LMFDB - Group of Dirichlet characters of modulus 1002

Show commands: PariGP / SageMath

sage: H = DirichletGroup(1002)

pari: g = idealstar(,1002,2)

Character group

sage: G.order() pari: g.no
Order	=	332
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{166}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{1002}(335,\cdot)$, $\chi_{1002}(673,\cdot)$

First 32 of 332 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	$-1$	$1$	$5$	$7$	$11$	$13$	$17$	$19$	$23$	$25$	$29$	$31$
$\chi_{1002}(1,\cdot)$	1002.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{1002}(5,\cdot)$	1002.f	166	no	$1$	$1$	$e\left(\frac{42}{83}\right)$	$e\left(\frac{59}{83}\right)$	$e\left(\frac{111}{166}\right)$	$e\left(\frac{103}{166}\right)$	$e\left(\frac{68}{83}\right)$	$e\left(\frac{29}{83}\right)$	$e\left(\frac{8}{83}\right)$	$e\left(\frac{1}{83}\right)$	$e\left(\frac{67}{166}\right)$	$e\left(\frac{45}{83}\right)$
$\chi_{1002}(7,\cdot)$	1002.e	83	no	$1$	$1$	$e\left(\frac{59}{83}\right)$	$e\left(\frac{73}{83}\right)$	$e\left(\frac{75}{83}\right)$	$e\left(\frac{18}{83}\right)$	$e\left(\frac{56}{83}\right)$	$e\left(\frac{19}{83}\right)$	$e\left(\frac{31}{83}\right)$	$e\left(\frac{35}{83}\right)$	$e\left(\frac{52}{83}\right)$	$e\left(\frac{81}{83}\right)$
$\chi_{1002}(11,\cdot)$	1002.h	166	no	$-1$	$1$	$e\left(\frac{111}{166}\right)$	$e\left(\frac{75}{83}\right)$	$e\left(\frac{37}{166}\right)$	$e\left(\frac{31}{83}\right)$	$e\left(\frac{73}{166}\right)$	$e\left(\frac{65}{83}\right)$	$e\left(\frac{33}{166}\right)$	$e\left(\frac{28}{83}\right)$	$e\left(\frac{133}{166}\right)$	$e\left(\frac{15}{83}\right)$
$\chi_{1002}(13,\cdot)$	1002.g	166	no	$-1$	$1$	$e\left(\frac{103}{166}\right)$	$e\left(\frac{18}{83}\right)$	$e\left(\frac{31}{83}\right)$	$e\left(\frac{151}{166}\right)$	$e\left(\frac{147}{166}\right)$	$e\left(\frac{82}{83}\right)$	$e\left(\frac{71}{166}\right)$	$e\left(\frac{20}{83}\right)$	$e\left(\frac{6}{83}\right)$	$e\left(\frac{70}{83}\right)$
$\chi_{1002}(17,\cdot)$	1002.f	166	no	$1$	$1$	$e\left(\frac{68}{83}\right)$	$e\left(\frac{56}{83}\right)$	$e\left(\frac{73}{166}\right)$	$e\left(\frac{147}{166}\right)$	$e\left(\frac{35}{83}\right)$	$e\left(\frac{43}{83}\right)$	$e\left(\frac{9}{83}\right)$	$e\left(\frac{53}{83}\right)$	$e\left(\frac{65}{166}\right)$	$e\left(\frac{61}{83}\right)$
$\chi_{1002}(19,\cdot)$	1002.e	83	no	$1$	$1$	$e\left(\frac{29}{83}\right)$	$e\left(\frac{19}{83}\right)$	$e\left(\frac{65}{83}\right)$	$e\left(\frac{82}{83}\right)$	$e\left(\frac{43}{83}\right)$	$e\left(\frac{22}{83}\right)$	$e\left(\frac{49}{83}\right)$	$e\left(\frac{58}{83}\right)$	$e\left(\frac{34}{83}\right)$	$e\left(\frac{37}{83}\right)$
$\chi_{1002}(23,\cdot)$	1002.f	166	no	$1$	$1$	$e\left(\frac{8}{83}\right)$	$e\left(\frac{31}{83}\right)$	$e\left(\frac{33}{166}\right)$	$e\left(\frac{71}{166}\right)$	$e\left(\frac{9}{83}\right)$	$e\left(\frac{49}{83}\right)$	$e\left(\frac{45}{83}\right)$	$e\left(\frac{16}{83}\right)$	$e\left(\frac{159}{166}\right)$	$e\left(\frac{56}{83}\right)$
