LMFDB - Group of Dirichlet characters of modulus 10008

Show commands: PariGP / SageMath

sage: H = DirichletGroup(10008)

pari: g = idealstar(,10008,2)

Character group

sage: G.order() pari: g.no
Order	=	3312
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{2}\times C_{6}\times C_{138}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{10008}(2503,\cdot)$, $\chi_{10008}(5005,\cdot)$, $\chi_{10008}(2225,\cdot)$, $\chi_{10008}(4033,\cdot)$

First 32 of 3312 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	$-1$	$1$	$5$	$7$	$11$	$13$	$17$	$19$	$23$	$25$	$29$	$31$
$\chi_{10008}(1,\cdot)$	10008.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{10008}(5,\cdot)$	10008.ea	138	yes	$-1$	$1$	$e\left(\frac{6}{23}\right)$	$e\left(\frac{34}{69}\right)$	$e\left(\frac{16}{23}\right)$	$e\left(\frac{7}{138}\right)$	$e\left(\frac{25}{138}\right)$	$e\left(\frac{71}{138}\right)$	$e\left(\frac{137}{138}\right)$	$e\left(\frac{12}{23}\right)$	$e\left(\frac{21}{23}\right)$	$e\left(\frac{13}{23}\right)$
$\chi_{10008}(7,\cdot)$	10008.ft	138	no	$-1$	$1$	$e\left(\frac{34}{69}\right)$	$e\left(\frac{13}{46}\right)$	$e\left(\frac{97}{138}\right)$	$e\left(\frac{12}{23}\right)$	$e\left(\frac{53}{69}\right)$	$e\left(\frac{83}{138}\right)$	$e\left(\frac{85}{138}\right)$	$e\left(\frac{68}{69}\right)$	$e\left(\frac{50}{69}\right)$	$e\left(\frac{17}{138}\right)$
$\chi_{10008}(11,\cdot)$	10008.dw	138	yes	$1$	$1$	$e\left(\frac{16}{23}\right)$	$e\left(\frac{97}{138}\right)$	$e\left(\frac{1}{46}\right)$	$e\left(\frac{11}{138}\right)$	$e\left(\frac{59}{138}\right)$	$e\left(\frac{41}{69}\right)$	$e\left(\frac{14}{69}\right)$	$e\left(\frac{9}{23}\right)$	$e\left(\frac{10}{23}\right)$	$e\left(\frac{31}{46}\right)$
$\chi_{10008}(13,\cdot)$	10008.eg	138	yes	$1$	$1$	$e\left(\frac{7}{138}\right)$	$e\left(\frac{12}{23}\right)$	$e\left(\frac{11}{138}\right)$	$e\left(\frac{39}{46}\right)$	$e\left(\frac{43}{69}\right)$	$e\left(\frac{109}{138}\right)$	$e\left(\frac{13}{69}\right)$	$e\left(\frac{7}{69}\right)$	$e\left(\frac{59}{138}\right)$	$e\left(\frac{44}{69}\right)$
$\chi_{10008}(17,\cdot)$	10008.ev	138	no	$1$	$1$	$e\left(\frac{25}{138}\right)$	$e\left(\frac{53}{69}\right)$	$e\left(\frac{59}{138}\right)$	$e\left(\frac{43}{69}\right)$	$e\left(\frac{32}{69}\right)$	$e\left(\frac{41}{138}\right)$	$e\left(\frac{10}{23}\right)$	$e\left(\frac{25}{69}\right)$	$e\left(\frac{53}{138}\right)$	$e\left(\frac{29}{69}\right)$
$\chi_{10008}(19,\cdot)$	10008.ei	138	no	$1$	$1$	$e\left(\frac{71}{138}\right)$	$e\left(\frac{83}{138}\right)$	$e\left(\frac{41}{69}\right)$	$e\left(\frac{109}{138}\right)$	$e\left(\frac{41}{138}\right)$	$e\left(\frac{133}{138}\right)$	$e\left(\frac{10}{23}\right)$	$e\left(\frac{2}{69}\right)$	$e\left(\frac{7}{138}\right)$	$e\left(\frac{35}{138}\right)$
