LMFDB - Group of Dirichlet characters of modulus 8040

Show commands: PariGP / SageMath

sage: H = DirichletGroup(8040)

pari: g = idealstar(,8040,2)

Character group

sage: G.order() pari: g.no
Order	=	2112
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{2}\times C_{2}\times C_{2}\times C_{132}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{8040}(6031,\cdot)$, $\chi_{8040}(4021,\cdot)$, $\chi_{8040}(2681,\cdot)$, $\chi_{8040}(3217,\cdot)$, $\chi_{8040}(5161,\cdot)$

First 32 of 2112 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	$-1$	$1$	$7$	$11$	$13$	$17$	$19$	$23$	$29$	$31$	$37$	$41$
$\chi_{8040}(1,\cdot)$	8040.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{8040}(7,\cdot)$	8040.hi	132	no	$-1$	$1$	$e\left(\frac{101}{132}\right)$	$e\left(\frac{2}{33}\right)$	$e\left(\frac{49}{132}\right)$	$e\left(\frac{73}{132}\right)$	$e\left(\frac{16}{33}\right)$	$e\left(\frac{1}{132}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{29}{33}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{31}{66}\right)$
$\chi_{8040}(11,\cdot)$	8040.gr	66	no	$-1$	$1$	$e\left(\frac{2}{33}\right)$	$e\left(\frac{8}{33}\right)$	$e\left(\frac{16}{33}\right)$	$e\left(\frac{47}{66}\right)$	$e\left(\frac{31}{33}\right)$	$e\left(\frac{1}{33}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{17}{33}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{29}{33}\right)$
$\chi_{8040}(13,\cdot)$	8040.hg	132	no	$1$	$1$	$e\left(\frac{49}{132}\right)$	$e\left(\frac{16}{33}\right)$	$e\left(\frac{29}{132}\right)$	$e\left(\frac{23}{132}\right)$	$e\left(\frac{29}{33}\right)$	$e\left(\frac{41}{132}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{35}{66}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{17}{66}\right)$
$\chi_{8040}(17,\cdot)$	8040.gu	132	no	$1$	$1$	$e\left(\frac{73}{132}\right)$	$e\left(\frac{47}{66}\right)$	$e\left(\frac{23}{132}\right)$	$e\left(\frac{107}{132}\right)$	$e\left(\frac{13}{66}\right)$	$e\left(\frac{53}{132}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{19}{33}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{59}{66}\right)$
$\chi_{8040}(19,\cdot)$	8040.gs	66	no	$-1$	$1$	$e\left(\frac{16}{33}\right)$	$e\left(\frac{31}{33}\right)$	$e\left(\frac{29}{33}\right)$	$e\left(\frac{13}{66}\right)$	$e\left(\frac{17}{33}\right)$	$e\left(\frac{8}{33}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{41}{66}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{33}\right)$
$\chi_{8040}(23,\cdot)$	8040.hh	132	no	$-1$	$1$	$e\left(\frac{1}{132}\right)$	$e\left(\frac{1}{33}\right)$	$e\left(\frac{41}{132}\right)$	$e\left(\frac{53}{132}\right)$	$e\left(\frac{8}{33}\right)$	$e\left(\frac{17}{132}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{29}{66}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{65}{66}\right)$
$\chi_{8040}(29,\cdot)$	8040.cm	6	yes	$-1$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{8040}(31,\cdot)$	8040.gp	66	no	$1$	$1$	$e\left(\frac{29}{33}\right)$	$e\left(\frac{17}{33}\right)$	$e\left(\frac{35}{66}\right)$	$e\left(\frac{19}{33}\right)$	$e\left(\frac{41}{66}\right)$	$e\left(\frac{29}{66}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{32}{33}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{49}{66}\right)$
