LMFDB - Group of Dirichlet characters of modulus 2023

Show commands: PariGP / SageMath

sage: H = DirichletGroup(2023)

pari: g = idealstar(,2023,2)

Character group

sage: G.order() pari: g.no
Order	=	1632
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{816}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{2023}(290,\cdot)$, $\chi_{2023}(1737,\cdot)$

First 32 of 1632 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	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$8$	$9$	$10$	$11$	$12$
$\chi_{2023}(1,\cdot)$	2023.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{2023}(2,\cdot)$	2023.bl	408	yes	$1$	$1$	$e\left(\frac{79}{204}\right)$	$e\left(\frac{13}{408}\right)$	$e\left(\frac{79}{102}\right)$	$e\left(\frac{257}{408}\right)$	$e\left(\frac{57}{136}\right)$	$e\left(\frac{11}{68}\right)$	$e\left(\frac{13}{204}\right)$	$e\left(\frac{7}{408}\right)$	$e\left(\frac{163}{408}\right)$	$e\left(\frac{329}{408}\right)$
$\chi_{2023}(3,\cdot)$	2023.bn	816	yes	$1$	$1$	$e\left(\frac{13}{408}\right)$	$e\left(\frac{139}{816}\right)$	$e\left(\frac{13}{204}\right)$	$e\left(\frac{551}{816}\right)$	$e\left(\frac{55}{272}\right)$	$e\left(\frac{13}{136}\right)$	$e\left(\frac{139}{408}\right)$	$e\left(\frac{577}{816}\right)$	$e\left(\frac{613}{816}\right)$	$e\left(\frac{191}{816}\right)$
$\chi_{2023}(4,\cdot)$	2023.bg	204	yes	$1$	$1$	$e\left(\frac{79}{102}\right)$	$e\left(\frac{13}{204}\right)$	$e\left(\frac{28}{51}\right)$	$e\left(\frac{53}{204}\right)$	$e\left(\frac{57}{68}\right)$	$e\left(\frac{11}{34}\right)$	$e\left(\frac{13}{102}\right)$	$e\left(\frac{7}{204}\right)$	$e\left(\frac{163}{204}\right)$	$e\left(\frac{125}{204}\right)$
$\chi_{2023}(5,\cdot)$	2023.bn	816	yes	$1$	$1$	$e\left(\frac{257}{408}\right)$	$e\left(\frac{551}{816}\right)$	$e\left(\frac{53}{204}\right)$	$e\left(\frac{787}{816}\right)$	$e\left(\frac{83}{272}\right)$	$e\left(\frac{121}{136}\right)$	$e\left(\frac{143}{408}\right)$	$e\left(\frac{485}{816}\right)$	$e\left(\frac{569}{816}\right)$	$e\left(\frac{763}{816}\right)$
$\chi_{2023}(6,\cdot)$	2023.bi	272	yes	$1$	$1$	$e\left(\frac{57}{136}\right)$	$e\left(\frac{55}{272}\right)$	$e\left(\frac{57}{68}\right)$	$e\left(\frac{83}{272}\right)$	$e\left(\frac{169}{272}\right)$	$e\left(\frac{35}{136}\right)$	$e\left(\frac{55}{136}\right)$	$e\left(\frac{197}{272}\right)$	$e\left(\frac{41}{272}\right)$	$e\left(\frac{11}{272}\right)$
$\chi_{2023}(8,\cdot)$	2023.bf	136	no	$1$	$1$	$e\left(\frac{11}{68}\right)$	$e\left(\frac{13}{136}\right)$	$e\left(\frac{11}{34}\right)$	$e\left(\frac{121}{136}\right)$	$e\left(\frac{35}{136}\right)$	$e\left(\frac{33}{68}\right)$	$e\left(\frac{13}{68}\right)$	$e\left(\frac{7}{136}\right)$	$e\left(\frac{27}{136}\right)$	$e\left(\frac{57}{136}\right)$