$\chi_{1002}(25,\cdot)$	1002.e	83	no	$1$	$1$	$e\left(\frac{1}{83}\right)$	$e\left(\frac{35}{83}\right)$	$e\left(\frac{28}{83}\right)$	$e\left(\frac{20}{83}\right)$	$e\left(\frac{53}{83}\right)$	$e\left(\frac{58}{83}\right)$	$e\left(\frac{16}{83}\right)$	$e\left(\frac{2}{83}\right)$	$e\left(\frac{67}{83}\right)$	$e\left(\frac{7}{83}\right)$
$\chi_{1002}(29,\cdot)$	1002.h	166	no	$-1$	$1$	$e\left(\frac{67}{166}\right)$	$e\left(\frac{52}{83}\right)$	$e\left(\frac{133}{166}\right)$	$e\left(\frac{6}{83}\right)$	$e\left(\frac{65}{166}\right)$	$e\left(\frac{34}{83}\right)$	$e\left(\frac{159}{166}\right)$	$e\left(\frac{67}{83}\right)$	$e\left(\frac{7}{166}\right)$	$e\left(\frac{27}{83}\right)$
$\chi_{1002}(31,\cdot)$	1002.e	83	no	$1$	$1$	$e\left(\frac{45}{83}\right)$	$e\left(\frac{81}{83}\right)$	$e\left(\frac{15}{83}\right)$	$e\left(\frac{70}{83}\right)$	$e\left(\frac{61}{83}\right)$	$e\left(\frac{37}{83}\right)$	$e\left(\frac{56}{83}\right)$	$e\left(\frac{7}{83}\right)$	$e\left(\frac{27}{83}\right)$	$e\left(\frac{66}{83}\right)$
$\chi_{1002}(35,\cdot)$	1002.f	166	no	$1$	$1$	$e\left(\frac{18}{83}\right)$	$e\left(\frac{49}{83}\right)$	$e\left(\frac{95}{166}\right)$	$e\left(\frac{139}{166}\right)$	$e\left(\frac{41}{83}\right)$	$e\left(\frac{48}{83}\right)$	$e\left(\frac{39}{83}\right)$	$e\left(\frac{36}{83}\right)$	$e\left(\frac{5}{166}\right)$	$e\left(\frac{43}{83}\right)$
$\chi_{1002}(37,\cdot)$	1002.g	166	no	$-1$	$1$	$e\left(\frac{61}{166}\right)$	$e\left(\frac{30}{83}\right)$	$e\left(\frac{24}{83}\right)$	$e\left(\frac{141}{166}\right)$	$e\left(\frac{79}{166}\right)$	$e\left(\frac{26}{83}\right)$	$e\left(\frac{63}{166}\right)$	$e\left(\frac{61}{83}\right)$	$e\left(\frac{10}{83}\right)$	$e\left(\frac{6}{83}\right)$
$\chi_{1002}(41,\cdot)$	1002.f	166	no	$1$	$1$	$e\left(\frac{7}{83}\right)$	$e\left(\frac{79}{83}\right)$	$e\left(\frac{143}{166}\right)$	$e\left(\frac{31}{166}\right)$	$e\left(\frac{39}{83}\right)$	$e\left(\frac{74}{83}\right)$	$e\left(\frac{29}{83}\right)$	$e\left(\frac{14}{83}\right)$	$e\left(\frac{25}{166}\right)$	$e\left(\frac{49}{83}\right)$
$\chi_{1002}(43,\cdot)$	1002.g	166	no	$-1$	$1$	$e\left(\frac{87}{166}\right)$	$e\left(\frac{70}{83}\right)$	$e\left(\frac{56}{83}\right)$	$e\left(\frac{163}{166}\right)$	$e\left(\frac{129}{166}\right)$	$e\left(\frac{33}{83}\right)$	$e\left(\frac{147}{166}\right)$	$e\left(\frac{4}{83}\right)$	$e\left(\frac{51}{83}\right)$	$e\left(\frac{14}{83}\right)$
$\chi_{1002}(47,\cdot)$	1002.h	166	no	$-1$	$1$	$e\left(\frac{49}{166}\right)$	$e\left(\frac{69}{83}\right)$	$e\left(\frac{127}{166}\right)$	$e\left(\frac{75}{83}\right)$	$e\left(\frac{107}{166}\right)$	$e\left(\frac{10}{83}\right)$	$e\left(\frac{37}{166}\right)$	$e\left(\frac{49}{83}\right)$	$e\left(\frac{129}{166}\right)$	$e\left(\frac{47}{83}\right)$
