LMFDB - Group of Dirichlet characters of modulus 7728

Show commands: PariGP / SageMath

sage: H = DirichletGroup(7728)

pari: g = idealstar(,7728,2)

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	=	$\chi_{7728}(4831,\cdot)$, $\chi_{7728}(5797,\cdot)$, $\chi_{7728}(5153,\cdot)$, $\chi_{7728}(6625,\cdot)$, $\chi_{7728}(6721,\cdot)$

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	$-1$	$1$	$5$	$11$	$13$	$17$	$19$	$25$	$29$	$31$	$37$	$41$
$\chi_{7728}(1,\cdot)$	7728.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{7728}(5,\cdot)$	7728.gw	132	yes	$-1$	$1$	$e\left(\frac{127}{132}\right)$	$e\left(\frac{65}{132}\right)$	$e\left(\frac{39}{44}\right)$	$e\left(\frac{43}{66}\right)$	$e\left(\frac{79}{132}\right)$	$e\left(\frac{61}{66}\right)$	$e\left(\frac{3}{44}\right)$	$e\left(\frac{7}{66}\right)$	$e\left(\frac{115}{132}\right)$	$e\left(\frac{1}{22}\right)$
$\chi_{7728}(11,\cdot)$	7728.hc	132	yes	$-1$	$1$	$e\left(\frac{65}{132}\right)$	$e\left(\frac{79}{132}\right)$	$e\left(\frac{21}{44}\right)$	$e\left(\frac{1}{33}\right)$	$e\left(\frac{95}{132}\right)$	$e\left(\frac{65}{66}\right)$	$e\left(\frac{27}{44}\right)$	$e\left(\frac{41}{66}\right)$	$e\left(\frac{23}{132}\right)$	$e\left(\frac{10}{11}\right)$
$\chi_{7728}(13,\cdot)$	7728.fl	44	no	$-1$	$1$	$e\left(\frac{39}{44}\right)$	$e\left(\frac{21}{44}\right)$	$e\left(\frac{29}{44}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{13}{44}\right)$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{31}{44}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{5}{44}\right)$	$e\left(\frac{7}{11}\right)$
$\chi_{7728}(17,\cdot)$	7728.gc	66	no	$-1$	$1$	$e\left(\frac{43}{66}\right)$	$e\left(\frac{1}{33}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{59}{66}\right)$	$e\left(\frac{20}{33}\right)$	$e\left(\frac{10}{33}\right)$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{5}{66}\right)$	$e\left(\frac{1}{66}\right)$	$e\left(\frac{9}{11}\right)$
$\chi_{7728}(19,\cdot)$	7728.hg	132	no	$-1$	$1$	$e\left(\frac{79}{132}\right)$	$e\left(\frac{95}{132}\right)$	$e\left(\frac{13}{44}\right)$	$e\left(\frac{20}{33}\right)$	$e\left(\frac{19}{132}\right)$	$e\left(\frac{13}{66}\right)$	$e\left(\frac{23}{44}\right)$	$e\left(\frac{14}{33}\right)$	$e\left(\frac{97}{132}\right)$	$e\left(\frac{2}{11}\right)$
$\chi_{7728}(25,\cdot)$	7728.fv	66	no	$1$	$1$	$e\left(\frac{61}{66}\right)$	$e\left(\frac{65}{66}\right)$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{10}{33}\right)$	$e\left(\frac{13}{66}\right)$	$e\left(\frac{28}{33}\right)$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{7}{33}\right)$	$e\left(\frac{49}{66}\right)$	$e\left(\frac{1}{11}\right)$
$\chi_{7728}(29,\cdot)$	7728.fh	44	no	$-1$	$1$	$e\left(\frac{3}{44}\right)$	$e\left(\frac{27}{44}\right)$	$e\left(\frac{31}{44}\right)$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{23}{44}\right)$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{21}{44}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{41}{44}\right)$	$e\left(\frac{9}{11}\right)$
$\chi_{7728}(31,\cdot)$	7728.fu	66	no	$1$	$1$	$e\left(\frac{7}{66}\right)$	$e\left(\frac{41}{66}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{5}{66}\right)$	$e\left(\frac{14}{33}\right)$	$e\left(\frac{7}{33}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{10}{33}\right)$	$e\left(\frac{2}{33}\right)$	$e\left(\frac{17}{22}\right)$