$\chi_{2023}(9,\cdot)$	2023.bl	408	yes	$1$	$1$	$e\left(\frac{13}{204}\right)$	$e\left(\frac{139}{408}\right)$	$e\left(\frac{13}{102}\right)$	$e\left(\frac{143}{408}\right)$	$e\left(\frac{55}{136}\right)$	$e\left(\frac{13}{68}\right)$	$e\left(\frac{139}{204}\right)$	$e\left(\frac{169}{408}\right)$	$e\left(\frac{205}{408}\right)$	$e\left(\frac{191}{408}\right)$
$\chi_{2023}(10,\cdot)$	2023.bn	816	yes	$1$	$1$	$e\left(\frac{7}{408}\right)$	$e\left(\frac{577}{816}\right)$	$e\left(\frac{7}{204}\right)$	$e\left(\frac{485}{816}\right)$	$e\left(\frac{197}{272}\right)$	$e\left(\frac{7}{136}\right)$	$e\left(\frac{169}{408}\right)$	$e\left(\frac{499}{816}\right)$	$e\left(\frac{79}{816}\right)$	$e\left(\frac{605}{816}\right)$
$\chi_{2023}(11,\cdot)$	2023.bm	816	yes	$-1$	$1$	$e\left(\frac{163}{408}\right)$	$e\left(\frac{613}{816}\right)$	$e\left(\frac{163}{204}\right)$	$e\left(\frac{569}{816}\right)$	$e\left(\frac{41}{272}\right)$	$e\left(\frac{27}{136}\right)$	$e\left(\frac{205}{408}\right)$	$e\left(\frac{79}{816}\right)$	$e\left(\frac{499}{816}\right)$	$e\left(\frac{449}{816}\right)$
$\chi_{2023}(12,\cdot)$	2023.bn	816	yes	$1$	$1$	$e\left(\frac{329}{408}\right)$	$e\left(\frac{191}{816}\right)$	$e\left(\frac{125}{204}\right)$	$e\left(\frac{763}{816}\right)$	$e\left(\frac{11}{272}\right)$	$e\left(\frac{57}{136}\right)$	$e\left(\frac{191}{408}\right)$	$e\left(\frac{605}{816}\right)$	$e\left(\frac{449}{816}\right)$	$e\left(\frac{691}{816}\right)$
$\chi_{2023}(13,\cdot)$	2023.ba	68	yes	$-1$	$1$	$e\left(\frac{31}{34}\right)$	$e\left(\frac{15}{68}\right)$	$e\left(\frac{14}{17}\right)$	$e\left(\frac{35}{68}\right)$	$e\left(\frac{9}{68}\right)$	$e\left(\frac{25}{34}\right)$	$e\left(\frac{15}{34}\right)$	$e\left(\frac{29}{68}\right)$	$e\left(\frac{39}{68}\right)$	$e\left(\frac{3}{68}\right)$
$\chi_{2023}(15,\cdot)$	2023.bf	136	no	$1$	$1$	$e\left(\frac{45}{68}\right)$	$e\left(\frac{115}{136}\right)$	$e\left(\frac{11}{34}\right)$	$e\left(\frac{87}{136}\right)$	$e\left(\frac{69}{136}\right)$	$e\left(\frac{67}{68}\right)$	$e\left(\frac{47}{68}\right)$	$e\left(\frac{41}{136}\right)$	$e\left(\frac{61}{136}\right)$	$e\left(\frac{23}{136}\right)$
$\chi_{2023}(16,\cdot)$	2023.bb	102	yes	$1$	$1$	$e\left(\frac{28}{51}\right)$	$e\left(\frac{13}{102}\right)$	$e\left(\frac{5}{51}\right)$	$e\left(\frac{53}{102}\right)$	$e\left(\frac{23}{34}\right)$	$e\left(\frac{11}{17}\right)$	$e\left(\frac{13}{51}\right)$	$e\left(\frac{7}{102}\right)$	$e\left(\frac{61}{102}\right)$	$e\left(\frac{23}{102}\right)$
$\chi_{2023}(18,\cdot)$	2023.y	51	yes	$1$	$1$	$e\left(\frac{23}{51}\right)$	$e\left(\frac{19}{51}\right)$	$e\left(\frac{46}{51}\right)$	$e\left(\frac{50}{51}\right)$	$e\left(\frac{14}{17}\right)$	$e\left(\frac{6}{17}\right)$	$e\left(\frac{38}{51}\right)$	$e\left(\frac{22}{51}\right)$	$e\left(\frac{46}{51}\right)$	$e\left(\frac{14}{51}\right)$
$\chi_{2023}(19,\cdot)$	2023.bk	408	yes	$-1$	$1$	$e\left(\frac{91}{204}\right)$	$e\left(\frac{361}{408}\right)$	$e\left(\frac{91}{102}\right)$	$e\left(\frac{389}{408}\right)$	$e\left(\frac{45}{136}\right)$	$e\left(\frac{23}{68}\right)$	$e\left(\frac{157}{204}\right)$	$e\left(\frac{163}{408}\right)$	$e\left(\frac{211}{408}\right)$	$e\left(\frac{317}{408}\right)$
