LMFDB - Group of Dirichlet characters of modulus 1489

Show commands: PariGP / SageMath

sage: H = DirichletGroup(1489)

pari: g = idealstar(,1489,2)

Character group

sage: G.order() pari: g.no
Order	=	1488
sage: H.invariants() pari: g.cyc
Structure	=	$C_{1488}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{1489}(14,\cdot)$

First 32 of 1488 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	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$11$
$\chi_{1489}(1,\cdot)$	1489.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{1489}(2,\cdot)$	1489.s	744	yes	$1$	$1$	$e\left(\frac{205}{372}\right)$	$e\left(\frac{13}{372}\right)$	$e\left(\frac{19}{186}\right)$	$e\left(\frac{133}{186}\right)$	$e\left(\frac{109}{186}\right)$	$e\left(\frac{67}{248}\right)$	$e\left(\frac{81}{124}\right)$	$e\left(\frac{13}{186}\right)$	$e\left(\frac{33}{124}\right)$	$e\left(\frac{35}{124}\right)$
$\chi_{1489}(3,\cdot)$	1489.s	744	yes	$1$	$1$	$e\left(\frac{13}{372}\right)$	$e\left(\frac{97}{372}\right)$	$e\left(\frac{13}{186}\right)$	$e\left(\frac{91}{186}\right)$	$e\left(\frac{55}{186}\right)$	$e\left(\frac{23}{248}\right)$	$e\left(\frac{13}{124}\right)$	$e\left(\frac{97}{186}\right)$	$e\left(\frac{65}{124}\right)$	$e\left(\frac{99}{124}\right)$
$\chi_{1489}(4,\cdot)$	1489.q	372	yes	$1$	$1$	$e\left(\frac{19}{186}\right)$	$e\left(\frac{13}{186}\right)$	$e\left(\frac{19}{93}\right)$	$e\left(\frac{40}{93}\right)$	$e\left(\frac{16}{93}\right)$	$e\left(\frac{67}{124}\right)$	$e\left(\frac{19}{62}\right)$	$e\left(\frac{13}{93}\right)$	$e\left(\frac{33}{62}\right)$	$e\left(\frac{35}{62}\right)$
$\chi_{1489}(5,\cdot)$	1489.q	372	yes	$1$	$1$	$e\left(\frac{133}{186}\right)$	$e\left(\frac{91}{186}\right)$	$e\left(\frac{40}{93}\right)$	$e\left(\frac{1}{93}\right)$	$e\left(\frac{19}{93}\right)$	$e\left(\frac{97}{124}\right)$	$e\left(\frac{9}{62}\right)$	$e\left(\frac{91}{93}\right)$	$e\left(\frac{45}{62}\right)$	$e\left(\frac{59}{62}\right)$
$\chi_{1489}(6,\cdot)$	1489.q	372	yes	$1$	$1$	$e\left(\frac{109}{186}\right)$	$e\left(\frac{55}{186}\right)$	$e\left(\frac{16}{93}\right)$	$e\left(\frac{19}{93}\right)$	$e\left(\frac{82}{93}\right)$	$e\left(\frac{45}{124}\right)$	$e\left(\frac{47}{62}\right)$	$e\left(\frac{55}{93}\right)$	$e\left(\frac{49}{62}\right)$	$e\left(\frac{5}{62}\right)$
$\chi_{1489}(7,\cdot)$	1489.r	496	yes	$-1$	$1$	$e\left(\frac{67}{248}\right)$	$e\left(\frac{23}{248}\right)$	$e\left(\frac{67}{124}\right)$	$e\left(\frac{97}{124}\right)$	$e\left(\frac{45}{124}\right)$	$e\left(\frac{451}{496}\right)$	$e\left(\frac{201}{248}\right)$	$e\left(\frac{23}{124}\right)$	$e\left(\frac{13}{248}\right)$	$e\left(\frac{243}{248}\right)$
$\chi_{1489}(8,\cdot)$	1489.p	248	yes	$1$	$1$	$e\left(\frac{81}{124}\right)$	$e\left(\frac{13}{124}\right)$	$e\left(\frac{19}{62}\right)$	$e\left(\frac{9}{62}\right)$	$e\left(\frac{47}{62}\right)$	$e\left(\frac{201}{248}\right)$	$e\left(\frac{119}{124}\right)$	$e\left(\frac{13}{62}\right)$	$e\left(\frac{99}{124}\right)$	$e\left(\frac{105}{124}\right)$