$\chi_{7728}(37,\cdot)$	7728.ha	132	no	$-1$	$1$	$e\left(\frac{115}{132}\right)$	$e\left(\frac{23}{132}\right)$	$e\left(\frac{5}{44}\right)$	$e\left(\frac{1}{66}\right)$	$e\left(\frac{97}{132}\right)$	$e\left(\frac{49}{66}\right)$	$e\left(\frac{41}{44}\right)$	$e\left(\frac{2}{33}\right)$	$e\left(\frac{127}{132}\right)$	$e\left(\frac{21}{22}\right)$
$\chi_{7728}(41,\cdot)$	7728.ei	22	no	$1$	$1$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{6}{11}\right)$
$\chi_{7728}(43,\cdot)$	7728.fn	44	no	$1$	$1$	$e\left(\frac{21}{44}\right)$	$e\left(\frac{35}{44}\right)$	$e\left(\frac{41}{44}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{29}{44}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{37}{44}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{1}{44}\right)$	$e\left(\frac{5}{22}\right)$
$\chi_{7728}(47,\cdot)$	7728.bx	6	no	$-1$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$-1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$-1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$1$
$\chi_{7728}(53,\cdot)$	7728.hh	132	yes	$1$	$1$	$e\left(\frac{125}{132}\right)$	$e\left(\frac{25}{132}\right)$	$e\left(\frac{37}{44}\right)$	$e\left(\frac{7}{33}\right)$	$e\left(\frac{5}{132}\right)$	$e\left(\frac{59}{66}\right)$	$e\left(\frac{35}{44}\right)$	$e\left(\frac{28}{33}\right)$	$e\left(\frac{95}{132}\right)$	$e\left(\frac{4}{11}\right)$
$\chi_{7728}(55,\cdot)$	7728.dv	22	no	$1$	$1$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{21}{22}\right)$
$\chi_{7728}(59,\cdot)$	7728.hj	132	yes	$-1$	$1$	$e\left(\frac{29}{132}\right)$	$e\left(\frac{85}{132}\right)$	$e\left(\frac{7}{44}\right)$	$e\left(\frac{4}{33}\right)$	$e\left(\frac{83}{132}\right)$	$e\left(\frac{29}{66}\right)$	$e\left(\frac{31}{44}\right)$	$e\left(\frac{16}{33}\right)$	$e\left(\frac{125}{132}\right)$	$e\left(\frac{3}{22}\right)$
$\chi_{7728}(61,\cdot)$	7728.hd	132	no	$1$	$1$	$e\left(\frac{91}{132}\right)$	$e\left(\frac{5}{132}\right)$	$e\left(\frac{25}{44}\right)$	$e\left(\frac{8}{33}\right)$	$e\left(\frac{1}{132}\right)$	$e\left(\frac{25}{66}\right)$	$e\left(\frac{7}{44}\right)$	$e\left(\frac{31}{66}\right)$	$e\left(\frac{85}{132}\right)$	$e\left(\frac{3}{11}\right)$
$\chi_{7728}(65,\cdot)$	7728.gp	66	no	$1$	$1$	$e\left(\frac{28}{33}\right)$	$e\left(\frac{32}{33}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{20}{33}\right)$	$e\left(\frac{59}{66}\right)$	$e\left(\frac{23}{33}\right)$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{14}{33}\right)$	$e\left(\frac{65}{66}\right)$	$e\left(\frac{15}{22}\right)$
$\chi_{7728}(67,\cdot)$	7728.gx	132	no	$1$	$1$	$e\left(\frac{89}{132}\right)$	$e\left(\frac{31}{132}\right)$	$e\left(\frac{23}{44}\right)$	$e\left(\frac{53}{66}\right)$	$e\left(\frac{125}{132}\right)$	$e\left(\frac{23}{66}\right)$	$e\left(\frac{39}{44}\right)$	$e\left(\frac{47}{66}\right)$	$e\left(\frac{65}{132}\right)$	$e\left(\frac{13}{22}\right)$
$\chi_{7728}(71,\cdot)$	7728.eg	22	no	$1$	$1$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{13}{22}\right)$