$\chi_{10008}(23,\cdot)$	10008.el	138	no	$-1$	$1$	$e\left(\frac{137}{138}\right)$	$e\left(\frac{85}{138}\right)$	$e\left(\frac{14}{69}\right)$	$e\left(\frac{13}{69}\right)$	$e\left(\frac{10}{23}\right)$	$e\left(\frac{10}{23}\right)$	$e\left(\frac{131}{138}\right)$	$e\left(\frac{68}{69}\right)$	$e\left(\frac{31}{138}\right)$	$e\left(\frac{17}{138}\right)$
$\chi_{10008}(25,\cdot)$	10008.ds	69	no	$1$	$1$	$e\left(\frac{12}{23}\right)$	$e\left(\frac{68}{69}\right)$	$e\left(\frac{9}{23}\right)$	$e\left(\frac{7}{69}\right)$	$e\left(\frac{25}{69}\right)$	$e\left(\frac{2}{69}\right)$	$e\left(\frac{68}{69}\right)$	$e\left(\frac{1}{23}\right)$	$e\left(\frac{19}{23}\right)$	$e\left(\frac{3}{23}\right)$
$\chi_{10008}(29,\cdot)$	10008.ea	138	yes	$-1$	$1$	$e\left(\frac{21}{23}\right)$	$e\left(\frac{50}{69}\right)$	$e\left(\frac{10}{23}\right)$	$e\left(\frac{59}{138}\right)$	$e\left(\frac{53}{138}\right)$	$e\left(\frac{7}{138}\right)$	$e\left(\frac{31}{138}\right)$	$e\left(\frac{19}{23}\right)$	$e\left(\frac{16}{23}\right)$	$e\left(\frac{11}{23}\right)$
$\chi_{10008}(31,\cdot)$	10008.dz	138	no	$-1$	$1$	$e\left(\frac{13}{23}\right)$	$e\left(\frac{17}{138}\right)$	$e\left(\frac{31}{46}\right)$	$e\left(\frac{44}{69}\right)$	$e\left(\frac{29}{69}\right)$	$e\left(\frac{35}{138}\right)$	$e\left(\frac{17}{138}\right)$	$e\left(\frac{3}{23}\right)$	$e\left(\frac{11}{23}\right)$	$e\left(\frac{41}{46}\right)$
$\chi_{10008}(35,\cdot)$	10008.ff	138	no	$1$	$1$	$e\left(\frac{52}{69}\right)$	$e\left(\frac{107}{138}\right)$	$e\left(\frac{55}{138}\right)$	$e\left(\frac{79}{138}\right)$	$e\left(\frac{131}{138}\right)$	$e\left(\frac{8}{69}\right)$	$e\left(\frac{14}{23}\right)$	$e\left(\frac{35}{69}\right)$	$e\left(\frac{44}{69}\right)$	$e\left(\frac{95}{138}\right)$
$\chi_{10008}(37,\cdot)$	10008.er	138	no	$1$	$1$	$e\left(\frac{49}{138}\right)$	$e\left(\frac{68}{69}\right)$	$e\left(\frac{77}{138}\right)$	$e\left(\frac{83}{138}\right)$	$e\left(\frac{2}{69}\right)$	$e\left(\frac{119}{138}\right)$	$e\left(\frac{15}{23}\right)$	$e\left(\frac{49}{69}\right)$	$e\left(\frac{137}{138}\right)$	$e\left(\frac{32}{69}\right)$
$\chi_{10008}(41,\cdot)$	10008.gc	138	no	$-1$	$1$	$e\left(\frac{5}{46}\right)$	$e\left(\frac{64}{69}\right)$	$e\left(\frac{21}{46}\right)$	$e\left(\frac{35}{69}\right)$	$e\left(\frac{43}{138}\right)$	$e\left(\frac{10}{69}\right)$	$e\left(\frac{59}{138}\right)$	$e\left(\frac{5}{23}\right)$	$e\left(\frac{29}{46}\right)$	$e\left(\frac{15}{23}\right)$
$\chi_{10008}(43,\cdot)$	10008.bb	6	yes	$1$	$1$	$-1$	$e\left(\frac{5}{6}\right)$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{3}\right)$	$1$	$-1$	$-1$
$\chi_{10008}(47,\cdot)$	10008.ex	138	no	$1$	$1$	$e\left(\frac{125}{138}\right)$	$e\left(\frac{31}{46}\right)$	$e\left(\frac{44}{69}\right)$	$e\left(\frac{18}{23}\right)$	$e\left(\frac{67}{138}\right)$	$e\left(\frac{113}{138}\right)$	$e\left(\frac{35}{69}\right)$	$e\left(\frac{56}{69}\right)$	$e\left(\frac{127}{138}\right)$	$e\left(\frac{83}{138}\right)$