$\chi_{1002}(49,\cdot)$	1002.e	83	no	$1$	$1$	$e\left(\frac{35}{83}\right)$	$e\left(\frac{63}{83}\right)$	$e\left(\frac{67}{83}\right)$	$e\left(\frac{36}{83}\right)$	$e\left(\frac{29}{83}\right)$	$e\left(\frac{38}{83}\right)$	$e\left(\frac{62}{83}\right)$	$e\left(\frac{70}{83}\right)$	$e\left(\frac{21}{83}\right)$	$e\left(\frac{79}{83}\right)$
$\chi_{1002}(53,\cdot)$	1002.f	166	no	$1$	$1$	$e\left(\frac{13}{83}\right)$	$e\left(\frac{40}{83}\right)$	$e\left(\frac{147}{166}\right)$	$e\left(\frac{105}{166}\right)$	$e\left(\frac{25}{83}\right)$	$e\left(\frac{7}{83}\right)$	$e\left(\frac{42}{83}\right)$	$e\left(\frac{26}{83}\right)$	$e\left(\frac{165}{166}\right)$	$e\left(\frac{8}{83}\right)$
$\chi_{1002}(55,\cdot)$	1002.g	166	no	$-1$	$1$	$e\left(\frac{29}{166}\right)$	$e\left(\frac{51}{83}\right)$	$e\left(\frac{74}{83}\right)$	$e\left(\frac{165}{166}\right)$	$e\left(\frac{43}{166}\right)$	$e\left(\frac{11}{83}\right)$	$e\left(\frac{49}{166}\right)$	$e\left(\frac{29}{83}\right)$	$e\left(\frac{17}{83}\right)$	$e\left(\frac{60}{83}\right)$
$\chi_{1002}(59,\cdot)$	1002.f	166	no	$1$	$1$	$e\left(\frac{15}{83}\right)$	$e\left(\frac{27}{83}\right)$	$e\left(\frac{93}{166}\right)$	$e\left(\frac{19}{166}\right)$	$e\left(\frac{48}{83}\right)$	$e\left(\frac{40}{83}\right)$	$e\left(\frac{74}{83}\right)$	$e\left(\frac{30}{83}\right)$	$e\left(\frac{101}{166}\right)$	$e\left(\frac{22}{83}\right)$
$\chi_{1002}(61,\cdot)$	1002.e	83	no	$1$	$1$	$e\left(\frac{33}{83}\right)$	$e\left(\frac{76}{83}\right)$	$e\left(\frac{11}{83}\right)$	$e\left(\frac{79}{83}\right)$	$e\left(\frac{6}{83}\right)$	$e\left(\frac{5}{83}\right)$	$e\left(\frac{30}{83}\right)$	$e\left(\frac{66}{83}\right)$	$e\left(\frac{53}{83}\right)$	$e\left(\frac{65}{83}\right)$
$\chi_{1002}(65,\cdot)$	1002.h	166	no	$-1$	$1$	$e\left(\frac{21}{166}\right)$	$e\left(\frac{77}{83}\right)$	$e\left(\frac{7}{166}\right)$	$e\left(\frac{44}{83}\right)$	$e\left(\frac{117}{166}\right)$	$e\left(\frac{28}{83}\right)$	$e\left(\frac{87}{166}\right)$	$e\left(\frac{21}{83}\right)$	$e\left(\frac{79}{166}\right)$	$e\left(\frac{32}{83}\right)$
$\chi_{1002}(67,\cdot)$	1002.g	166	no	$-1$	$1$	$e\left(\frac{165}{166}\right)$	$e\left(\frac{24}{83}\right)$	$e\left(\frac{69}{83}\right)$	$e\left(\frac{63}{166}\right)$	$e\left(\frac{113}{166}\right)$	$e\left(\frac{54}{83}\right)$	$e\left(\frac{67}{166}\right)$	$e\left(\frac{82}{83}\right)$	$e\left(\frac{8}{83}\right)$	$e\left(\frac{38}{83}\right)$
$\chi_{1002}(71,\cdot)$	1002.f	166	no	$1$	$1$	$e\left(\frac{64}{83}\right)$	$e\left(\frac{82}{83}\right)$	$e\left(\frac{15}{166}\right)$	$e\left(\frac{153}{166}\right)$	$e\left(\frac{72}{83}\right)$	$e\left(\frac{60}{83}\right)$	$e\left(\frac{28}{83}\right)$	$e\left(\frac{45}{83}\right)$	$e\left(\frac{27}{166}\right)$	$e\left(\frac{33}{83}\right)$
$\chi_{1002}(73,\cdot)$	1002.g	166	no	$-1$	$1$	$e\left(\frac{89}{166}\right)$	$e\left(\frac{22}{83}\right)$	$e\left(\frac{1}{83}\right)$	$e\left(\frac{37}{166}\right)$	$e\left(\frac{69}{166}\right)$	$e\left(\frac{8}{83}\right)$	$e\left(\frac{13}{166}\right)$	$e\left(\frac{6}{83}\right)$	$e\left(\frac{35}{83}\right)$	$e\left(\frac{21}{83}\right)$