$\chi_{1489}(9,\cdot)$	1489.q	372	yes	$1$	$1$	$e\left(\frac{13}{186}\right)$	$e\left(\frac{97}{186}\right)$	$e\left(\frac{13}{93}\right)$	$e\left(\frac{91}{93}\right)$	$e\left(\frac{55}{93}\right)$	$e\left(\frac{23}{124}\right)$	$e\left(\frac{13}{62}\right)$	$e\left(\frac{4}{93}\right)$	$e\left(\frac{3}{62}\right)$	$e\left(\frac{37}{62}\right)$
$\chi_{1489}(10,\cdot)$	1489.p	248	yes	$1$	$1$	$e\left(\frac{33}{124}\right)$	$e\left(\frac{65}{124}\right)$	$e\left(\frac{33}{62}\right)$	$e\left(\frac{45}{62}\right)$	$e\left(\frac{49}{62}\right)$	$e\left(\frac{13}{248}\right)$	$e\left(\frac{99}{124}\right)$	$e\left(\frac{3}{62}\right)$	$e\left(\frac{123}{124}\right)$	$e\left(\frac{29}{124}\right)$
$\chi_{1489}(11,\cdot)$	1489.p	248	yes	$1$	$1$	$e\left(\frac{35}{124}\right)$	$e\left(\frac{99}{124}\right)$	$e\left(\frac{35}{62}\right)$	$e\left(\frac{59}{62}\right)$	$e\left(\frac{5}{62}\right)$	$e\left(\frac{243}{248}\right)$	$e\left(\frac{105}{124}\right)$	$e\left(\frac{37}{62}\right)$	$e\left(\frac{29}{124}\right)$	$e\left(\frac{27}{124}\right)$
$\chi_{1489}(12,\cdot)$	1489.p	248	yes	$1$	$1$	$e\left(\frac{17}{124}\right)$	$e\left(\frac{41}{124}\right)$	$e\left(\frac{17}{62}\right)$	$e\left(\frac{57}{62}\right)$	$e\left(\frac{29}{62}\right)$	$e\left(\frac{157}{248}\right)$	$e\left(\frac{51}{124}\right)$	$e\left(\frac{41}{62}\right)$	$e\left(\frac{7}{124}\right)$	$e\left(\frac{45}{124}\right)$
$\chi_{1489}(13,\cdot)$	1489.r	496	yes	$-1$	$1$	$e\left(\frac{209}{248}\right)$	$e\left(\frac{205}{248}\right)$	$e\left(\frac{85}{124}\right)$	$e\left(\frac{99}{124}\right)$	$e\left(\frac{83}{124}\right)$	$e\left(\frac{289}{496}\right)$	$e\left(\frac{131}{248}\right)$	$e\left(\frac{81}{124}\right)$	$e\left(\frac{159}{248}\right)$	$e\left(\frac{225}{248}\right)$
$\chi_{1489}(14,\cdot)$	1489.t	1488	yes	$-1$	$1$	$e\left(\frac{611}{744}\right)$	$e\left(\frac{95}{744}\right)$	$e\left(\frac{239}{372}\right)$	$e\left(\frac{185}{372}\right)$	$e\left(\frac{353}{372}\right)$	$e\left(\frac{89}{496}\right)$	$e\left(\frac{115}{248}\right)$	$e\left(\frac{95}{372}\right)$	$e\left(\frac{79}{248}\right)$	$e\left(\frac{65}{248}\right)$
$\chi_{1489}(15,\cdot)$	1489.f	8	yes	$1$	$1$	$-i$	$-i$	$-1$	$-1$	$-1$	$e\left(\frac{7}{8}\right)$	$i$	$-1$	$i$	$-i$
$\chi_{1489}(16,\cdot)$	1489.o	186	yes	$1$	$1$	$e\left(\frac{19}{93}\right)$	$e\left(\frac{13}{93}\right)$	$e\left(\frac{38}{93}\right)$	$e\left(\frac{80}{93}\right)$	$e\left(\frac{32}{93}\right)$	$e\left(\frac{5}{62}\right)$	$e\left(\frac{19}{31}\right)$	$e\left(\frac{26}{93}\right)$	$e\left(\frac{2}{31}\right)$	$e\left(\frac{4}{31}\right)$