$\chi_{2023}(20,\cdot)$	2023.bi	272	yes	$1$	$1$	$e\left(\frac{55}{136}\right)$	$e\left(\frac{201}{272}\right)$	$e\left(\frac{55}{68}\right)$	$e\left(\frac{61}{272}\right)$	$e\left(\frac{39}{272}\right)$	$e\left(\frac{29}{136}\right)$	$e\left(\frac{65}{136}\right)$	$e\left(\frac{171}{272}\right)$	$e\left(\frac{135}{272}\right)$	$e\left(\frac{149}{272}\right)$
$\chi_{2023}(22,\cdot)$	2023.bj	272	no	$-1$	$1$	$e\left(\frac{107}{136}\right)$	$e\left(\frac{213}{272}\right)$	$e\left(\frac{39}{68}\right)$	$e\left(\frac{89}{272}\right)$	$e\left(\frac{155}{272}\right)$	$e\left(\frac{49}{136}\right)$	$e\left(\frac{77}{136}\right)$	$e\left(\frac{31}{272}\right)$	$e\left(\frac{3}{272}\right)$	$e\left(\frac{97}{272}\right)$
$\chi_{2023}(23,\cdot)$	2023.bm	816	yes	$-1$	$1$	$e\left(\frac{179}{408}\right)$	$e\left(\frac{125}{816}\right)$	$e\left(\frac{179}{204}\right)$	$e\left(\frac{337}{816}\right)$	$e\left(\frac{161}{272}\right)$	$e\left(\frac{43}{136}\right)$	$e\left(\frac{125}{408}\right)$	$e\left(\frac{695}{816}\right)$	$e\left(\frac{155}{816}\right)$	$e\left(\frac{25}{816}\right)$
$\chi_{2023}(24,\cdot)$	2023.bn	816	yes	$1$	$1$	$e\left(\frac{79}{408}\right)$	$e\left(\frac{217}{816}\right)$	$e\left(\frac{79}{204}\right)$	$e\left(\frac{461}{816}\right)$	$e\left(\frac{125}{272}\right)$	$e\left(\frac{79}{136}\right)$	$e\left(\frac{217}{408}\right)$	$e\left(\frac{619}{816}\right)$	$e\left(\frac{775}{816}\right)$	$e\left(\frac{533}{816}\right)$
$\chi_{2023}(25,\cdot)$	2023.bl	408	yes	$1$	$1$	$e\left(\frac{53}{204}\right)$	$e\left(\frac{143}{408}\right)$	$e\left(\frac{53}{102}\right)$	$e\left(\frac{379}{408}\right)$	$e\left(\frac{83}{136}\right)$	$e\left(\frac{53}{68}\right)$	$e\left(\frac{143}{204}\right)$	$e\left(\frac{77}{408}\right)$	$e\left(\frac{161}{408}\right)$	$e\left(\frac{355}{408}\right)$
$\chi_{2023}(26,\cdot)$	2023.bk	408	yes	$-1$	$1$	$e\left(\frac{61}{204}\right)$	$e\left(\frac{103}{408}\right)$	$e\left(\frac{61}{102}\right)$	$e\left(\frac{59}{408}\right)$	$e\left(\frac{75}{136}\right)$	$e\left(\frac{61}{68}\right)$	$e\left(\frac{103}{204}\right)$	$e\left(\frac{181}{408}\right)$	$e\left(\frac{397}{408}\right)$	$e\left(\frac{347}{408}\right)$
$\chi_{2023}(27,\cdot)$	2023.bi	272	yes	$1$	$1$	$e\left(\frac{13}{136}\right)$	$e\left(\frac{139}{272}\right)$	$e\left(\frac{13}{68}\right)$	$e\left(\frac{7}{272}\right)$	$e\left(\frac{165}{272}\right)$	$e\left(\frac{39}{136}\right)$	$e\left(\frac{3}{136}\right)$	$e\left(\frac{33}{272}\right)$	$e\left(\frac{69}{272}\right)$	$e\left(\frac{191}{272}\right)$