$\chi_{7728}(73,\cdot)$	7728.gg	66	no	$-1$	$1$	$e\left(\frac{17}{33}\right)$	$e\left(\frac{53}{66}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{29}{66}\right)$	$e\left(\frac{2}{33}\right)$	$e\left(\frac{1}{33}\right)$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{17}{66}\right)$	$e\left(\frac{43}{66}\right)$	$e\left(\frac{15}{22}\right)$
$\chi_{7728}(79,\cdot)$	7728.fy	66	no	$1$	$1$	$e\left(\frac{53}{66}\right)$	$e\left(\frac{2}{33}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{19}{66}\right)$	$e\left(\frac{7}{33}\right)$	$e\left(\frac{20}{33}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{43}{66}\right)$	$e\left(\frac{35}{66}\right)$	$e\left(\frac{7}{11}\right)$
$\chi_{7728}(83,\cdot)$	7728.fj	44	yes	$1$	$1$	$e\left(\frac{31}{44}\right)$	$e\left(\frac{15}{44}\right)$	$e\left(\frac{5}{44}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{25}{44}\right)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{41}{44}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{35}{44}\right)$	$e\left(\frac{21}{22}\right)$
$\chi_{7728}(85,\cdot)$	7728.fc	44	no	$1$	$1$	$e\left(\frac{27}{44}\right)$	$e\left(\frac{23}{44}\right)$	$e\left(\frac{37}{44}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{9}{44}\right)$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{13}{44}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{39}{44}\right)$	$e\left(\frac{19}{22}\right)$
$\chi_{7728}(89,\cdot)$	7728.gf	66	no	$-1$	$1$	$e\left(\frac{13}{33}\right)$	$e\left(\frac{25}{66}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{61}{66}\right)$	$e\left(\frac{5}{66}\right)$	$e\left(\frac{26}{33}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{13}{66}\right)$	$e\left(\frac{31}{33}\right)$	$e\left(\frac{8}{11}\right)$
$\chi_{7728}(95,\cdot)$	7728.fx	66	no	$1$	$1$	$e\left(\frac{37}{66}\right)$	$e\left(\frac{7}{33}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{17}{66}\right)$	$e\left(\frac{49}{66}\right)$	$e\left(\frac{4}{33}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{35}{66}\right)$	$e\left(\frac{20}{33}\right)$	$e\left(\frac{5}{22}\right)$
$\chi_{7728}(97,\cdot)$	7728.ee	22	no	$1$	$1$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{1}{22}\right)$
$\chi_{7728}(101,\cdot)$	7728.he	132	yes	$1$	$1$	$e\left(\frac{5}{132}\right)$	$e\left(\frac{67}{132}\right)$	$e\left(\frac{27}{44}\right)$	$e\left(\frac{28}{33}\right)$	$e\left(\frac{53}{132}\right)$	$e\left(\frac{5}{66}\right)$	$e\left(\frac{19}{44}\right)$	$e\left(\frac{59}{66}\right)$	$e\left(\frac{17}{132}\right)$	$e\left(\frac{21}{22}\right)$
$\chi_{7728}(103,\cdot)$	7728.fs	66	no	$-1$	$1$	$e\left(\frac{5}{66}\right)$	$e\left(\frac{1}{66}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{23}{33}\right)$	$e\left(\frac{10}{33}\right)$	$e\left(\frac{5}{33}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{26}{33}\right)$	$e\left(\frac{25}{33}\right)$	$e\left(\frac{9}{22}\right)$
$\chi_{7728}(107,\cdot)$	7728.hc	132	yes	$-1$	$1$	$e\left(\frac{25}{132}\right)$	$e\left(\frac{71}{132}\right)$	$e\left(\frac{25}{44}\right)$	$e\left(\frac{8}{33}\right)$	$e\left(\frac{67}{132}\right)$	$e\left(\frac{25}{66}\right)$	$e\left(\frac{7}{44}\right)$	$e\left(\frac{31}{66}\right)$	$e\left(\frac{19}{132}\right)$	$e\left(\frac{3}{11}\right)$