$\chi_{8040}(37,\cdot)$	8040.dm	12	no	$-1$	$1$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{8040}(41,\cdot)$	8040.fy	66	no	$1$	$1$	$e\left(\frac{31}{66}\right)$	$e\left(\frac{29}{33}\right)$	$e\left(\frac{17}{66}\right)$	$e\left(\frac{59}{66}\right)$	$e\left(\frac{1}{33}\right)$	$e\left(\frac{65}{66}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{49}{66}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{33}\right)$
$\chi_{8040}(43,\cdot)$	8040.fo	44	no	$-1$	$1$	$e\left(\frac{17}{44}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{15}{44}\right)$	$e\left(\frac{21}{44}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{25}{44}\right)$	$1$	$e\left(\frac{10}{11}\right)$	$i$	$e\left(\frac{5}{22}\right)$
$\chi_{8040}(47,\cdot)$	8040.hh	132	no	$-1$	$1$	$e\left(\frac{23}{132}\right)$	$e\left(\frac{23}{33}\right)$	$e\left(\frac{19}{132}\right)$	$e\left(\frac{31}{132}\right)$	$e\left(\frac{19}{33}\right)$	$e\left(\frac{127}{132}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{7}{66}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{43}{66}\right)$
$\chi_{8040}(49,\cdot)$	8040.fx	66	no	$1$	$1$	$e\left(\frac{35}{66}\right)$	$e\left(\frac{4}{33}\right)$	$e\left(\frac{49}{66}\right)$	$e\left(\frac{7}{66}\right)$	$e\left(\frac{32}{33}\right)$	$e\left(\frac{1}{66}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{25}{33}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{31}{33}\right)$
$\chi_{8040}(53,\cdot)$	8040.fi	44	yes	$-1$	$1$	$e\left(\frac{27}{44}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{7}{44}\right)$	$e\left(\frac{23}{44}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{41}{44}\right)$	$-1$	$e\left(\frac{13}{22}\right)$	$i$	$e\left(\frac{3}{11}\right)$
$\chi_{8040}(59,\cdot)$	8040.eb	22	yes	$1$	$1$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{17}{22}\right)$	$1$	$e\left(\frac{3}{22}\right)$	$1$	$e\left(\frac{9}{22}\right)$
$\chi_{8040}(61,\cdot)$	8040.ge	66	no	$-1$	$1$	$e\left(\frac{29}{66}\right)$	$e\left(\frac{25}{33}\right)$	$e\left(\frac{17}{33}\right)$	$e\left(\frac{26}{33}\right)$	$e\left(\frac{37}{66}\right)$	$e\left(\frac{32}{33}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{65}{66}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{41}{66}\right)$
$\chi_{8040}(71,\cdot)$	8040.gc	66	no	$1$	$1$	$e\left(\frac{13}{66}\right)$	$e\left(\frac{26}{33}\right)$	$e\left(\frac{19}{33}\right)$	$e\left(\frac{29}{66}\right)$	$e\left(\frac{53}{66}\right)$	$e\left(\frac{28}{33}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{61}{66}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{7}{66}\right)$
$\chi_{8040}(73,\cdot)$	8040.hf	132	no	$-1$	$1$	$e\left(\frac{91}{132}\right)$	$e\left(\frac{25}{33}\right)$	$e\left(\frac{101}{132}\right)$	$e\left(\frac{71}{132}\right)$	$e\left(\frac{37}{66}\right)$	$e\left(\frac{29}{132}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{16}{33}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{4}{33}\right)$
$\chi_{8040}(77,\cdot)$	8040.hj	132	yes	$1$	$1$	$e\left(\frac{109}{132}\right)$	$e\left(\frac{10}{33}\right)$	$e\left(\frac{113}{132}\right)$	$e\left(\frac{35}{132}\right)$	$e\left(\frac{14}{33}\right)$	$e\left(\frac{5}{132}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{13}{33}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{23}{66}\right)$