$\chi_{1489}(17,\cdot)$	1489.r	496	yes	$-1$	$1$	$e\left(\frac{83}{248}\right)$	$e\left(\frac{47}{248}\right)$	$e\left(\frac{83}{124}\right)$	$e\left(\frac{85}{124}\right)$	$e\left(\frac{65}{124}\right)$	$e\left(\frac{59}{496}\right)$	$e\left(\frac{1}{248}\right)$	$e\left(\frac{47}{124}\right)$	$e\left(\frac{5}{248}\right)$	$e\left(\frac{227}{248}\right)$
$\chi_{1489}(18,\cdot)$	1489.p	248	yes	$1$	$1$	$e\left(\frac{77}{124}\right)$	$e\left(\frac{69}{124}\right)$	$e\left(\frac{15}{62}\right)$	$e\left(\frac{43}{62}\right)$	$e\left(\frac{11}{62}\right)$	$e\left(\frac{113}{248}\right)$	$e\left(\frac{107}{124}\right)$	$e\left(\frac{7}{62}\right)$	$e\left(\frac{39}{124}\right)$	$e\left(\frac{109}{124}\right)$
$\chi_{1489}(19,\cdot)$	1489.s	744	yes	$1$	$1$	$e\left(\frac{313}{372}\right)$	$e\left(\frac{361}{372}\right)$	$e\left(\frac{127}{186}\right)$	$e\left(\frac{145}{186}\right)$	$e\left(\frac{151}{186}\right)$	$e\left(\frac{115}{248}\right)$	$e\left(\frac{65}{124}\right)$	$e\left(\frac{175}{186}\right)$	$e\left(\frac{77}{124}\right)$	$e\left(\frac{123}{124}\right)$
$\chi_{1489}(20,\cdot)$	1489.m	93	yes	$1$	$1$	$e\left(\frac{76}{93}\right)$	$e\left(\frac{52}{93}\right)$	$e\left(\frac{59}{93}\right)$	$e\left(\frac{41}{93}\right)$	$e\left(\frac{35}{93}\right)$	$e\left(\frac{10}{31}\right)$	$e\left(\frac{14}{31}\right)$	$e\left(\frac{11}{93}\right)$	$e\left(\frac{8}{31}\right)$	$e\left(\frac{16}{31}\right)$
$\chi_{1489}(21,\cdot)$	1489.t	1488	yes	$-1$	$1$	$e\left(\frac{227}{744}\right)$	$e\left(\frac{263}{744}\right)$	$e\left(\frac{227}{372}\right)$	$e\left(\frac{101}{372}\right)$	$e\left(\frac{245}{372}\right)$	$e\left(\frac{1}{496}\right)$	$e\left(\frac{227}{248}\right)$	$e\left(\frac{263}{372}\right)$	$e\left(\frac{143}{248}\right)$	$e\left(\frac{193}{248}\right)$
$\chi_{1489}(22,\cdot)$	1489.g	12	yes	$1$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$	$i$	$-1$	$e\left(\frac{2}{3}\right)$	$-1$	$-1$
$\chi_{1489}(23,\cdot)$	1489.r	496	yes	$-1$	$1$	$e\left(\frac{7}{248}\right)$	$e\left(\frac{243}{248}\right)$	$e\left(\frac{7}{124}\right)$	$e\left(\frac{49}{124}\right)$	$e\left(\frac{1}{124}\right)$	$e\left(\frac{495}{496}\right)$	$e\left(\frac{21}{248}\right)$	$e\left(\frac{119}{124}\right)$	$e\left(\frac{105}{248}\right)$	$e\left(\frac{55}{248}\right)$
$\chi_{1489}(24,\cdot)$	1489.m	93	yes	$1$	$1$	$e\left(\frac{64}{93}\right)$	$e\left(\frac{34}{93}\right)$	$e\left(\frac{35}{93}\right)$	$e\left(\frac{59}{93}\right)$	$e\left(\frac{5}{93}\right)$	$e\left(\frac{28}{31}\right)$	$e\left(\frac{2}{31}\right)$	$e\left(\frac{68}{93}\right)$	$e\left(\frac{10}{31}\right)$	$e\left(\frac{20}{31}\right)$
$\chi_{1489}(25,\cdot)$	1489.o	186	yes	$1$	$1$	$e\left(\frac{40}{93}\right)$	$e\left(\frac{91}{93}\right)$	$e\left(\frac{80}{93}\right)$	$e\left(\frac{2}{93}\right)$	$e\left(\frac{38}{93}\right)$	$e\left(\frac{35}{62}\right)$	$e\left(\frac{9}{31}\right)$	$e\left(\frac{89}{93}\right)$	$e\left(\frac{14}{31}\right)$	$e\left(\frac{28}{31}\right)$