$\chi_{2023}(29,\cdot)$	2023.bj	272	no	$-1$	$1$	$e\left(\frac{43}{136}\right)$	$e\left(\frac{125}{272}\right)$	$e\left(\frac{43}{68}\right)$	$e\left(\frac{65}{272}\right)$	$e\left(\frac{211}{272}\right)$	$e\left(\frac{129}{136}\right)$	$e\left(\frac{125}{136}\right)$	$e\left(\frac{151}{272}\right)$	$e\left(\frac{155}{272}\right)$	$e\left(\frac{25}{272}\right)$
$\chi_{2023}(30,\cdot)$	2023.bg	204	yes	$1$	$1$	$e\left(\frac{5}{102}\right)$	$e\left(\frac{179}{204}\right)$	$e\left(\frac{5}{51}\right)$	$e\left(\frac{55}{204}\right)$	$e\left(\frac{63}{68}\right)$	$e\left(\frac{5}{34}\right)$	$e\left(\frac{77}{102}\right)$	$e\left(\frac{65}{204}\right)$	$e\left(\frac{173}{204}\right)$	$e\left(\frac{199}{204}\right)$
$\chi_{2023}(31,\cdot)$	2023.bn	816	yes	$1$	$1$	$e\left(\frac{253}{408}\right)$	$e\left(\frac{163}{816}\right)$	$e\left(\frac{49}{204}\right)$	$e\left(\frac{335}{816}\right)$	$e\left(\frac{223}{272}\right)$	$e\left(\frac{117}{136}\right)$	$e\left(\frac{163}{408}\right)$	$e\left(\frac{25}{816}\right)$	$e\left(\frac{349}{816}\right)$	$e\left(\frac{359}{816}\right)$
$\chi_{2023}(32,\cdot)$	2023.bl	408	yes	$1$	$1$	$e\left(\frac{191}{204}\right)$	$e\left(\frac{65}{408}\right)$	$e\left(\frac{89}{102}\right)$	$e\left(\frac{61}{408}\right)$	$e\left(\frac{13}{136}\right)$	$e\left(\frac{55}{68}\right)$	$e\left(\frac{65}{204}\right)$	$e\left(\frac{35}{408}\right)$	$e\left(\frac{407}{408}\right)$	$e\left(\frac{13}{408}\right)$
$\chi_{2023}(33,\cdot)$	2023.bd	102	yes	$-1$	$1$	$e\left(\frac{22}{51}\right)$	$e\left(\frac{47}{51}\right)$	$e\left(\frac{44}{51}\right)$	$e\left(\frac{19}{51}\right)$	$e\left(\frac{6}{17}\right)$	$e\left(\frac{5}{17}\right)$	$e\left(\frac{43}{51}\right)$	$e\left(\frac{41}{51}\right)$	$e\left(\frac{37}{102}\right)$	$e\left(\frac{40}{51}\right)$
$\chi_{2023}(36,\cdot)$	2023.bf	136	no	$1$	$1$	$e\left(\frac{57}{68}\right)$	$e\left(\frac{55}{136}\right)$	$e\left(\frac{23}{34}\right)$	$e\left(\frac{83}{136}\right)$	$e\left(\frac{33}{136}\right)$	$e\left(\frac{35}{68}\right)$	$e\left(\frac{55}{68}\right)$	$e\left(\frac{61}{136}\right)$	$e\left(\frac{41}{136}\right)$	$e\left(\frac{11}{136}\right)$
$\chi_{2023}(37,\cdot)$	2023.bm	816	yes	$-1$	$1$	$e\left(\frac{317}{408}\right)$	$e\left(\frac{659}{816}\right)$	$e\left(\frac{113}{204}\right)$	$e\left(\frac{223}{816}\right)$	$e\left(\frac{159}{272}\right)$	$e\left(\frac{45}{136}\right)$	$e\left(\frac{251}{408}\right)$	$e\left(\frac{41}{816}\right)$	$e\left(\frac{197}{816}\right)$	$e\left(\frac{295}{816}\right)$
$\chi_{2023}(38,\cdot)$	2023.m	12	no	$-1$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{7}{12}\right)$	$-i$	$-1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{7}{12}\right)$
$\chi_{2023}(39,\cdot)$	2023.bm	816	yes	$-1$	$1$	$e\left(\frac{385}{408}\right)$	$e\left(\frac{319}{816}\right)$	$e\left(\frac{181}{204}\right)$	$e\left(\frac{155}{816}\right)$	$e\left(\frac{91}{272}\right)$	$e\left(\frac{113}{136}\right)$	$e\left(\frac{319}{408}\right)$	$e\left(\frac{109}{816}\right)$	$e\left(\frac{265}{816}\right)$	$e\left(\frac{227}{816}\right)$