$\chi_{8040}(79,\cdot)$	8040.gb	66	no	$1$	$1$	$e\left(\frac{19}{66}\right)$	$e\left(\frac{5}{33}\right)$	$e\left(\frac{10}{33}\right)$	$e\left(\frac{17}{66}\right)$	$e\left(\frac{47}{66}\right)$	$e\left(\frac{13}{33}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{23}{33}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{61}{66}\right)$
$\chi_{8040}(83,\cdot)$	8040.gw	132	yes	$-1$	$1$	$e\left(\frac{85}{132}\right)$	$e\left(\frac{5}{66}\right)$	$e\left(\frac{119}{132}\right)$	$e\left(\frac{17}{132}\right)$	$e\left(\frac{7}{66}\right)$	$e\left(\frac{125}{132}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{23}{66}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{47}{66}\right)$
$\chi_{8040}(89,\cdot)$	8040.eu	22	no	$-1$	$1$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{5}{11}\right)$	$-1$	$e\left(\frac{8}{11}\right)$	$-1$	$e\left(\frac{15}{22}\right)$
$\chi_{8040}(91,\cdot)$	8040.em	22	no	$-1$	$1$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{7}{22}\right)$	$-1$	$e\left(\frac{9}{22}\right)$	$-1$	$e\left(\frac{8}{11}\right)$
$\chi_{8040}(97,\cdot)$	8040.dr	12	no	$1$	$1$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{6}\right)$
$\chi_{8040}(101,\cdot)$	8040.ft	66	no	$1$	$1$	$e\left(\frac{43}{66}\right)$	$e\left(\frac{7}{66}\right)$	$e\left(\frac{7}{33}\right)$	$e\left(\frac{35}{66}\right)$	$e\left(\frac{23}{66}\right)$	$e\left(\frac{5}{66}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{19}{66}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{23}{33}\right)$
$\chi_{8040}(103,\cdot)$	8040.ha	132	no	$1$	$1$	$e\left(\frac{17}{132}\right)$	$e\left(\frac{1}{66}\right)$	$e\left(\frac{37}{132}\right)$	$e\left(\frac{43}{132}\right)$	$e\left(\frac{4}{33}\right)$	$e\left(\frac{91}{132}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{31}{66}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{8}{33}\right)$
$\chi_{8040}(107,\cdot)$	8040.fl	44	yes	$-1$	$1$	$e\left(\frac{1}{44}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{19}{44}\right)$	$e\left(\frac{9}{44}\right)$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{17}{44}\right)$	$-1$	$e\left(\frac{7}{22}\right)$	$-i$	$e\left(\frac{21}{22}\right)$
$\chi_{8040}(109,\cdot)$	8040.dy	22	no	$-1$	$1$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{5}{22}\right)$	$-1$	$e\left(\frac{19}{22}\right)$	$1$	$e\left(\frac{13}{22}\right)$
$\chi_{8040}(113,\cdot)$	8040.hc	132	no	$-1$	$1$	$e\left(\frac{113}{132}\right)$	$e\left(\frac{14}{33}\right)$	$e\left(\frac{79}{132}\right)$	$e\left(\frac{49}{132}\right)$	$e\left(\frac{59}{66}\right)$	$e\left(\frac{7}{132}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{43}{66}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{26}{33}\right)$
$\chi_{8040}(119,\cdot)$	8040.eq	22	no	$-1$	$1$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{9}{22}\right)$	$-1$	$e\left(\frac{5}{11}\right)$	$-1$	$e\left(\frac{4}{11}\right)$
$\chi_{8040}(121,\cdot)$	8040.ey	33	no	$1$	$1$	$e\left(\frac{4}{33}\right)$	$e\left(\frac{16}{33}\right)$	$e\left(\frac{32}{33}\right)$	$e\left(\frac{14}{33}\right)$	$e\left(\frac{29}{33}\right)$	$e\left(\frac{2}{33}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{33}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{25}{33}\right)$