$\chi_{1489}(26,\cdot)$	1489.t	1488	yes	$-1$	$1$	$e\left(\frac{293}{744}\right)$	$e\left(\frac{641}{744}\right)$	$e\left(\frac{293}{372}\right)$	$e\left(\frac{191}{372}\right)$	$e\left(\frac{95}{372}\right)$	$e\left(\frac{423}{496}\right)$	$e\left(\frac{45}{248}\right)$	$e\left(\frac{269}{372}\right)$	$e\left(\frac{225}{248}\right)$	$e\left(\frac{47}{248}\right)$
$\chi_{1489}(27,\cdot)$	1489.p	248	yes	$1$	$1$	$e\left(\frac{13}{124}\right)$	$e\left(\frac{97}{124}\right)$	$e\left(\frac{13}{62}\right)$	$e\left(\frac{29}{62}\right)$	$e\left(\frac{55}{62}\right)$	$e\left(\frac{69}{248}\right)$	$e\left(\frac{39}{124}\right)$	$e\left(\frac{35}{62}\right)$	$e\left(\frac{71}{124}\right)$	$e\left(\frac{49}{124}\right)$
$\chi_{1489}(28,\cdot)$	1489.t	1488	yes	$-1$	$1$	$e\left(\frac{277}{744}\right)$	$e\left(\frac{121}{744}\right)$	$e\left(\frac{277}{372}\right)$	$e\left(\frac{79}{372}\right)$	$e\left(\frac{199}{372}\right)$	$e\left(\frac{223}{496}\right)$	$e\left(\frac{29}{248}\right)$	$e\left(\frac{121}{372}\right)$	$e\left(\frac{145}{248}\right)$	$e\left(\frac{135}{248}\right)$
$\chi_{1489}(29,\cdot)$	1489.t	1488	yes	$-1$	$1$	$e\left(\frac{667}{744}\right)$	$e\left(\frac{55}{744}\right)$	$e\left(\frac{295}{372}\right)$	$e\left(\frac{205}{372}\right)$	$e\left(\frac{361}{372}\right)$	$e\left(\frac{169}{496}\right)$	$e\left(\frac{171}{248}\right)$	$e\left(\frac{55}{372}\right)$	$e\left(\frac{111}{248}\right)$	$e\left(\frac{129}{248}\right)$
$\chi_{1489}(30,\cdot)$	1489.o	186	yes	$1$	$1$	$e\left(\frac{28}{93}\right)$	$e\left(\frac{73}{93}\right)$	$e\left(\frac{56}{93}\right)$	$e\left(\frac{20}{93}\right)$	$e\left(\frac{8}{93}\right)$	$e\left(\frac{9}{62}\right)$	$e\left(\frac{28}{31}\right)$	$e\left(\frac{53}{93}\right)$	$e\left(\frac{16}{31}\right)$	$e\left(\frac{1}{31}\right)$
$\chi_{1489}(31,\cdot)$	1489.s	744	yes	$1$	$1$	$e\left(\frac{283}{372}\right)$	$e\left(\frac{223}{372}\right)$	$e\left(\frac{97}{186}\right)$	$e\left(\frac{121}{186}\right)$	$e\left(\frac{67}{186}\right)$	$e\left(\frac{81}{248}\right)$	$e\left(\frac{35}{124}\right)$	$e\left(\frac{37}{186}\right)$	$e\left(\frac{51}{124}\right)$	$e\left(\frac{9}{124}\right)$
$\chi_{1489}(32,\cdot)$	1489.s	744	yes	$1$	$1$	$e\left(\frac{281}{372}\right)$	$e\left(\frac{65}{372}\right)$	$e\left(\frac{95}{186}\right)$	$e\left(\frac{107}{186}\right)$	$e\left(\frac{173}{186}\right)$	$e\left(\frac{87}{248}\right)$	$e\left(\frac{33}{124}\right)$	$e\left(\frac{65}{186}\right)$	$e\left(\frac{41}{124}\right)$	$e\left(\frac{51}{124}\right)$

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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	$1489$
Structure	\(C_{1488}\)
Order	$1488$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(7\)	\(8\)	\(9\)	\(10\)	\(11\)