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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	$2023$
Structure	\(C_{2}\times C_{816}\)
Order	$1632$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(8\)	\(9\)	\(10\)	\(11\)	\(12\)
\(\chi_{2023}(1,\cdot)\)	2023.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{2023}(2,\cdot)\)	2023.bl	408	yes	\(1\)	\(1\)	\(e\left(\frac{79}{204}\right)\)	\(e\left(\frac{13}{408}\right)\)	\(e\left(\frac{79}{102}\right)\)	\(e\left(\frac{257}{408}\right)\)	\(e\left(\frac{57}{136}\right)\)	\(e\left(\frac{11}{68}\right)\)	\(e\left(\frac{13}{204}\right)\)	\(e\left(\frac{7}{408}\right)\)	\(e\left(\frac{163}{408}\right)\)	\(e\left(\frac{329}{408}\right)\)
\(\chi_{2023}(3,\cdot)\)	2023.bn	816	yes	\(1\)	\(1\)	\(e\left(\frac{13}{408}\right)\)	\(e\left(\frac{139}{816}\right)\)	\(e\left(\frac{13}{204}\right)\)	\(e\left(\frac{551}{816}\right)\)	\(e\left(\frac{55}{272}\right)\)	\(e\left(\frac{13}{136}\right)\)	\(e\left(\frac{139}{408}\right)\)	\(e\left(\frac{577}{816}\right)\)	\(e\left(\frac{613}{816}\right)\)	\(e\left(\frac{191}{816}\right)\)
\(\chi_{2023}(4,\cdot)\)	2023.bg	204	yes	\(1\)	\(1\)	\(e\left(\frac{79}{102}\right)\)	\(e\left(\frac{13}{204}\right)\)	\(e\left(\frac{28}{51}\right)\)	\(e\left(\frac{53}{204}\right)\)	\(e\left(\frac{57}{68}\right)\)	\(e\left(\frac{11}{34}\right)\)	\(e\left(\frac{13}{102}\right)\)	\(e\left(\frac{7}{204}\right)\)	\(e\left(\frac{163}{204}\right)\)	\(e\left(\frac{125}{204}\right)\)
\(\chi_{2023}(5,\cdot)\)	2023.bn	816	yes	\(1\)	\(1\)	\(e\left(\frac{257}{408}\right)\)	\(e\left(\frac{551}{816}\right)\)	\(e\left(\frac{53}{204}\right)\)	\(e\left(\frac{787}{816}\right)\)	\(e\left(\frac{83}{272}\right)\)	\(e\left(\frac{121}{136}\right)\)	\(e\left(\frac{143}{408}\right)\)	\(e\left(\frac{485}{816}\right)\)	\(e\left(\frac{569}{816}\right)\)	\(e\left(\frac{763}{816}\right)\)
\(\chi_{2023}(6,\cdot)\)	2023.bi	272	yes	\(1\)	\(1\)	\(e\left(\frac{57}{136}\right)\)	\(e\left(\frac{55}{272}\right)\)	\(e\left(\frac{57}{68}\right)\)	\(e\left(\frac{83}{272}\right)\)	\(e\left(\frac{169}{272}\right)\)	\(e\left(\frac{35}{136}\right)\)	\(e\left(\frac{55}{136}\right)\)	\(e\left(\frac{197}{272}\right)\)	\(e\left(\frac{41}{272}\right)\)	\(e\left(\frac{11}{272}\right)\)
\(\chi_{2023}(8,\cdot)\)	2023.bf	136	no	\(1\)	\(1\)	\(e\left(\frac{11}{68}\right)\)	\(e\left(\frac{13}{136}\right)\)	\(e\left(\frac{11}{34}\right)\)	\(e\left(\frac{121}{136}\right)\)	\(e\left(\frac{35}{136}\right)\)	\(e\left(\frac{33}{68}\right)\)	\(e\left(\frac{13}{68}\right)\)	\(e\left(\frac{7}{136}\right)\)	\(e\left(\frac{27}{136}\right)\)	\(e\left(\frac{57}{136}\right)\)
\(\chi_{2023}(9,\cdot)\)	2023.bl	408	yes	\(1\)	\(1\)	\(e\left(\frac{13}{204}\right)\)	\(e\left(\frac{139}{408}\right)\)	\(e\left(\frac{13}{102}\right)\)	\(e\left(\frac{143}{408}\right)\)	\(e\left(\frac{55}{136}\right)\)	\(e\left(\frac{13}{68}\right)\)	\(e\left(\frac{139}{204}\right)\)	\(e\left(\frac{169}{408}\right)\)	\(e\left(\frac{205}{408}\right)\)	\(e\left(\frac{191}{408}\right)\)