$\chi_{10008}(49,\cdot)$	10008.dt	69	no	$1$	$1$	$e\left(\frac{68}{69}\right)$	$e\left(\frac{13}{23}\right)$	$e\left(\frac{28}{69}\right)$	$e\left(\frac{1}{23}\right)$	$e\left(\frac{37}{69}\right)$	$e\left(\frac{14}{69}\right)$	$e\left(\frac{16}{69}\right)$	$e\left(\frac{67}{69}\right)$	$e\left(\frac{31}{69}\right)$	$e\left(\frac{17}{69}\right)$
$\chi_{10008}(53,\cdot)$	10008.fo	138	no	$1$	$1$	$e\left(\frac{20}{69}\right)$	$e\left(\frac{2}{69}\right)$	$e\left(\frac{61}{69}\right)$	$e\left(\frac{41}{138}\right)$	$e\left(\frac{65}{69}\right)$	$e\left(\frac{19}{69}\right)$	$e\left(\frac{16}{23}\right)$	$e\left(\frac{40}{69}\right)$	$e\left(\frac{1}{69}\right)$	$e\left(\frac{5}{69}\right)$
$\chi_{10008}(55,\cdot)$	10008.dg	46	no	$-1$	$1$	$e\left(\frac{22}{23}\right)$	$e\left(\frac{9}{46}\right)$	$e\left(\frac{33}{46}\right)$	$e\left(\frac{3}{23}\right)$	$e\left(\frac{14}{23}\right)$	$e\left(\frac{5}{46}\right)$	$e\left(\frac{9}{46}\right)$	$e\left(\frac{21}{23}\right)$	$e\left(\frac{8}{23}\right)$	$e\left(\frac{11}{46}\right)$
$\chi_{10008}(59,\cdot)$	10008.fe	138	yes	$-1$	$1$	$e\left(\frac{52}{69}\right)$	$e\left(\frac{61}{138}\right)$	$e\left(\frac{55}{138}\right)$	$e\left(\frac{125}{138}\right)$	$e\left(\frac{18}{23}\right)$	$e\left(\frac{13}{46}\right)$	$e\left(\frac{107}{138}\right)$	$e\left(\frac{35}{69}\right)$	$e\left(\frac{44}{69}\right)$	$e\left(\frac{95}{138}\right)$
$\chi_{10008}(61,\cdot)$	10008.ga	138	yes	$-1$	$1$	$e\left(\frac{41}{46}\right)$	$e\left(\frac{5}{69}\right)$	$e\left(\frac{25}{46}\right)$	$e\left(\frac{137}{138}\right)$	$e\left(\frac{95}{138}\right)$	$e\left(\frac{59}{69}\right)$	$e\left(\frac{79}{138}\right)$	$e\left(\frac{18}{23}\right)$	$e\left(\frac{17}{46}\right)$	$e\left(\frac{8}{23}\right)$
$\chi_{10008}(65,\cdot)$	10008.ew	138	no	$-1$	$1$	$e\left(\frac{43}{138}\right)$	$e\left(\frac{1}{69}\right)$	$e\left(\frac{107}{138}\right)$	$e\left(\frac{62}{69}\right)$	$e\left(\frac{37}{46}\right)$	$e\left(\frac{7}{23}\right)$	$e\left(\frac{25}{138}\right)$	$e\left(\frac{43}{69}\right)$	$e\left(\frac{47}{138}\right)$	$e\left(\frac{14}{69}\right)$
$\chi_{10008}(67,\cdot)$	10008.fa	138	yes	$-1$	$1$	$e\left(\frac{19}{138}\right)$	$e\left(\frac{29}{46}\right)$	$e\left(\frac{10}{69}\right)$	$e\left(\frac{27}{46}\right)$	$e\left(\frac{28}{69}\right)$	$e\left(\frac{5}{69}\right)$	$e\left(\frac{41}{138}\right)$	$e\left(\frac{19}{69}\right)$	$e\left(\frac{101}{138}\right)$	$e\left(\frac{91}{138}\right)$
$\chi_{10008}(71,\cdot)$	10008.em	138	no	$1$	$1$	$e\left(\frac{59}{138}\right)$	$e\left(\frac{137}{138}\right)$	$e\left(\frac{2}{69}\right)$	$e\left(\frac{38}{69}\right)$	$e\left(\frac{71}{138}\right)$	$e\left(\frac{25}{138}\right)$	$e\left(\frac{19}{23}\right)$	$e\left(\frac{59}{69}\right)$	$e\left(\frac{103}{138}\right)$	$e\left(\frac{101}{138}\right)$
$\chi_{10008}(73,\cdot)$	10008.fq	138	no	$-1$	$1$	$e\left(\frac{37}{69}\right)$	$e\left(\frac{52}{69}\right)$	$e\left(\frac{68}{69}\right)$	$e\left(\frac{50}{69}\right)$	$e\left(\frac{137}{138}\right)$	$e\left(\frac{91}{138}\right)$	$e\left(\frac{27}{46}\right)$	$e\left(\frac{5}{69}\right)$	$e\left(\frac{26}{69}\right)$	$e\left(\frac{61}{69}\right)$