$\chi_{1002}(77,\cdot)$	1002.h	166	no	$-1$	$1$	$e\left(\frac{63}{166}\right)$	$e\left(\frac{65}{83}\right)$	$e\left(\frac{21}{166}\right)$	$e\left(\frac{49}{83}\right)$	$e\left(\frac{19}{166}\right)$	$e\left(\frac{1}{83}\right)$	$e\left(\frac{95}{166}\right)$	$e\left(\frac{63}{83}\right)$	$e\left(\frac{71}{166}\right)$	$e\left(\frac{13}{83}\right)$
$\chi_{1002}(79,\cdot)$	1002.g	166	no	$-1$	$1$	$e\left(\frac{65}{166}\right)$	$e\left(\frac{17}{83}\right)$	$e\left(\frac{80}{83}\right)$	$e\left(\frac{55}{166}\right)$	$e\left(\frac{125}{166}\right)$	$e\left(\frac{59}{83}\right)$	$e\left(\frac{127}{166}\right)$	$e\left(\frac{65}{83}\right)$	$e\left(\frac{61}{83}\right)$	$e\left(\frac{20}{83}\right)$
$\chi_{1002}(83,\cdot)$	1002.f	166	no	$1$	$1$	$e\left(\frac{63}{83}\right)$	$e\left(\frac{47}{83}\right)$	$e\left(\frac{125}{166}\right)$	$e\left(\frac{113}{166}\right)$	$e\left(\frac{19}{83}\right)$	$e\left(\frac{2}{83}\right)$	$e\left(\frac{12}{83}\right)$	$e\left(\frac{43}{83}\right)$	$e\left(\frac{59}{166}\right)$	$e\left(\frac{26}{83}\right)$
$\chi_{1002}(85,\cdot)$	1002.e	83	no	$1$	$1$	$e\left(\frac{27}{83}\right)$	$e\left(\frac{32}{83}\right)$	$e\left(\frac{9}{83}\right)$	$e\left(\frac{42}{83}\right)$	$e\left(\frac{20}{83}\right)$	$e\left(\frac{72}{83}\right)$	$e\left(\frac{17}{83}\right)$	$e\left(\frac{54}{83}\right)$	$e\left(\frac{66}{83}\right)$	$e\left(\frac{23}{83}\right)$
$\chi_{1002}(89,\cdot)$	1002.h	166	no	$-1$	$1$	$e\left(\frac{71}{166}\right)$	$e\left(\frac{39}{83}\right)$	$e\left(\frac{79}{166}\right)$	$e\left(\frac{46}{83}\right)$	$e\left(\frac{111}{166}\right)$	$e\left(\frac{67}{83}\right)$	$e\left(\frac{57}{166}\right)$	$e\left(\frac{71}{83}\right)$	$e\left(\frac{109}{166}\right)$	$e\left(\frac{41}{83}\right)$
$\chi_{1002}(91,\cdot)$	1002.g	166	no	$-1$	$1$	$e\left(\frac{55}{166}\right)$	$e\left(\frac{8}{83}\right)$	$e\left(\frac{23}{83}\right)$	$e\left(\frac{21}{166}\right)$	$e\left(\frac{93}{166}\right)$	$e\left(\frac{18}{83}\right)$	$e\left(\frac{133}{166}\right)$	$e\left(\frac{55}{83}\right)$	$e\left(\frac{58}{83}\right)$	$e\left(\frac{68}{83}\right)$
$\chi_{1002}(95,\cdot)$	1002.f	166	no	$1$	$1$	$e\left(\frac{71}{83}\right)$	$e\left(\frac{78}{83}\right)$	$e\left(\frac{75}{166}\right)$	$e\left(\frac{101}{166}\right)$	$e\left(\frac{28}{83}\right)$	$e\left(\frac{51}{83}\right)$	$e\left(\frac{57}{83}\right)$	$e\left(\frac{59}{83}\right)$	$e\left(\frac{135}{166}\right)$	$e\left(\frac{82}{83}\right)$

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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	$1002$
Structure	\(C_{2}\times C_{166}\)
Order	$332$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(5\)	\(7\)	\(11\)	\(13\)	\(17\)	\(19\)	\(23\)	\(25\)	\(29\)	\(31\)