$\chi_{7728}(109,\cdot)$	7728.ha	132	no	$-1$	$1$	$e\left(\frac{53}{132}\right)$	$e\left(\frac{37}{132}\right)$	$e\left(\frac{31}{44}\right)$	$e\left(\frac{59}{66}\right)$	$e\left(\frac{47}{132}\right)$	$e\left(\frac{53}{66}\right)$	$e\left(\frac{43}{44}\right)$	$e\left(\frac{19}{33}\right)$	$e\left(\frac{101}{132}\right)$	$e\left(\frac{7}{22}\right)$
$\chi_{7728}(113,\cdot)$	7728.dt	22	no	$1$	$1$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{13}{22}\right)$

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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	$7728$
Structure	\(C_{2}\times C_{2}\times C_{2}\times C_{2}\times C_{132}\)
Order	$2112$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(5\)	\(11\)	\(13\)	\(17\)	\(19\)	\(25\)	\(29\)	\(31\)	\(37\)	\(41\)
\(\chi_{7728}(1,\cdot)\)	7728.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{7728}(5,\cdot)\)	7728.gw	132	yes	\(-1\)	\(1\)	\(e\left(\frac{127}{132}\right)\)	\(e\left(\frac{65}{132}\right)\)	\(e\left(\frac{39}{44}\right)\)	\(e\left(\frac{43}{66}\right)\)	\(e\left(\frac{79}{132}\right)\)	\(e\left(\frac{61}{66}\right)\)	\(e\left(\frac{3}{44}\right)\)	\(e\left(\frac{7}{66}\right)\)	\(e\left(\frac{115}{132}\right)\)	\(e\left(\frac{1}{22}\right)\)
\(\chi_{7728}(11,\cdot)\)	7728.hc	132	yes	\(-1\)	\(1\)	\(e\left(\frac{65}{132}\right)\)	\(e\left(\frac{79}{132}\right)\)	\(e\left(\frac{21}{44}\right)\)	\(e\left(\frac{1}{33}\right)\)	\(e\left(\frac{95}{132}\right)\)	\(e\left(\frac{65}{66}\right)\)	\(e\left(\frac{27}{44}\right)\)	\(e\left(\frac{41}{66}\right)\)	\(e\left(\frac{23}{132}\right)\)	\(e\left(\frac{10}{11}\right)\)
\(\chi_{7728}(13,\cdot)\)	7728.fl	44	no	\(-1\)	\(1\)	\(e\left(\frac{39}{44}\right)\)	\(e\left(\frac{21}{44}\right)\)	\(e\left(\frac{29}{44}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{13}{44}\right)\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{31}{44}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{5}{44}\right)\)	\(e\left(\frac{7}{11}\right)\)
\(\chi_{7728}(17,\cdot)\)	7728.gc	66	no	\(-1\)	\(1\)	\(e\left(\frac{43}{66}\right)\)	\(e\left(\frac{1}{33}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{59}{66}\right)\)	\(e\left(\frac{20}{33}\right)\)	\(e\left(\frac{10}{33}\right)\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{5}{66}\right)\)	\(e\left(\frac{1}{66}\right)\)	\(e\left(\frac{9}{11}\right)\)
\(\chi_{7728}(19,\cdot)\)	7728.hg	132	no	\(-1\)	\(1\)	\(e\left(\frac{79}{132}\right)\)	\(e\left(\frac{95}{132}\right)\)	\(e\left(\frac{13}{44}\right)\)	\(e\left(\frac{20}{33}\right)\)	\(e\left(\frac{19}{132}\right)\)	\(e\left(\frac{13}{66}\right)\)	\(e\left(\frac{23}{44}\right)\)	\(e\left(\frac{14}{33}\right)\)	\(e\left(\frac{97}{132}\right)\)	\(e\left(\frac{2}{11}\right)\)
\(\chi_{7728}(25,\cdot)\)	7728.fv	66	no	\(1\)	\(1\)	\(e\left(\frac{61}{66}\right)\)	\(e\left(\frac{65}{66}\right)\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{10}{33}\right)\)	\(e\left(\frac{13}{66}\right)\)	\(e\left(\frac{28}{33}\right)\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{7}{33}\right)\)	\(e\left(\frac{49}{66}\right)\)	\(e\left(\frac{1}{11}\right)\)
\(\chi_{7728}(29,\cdot)\)	7728.fh	44	no	\(-1\)	\(1\)	\(e\left(\frac{3}{44}\right)\)	\(e\left(\frac{27}{44}\right)\)	\(e\left(\frac{31}{44}\right)\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{23}{44}\right)\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{21}{44}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{41}{44}\right)\)	\(e\left(\frac{9}{11}\right)\)