$\chi_{10008}(77,\cdot)$	10008.fp	138	yes	$-1$	$1$	$e\left(\frac{13}{69}\right)$	$e\left(\frac{68}{69}\right)$	$e\left(\frac{50}{69}\right)$	$e\left(\frac{83}{138}\right)$	$e\left(\frac{9}{46}\right)$	$e\left(\frac{9}{46}\right)$	$e\left(\frac{113}{138}\right)$	$e\left(\frac{26}{69}\right)$	$e\left(\frac{11}{69}\right)$	$e\left(\frac{55}{69}\right)$
$\chi_{10008}(79,\cdot)$	10008.fi	138	no	$-1$	$1$	$e\left(\frac{50}{69}\right)$	$e\left(\frac{125}{138}\right)$	$e\left(\frac{29}{138}\right)$	$e\left(\frac{11}{69}\right)$	$e\left(\frac{12}{23}\right)$	$e\left(\frac{1}{46}\right)$	$e\left(\frac{79}{138}\right)$	$e\left(\frac{31}{69}\right)$	$e\left(\frac{37}{69}\right)$	$e\left(\frac{25}{138}\right)$
$\chi_{10008}(83,\cdot)$	10008.fu	138	yes	$1$	$1$	$e\left(\frac{25}{69}\right)$	$e\left(\frac{17}{46}\right)$	$e\left(\frac{49}{138}\right)$	$e\left(\frac{19}{46}\right)$	$e\left(\frac{13}{138}\right)$	$e\left(\frac{64}{69}\right)$	$e\left(\frac{14}{69}\right)$	$e\left(\frac{50}{69}\right)$	$e\left(\frac{53}{69}\right)$	$e\left(\frac{47}{138}\right)$
$\chi_{10008}(85,\cdot)$	10008.ef	138	yes	$-1$	$1$	$e\left(\frac{61}{138}\right)$	$e\left(\frac{6}{23}\right)$	$e\left(\frac{17}{138}\right)$	$e\left(\frac{31}{46}\right)$	$e\left(\frac{89}{138}\right)$	$e\left(\frac{56}{69}\right)$	$e\left(\frac{59}{138}\right)$	$e\left(\frac{61}{69}\right)$	$e\left(\frac{41}{138}\right)$	$e\left(\frac{68}{69}\right)$
$\chi_{10008}(89,\cdot)$	10008.eu	138	no	$-1$	$1$	$e\left(\frac{43}{138}\right)$	$e\left(\frac{47}{69}\right)$	$e\left(\frac{107}{138}\right)$	$e\left(\frac{16}{69}\right)$	$e\left(\frac{19}{138}\right)$	$e\left(\frac{67}{69}\right)$	$e\left(\frac{39}{46}\right)$	$e\left(\frac{43}{69}\right)$	$e\left(\frac{47}{138}\right)$	$e\left(\frac{14}{69}\right)$
$\chi_{10008}(91,\cdot)$	10008.dq	46	no	$-1$	$1$	$e\left(\frac{25}{46}\right)$	$e\left(\frac{37}{46}\right)$	$e\left(\frac{18}{23}\right)$	$e\left(\frac{17}{46}\right)$	$e\left(\frac{9}{23}\right)$	$e\left(\frac{9}{23}\right)$	$e\left(\frac{37}{46}\right)$	$e\left(\frac{2}{23}\right)$	$e\left(\frac{7}{46}\right)$	$e\left(\frac{35}{46}\right)$
$\chi_{10008}(95,\cdot)$	10008.el	138	no	$-1$	$1$	$e\left(\frac{107}{138}\right)$	$e\left(\frac{13}{138}\right)$	$e\left(\frac{20}{69}\right)$	$e\left(\frac{58}{69}\right)$	$e\left(\frac{11}{23}\right)$	$e\left(\frac{11}{23}\right)$	$e\left(\frac{59}{138}\right)$	$e\left(\frac{38}{69}\right)$	$e\left(\frac{133}{138}\right)$	$e\left(\frac{113}{138}\right)$

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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	$10008$
Structure	\(C_{2}\times C_{2}\times C_{6}\times C_{138}\)
Order	$3312$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(5\)	\(7\)	\(11\)	\(13\)	\(17\)	\(19\)	\(23\)	\(25\)	\(29\)	\(31\)