\(\chi_{1002}(1,\cdot)\)	1002.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{1002}(5,\cdot)\)	1002.f	166	no	\(1\)	\(1\)	\(e\left(\frac{42}{83}\right)\)	\(e\left(\frac{59}{83}\right)\)	\(e\left(\frac{111}{166}\right)\)	\(e\left(\frac{103}{166}\right)\)	\(e\left(\frac{68}{83}\right)\)	\(e\left(\frac{29}{83}\right)\)	\(e\left(\frac{8}{83}\right)\)	\(e\left(\frac{1}{83}\right)\)	\(e\left(\frac{67}{166}\right)\)	\(e\left(\frac{45}{83}\right)\)
\(\chi_{1002}(7,\cdot)\)	1002.e	83	no	\(1\)	\(1\)	\(e\left(\frac{59}{83}\right)\)	\(e\left(\frac{73}{83}\right)\)	\(e\left(\frac{75}{83}\right)\)	\(e\left(\frac{18}{83}\right)\)	\(e\left(\frac{56}{83}\right)\)	\(e\left(\frac{19}{83}\right)\)	\(e\left(\frac{31}{83}\right)\)	\(e\left(\frac{35}{83}\right)\)	\(e\left(\frac{52}{83}\right)\)	\(e\left(\frac{81}{83}\right)\)
\(\chi_{1002}(11,\cdot)\)	1002.h	166	no	\(-1\)	\(1\)	\(e\left(\frac{111}{166}\right)\)	\(e\left(\frac{75}{83}\right)\)	\(e\left(\frac{37}{166}\right)\)	\(e\left(\frac{31}{83}\right)\)	\(e\left(\frac{73}{166}\right)\)	\(e\left(\frac{65}{83}\right)\)	\(e\left(\frac{33}{166}\right)\)	\(e\left(\frac{28}{83}\right)\)	\(e\left(\frac{133}{166}\right)\)	\(e\left(\frac{15}{83}\right)\)
\(\chi_{1002}(13,\cdot)\)	1002.g	166	no	\(-1\)	\(1\)	\(e\left(\frac{103}{166}\right)\)	\(e\left(\frac{18}{83}\right)\)	\(e\left(\frac{31}{83}\right)\)	\(e\left(\frac{151}{166}\right)\)	\(e\left(\frac{147}{166}\right)\)	\(e\left(\frac{82}{83}\right)\)	\(e\left(\frac{71}{166}\right)\)	\(e\left(\frac{20}{83}\right)\)	\(e\left(\frac{6}{83}\right)\)	\(e\left(\frac{70}{83}\right)\)
\(\chi_{1002}(17,\cdot)\)	1002.f	166	no	\(1\)	\(1\)	\(e\left(\frac{68}{83}\right)\)	\(e\left(\frac{56}{83}\right)\)	\(e\left(\frac{73}{166}\right)\)	\(e\left(\frac{147}{166}\right)\)	\(e\left(\frac{35}{83}\right)\)	\(e\left(\frac{43}{83}\right)\)	\(e\left(\frac{9}{83}\right)\)	\(e\left(\frac{53}{83}\right)\)	\(e\left(\frac{65}{166}\right)\)	\(e\left(\frac{61}{83}\right)\)
\(\chi_{1002}(19,\cdot)\)	1002.e	83	no	\(1\)	\(1\)	\(e\left(\frac{29}{83}\right)\)	\(e\left(\frac{19}{83}\right)\)	\(e\left(\frac{65}{83}\right)\)	\(e\left(\frac{82}{83}\right)\)	\(e\left(\frac{43}{83}\right)\)	\(e\left(\frac{22}{83}\right)\)	\(e\left(\frac{49}{83}\right)\)	\(e\left(\frac{58}{83}\right)\)	\(e\left(\frac{34}{83}\right)\)	\(e\left(\frac{37}{83}\right)\)
\(\chi_{1002}(23,\cdot)\)	1002.f	166	no	\(1\)	\(1\)	\(e\left(\frac{8}{83}\right)\)	\(e\left(\frac{31}{83}\right)\)	\(e\left(\frac{33}{166}\right)\)	\(e\left(\frac{71}{166}\right)\)	\(e\left(\frac{9}{83}\right)\)	\(e\left(\frac{49}{83}\right)\)	\(e\left(\frac{45}{83}\right)\)	\(e\left(\frac{16}{83}\right)\)	\(e\left(\frac{159}{166}\right)\)	\(e\left(\frac{56}{83}\right)\)
\(\chi_{1002}(25,\cdot)\)	1002.e	83	no	\(1\)	\(1\)	\(e\left(\frac{1}{83}\right)\)	\(e\left(\frac{35}{83}\right)\)	\(e\left(\frac{28}{83}\right)\)	\(e\left(\frac{20}{83}\right)\)	\(e\left(\frac{53}{83}\right)\)	\(e\left(\frac{58}{83}\right)\)	\(e\left(\frac{16}{83}\right)\)	\(e\left(\frac{2}{83}\right)\)	\(e\left(\frac{67}{83}\right)\)	\(e\left(\frac{7}{83}\right)\)
