\)	\(e\left(\frac{26}{111}\right)\)	\(e\left(\frac{31}{111}\right)\)
\(\chi_{4023}(38,\cdot)\)	4023.bi	1332	yes	\(1\)	\(1\)	\(e\left(\frac{395}{1332}\right)\)	\(e\left(\frac{395}{666}\right)\)	\(e\left(\frac{227}{666}\right)\)	\(e\left(\frac{73}{666}\right)\)	\(e\left(\frac{395}{444}\right)\)	\(e\left(\frac{283}{444}\right)\)	\(e\left(\frac{1319}{1332}\right)\)	\(e\left(\frac{289}{1332}\right)\)	\(e\left(\frac{541}{1332}\right)\)	\(e\left(\frac{62}{333}\right)\)
\(\chi_{4023}(40,\cdot)\)	4023.bj	1332	yes	\(-1\)	\(1\)	\(e\left(\frac{223}{1332}\right)\)	\(e\left(\frac{223}{666}\right)\)	\(e\left(\frac{137}{333}\right)\)	\(e\left(\frac{515}{666}\right)\)	\(e\left(\frac{223}{444}\right)\)	\(e\left(\frac{257}{444}\right)\)	\(e\left(\frac{775}{1332}\right)\)	\(e\left(\frac{1163}{1332}\right)\)	\(e\left(\frac{1253}{1332}\right)\)	\(e\left(\frac{223}{333}\right)\)
\(\chi_{4023}(41,\cdot)\)	4023.bi	1332	yes	\(1\)	\(1\)	\(e\left(\frac{295}{1332}\right)\)	\(e\left(\frac{295}{666}\right)\)	\(e\left(\frac{355}{666}\right)\)	\(e\left(\frac{299}{666}\right)\)	\(e\left(\frac{295}{444}\right)\)	\(e\left(\frac{335}{444}\right)\)	\(e\left(\frac{631}{1332}\right)\)	\(e\left(\frac{317}{1332}\right)\)	\(e\left(\frac{893}{1332}\right)\)	\(e\left(\frac{295}{333}\right)\)
\(\chi_{4023}(43,\cdot)\)	4023.bj	1332	yes	\(-1\)	\(1\)	\(e\left(\frac{1133}{1332}\right)\)	\(e\left(\frac{467}{666}\right)\)	\(e\left(\frac{154}{333}\right)\)	\(e\left(\frac{523}{666}\right)\)	\(e\left(\frac{245}{444}\right)\)	\(e\left(\frac{139}{444}\right)\)	\(e\left(\frac{509}{1332}\right)\)	\(e\left(\frac{109}{1332}\right)\)	\(e\left(\frac{847}{1332}\right)\)	\(e\left(\frac{134}{333}\right)\)
\(\chi_{4023}(44,\cdot)\)	4023.m	12	no	\(1\)	\(1\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(-i\)	\(-i\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{4023}(46,\cdot)\)	4023.w	111	no	\(1\)	\(1\)	\(e\left(\frac{35}{111}\right)\)	\(e\left(\frac{70}{111}\right)\)	\(e\left(\frac{88}{111}\right)\)	\(e\left(\frac{86}{111}\right)\)	\(e\left(\frac{35}{37}\right)\)	\(e\left(\frac{4}{37}\right)\)	\(e\left(\frac{41}{111}\right)\)	\(e\left(\frac{79}{111}\right)\)	\(e\left(\frac{10}{111}\right)\)	\(e\left(\frac{29}{111}\right)\)
\(\chi_{4023}(47,\cdot)\)	4023.bh	666	yes	\(-1\)	\(1\)	\(e\left(\frac{107}{333}\right)\)	\(e\left(\frac{214}{333}\right)\)	\(e\left(\frac{611}{666}\right)\)	\(e\left(\frac{209}{333}\right)\)	\(e\left(\frac{107}{111}\right)\)	\(e\left(\frac{53}{222}\right)\)	\(e\left(\frac{230}{333}\right)\)	\(e\left(\frac{353}{666}\right)\)	\(e\left(\frac{316}{333}\right)\)	\(e\left(\frac{95}{333}\right)\)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Learn more

Character group

First 32 of 2664 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.