\(\chi_{1489}(1,\cdot)\)	1489.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{1489}(2,\cdot)\)	1489.s	744	yes	\(1\)	\(1\)	\(e\left(\frac{205}{372}\right)\)	\(e\left(\frac{13}{372}\right)\)	\(e\left(\frac{19}{186}\right)\)	\(e\left(\frac{133}{186}\right)\)	\(e\left(\frac{109}{186}\right)\)	\(e\left(\frac{67}{248}\right)\)	\(e\left(\frac{81}{124}\right)\)	\(e\left(\frac{13}{186}\right)\)	\(e\left(\frac{33}{124}\right)\)	\(e\left(\frac{35}{124}\right)\)
\(\chi_{1489}(3,\cdot)\)	1489.s	744	yes	\(1\)	\(1\)	\(e\left(\frac{13}{372}\right)\)	\(e\left(\frac{97}{372}\right)\)	\(e\left(\frac{13}{186}\right)\)	\(e\left(\frac{91}{186}\right)\)	\(e\left(\frac{55}{186}\right)\)	\(e\left(\frac{23}{248}\right)\)	\(e\left(\frac{13}{124}\right)\)	\(e\left(\frac{97}{186}\right)\)	\(e\left(\frac{65}{124}\right)\)	\(e\left(\frac{99}{124}\right)\)
\(\chi_{1489}(4,\cdot)\)	1489.q	372	yes	\(1\)	\(1\)	\(e\left(\frac{19}{186}\right)\)	\(e\left(\frac{13}{186}\right)\)	\(e\left(\frac{19}{93}\right)\)	\(e\left(\frac{40}{93}\right)\)	\(e\left(\frac{16}{93}\right)\)	\(e\left(\frac{67}{124}\right)\)	\(e\left(\frac{19}{62}\right)\)	\(e\left(\frac{13}{93}\right)\)	\(e\left(\frac{33}{62}\right)\)	\(e\left(\frac{35}{62}\right)\)
\(\chi_{1489}(5,\cdot)\)	1489.q	372	yes	\(1\)	\(1\)	\(e\left(\frac{133}{186}\right)\)	\(e\left(\frac{91}{186}\right)\)	\(e\left(\frac{40}{93}\right)\)	\(e\left(\frac{1}{93}\right)\)	\(e\left(\frac{19}{93}\right)\)	\(e\left(\frac{97}{124}\right)\)	\(e\left(\frac{9}{62}\right)\)	\(e\left(\frac{91}{93}\right)\)	\(e\left(\frac{45}{62}\right)\)	\(e\left(\frac{59}{62}\right)\)
\(\chi_{1489}(6,\cdot)\)	1489.q	372	yes	\(1\)	\(1\)	\(e\left(\frac{109}{186}\right)\)	\(e\left(\frac{55}{186}\right)\)	\(e\left(\frac{16}{93}\right)\)	\(e\left(\frac{19}{93}\right)\)	\(e\left(\frac{82}{93}\right)\)	\(e\left(\frac{45}{124}\right)\)	\(e\left(\frac{47}{62}\right)\)	\(e\left(\frac{55}{93}\right)\)	\(e\left(\frac{49}{62}\right)\)	\(e\left(\frac{5}{62}\right)\)
\(\chi_{1489}(7,\cdot)\)	1489.r	496	yes	\(-1\)	\(1\)	\(e\left(\frac{67}{248}\right)\)	\(e\left(\frac{23}{248}\right)\)	\(e\left(\frac{67}{124}\right)\)	\(e\left(\frac{97}{124}\right)\)	\(e\left(\frac{45}{124}\right)\)	\(e\left(\frac{451}{496}\right)\)	\(e\left(\frac{201}{248}\right)\)	\(e\left(\frac{23}{124}\right)\)	\(e\left(\frac{13}{248}\right)\)	\(e\left(\frac{243}{248}\right)\)
\(\chi_{1489}(8,\cdot)\)	1489.p	248	yes	\(1\)	\(1\)	\(e\left(\frac{81}{124}\right)\)	\(e\left(\frac{13}{124}\right)\)	\(e\left(\frac{19}{62}\right)\)	\(e\left(\frac{9}{62}\right)\)	\(e\left(\frac{47}{62}\right)\)	\(e\left(\frac{201}{248}\right)\)	\(e\left(\frac{119}{124}\right)\)	\(e\left(\frac{13}{62}\right)\)	\(e\left(\frac{99}{124}\right)\)	\(e\left(\frac{105}{124}\right)\)
\(\chi_{1489}(9,\cdot)\)	1489.q	372	yes	\(1\)	\(1\)	\(e\left(\frac{13}{186}\right)\)	\(e\left(\frac{97}{186}\right)\)	\(e\left(\frac{13}{93}\right)\)	\(e\left(\frac{91}{93}\right)\)	\(e\left(\frac{55}{93}\right)\)	\(e\left(\frac{23}{124}\right)\)	\(e\left(\frac{13}{62}\right)\)	\(e\left(\frac{4}{93}\right)\)	\(e\left(\frac{3}{62}\right)\)	\(e\left(\frac{37}{62}\right)\)