\(\chi_{1002}(29,\cdot)\)	1002.h	166	no	\(-1\)	\(1\)	\(e\left(\frac{67}{166}\right)\)	\(e\left(\frac{52}{83}\right)\)	\(e\left(\frac{133}{166}\right)\)	\(e\left(\frac{6}{83}\right)\)	\(e\left(\frac{65}{166}\right)\)	\(e\left(\frac{34}{83}\right)\)	\(e\left(\frac{159}{166}\right)\)	\(e\left(\frac{67}{83}\right)\)	\(e\left(\frac{7}{166}\right)\)	\(e\left(\frac{27}{83}\right)\)
\(\chi_{1002}(31,\cdot)\)	1002.e	83	no	\(1\)	\(1\)	\(e\left(\frac{45}{83}\right)\)	\(e\left(\frac{81}{83}\right)\)	\(e\left(\frac{15}{83}\right)\)	\(e\left(\frac{70}{83}\right)\)	\(e\left(\frac{61}{83}\right)\)	\(e\left(\frac{37}{83}\right)\)	\(e\left(\frac{56}{83}\right)\)	\(e\left(\frac{7}{83}\right)\)	\(e\left(\frac{27}{83}\right)\)	\(e\left(\frac{66}{83}\right)\)
\(\chi_{1002}(35,\cdot)\)	1002.f	166	no	\(1\)	\(1\)	\(e\left(\frac{18}{83}\right)\)	\(e\left(\frac{49}{83}\right)\)	\(e\left(\frac{95}{166}\right)\)	\(e\left(\frac{139}{166}\right)\)	\(e\left(\frac{41}{83}\right)\)	\(e\left(\frac{48}{83}\right)\)	\(e\left(\frac{39}{83}\right)\)	\(e\left(\frac{36}{83}\right)\)	\(e\left(\frac{5}{166}\right)\)	\(e\left(\frac{43}{83}\right)\)
\(\chi_{1002}(37,\cdot)\)	1002.g	166	no	\(-1\)	\(1\)	\(e\left(\frac{61}{166}\right)\)	\(e\left(\frac{30}{83}\right)\)	\(e\left(\frac{24}{83}\right)\)	\(e\left(\frac{141}{166}\right)\)	\(e\left(\frac{79}{166}\right)\)	\(e\left(\frac{26}{83}\right)\)	\(e\left(\frac{63}{166}\right)\)	\(e\left(\frac{61}{83}\right)\)	\(e\left(\frac{10}{83}\right)\)	\(e\left(\frac{6}{83}\right)\)
\(\chi_{1002}(41,\cdot)\)	1002.f	166	no	\(1\)	\(1\)	\(e\left(\frac{7}{83}\right)\)	\(e\left(\frac{79}{83}\right)\)	\(e\left(\frac{143}{166}\right)\)	\(e\left(\frac{31}{166}\right)\)	\(e\left(\frac{39}{83}\right)\)	\(e\left(\frac{74}{83}\right)\)	\(e\left(\frac{29}{83}\right)\)	\(e\left(\frac{14}{83}\right)\)	\(e\left(\frac{25}{166}\right)\)	\(e\left(\frac{49}{83}\right)\)
\(\chi_{1002}(43,\cdot)\)	1002.g	166	no	\(-1\)	\(1\)	\(e\left(\frac{87}{166}\right)\)	\(e\left(\frac{70}{83}\right)\)	\(e\left(\frac{56}{83}\right)\)	\(e\left(\frac{163}{166}\right)\)	\(e\left(\frac{129}{166}\right)\)	\(e\left(\frac{33}{83}\right)\)	\(e\left(\frac{147}{166}\right)\)	\(e\left(\frac{4}{83}\right)\)	\(e\left(\frac{51}{83}\right)\)	\(e\left(\frac{14}{83}\right)\)
\(\chi_{1002}(47,\cdot)\)	1002.h	166	no	\(-1\)	\(1\)	\(e\left(\frac{49}{166}\right)\)	\(e\left(\frac{69}{83}\right)\)	\(e\left(\frac{127}{166}\right)\)	\(e\left(\frac{75}{83}\right)\)	\(e\left(\frac{107}{166}\right)\)	\(e\left(\frac{10}{83}\right)\)	\(e\left(\frac{37}{166}\right)\)	\(e\left(\frac{49}{83}\right)\)	\(e\left(\frac{129}{166}\right)\)	\(e\left(\frac{47}{83}\right)\)
\(\chi_{1002}(49,\cdot)\)	1002.e	83	no	\(1\)	\(1\)	\(e\left(\frac{35}{83}\right)\)	\(e\left(\frac{63}{83}\right)\)	\(e\left(\frac{67}{83}\right)\)	\(e\left(\frac{36}{83}\right)\)	\(e\left(\frac{29}{83}\right)\)	\(e\left(\frac{38}{83}\right)\)	\(e\left(\frac{62}{83}\right)\)	\(e\left(\frac{70}{83}\right)\)	\(e\left(\frac{21}{83}\right)\)	\(e\left(\frac{79}{83}\right)\)