\(\chi_{10008}(1,\cdot)\)	10008.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{10008}(5,\cdot)\)	10008.ea	138	yes	\(-1\)	\(1\)	\(e\left(\frac{6}{23}\right)\)	\(e\left(\frac{34}{69}\right)\)	\(e\left(\frac{16}{23}\right)\)	\(e\left(\frac{7}{138}\right)\)	\(e\left(\frac{25}{138}\right)\)	\(e\left(\frac{71}{138}\right)\)	\(e\left(\frac{137}{138}\right)\)	\(e\left(\frac{12}{23}\right)\)	\(e\left(\frac{21}{23}\right)\)	\(e\left(\frac{13}{23}\right)\)
\(\chi_{10008}(7,\cdot)\)	10008.ft	138	no	\(-1\)	\(1\)	\(e\left(\frac{34}{69}\right)\)	\(e\left(\frac{13}{46}\right)\)	\(e\left(\frac{97}{138}\right)\)	\(e\left(\frac{12}{23}\right)\)	\(e\left(\frac{53}{69}\right)\)	\(e\left(\frac{83}{138}\right)\)	\(e\left(\frac{85}{138}\right)\)	\(e\left(\frac{68}{69}\right)\)	\(e\left(\frac{50}{69}\right)\)	\(e\left(\frac{17}{138}\right)\)
\(\chi_{10008}(11,\cdot)\)	10008.dw	138	yes	\(1\)	\(1\)	\(e\left(\frac{16}{23}\right)\)	\(e\left(\frac{97}{138}\right)\)	\(e\left(\frac{1}{46}\right)\)	\(e\left(\frac{11}{138}\right)\)	\(e\left(\frac{59}{138}\right)\)	\(e\left(\frac{41}{69}\right)\)	\(e\left(\frac{14}{69}\right)\)	\(e\left(\frac{9}{23}\right)\)	\(e\left(\frac{10}{23}\right)\)	\(e\left(\frac{31}{46}\right)\)
\(\chi_{10008}(13,\cdot)\)	10008.eg	138	yes	\(1\)	\(1\)	\(e\left(\frac{7}{138}\right)\)	\(e\left(\frac{12}{23}\right)\)	\(e\left(\frac{11}{138}\right)\)	\(e\left(\frac{39}{46}\right)\)	\(e\left(\frac{43}{69}\right)\)	\(e\left(\frac{109}{138}\right)\)	\(e\left(\frac{13}{69}\right)\)	\(e\left(\frac{7}{69}\right)\)	\(e\left(\frac{59}{138}\right)\)	\(e\left(\frac{44}{69}\right)\)
\(\chi_{10008}(17,\cdot)\)	10008.ev	138	no	\(1\)	\(1\)	\(e\left(\frac{25}{138}\right)\)	\(e\left(\frac{53}{69}\right)\)	\(e\left(\frac{59}{138}\right)\)	\(e\left(\frac{43}{69}\right)\)	\(e\left(\frac{32}{69}\right)\)	\(e\left(\frac{41}{138}\right)\)	\(e\left(\frac{10}{23}\right)\)	\(e\left(\frac{25}{69}\right)\)	\(e\left(\frac{53}{138}\right)\)	\(e\left(\frac{29}{69}\right)\)
\(\chi_{10008}(19,\cdot)\)	10008.ei	138	no	\(1\)	\(1\)	\(e\left(\frac{71}{138}\right)\)	\(e\left(\frac{83}{138}\right)\)	\(e\left(\frac{41}{69}\right)\)	\(e\left(\frac{109}{138}\right)\)	\(e\left(\frac{41}{138}\right)\)	\(e\left(\frac{133}{138}\right)\)	\(e\left(\frac{10}{23}\right)\)	\(e\left(\frac{2}{69}\right)\)	\(e\left(\frac{7}{138}\right)\)	\(e\left(\frac{35}{138}\right)\)
\(\chi_{10008}(23,\cdot)\)	10008.el	138	no	\(-1\)	\(1\)	\(e\left(\frac{137}{138}\right)\)	\(e\left(\frac{85}{138}\right)\)	\(e\left(\frac{14}{69}\right)\)	\(e\left(\frac{13}{69}\right)\)	\(e\left(\frac{10}{23}\right)\)	\(e\left(\frac{10}{23}\right)\)	\(e\left(\frac{131}{138}\right)\)	\(e\left(\frac{68}{69}\right)\)	\(e\left(\frac{31}{138}\right)\)	\(e\left(\frac{17}{138}\right)\)
\(\chi_{10008}(25,\cdot)\)	10008.ds	69	no	\(1\)	\(1\)	\(e\left(\frac{12}{23}\right)\)	\(e\left(\frac{68}{69}\right)\)	\(e\left(\frac{9}{23}\right)\)	\(e\left(\frac{7}{69}\right)\)	\(e\left(\frac{25}{69}\right)\)	\(e\left(\frac{2}{69}\right)\)	\(e\left(\frac{68}{69}\right)\)	\(e\left(\frac{1}{23}\right)\)	\(e\left(\frac{19}{23}\right)\)	\(e\left(\frac{3}{23}\right)\)