\(\chi_{2023}(10,\cdot)\)	2023.bn	816	yes	\(1\)	\(1\)	\(e\left(\frac{7}{408}\right)\)	\(e\left(\frac{577}{816}\right)\)	\(e\left(\frac{7}{204}\right)\)	\(e\left(\frac{485}{816}\right)\)	\(e\left(\frac{197}{272}\right)\)	\(e\left(\frac{7}{136}\right)\)	\(e\left(\frac{169}{408}\right)\)	\(e\left(\frac{499}{816}\right)\)	\(e\left(\frac{79}{816}\right)\)	\(e\left(\frac{605}{816}\right)\)
\(\chi_{2023}(11,\cdot)\)	2023.bm	816	yes	\(-1\)	\(1\)	\(e\left(\frac{163}{408}\right)\)	\(e\left(\frac{613}{816}\right)\)	\(e\left(\frac{163}{204}\right)\)	\(e\left(\frac{569}{816}\right)\)	\(e\left(\frac{41}{272}\right)\)	\(e\left(\frac{27}{136}\right)\)	\(e\left(\frac{205}{408}\right)\)	\(e\left(\frac{79}{816}\right)\)	\(e\left(\frac{499}{816}\right)\)	\(e\left(\frac{449}{816}\right)\)
\(\chi_{2023}(12,\cdot)\)	2023.bn	816	yes	\(1\)	\(1\)	\(e\left(\frac{329}{408}\right)\)	\(e\left(\frac{191}{816}\right)\)	\(e\left(\frac{125}{204}\right)\)	\(e\left(\frac{763}{816}\right)\)	\(e\left(\frac{11}{272}\right)\)	\(e\left(\frac{57}{136}\right)\)	\(e\left(\frac{191}{408}\right)\)	\(e\left(\frac{605}{816}\right)\)	\(e\left(\frac{449}{816}\right)\)	\(e\left(\frac{691}{816}\right)\)
\(\chi_{2023}(13,\cdot)\)	2023.ba	68	yes	\(-1\)	\(1\)	\(e\left(\frac{31}{34}\right)\)	\(e\left(\frac{15}{68}\right)\)	\(e\left(\frac{14}{17}\right)\)	\(e\left(\frac{35}{68}\right)\)	\(e\left(\frac{9}{68}\right)\)	\(e\left(\frac{25}{34}\right)\)	\(e\left(\frac{15}{34}\right)\)	\(e\left(\frac{29}{68}\right)\)	\(e\left(\frac{39}{68}\right)\)	\(e\left(\frac{3}{68}\right)\)
\(\chi_{2023}(15,\cdot)\)	2023.bf	136	no	\(1\)	\(1\)	\(e\left(\frac{45}{68}\right)\)	\(e\left(\frac{115}{136}\right)\)	\(e\left(\frac{11}{34}\right)\)	\(e\left(\frac{87}{136}\right)\)	\(e\left(\frac{69}{136}\right)\)	\(e\left(\frac{67}{68}\right)\)	\(e\left(\frac{47}{68}\right)\)	\(e\left(\frac{41}{136}\right)\)	\(e\left(\frac{61}{136}\right)\)	\(e\left(\frac{23}{136}\right)\)
\(\chi_{2023}(16,\cdot)\)	2023.bb	102	yes	\(1\)	\(1\)	\(e\left(\frac{28}{51}\right)\)	\(e\left(\frac{13}{102}\right)\)	\(e\left(\frac{5}{51}\right)\)	\(e\left(\frac{53}{102}\right)\)	\(e\left(\frac{23}{34}\right)\)	\(e\left(\frac{11}{17}\right)\)	\(e\left(\frac{13}{51}\right)\)	\(e\left(\frac{7}{102}\right)\)	\(e\left(\frac{61}{102}\right)\)	\(e\left(\frac{23}{102}\right)\)
\(\chi_{2023}(18,\cdot)\)	2023.y	51	yes	\(1\)	\(1\)	\(e\left(\frac{23}{51}\right)\)	\(e\left(\frac{19}{51}\right)\)	\(e\left(\frac{46}{51}\right)\)	\(e\left(\frac{50}{51}\right)\)	\(e\left(\frac{14}{17}\right)\)	\(e\left(\frac{6}{17}\right)\)	\(e\left(\frac{38}{51}\right)\)	\(e\left(\frac{22}{51}\right)\)	\(e\left(\frac{46}{51}\right)\)	\(e\left(\frac{14}{51}\right)\)
\(\chi_{2023}(19,\cdot)\)	2023.bk	408	yes	\(-1\)	\(1\)	\(e\left(\frac{91}{204}\right)\)	\(e\left(\frac{361}{408}\right)\)	\(e\left(\frac{91}{102}\right)\)	\(e\left(\frac{389}{408}\right)\)	\(e\left(\frac{45}{136}\right)\)	\(e\left(\frac{23}{68}\right)\)	\(e\left(\frac{157}{204}\right)\)	\(e\left(\frac{163}{408}\right)\)	\(e\left(\frac{211}{408}\right)\)	\(e\left(\frac{317}{408}\right)\)