\(\chi_{1489}(10,\cdot)\)	1489.p	248	yes	\(1\)	\(1\)	\(e\left(\frac{33}{124}\right)\)	\(e\left(\frac{65}{124}\right)\)	\(e\left(\frac{33}{62}\right)\)	\(e\left(\frac{45}{62}\right)\)	\(e\left(\frac{49}{62}\right)\)	\(e\left(\frac{13}{248}\right)\)	\(e\left(\frac{99}{124}\right)\)	\(e\left(\frac{3}{62}\right)\)	\(e\left(\frac{123}{124}\right)\)	\(e\left(\frac{29}{124}\right)\)
\(\chi_{1489}(11,\cdot)\)	1489.p	248	yes	\(1\)	\(1\)	\(e\left(\frac{35}{124}\right)\)	\(e\left(\frac{99}{124}\right)\)	\(e\left(\frac{35}{62}\right)\)	\(e\left(\frac{59}{62}\right)\)	\(e\left(\frac{5}{62}\right)\)	\(e\left(\frac{243}{248}\right)\)	\(e\left(\frac{105}{124}\right)\)	\(e\left(\frac{37}{62}\right)\)	\(e\left(\frac{29}{124}\right)\)	\(e\left(\frac{27}{124}\right)\)
\(\chi_{1489}(12,\cdot)\)	1489.p	248	yes	\(1\)	\(1\)	\(e\left(\frac{17}{124}\right)\)	\(e\left(\frac{41}{124}\right)\)	\(e\left(\frac{17}{62}\right)\)	\(e\left(\frac{57}{62}\right)\)	\(e\left(\frac{29}{62}\right)\)	\(e\left(\frac{157}{248}\right)\)	\(e\left(\frac{51}{124}\right)\)	\(e\left(\frac{41}{62}\right)\)	\(e\left(\frac{7}{124}\right)\)	\(e\left(\frac{45}{124}\right)\)
\(\chi_{1489}(13,\cdot)\)	1489.r	496	yes	\(-1\)	\(1\)	\(e\left(\frac{209}{248}\right)\)	\(e\left(\frac{205}{248}\right)\)	\(e\left(\frac{85}{124}\right)\)	\(e\left(\frac{99}{124}\right)\)	\(e\left(\frac{83}{124}\right)\)	\(e\left(\frac{289}{496}\right)\)	\(e\left(\frac{131}{248}\right)\)	\(e\left(\frac{81}{124}\right)\)	\(e\left(\frac{159}{248}\right)\)	\(e\left(\frac{225}{248}\right)\)
\(\chi_{1489}(14,\cdot)\)	1489.t	1488	yes	\(-1\)	\(1\)	\(e\left(\frac{611}{744}\right)\)	\(e\left(\frac{95}{744}\right)\)	\(e\left(\frac{239}{372}\right)\)	\(e\left(\frac{185}{372}\right)\)	\(e\left(\frac{353}{372}\right)\)	\(e\left(\frac{89}{496}\right)\)	\(e\left(\frac{115}{248}\right)\)	\(e\left(\frac{95}{372}\right)\)	\(e\left(\frac{79}{248}\right)\)	\(e\left(\frac{65}{248}\right)\)
\(\chi_{1489}(15,\cdot)\)	1489.f	8	yes	\(1\)	\(1\)	\(-i\)	\(-i\)	\(-1\)	\(-1\)	\(-1\)	\(e\left(\frac{7}{8}\right)\)	\(i\)	\(-1\)	\(i\)	\(-i\)
\(\chi_{1489}(16,\cdot)\)	1489.o	186	yes	\(1\)	\(1\)	\(e\left(\frac{19}{93}\right)\)	\(e\left(\frac{13}{93}\right)\)	\(e\left(\frac{38}{93}\right)\)	\(e\left(\frac{80}{93}\right)\)	\(e\left(\frac{32}{93}\right)\)	\(e\left(\frac{5}{62}\right)\)	\(e\left(\frac{19}{31}\right)\)	\(e\left(\frac{26}{93}\right)\)	\(e\left(\frac{2}{31}\right)\)	\(e\left(\frac{4}{31}\right)\)
\(\chi_{1489}(17,\cdot)\)	1489.r	496	yes	\(-1\)	\(1\)	\(e\left(\frac{83}{248}\right)\)	\(e\left(\frac{47}{248}\right)\)	\(e\left(\frac{83}{124}\right)\)	\(e\left(\frac{85}{124}\right)\)	\(e\left(\frac{65}{124}\right)\)	\(e\left(\frac{59}{496}\right)\)	\(e\left(\frac{1}{248}\right)\)	\(e\left(\frac{47}{124}\right)\)	\(e\left(\frac{5}{248}\right)\)	\(e\left(\frac{227}{248}\right)\)