\(\chi_{10008}(29,\cdot)\)	10008.ea	138	yes	\(-1\)	\(1\)	\(e\left(\frac{21}{23}\right)\)	\(e\left(\frac{50}{69}\right)\)	\(e\left(\frac{10}{23}\right)\)	\(e\left(\frac{59}{138}\right)\)	\(e\left(\frac{53}{138}\right)\)	\(e\left(\frac{7}{138}\right)\)	\(e\left(\frac{31}{138}\right)\)	\(e\left(\frac{19}{23}\right)\)	\(e\left(\frac{16}{23}\right)\)	\(e\left(\frac{11}{23}\right)\)
\(\chi_{10008}(31,\cdot)\)	10008.dz	138	no	\(-1\)	\(1\)	\(e\left(\frac{13}{23}\right)\)	\(e\left(\frac{17}{138}\right)\)	\(e\left(\frac{31}{46}\right)\)	\(e\left(\frac{44}{69}\right)\)	\(e\left(\frac{29}{69}\right)\)	\(e\left(\frac{35}{138}\right)\)	\(e\left(\frac{17}{138}\right)\)	\(e\left(\frac{3}{23}\right)\)	\(e\left(\frac{11}{23}\right)\)	\(e\left(\frac{41}{46}\right)\)
\(\chi_{10008}(35,\cdot)\)	10008.ff	138	no	\(1\)	\(1\)	\(e\left(\frac{52}{69}\right)\)	\(e\left(\frac{107}{138}\right)\)	\(e\left(\frac{55}{138}\right)\)	\(e\left(\frac{79}{138}\right)\)	\(e\left(\frac{131}{138}\right)\)	\(e\left(\frac{8}{69}\right)\)	\(e\left(\frac{14}{23}\right)\)	\(e\left(\frac{35}{69}\right)\)	\(e\left(\frac{44}{69}\right)\)	\(e\left(\frac{95}{138}\right)\)
\(\chi_{10008}(37,\cdot)\)	10008.er	138	no	\(1\)	\(1\)	\(e\left(\frac{49}{138}\right)\)	\(e\left(\frac{68}{69}\right)\)	\(e\left(\frac{77}{138}\right)\)	\(e\left(\frac{83}{138}\right)\)	\(e\left(\frac{2}{69}\right)\)	\(e\left(\frac{119}{138}\right)\)	\(e\left(\frac{15}{23}\right)\)	\(e\left(\frac{49}{69}\right)\)	\(e\left(\frac{137}{138}\right)\)	\(e\left(\frac{32}{69}\right)\)
\(\chi_{10008}(41,\cdot)\)	10008.gc	138	no	\(-1\)	\(1\)	\(e\left(\frac{5}{46}\right)\)	\(e\left(\frac{64}{69}\right)\)	\(e\left(\frac{21}{46}\right)\)	\(e\left(\frac{35}{69}\right)\)	\(e\left(\frac{43}{138}\right)\)	\(e\left(\frac{10}{69}\right)\)	\(e\left(\frac{59}{138}\right)\)	\(e\left(\frac{5}{23}\right)\)	\(e\left(\frac{29}{46}\right)\)	\(e\left(\frac{15}{23}\right)\)
\(\chi_{10008}(43,\cdot)\)	10008.bb	6	yes	\(1\)	\(1\)	\(-1\)	\(e\left(\frac{5}{6}\right)\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(1\)	\(-1\)	\(-1\)
\(\chi_{10008}(47,\cdot)\)	10008.ex	138	no	\(1\)	\(1\)	\(e\left(\frac{125}{138}\right)\)	\(e\left(\frac{31}{46}\right)\)	\(e\left(\frac{44}{69}\right)\)	\(e\left(\frac{18}{23}\right)\)	\(e\left(\frac{67}{138}\right)\)	\(e\left(\frac{113}{138}\right)\)	\(e\left(\frac{35}{69}\right)\)	\(e\left(\frac{56}{69}\right)\)	\(e\left(\frac{127}{138}\right)\)	\(e\left(\frac{83}{138}\right)\)
\(\chi_{10008}(49,\cdot)\)	10008.dt	69	no	\(1\)	\(1\)	\(e\left(\frac{68}{69}\right)\)	\(e\left(\frac{13}{23}\right)\)	\(e\left(\frac{28}{69}\right)\)	\(e\left(\frac{1}{23}\right)\)	\(e\left(\frac{37}{69}\right)\)	\(e\left(\frac{14}{69}\right)\)	\(e\left(\frac{16}{69}\right)\)	\(e\left(\frac{67}{69}\right)\)	\(e\left(\frac{31}{69}\right)\)	\(e\left(\frac{17}{69}\right)\)