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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	$8040$
Structure	\(C_{2}\times C_{2}\times C_{2}\times C_{2}\times C_{132}\)
Order	$2112$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(7\)	\(11\)	\(13\)	\(17\)	\(19\)	\(23\)	\(29\)	\(31\)	\(37\)	\(41\)
\(\chi_{8040}(1,\cdot)\)	8040.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{8040}(7,\cdot)\)	8040.hi	132	no	\(-1\)	\(1\)	\(e\left(\frac{101}{132}\right)\)	\(e\left(\frac{2}{33}\right)\)	\(e\left(\frac{49}{132}\right)\)	\(e\left(\frac{73}{132}\right)\)	\(e\left(\frac{16}{33}\right)\)	\(e\left(\frac{1}{132}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{29}{33}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{31}{66}\right)\)
\(\chi_{8040}(11,\cdot)\)	8040.gr	66	no	\(-1\)	\(1\)	\(e\left(\frac{2}{33}\right)\)	\(e\left(\frac{8}{33}\right)\)	\(e\left(\frac{16}{33}\right)\)	\(e\left(\frac{47}{66}\right)\)	\(e\left(\frac{31}{33}\right)\)	\(e\left(\frac{1}{33}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{17}{33}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{29}{33}\right)\)
\(\chi_{8040}(13,\cdot)\)	8040.hg	132	no	\(1\)	\(1\)	\(e\left(\frac{49}{132}\right)\)	\(e\left(\frac{16}{33}\right)\)	\(e\left(\frac{29}{132}\right)\)	\(e\left(\frac{23}{132}\right)\)	\(e\left(\frac{29}{33}\right)\)	\(e\left(\frac{41}{132}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{35}{66}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{17}{66}\right)\)
\(\chi_{8040}(17,\cdot)\)	8040.gu	132	no	\(1\)	\(1\)	\(e\left(\frac{73}{132}\right)\)	\(e\left(\frac{47}{66}\right)\)	\(e\left(\frac{23}{132}\right)\)	\(e\left(\frac{107}{132}\right)\)	\(e\left(\frac{13}{66}\right)\)	\(e\left(\frac{53}{132}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{19}{33}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{59}{66}\right)\)
\(\chi_{8040}(19,\cdot)\)	8040.gs	66	no	\(-1\)	\(1\)	\(e\left(\frac{16}{33}\right)\)	\(e\left(\frac{31}{33}\right)\)	\(e\left(\frac{29}{33}\right)\)	\(e\left(\frac{13}{66}\right)\)	\(e\left(\frac{17}{33}\right)\)	\(e\left(\frac{8}{33}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{41}{66}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{33}\right)\)
\(\chi_{8040}(23,\cdot)\)	8040.hh	132	no	\(-1\)	\(1\)	\(e\left(\frac{1}{132}\right)\)	\(e\left(\frac{1}{33}\right)\)	\(e\left(\frac{41}{132}\right)\)	\(e\left(\frac{53}{132}\right)\)	\(e\left(\frac{8}{33}\right)\)	\(e\left(\frac{17}{132}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{29}{66}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{65}{66}\right)\)
\(\chi_{8040}(29,\cdot)\)	8040.cm	6	yes	\(-1\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{8040}(31,\cdot)\)	8040.gp	66	no	\(1\)	\(1\)	\(e\left(\frac{29}{33}\right)\)	\(e\left(\frac{17}{33}\right)\)	\(e\left(\frac{35}{66}\right)\)	\(e\left(\frac{19}{33}\right)\)	\(e\left(\frac{41}{66}\right)\)	\(e\left(\frac{29}{66}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{32}{33}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{49}{66}\right)\)
\(\chi_{8040}(37,\cdot)\)	8040.dm	12	no	\(-1\)	\(1\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{8040}(41,\cdot)\)	8040.fy	66	no	\(1\)	\(1\)	\(e\left(\frac{31}{66}\right)\)	\(e\left(\frac{29}{33}\right)\)	\(e\left(\frac{17}{66}\right)\)	\(e\left(\frac{59}{66}\right)\)	\(e\left(\frac{1}{33}\right)\)	\(e\left(\frac{65}{66}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{49}{66}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{2}{33}\right)\)