\(\chi_{1489}(18,\cdot)\)	1489.p	248	yes	\(1\)	\(1\)	\(e\left(\frac{77}{124}\right)\)	\(e\left(\frac{69}{124}\right)\)	\(e\left(\frac{15}{62}\right)\)	\(e\left(\frac{43}{62}\right)\)	\(e\left(\frac{11}{62}\right)\)	\(e\left(\frac{113}{248}\right)\)	\(e\left(\frac{107}{124}\right)\)	\(e\left(\frac{7}{62}\right)\)	\(e\left(\frac{39}{124}\right)\)	\(e\left(\frac{109}{124}\right)\)
\(\chi_{1489}(19,\cdot)\)	1489.s	744	yes	\(1\)	\(1\)	\(e\left(\frac{313}{372}\right)\)	\(e\left(\frac{361}{372}\right)\)	\(e\left(\frac{127}{186}\right)\)	\(e\left(\frac{145}{186}\right)\)	\(e\left(\frac{151}{186}\right)\)	\(e\left(\frac{115}{248}\right)\)	\(e\left(\frac{65}{124}\right)\)	\(e\left(\frac{175}{186}\right)\)	\(e\left(\frac{77}{124}\right)\)	\(e\left(\frac{123}{124}\right)\)
\(\chi_{1489}(20,\cdot)\)	1489.m	93	yes	\(1\)	\(1\)	\(e\left(\frac{76}{93}\right)\)	\(e\left(\frac{52}{93}\right)\)	\(e\left(\frac{59}{93}\right)\)	\(e\left(\frac{41}{93}\right)\)	\(e\left(\frac{35}{93}\right)\)	\(e\left(\frac{10}{31}\right)\)	\(e\left(\frac{14}{31}\right)\)	\(e\left(\frac{11}{93}\right)\)	\(e\left(\frac{8}{31}\right)\)	\(e\left(\frac{16}{31}\right)\)
\(\chi_{1489}(21,\cdot)\)	1489.t	1488	yes	\(-1\)	\(1\)	\(e\left(\frac{227}{744}\right)\)	\(e\left(\frac{263}{744}\right)\)	\(e\left(\frac{227}{372}\right)\)	\(e\left(\frac{101}{372}\right)\)	\(e\left(\frac{245}{372}\right)\)	\(e\left(\frac{1}{496}\right)\)	\(e\left(\frac{227}{248}\right)\)	\(e\left(\frac{263}{372}\right)\)	\(e\left(\frac{143}{248}\right)\)	\(e\left(\frac{193}{248}\right)\)
\(\chi_{1489}(22,\cdot)\)	1489.g	12	yes	\(1\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(i\)	\(-1\)	\(e\left(\frac{2}{3}\right)\)	\(-1\)	\(-1\)
\(\chi_{1489}(23,\cdot)\)	1489.r	496	yes	\(-1\)	\(1\)	\(e\left(\frac{7}{248}\right)\)	\(e\left(\frac{243}{248}\right)\)	\(e\left(\frac{7}{124}\right)\)	\(e\left(\frac{49}{124}\right)\)	\(e\left(\frac{1}{124}\right)\)	\(e\left(\frac{495}{496}\right)\)	\(e\left(\frac{21}{248}\right)\)	\(e\left(\frac{119}{124}\right)\)	\(e\left(\frac{105}{248}\right)\)	\(e\left(\frac{55}{248}\right)\)
\(\chi_{1489}(24,\cdot)\)	1489.m	93	yes	\(1\)	\(1\)	\(e\left(\frac{64}{93}\right)\)	\(e\left(\frac{34}{93}\right)\)	\(e\left(\frac{35}{93}\right)\)	\(e\left(\frac{59}{93}\right)\)	\(e\left(\frac{5}{93}\right)\)	\(e\left(\frac{28}{31}\right)\)	\(e\left(\frac{2}{31}\right)\)	\(e\left(\frac{68}{93}\right)\)	\(e\left(\frac{10}{31}\right)\)	\(e\left(\frac{20}{31}\right)\)
\(\chi_{1489}(25,\cdot)\)	1489.o	186	yes	\(1\)	\(1\)	\(e\left(\frac{40}{93}\right)\)	\(e\left(\frac{91}{93}\right)\)	\(e\left(\frac{80}{93}\right)\)	\(e\left(\frac{2}{93}\right)\)	\(e\left(\frac{38}{93}\right)\)	\(e\left(\frac{35}{62}\right)\)	\(e\left(\frac{9}{31}\right)\)	\(e\left(\frac{89}{93}\right)\)	\(e\left(\frac{14}{31}\right)\)	\(e\left(\frac{28}{31}\right)\)