\(\chi_{10008}(53,\cdot)\)	10008.fo	138	no	\(1\)	\(1\)	\(e\left(\frac{20}{69}\right)\)	\(e\left(\frac{2}{69}\right)\)	\(e\left(\frac{61}{69}\right)\)	\(e\left(\frac{41}{138}\right)\)	\(e\left(\frac{65}{69}\right)\)	\(e\left(\frac{19}{69}\right)\)	\(e\left(\frac{16}{23}\right)\)	\(e\left(\frac{40}{69}\right)\)	\(e\left(\frac{1}{69}\right)\)	\(e\left(\frac{5}{69}\right)\)
\(\chi_{10008}(55,\cdot)\)	10008.dg	46	no	\(-1\)	\(1\)	\(e\left(\frac{22}{23}\right)\)	\(e\left(\frac{9}{46}\right)\)	\(e\left(\frac{33}{46}\right)\)	\(e\left(\frac{3}{23}\right)\)	\(e\left(\frac{14}{23}\right)\)	\(e\left(\frac{5}{46}\right)\)	\(e\left(\frac{9}{46}\right)\)	\(e\left(\frac{21}{23}\right)\)	\(e\left(\frac{8}{23}\right)\)	\(e\left(\frac{11}{46}\right)\)
\(\chi_{10008}(59,\cdot)\)	10008.fe	138	yes	\(-1\)	\(1\)	\(e\left(\frac{52}{69}\right)\)	\(e\left(\frac{61}{138}\right)\)	\(e\left(\frac{55}{138}\right)\)	\(e\left(\frac{125}{138}\right)\)	\(e\left(\frac{18}{23}\right)\)	\(e\left(\frac{13}{46}\right)\)	\(e\left(\frac{107}{138}\right)\)	\(e\left(\frac{35}{69}\right)\)	\(e\left(\frac{44}{69}\right)\)	\(e\left(\frac{95}{138}\right)\)
\(\chi_{10008}(61,\cdot)\)	10008.ga	138	yes	\(-1\)	\(1\)	\(e\left(\frac{41}{46}\right)\)	\(e\left(\frac{5}{69}\right)\)	\(e\left(\frac{25}{46}\right)\)	\(e\left(\frac{137}{138}\right)\)	\(e\left(\frac{95}{138}\right)\)	\(e\left(\frac{59}{69}\right)\)	\(e\left(\frac{79}{138}\right)\)	\(e\left(\frac{18}{23}\right)\)	\(e\left(\frac{17}{46}\right)\)	\(e\left(\frac{8}{23}\right)\)
\(\chi_{10008}(65,\cdot)\)	10008.ew	138	no	\(-1\)	\(1\)	\(e\left(\frac{43}{138}\right)\)	\(e\left(\frac{1}{69}\right)\)	\(e\left(\frac{107}{138}\right)\)	\(e\left(\frac{62}{69}\right)\)	\(e\left(\frac{37}{46}\right)\)	\(e\left(\frac{7}{23}\right)\)	\(e\left(\frac{25}{138}\right)\)	\(e\left(\frac{43}{69}\right)\)	\(e\left(\frac{47}{138}\right)\)	\(e\left(\frac{14}{69}\right)\)
\(\chi_{10008}(67,\cdot)\)	10008.fa	138	yes	\(-1\)	\(1\)	\(e\left(\frac{19}{138}\right)\)	\(e\left(\frac{29}{46}\right)\)	\(e\left(\frac{10}{69}\right)\)	\(e\left(\frac{27}{46}\right)\)	\(e\left(\frac{28}{69}\right)\)	\(e\left(\frac{5}{69}\right)\)	\(e\left(\frac{41}{138}\right)\)	\(e\left(\frac{19}{69}\right)\)	\(e\left(\frac{101}{138}\right)\)	\(e\left(\frac{91}{138}\right)\)
\(\chi_{10008}(71,\cdot)\)	10008.em	138	no	\(1\)	\(1\)	\(e\left(\frac{59}{138}\right)\)	\(e\left(\frac{137}{138}\right)\)	\(e\left(\frac{2}{69}\right)\)	\(e\left(\frac{38}{69}\right)\)	\(e\left(\frac{71}{138}\right)\)	\(e\left(\frac{25}{138}\right)\)	\(e\left(\frac{19}{23}\right)\)	\(e\left(\frac{59}{69}\right)\)	\(e\left(\frac{103}{138}\right)\)	\(e\left(\frac{101}{138}\right)\)
\(\chi_{10008}(73,\cdot)\)	10008.fq	138	no	\(-1\)	\(1\)	\(e\left(\frac{37}{69}\right)\)	\(e\left(\frac{52}{69}\right)\)	\(e\left(\frac{68}{69}\right)\)	\(e\left(\frac{50}{69}\right)\)	\(e\left(\frac{137}{138}\right)\)	\(e\left(\frac{91}{138}\right)\)	\(e\left(\frac{27}{46}\right)\)	\(e\left(\frac{5}{69}\right)\)	\(e\left(\frac{26}{69}\right)\)	\(e\left(\frac{61}{69}\right)\)