\(\chi_{2023}(20,\cdot)\)	2023.bi	272	yes	\(1\)	\(1\)	\(e\left(\frac{55}{136}\right)\)	\(e\left(\frac{201}{272}\right)\)	\(e\left(\frac{55}{68}\right)\)	\(e\left(\frac{61}{272}\right)\)	\(e\left(\frac{39}{272}\right)\)	\(e\left(\frac{29}{136}\right)\)	\(e\left(\frac{65}{136}\right)\)	\(e\left(\frac{171}{272}\right)\)	\(e\left(\frac{135}{272}\right)\)	\(e\left(\frac{149}{272}\right)\)
\(\chi_{2023}(22,\cdot)\)	2023.bj	272	no	\(-1\)	\(1\)	\(e\left(\frac{107}{136}\right)\)	\(e\left(\frac{213}{272}\right)\)	\(e\left(\frac{39}{68}\right)\)	\(e\left(\frac{89}{272}\right)\)	\(e\left(\frac{155}{272}\right)\)	\(e\left(\frac{49}{136}\right)\)	\(e\left(\frac{77}{136}\right)\)	\(e\left(\frac{31}{272}\right)\)	\(e\left(\frac{3}{272}\right)\)	\(e\left(\frac{97}{272}\right)\)
\(\chi_{2023}(23,\cdot)\)	2023.bm	816	yes	\(-1\)	\(1\)	\(e\left(\frac{179}{408}\right)\)	\(e\left(\frac{125}{816}\right)\)	\(e\left(\frac{179}{204}\right)\)	\(e\left(\frac{337}{816}\right)\)	\(e\left(\frac{161}{272}\right)\)	\(e\left(\frac{43}{136}\right)\)	\(e\left(\frac{125}{408}\right)\)	\(e\left(\frac{695}{816}\right)\)	\(e\left(\frac{155}{816}\right)\)	\(e\left(\frac{25}{816}\right)\)
\(\chi_{2023}(24,\cdot)\)	2023.bn	816	yes	\(1\)	\(1\)	\(e\left(\frac{79}{408}\right)\)	\(e\left(\frac{217}{816}\right)\)	\(e\left(\frac{79}{204}\right)\)	\(e\left(\frac{461}{816}\right)\)	\(e\left(\frac{125}{272}\right)\)	\(e\left(\frac{79}{136}\right)\)	\(e\left(\frac{217}{408}\right)\)	\(e\left(\frac{619}{816}\right)\)	\(e\left(\frac{775}{816}\right)\)	\(e\left(\frac{533}{816}\right)\)
\(\chi_{2023}(25,\cdot)\)	2023.bl	408	yes	\(1\)	\(1\)	\(e\left(\frac{53}{204}\right)\)	\(e\left(\frac{143}{408}\right)\)	\(e\left(\frac{53}{102}\right)\)	\(e\left(\frac{379}{408}\right)\)	\(e\left(\frac{83}{136}\right)\)	\(e\left(\frac{53}{68}\right)\)	\(e\left(\frac{143}{204}\right)\)	\(e\left(\frac{77}{408}\right)\)	\(e\left(\frac{161}{408}\right)\)	\(e\left(\frac{355}{408}\right)\)
\(\chi_{2023}(26,\cdot)\)	2023.bk	408	yes	\(-1\)	\(1\)	\(e\left(\frac{61}{204}\right)\)	\(e\left(\frac{103}{408}\right)\)	\(e\left(\frac{61}{102}\right)\)	\(e\left(\frac{59}{408}\right)\)	\(e\left(\frac{75}{136}\right)\)	\(e\left(\frac{61}{68}\right)\)	\(e\left(\frac{103}{204}\right)\)	\(e\left(\frac{181}{408}\right)\)	\(e\left(\frac{397}{408}\right)\)	\(e\left(\frac{347}{408}\right)\)
\(\chi_{2023}(27,\cdot)\)	2023.bi	272	yes	\(1\)	\(1\)	\(e\left(\frac{13}{136}\right)\)	\(e\left(\frac{139}{272}\right)\)	\(e\left(\frac{13}{68}\right)\)	\(e\left(\frac{7}{272}\right)\)	\(e\left(\frac{165}{272}\right)\)	\(e\left(\frac{39}{136}\right)\)	\(e\left(\frac{3}{136}\right)\)	\(e\left(\frac{33}{272}\right)\)	\(e\left(\frac{69}{272}\right)\)	\(e\left(\frac{191}{272}\right)\)
\(\chi_{2023}(29,\cdot)\)	2023.bj	272	no	\(-1\)	\(1\)	\(e\left(\frac{43}{136}\right)\)	\(e\left(\frac{125}{272}\right)\)	\(e\left(\frac{43}{68}\right)\)	\(e\left(\frac{65}{272}\right)\)	\(e\left(\frac{211}{272}\right)\)	\(e\left(\frac{129}{136}\right)\)	\(e\left(\frac{125}{136}\right)\)	\(e\left(\frac{151}{272}\right)\)	\(e\left(\frac{155}{272}\right)\)	\(e\left(\frac{25}{272}\right)\)