\(\chi_{1002}(53,\cdot)\)	1002.f	166	no	\(1\)	\(1\)	\(e\left(\frac{13}{83}\right)\)	\(e\left(\frac{40}{83}\right)\)	\(e\left(\frac{147}{166}\right)\)	\(e\left(\frac{105}{166}\right)\)	\(e\left(\frac{25}{83}\right)\)	\(e\left(\frac{7}{83}\right)\)	\(e\left(\frac{42}{83}\right)\)	\(e\left(\frac{26}{83}\right)\)	\(e\left(\frac{165}{166}\right)\)	\(e\left(\frac{8}{83}\right)\)
\(\chi_{1002}(55,\cdot)\)	1002.g	166	no	\(-1\)	\(1\)	\(e\left(\frac{29}{166}\right)\)	\(e\left(\frac{51}{83}\right)\)	\(e\left(\frac{74}{83}\right)\)	\(e\left(\frac{165}{166}\right)\)	\(e\left(\frac{43}{166}\right)\)	\(e\left(\frac{11}{83}\right)\)	\(e\left(\frac{49}{166}\right)\)	\(e\left(\frac{29}{83}\right)\)	\(e\left(\frac{17}{83}\right)\)	\(e\left(\frac{60}{83}\right)\)
\(\chi_{1002}(59,\cdot)\)	1002.f	166	no	\(1\)	\(1\)	\(e\left(\frac{15}{83}\right)\)	\(e\left(\frac{27}{83}\right)\)	\(e\left(\frac{93}{166}\right)\)	\(e\left(\frac{19}{166}\right)\)	\(e\left(\frac{48}{83}\right)\)	\(e\left(\frac{40}{83}\right)\)	\(e\left(\frac{74}{83}\right)\)	\(e\left(\frac{30}{83}\right)\)	\(e\left(\frac{101}{166}\right)\)	\(e\left(\frac{22}{83}\right)\)
\(\chi_{1002}(61,\cdot)\)	1002.e	83	no	\(1\)	\(1\)	\(e\left(\frac{33}{83}\right)\)	\(e\left(\frac{76}{83}\right)\)	\(e\left(\frac{11}{83}\right)\)	\(e\left(\frac{79}{83}\right)\)	\(e\left(\frac{6}{83}\right)\)	\(e\left(\frac{5}{83}\right)\)	\(e\left(\frac{30}{83}\right)\)	\(e\left(\frac{66}{83}\right)\)	\(e\left(\frac{53}{83}\right)\)	\(e\left(\frac{65}{83}\right)\)
\(\chi_{1002}(65,\cdot)\)	1002.h	166	no	\(-1\)	\(1\)	\(e\left(\frac{21}{166}\right)\)	\(e\left(\frac{77}{83}\right)\)	\(e\left(\frac{7}{166}\right)\)	\(e\left(\frac{44}{83}\right)\)	\(e\left(\frac{117}{166}\right)\)	\(e\left(\frac{28}{83}\right)\)	\(e\left(\frac{87}{166}\right)\)	\(e\left(\frac{21}{83}\right)\)	\(e\left(\frac{79}{166}\right)\)	\(e\left(\frac{32}{83}\right)\)
\(\chi_{1002}(67,\cdot)\)	1002.g	166	no	\(-1\)	\(1\)	\(e\left(\frac{165}{166}\right)\)	\(e\left(\frac{24}{83}\right)\)	\(e\left(\frac{69}{83}\right)\)	\(e\left(\frac{63}{166}\right)\)	\(e\left(\frac{113}{166}\right)\)	\(e\left(\frac{54}{83}\right)\)	\(e\left(\frac{67}{166}\right)\)	\(e\left(\frac{82}{83}\right)\)	\(e\left(\frac{8}{83}\right)\)	\(e\left(\frac{38}{83}\right)\)
\(\chi_{1002}(71,\cdot)\)	1002.f	166	no	\(1\)	\(1\)	\(e\left(\frac{64}{83}\right)\)	\(e\left(\frac{82}{83}\right)\)	\(e\left(\frac{15}{166}\right)\)	\(e\left(\frac{153}{166}\right)\)	\(e\left(\frac{72}{83}\right)\)	\(e\left(\frac{60}{83}\right)\)	\(e\left(\frac{28}{83}\right)\)	\(e\left(\frac{45}{83}\right)\)	\(e\left(\frac{27}{166}\right)\)	\(e\left(\frac{33}{83}\right)\)
\(\chi_{1002}(73,\cdot)\)	1002.g	166	no	\(-1\)	\(1\)	\(e\left(\frac{89}{166}\right)\)	\(e\left(\frac{22}{83}\right)\)	\(e\left(\frac{1}{83}\right)\)	\(e\left(\frac{37}{166}\right)\)	\(e\left(\frac{69}{166}\right)\)	\(e\left(\frac{8}{83}\right)\)	\(e\left(\frac{13}{166}\right)\)	\(e\left(\frac{6}{83}\right)\)	\(e\left(\frac{35}{83}\right)\)	\(e\left(\frac{21}{83}\right)\)