\(\chi_{10008}(77,\cdot)\)	10008.fp	138	yes	\(-1\)	\(1\)	\(e\left(\frac{13}{69}\right)\)	\(e\left(\frac{68}{69}\right)\)	\(e\left(\frac{50}{69}\right)\)	\(e\left(\frac{83}{138}\right)\)	\(e\left(\frac{9}{46}\right)\)	\(e\left(\frac{9}{46}\right)\)	\(e\left(\frac{113}{138}\right)\)	\(e\left(\frac{26}{69}\right)\)	\(e\left(\frac{11}{69}\right)\)	\(e\left(\frac{55}{69}\right)\)
\(\chi_{10008}(79,\cdot)\)	10008.fi	138	no	\(-1\)	\(1\)	\(e\left(\frac{50}{69}\right)\)	\(e\left(\frac{125}{138}\right)\)	\(e\left(\frac{29}{138}\right)\)	\(e\left(\frac{11}{69}\right)\)	\(e\left(\frac{12}{23}\right)\)	\(e\left(\frac{1}{46}\right)\)	\(e\left(\frac{79}{138}\right)\)	\(e\left(\frac{31}{69}\right)\)	\(e\left(\frac{37}{69}\right)\)	\(e\left(\frac{25}{138}\right)\)
\(\chi_{10008}(83,\cdot)\)	10008.fu	138	yes	\(1\)	\(1\)	\(e\left(\frac{25}{69}\right)\)	\(e\left(\frac{17}{46}\right)\)	\(e\left(\frac{49}{138}\right)\)	\(e\left(\frac{19}{46}\right)\)	\(e\left(\frac{13}{138}\right)\)	\(e\left(\frac{64}{69}\right)\)	\(e\left(\frac{14}{69}\right)\)	\(e\left(\frac{50}{69}\right)\)	\(e\left(\frac{53}{69}\right)\)	\(e\left(\frac{47}{138}\right)\)
\(\chi_{10008}(85,\cdot)\)	10008.ef	138	yes	\(-1\)	\(1\)	\(e\left(\frac{61}{138}\right)\)	\(e\left(\frac{6}{23}\right)\)	\(e\left(\frac{17}{138}\right)\)	\(e\left(\frac{31}{46}\right)\)	\(e\left(\frac{89}{138}\right)\)	\(e\left(\frac{56}{69}\right)\)	\(e\left(\frac{59}{138}\right)\)	\(e\left(\frac{61}{69}\right)\)	\(e\left(\frac{41}{138}\right)\)	\(e\left(\frac{68}{69}\right)\)
\(\chi_{10008}(89,\cdot)\)	10008.eu	138	no	\(-1\)	\(1\)	\(e\left(\frac{43}{138}\right)\)	\(e\left(\frac{47}{69}\right)\)	\(e\left(\frac{107}{138}\right)\)	\(e\left(\frac{16}{69}\right)\)	\(e\left(\frac{19}{138}\right)\)	\(e\left(\frac{67}{69}\right)\)	\(e\left(\frac{39}{46}\right)\)	\(e\left(\frac{43}{69}\right)\)	\(e\left(\frac{47}{138}\right)\)	\(e\left(\frac{14}{69}\right)\)
\(\chi_{10008}(91,\cdot)\)	10008.dq	46	no	\(-1\)	\(1\)	\(e\left(\frac{25}{46}\right)\)	\(e\left(\frac{37}{46}\right)\)	\(e\left(\frac{18}{23}\right)\)	\(e\left(\frac{17}{46}\right)\)	\(e\left(\frac{9}{23}\right)\)	\(e\left(\frac{9}{23}\right)\)	\(e\left(\frac{37}{46}\right)\)	\(e\left(\frac{2}{23}\right)\)	\(e\left(\frac{7}{46}\right)\)	\(e\left(\frac{35}{46}\right)\)
\(\chi_{10008}(95,\cdot)\)	10008.el	138	no	\(-1\)	\(1\)	\(e\left(\frac{107}{138}\right)\)	\(e\left(\frac{13}{138}\right)\)	\(e\left(\frac{20}{69}\right)\)	\(e\left(\frac{58}{69}\right)\)	\(e\left(\frac{11}{23}\right)\)	\(e\left(\frac{11}{23}\right)\)	\(e\left(\frac{59}{138}\right)\)	\(e\left(\frac{38}{69}\right)\)	\(e\left(\frac{133}{138}\right)\)	\(e\left(\frac{113}{138}\right)\)

Introduction

L-functions

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Character group

First 32 of 3312 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.