\(\chi_{8040}(43,\cdot)\)	8040.fo	44	no	\(-1\)	\(1\)	\(e\left(\frac{17}{44}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{15}{44}\right)\)	\(e\left(\frac{21}{44}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{25}{44}\right)\)	\(1\)	\(e\left(\frac{10}{11}\right)\)	\(i\)	\(e\left(\frac{5}{22}\right)\)
\(\chi_{8040}(47,\cdot)\)	8040.hh	132	no	\(-1\)	\(1\)	\(e\left(\frac{23}{132}\right)\)	\(e\left(\frac{23}{33}\right)\)	\(e\left(\frac{19}{132}\right)\)	\(e\left(\frac{31}{132}\right)\)	\(e\left(\frac{19}{33}\right)\)	\(e\left(\frac{127}{132}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{7}{66}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{43}{66}\right)\)
\(\chi_{8040}(49,\cdot)\)	8040.fx	66	no	\(1\)	\(1\)	\(e\left(\frac{35}{66}\right)\)	\(e\left(\frac{4}{33}\right)\)	\(e\left(\frac{49}{66}\right)\)	\(e\left(\frac{7}{66}\right)\)	\(e\left(\frac{32}{33}\right)\)	\(e\left(\frac{1}{66}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{25}{33}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{31}{33}\right)\)
\(\chi_{8040}(53,\cdot)\)	8040.fi	44	yes	\(-1\)	\(1\)	\(e\left(\frac{27}{44}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{7}{44}\right)\)	\(e\left(\frac{23}{44}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{41}{44}\right)\)	\(-1\)	\(e\left(\frac{13}{22}\right)\)	\(i\)	\(e\left(\frac{3}{11}\right)\)
\(\chi_{8040}(59,\cdot)\)	8040.eb	22	yes	\(1\)	\(1\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{17}{22}\right)\)	\(1\)	\(e\left(\frac{3}{22}\right)\)	\(1\)	\(e\left(\frac{9}{22}\right)\)
\(\chi_{8040}(61,\cdot)\)	8040.ge	66	no	\(-1\)	\(1\)	\(e\left(\frac{29}{66}\right)\)	\(e\left(\frac{25}{33}\right)\)	\(e\left(\frac{17}{33}\right)\)	\(e\left(\frac{26}{33}\right)\)	\(e\left(\frac{37}{66}\right)\)	\(e\left(\frac{32}{33}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{65}{66}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{41}{66}\right)\)
\(\chi_{8040}(71,\cdot)\)	8040.gc	66	no	\(1\)	\(1\)	\(e\left(\frac{13}{66}\right)\)	\(e\left(\frac{26}{33}\right)\)	\(e\left(\frac{19}{33}\right)\)	\(e\left(\frac{29}{66}\right)\)	\(e\left(\frac{53}{66}\right)\)	\(e\left(\frac{28}{33}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{61}{66}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{7}{66}\right)\)
\(\chi_{8040}(73,\cdot)\)	8040.hf	132	no	\(-1\)	\(1\)	\(e\left(\frac{91}{132}\right)\)	\(e\left(\frac{25}{33}\right)\)	\(e\left(\frac{101}{132}\right)\)	\(e\left(\frac{71}{132}\right)\)	\(e\left(\frac{37}{66}\right)\)	\(e\left(\frac{29}{132}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{16}{33}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{4}{33}\right)\)
\(\chi_{8040}(77,\cdot)\)	8040.hj	132	yes	\(1\)	\(1\)	\(e\left(\frac{109}{132}\right)\)	\(e\left(\frac{10}{33}\right)\)	\(e\left(\frac{113}{132}\right)\)	\(e\left(\frac{35}{132}\right)\)	\(e\left(\frac{14}{33}\right)\)	\(e\left(\frac{5}{132}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{13}{33}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{23}{66}\right)\)