\(\chi_{1002}(77,\cdot)\)	1002.h	166	no	\(-1\)	\(1\)	\(e\left(\frac{63}{166}\right)\)	\(e\left(\frac{65}{83}\right)\)	\(e\left(\frac{21}{166}\right)\)	\(e\left(\frac{49}{83}\right)\)	\(e\left(\frac{19}{166}\right)\)	\(e\left(\frac{1}{83}\right)\)	\(e\left(\frac{95}{166}\right)\)	\(e\left(\frac{63}{83}\right)\)	\(e\left(\frac{71}{166}\right)\)	\(e\left(\frac{13}{83}\right)\)
\(\chi_{1002}(79,\cdot)\)	1002.g	166	no	\(-1\)	\(1\)	\(e\left(\frac{65}{166}\right)\)	\(e\left(\frac{17}{83}\right)\)	\(e\left(\frac{80}{83}\right)\)	\(e\left(\frac{55}{166}\right)\)	\(e\left(\frac{125}{166}\right)\)	\(e\left(\frac{59}{83}\right)\)	\(e\left(\frac{127}{166}\right)\)	\(e\left(\frac{65}{83}\right)\)	\(e\left(\frac{61}{83}\right)\)	\(e\left(\frac{20}{83}\right)\)
\(\chi_{1002}(83,\cdot)\)	1002.f	166	no	\(1\)	\(1\)	\(e\left(\frac{63}{83}\right)\)	\(e\left(\frac{47}{83}\right)\)	\(e\left(\frac{125}{166}\right)\)	\(e\left(\frac{113}{166}\right)\)	\(e\left(\frac{19}{83}\right)\)	\(e\left(\frac{2}{83}\right)\)	\(e\left(\frac{12}{83}\right)\)	\(e\left(\frac{43}{83}\right)\)	\(e\left(\frac{59}{166}\right)\)	\(e\left(\frac{26}{83}\right)\)
\(\chi_{1002}(85,\cdot)\)	1002.e	83	no	\(1\)	\(1\)	\(e\left(\frac{27}{83}\right)\)	\(e\left(\frac{32}{83}\right)\)	\(e\left(\frac{9}{83}\right)\)	\(e\left(\frac{42}{83}\right)\)	\(e\left(\frac{20}{83}\right)\)	\(e\left(\frac{72}{83}\right)\)	\(e\left(\frac{17}{83}\right)\)	\(e\left(\frac{54}{83}\right)\)	\(e\left(\frac{66}{83}\right)\)	\(e\left(\frac{23}{83}\right)\)
\(\chi_{1002}(89,\cdot)\)	1002.h	166	no	\(-1\)	\(1\)	\(e\left(\frac{71}{166}\right)\)	\(e\left(\frac{39}{83}\right)\)	\(e\left(\frac{79}{166}\right)\)	\(e\left(\frac{46}{83}\right)\)	\(e\left(\frac{111}{166}\right)\)	\(e\left(\frac{67}{83}\right)\)	\(e\left(\frac{57}{166}\right)\)	\(e\left(\frac{71}{83}\right)\)	\(e\left(\frac{109}{166}\right)\)	\(e\left(\frac{41}{83}\right)\)
\(\chi_{1002}(91,\cdot)\)	1002.g	166	no	\(-1\)	\(1\)	\(e\left(\frac{55}{166}\right)\)	\(e\left(\frac{8}{83}\right)\)	\(e\left(\frac{23}{83}\right)\)	\(e\left(\frac{21}{166}\right)\)	\(e\left(\frac{93}{166}\right)\)	\(e\left(\frac{18}{83}\right)\)	\(e\left(\frac{133}{166}\right)\)	\(e\left(\frac{55}{83}\right)\)	\(e\left(\frac{58}{83}\right)\)	\(e\left(\frac{68}{83}\right)\)
\(\chi_{1002}(95,\cdot)\)	1002.f	166	no	\(1\)	\(1\)	\(e\left(\frac{71}{83}\right)\)	\(e\left(\frac{78}{83}\right)\)	\(e\left(\frac{75}{166}\right)\)	\(e\left(\frac{101}{166}\right)\)	\(e\left(\frac{28}{83}\right)\)	\(e\left(\frac{51}{83}\right)\)	\(e\left(\frac{57}{83}\right)\)	\(e\left(\frac{59}{83}\right)\)	\(e\left(\frac{135}{166}\right)\)	\(e\left(\frac{82}{83}\right)\)

Introduction

L-functions

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This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.