\(\chi_{2023}(30,\cdot)\)	2023.bg	204	yes	\(1\)	\(1\)	\(e\left(\frac{5}{102}\right)\)	\(e\left(\frac{179}{204}\right)\)	\(e\left(\frac{5}{51}\right)\)	\(e\left(\frac{55}{204}\right)\)	\(e\left(\frac{63}{68}\right)\)	\(e\left(\frac{5}{34}\right)\)	\(e\left(\frac{77}{102}\right)\)	\(e\left(\frac{65}{204}\right)\)	\(e\left(\frac{173}{204}\right)\)	\(e\left(\frac{199}{204}\right)\)
\(\chi_{2023}(31,\cdot)\)	2023.bn	816	yes	\(1\)	\(1\)	\(e\left(\frac{253}{408}\right)\)	\(e\left(\frac{163}{816}\right)\)	\(e\left(\frac{49}{204}\right)\)	\(e\left(\frac{335}{816}\right)\)	\(e\left(\frac{223}{272}\right)\)	\(e\left(\frac{117}{136}\right)\)	\(e\left(\frac{163}{408}\right)\)	\(e\left(\frac{25}{816}\right)\)	\(e\left(\frac{349}{816}\right)\)	\(e\left(\frac{359}{816}\right)\)
\(\chi_{2023}(32,\cdot)\)	2023.bl	408	yes	\(1\)	\(1\)	\(e\left(\frac{191}{204}\right)\)	\(e\left(\frac{65}{408}\right)\)	\(e\left(\frac{89}{102}\right)\)	\(e\left(\frac{61}{408}\right)\)	\(e\left(\frac{13}{136}\right)\)	\(e\left(\frac{55}{68}\right)\)	\(e\left(\frac{65}{204}\right)\)	\(e\left(\frac{35}{408}\right)\)	\(e\left(\frac{407}{408}\right)\)	\(e\left(\frac{13}{408}\right)\)
\(\chi_{2023}(33,\cdot)\)	2023.bd	102	yes	\(-1\)	\(1\)	\(e\left(\frac{22}{51}\right)\)	\(e\left(\frac{47}{51}\right)\)	\(e\left(\frac{44}{51}\right)\)	\(e\left(\frac{19}{51}\right)\)	\(e\left(\frac{6}{17}\right)\)	\(e\left(\frac{5}{17}\right)\)	\(e\left(\frac{43}{51}\right)\)	\(e\left(\frac{41}{51}\right)\)	\(e\left(\frac{37}{102}\right)\)	\(e\left(\frac{40}{51}\right)\)
\(\chi_{2023}(36,\cdot)\)	2023.bf	136	no	\(1\)	\(1\)	\(e\left(\frac{57}{68}\right)\)	\(e\left(\frac{55}{136}\right)\)	\(e\left(\frac{23}{34}\right)\)	\(e\left(\frac{83}{136}\right)\)	\(e\left(\frac{33}{136}\right)\)	\(e\left(\frac{35}{68}\right)\)	\(e\left(\frac{55}{68}\right)\)	\(e\left(\frac{61}{136}\right)\)	\(e\left(\frac{41}{136}\right)\)	\(e\left(\frac{11}{136}\right)\)
\(\chi_{2023}(37,\cdot)\)	2023.bm	816	yes	\(-1\)	\(1\)	\(e\left(\frac{317}{408}\right)\)	\(e\left(\frac{659}{816}\right)\)	\(e\left(\frac{113}{204}\right)\)	\(e\left(\frac{223}{816}\right)\)	\(e\left(\frac{159}{272}\right)\)	\(e\left(\frac{45}{136}\right)\)	\(e\left(\frac{251}{408}\right)\)	\(e\left(\frac{41}{816}\right)\)	\(e\left(\frac{197}{816}\right)\)	\(e\left(\frac{295}{816}\right)\)
\(\chi_{2023}(38,\cdot)\)	2023.m	12	no	\(-1\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(-i\)	\(-1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{7}{12}\right)\)
\(\chi_{2023}(39,\cdot)\)	2023.bm	816	yes	\(-1\)	\(1\)	\(e\left(\frac{385}{408}\right)\)	\(e\left(\frac{319}{816}\right)\)	\(e\left(\frac{181}{204}\right)\)	\(e\left(\frac{155}{816}\right)\)	\(e\left(\frac{91}{272}\right)\)	\(e\left(\frac{113}{136}\right)\)	\(e\left(\frac{319}{408}\right)\)	\(e\left(\frac{109}{816}\right)\)	\(e\left(\frac{265}{816}\right)\)	\(e\left(\frac{227}{816}\right)\)

Introduction

L-functions

Modular forms

Varieties

Fields

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Groups

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Properties

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Character group

First 32 of 1632 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.