\(\chi_{1489}(26,\cdot)\)	1489.t	1488	yes	\(-1\)	\(1\)	\(e\left(\frac{293}{744}\right)\)	\(e\left(\frac{641}{744}\right)\)	\(e\left(\frac{293}{372}\right)\)	\(e\left(\frac{191}{372}\right)\)	\(e\left(\frac{95}{372}\right)\)	\(e\left(\frac{423}{496}\right)\)	\(e\left(\frac{45}{248}\right)\)	\(e\left(\frac{269}{372}\right)\)	\(e\left(\frac{225}{248}\right)\)	\(e\left(\frac{47}{248}\right)\)
\(\chi_{1489}(27,\cdot)\)	1489.p	248	yes	\(1\)	\(1\)	\(e\left(\frac{13}{124}\right)\)	\(e\left(\frac{97}{124}\right)\)	\(e\left(\frac{13}{62}\right)\)	\(e\left(\frac{29}{62}\right)\)	\(e\left(\frac{55}{62}\right)\)	\(e\left(\frac{69}{248}\right)\)	\(e\left(\frac{39}{124}\right)\)	\(e\left(\frac{35}{62}\right)\)	\(e\left(\frac{71}{124}\right)\)	\(e\left(\frac{49}{124}\right)\)
\(\chi_{1489}(28,\cdot)\)	1489.t	1488	yes	\(-1\)	\(1\)	\(e\left(\frac{277}{744}\right)\)	\(e\left(\frac{121}{744}\right)\)	\(e\left(\frac{277}{372}\right)\)	\(e\left(\frac{79}{372}\right)\)	\(e\left(\frac{199}{372}\right)\)	\(e\left(\frac{223}{496}\right)\)	\(e\left(\frac{29}{248}\right)\)	\(e\left(\frac{121}{372}\right)\)	\(e\left(\frac{145}{248}\right)\)	\(e\left(\frac{135}{248}\right)\)
\(\chi_{1489}(29,\cdot)\)	1489.t	1488	yes	\(-1\)	\(1\)	\(e\left(\frac{667}{744}\right)\)	\(e\left(\frac{55}{744}\right)\)	\(e\left(\frac{295}{372}\right)\)	\(e\left(\frac{205}{372}\right)\)	\(e\left(\frac{361}{372}\right)\)	\(e\left(\frac{169}{496}\right)\)	\(e\left(\frac{171}{248}\right)\)	\(e\left(\frac{55}{372}\right)\)	\(e\left(\frac{111}{248}\right)\)	\(e\left(\frac{129}{248}\right)\)
\(\chi_{1489}(30,\cdot)\)	1489.o	186	yes	\(1\)	\(1\)	\(e\left(\frac{28}{93}\right)\)	\(e\left(\frac{73}{93}\right)\)	\(e\left(\frac{56}{93}\right)\)	\(e\left(\frac{20}{93}\right)\)	\(e\left(\frac{8}{93}\right)\)	\(e\left(\frac{9}{62}\right)\)	\(e\left(\frac{28}{31}\right)\)	\(e\left(\frac{53}{93}\right)\)	\(e\left(\frac{16}{31}\right)\)	\(e\left(\frac{1}{31}\right)\)
\(\chi_{1489}(31,\cdot)\)	1489.s	744	yes	\(1\)	\(1\)	\(e\left(\frac{283}{372}\right)\)	\(e\left(\frac{223}{372}\right)\)	\(e\left(\frac{97}{186}\right)\)	\(e\left(\frac{121}{186}\right)\)	\(e\left(\frac{67}{186}\right)\)	\(e\left(\frac{81}{248}\right)\)	\(e\left(\frac{35}{124}\right)\)	\(e\left(\frac{37}{186}\right)\)	\(e\left(\frac{51}{124}\right)\)	\(e\left(\frac{9}{124}\right)\)
\(\chi_{1489}(32,\cdot)\)	1489.s	744	yes	\(1\)	\(1\)	\(e\left(\frac{281}{372}\right)\)	\(e\left(\frac{65}{372}\right)\)	\(e\left(\frac{95}{186}\right)\)	\(e\left(\frac{107}{186}\right)\)	\(e\left(\frac{173}{186}\right)\)	\(e\left(\frac{87}{248}\right)\)	\(e\left(\frac{33}{124}\right)\)	\(e\left(\frac{65}{186}\right)\)	\(e\left(\frac{41}{124}\right)\)	\(e\left(\frac{51}{124}\right)\)

Introduction

L-functions

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Character group

First 32 of 1488 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.