\(\chi_{8040}(79,\cdot)\)	8040.gb	66	no	\(1\)	\(1\)	\(e\left(\frac{19}{66}\right)\)	\(e\left(\frac{5}{33}\right)\)	\(e\left(\frac{10}{33}\right)\)	\(e\left(\frac{17}{66}\right)\)	\(e\left(\frac{47}{66}\right)\)	\(e\left(\frac{13}{33}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{23}{33}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{61}{66}\right)\)
\(\chi_{8040}(83,\cdot)\)	8040.gw	132	yes	\(-1\)	\(1\)	\(e\left(\frac{85}{132}\right)\)	\(e\left(\frac{5}{66}\right)\)	\(e\left(\frac{119}{132}\right)\)	\(e\left(\frac{17}{132}\right)\)	\(e\left(\frac{7}{66}\right)\)	\(e\left(\frac{125}{132}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{23}{66}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{47}{66}\right)\)
\(\chi_{8040}(89,\cdot)\)	8040.eu	22	no	\(-1\)	\(1\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(-1\)	\(e\left(\frac{8}{11}\right)\)	\(-1\)	\(e\left(\frac{15}{22}\right)\)
\(\chi_{8040}(91,\cdot)\)	8040.em	22	no	\(-1\)	\(1\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(-1\)	\(e\left(\frac{9}{22}\right)\)	\(-1\)	\(e\left(\frac{8}{11}\right)\)
\(\chi_{8040}(97,\cdot)\)	8040.dr	12	no	\(1\)	\(1\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{8040}(101,\cdot)\)	8040.ft	66	no	\(1\)	\(1\)	\(e\left(\frac{43}{66}\right)\)	\(e\left(\frac{7}{66}\right)\)	\(e\left(\frac{7}{33}\right)\)	\(e\left(\frac{35}{66}\right)\)	\(e\left(\frac{23}{66}\right)\)	\(e\left(\frac{5}{66}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{19}{66}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{23}{33}\right)\)
\(\chi_{8040}(103,\cdot)\)	8040.ha	132	no	\(1\)	\(1\)	\(e\left(\frac{17}{132}\right)\)	\(e\left(\frac{1}{66}\right)\)	\(e\left(\frac{37}{132}\right)\)	\(e\left(\frac{43}{132}\right)\)	\(e\left(\frac{4}{33}\right)\)	\(e\left(\frac{91}{132}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{31}{66}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{8}{33}\right)\)
\(\chi_{8040}(107,\cdot)\)	8040.fl	44	yes	\(-1\)	\(1\)	\(e\left(\frac{1}{44}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{19}{44}\right)\)	\(e\left(\frac{9}{44}\right)\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{17}{44}\right)\)	\(-1\)	\(e\left(\frac{7}{22}\right)\)	\(-i\)	\(e\left(\frac{21}{22}\right)\)
\(\chi_{8040}(109,\cdot)\)	8040.dy	22	no	\(-1\)	\(1\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{5}{22}\right)\)	\(-1\)	\(e\left(\frac{19}{22}\right)\)	\(1\)	\(e\left(\frac{13}{22}\right)\)
\(\chi_{8040}(113,\cdot)\)	8040.hc	132	no	\(-1\)	\(1\)	\(e\left(\frac{113}{132}\right)\)	\(e\left(\frac{14}{33}\right)\)	\(e\left(\frac{79}{132}\right)\)	\(e\left(\frac{49}{132}\right)\)	\(e\left(\frac{59}{66}\right)\)	\(e\left(\frac{7}{132}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{43}{66}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{26}{33}\right)\)
\(\chi_{8040}(119,\cdot)\)	8040.eq	22	no	\(-1\)	\(1\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(-1\)	\(e\left(\frac{5}{11}\right)\)	\(-1\)	\(e\left(\frac{4}{11}\right)\)
\(\chi_{8040}(121,\cdot)\)	8040.ey	33	no	\(1\)	\(1\)	\(e\left(\frac{4}{33}\right)\)	\(e\left(\frac{16}{33}\right)\)	\(e\left(\frac{32}{33}\right)\)	\(e\left(\frac{14}{33}\right)\)	\(e\left(\frac{29}{33}\right)\)	\(e\left(\frac{2}{33}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{33}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{25}{33}\right)\)

Introduction

L-functions

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Character group

First 32 of 2112 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.