\(\chi_{7728}(31,\cdot)\)	7728.fu	66	no	\(1\)	\(1\)	\(e\left(\frac{7}{66}\right)\)	\(e\left(\frac{41}{66}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{5}{66}\right)\)	\(e\left(\frac{14}{33}\right)\)	\(e\left(\frac{7}{33}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{10}{33}\right)\)	\(e\left(\frac{2}{33}\right)\)	\(e\left(\frac{17}{22}\right)\)
\(\chi_{7728}(37,\cdot)\)	7728.ha	132	no	\(-1\)	\(1\)	\(e\left(\frac{115}{132}\right)\)	\(e\left(\frac{23}{132}\right)\)	\(e\left(\frac{5}{44}\right)\)	\(e\left(\frac{1}{66}\right)\)	\(e\left(\frac{97}{132}\right)\)	\(e\left(\frac{49}{66}\right)\)	\(e\left(\frac{41}{44}\right)\)	\(e\left(\frac{2}{33}\right)\)	\(e\left(\frac{127}{132}\right)\)	\(e\left(\frac{21}{22}\right)\)
\(\chi_{7728}(41,\cdot)\)	7728.ei	22	no	\(1\)	\(1\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{6}{11}\right)\)
\(\chi_{7728}(43,\cdot)\)	7728.fn	44	no	\(1\)	\(1\)	\(e\left(\frac{21}{44}\right)\)	\(e\left(\frac{35}{44}\right)\)	\(e\left(\frac{41}{44}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{29}{44}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{37}{44}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{1}{44}\right)\)	\(e\left(\frac{5}{22}\right)\)
\(\chi_{7728}(47,\cdot)\)	7728.bx	6	no	\(-1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(-1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(-1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(1\)
\(\chi_{7728}(53,\cdot)\)	7728.hh	132	yes	\(1\)	\(1\)	\(e\left(\frac{125}{132}\right)\)	\(e\left(\frac{25}{132}\right)\)	\(e\left(\frac{37}{44}\right)\)	\(e\left(\frac{7}{33}\right)\)	\(e\left(\frac{5}{132}\right)\)	\(e\left(\frac{59}{66}\right)\)	\(e\left(\frac{35}{44}\right)\)	\(e\left(\frac{28}{33}\right)\)	\(e\left(\frac{95}{132}\right)\)	\(e\left(\frac{4}{11}\right)\)
\(\chi_{7728}(55,\cdot)\)	7728.dv	22	no	\(1\)	\(1\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{21}{22}\right)\)
\(\chi_{7728}(59,\cdot)\)	7728.hj	132	yes	\(-1\)	\(1\)	\(e\left(\frac{29}{132}\right)\)	\(e\left(\frac{85}{132}\right)\)	\(e\left(\frac{7}{44}\right)\)	\(e\left(\frac{4}{33}\right)\)	\(e\left(\frac{83}{132}\right)\)	\(e\left(\frac{29}{66}\right)\)	\(e\left(\frac{31}{44}\right)\)	\(e\left(\frac{16}{33}\right)\)	\(e\left(\frac{125}{132}\right)\)	\(e\left(\frac{3}{22}\right)\)
\(\chi_{7728}(61,\cdot)\)	7728.hd	132	no	\(1\)	\(1\)	\(e\left(\frac{91}{132}\right)\)	\(e\left(\frac{5}{132}\right)\)	\(e\left(\frac{25}{44}\right)\)	\(e\left(\frac{8}{33}\right)\)	\(e\left(\frac{1}{132}\right)\)	\(e\left(\frac{25}{66}\right)\)	\(e\left(\frac{7}{44}\right)\)	\(e\left(\frac{31}{66}\right)\)	\(e\left(\frac{85}{132}\right)\)	\(e\left(\frac{3}{11}\right)\)
\(\chi_{7728}(65,\cdot)\)	7728.gp	66	no	\(1\)	\(1\)	\(e\left(\frac{28}{33}\right)\)	\(e\left(\frac{32}{33}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{20}{33}\right)\)	\(e\left(\frac{59}{66}\right)\)	\(e\left(\frac{23}{33}\right)\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{14}{33}\right)\)	\(e\left(\frac{65}{66}\right)\)	\(e\left(\frac{15}{22}\right)\)
\(\chi_{7728}(67,\cdot)\)	7728.gx	132	no	\(1\)	\(1\)	\(e\left(\frac{89}{132}\right)\)	\(e\left(\frac{31}{132}\right)\)	\(e\left(\frac{23}{44}\right)\)	\(e\left(\frac{53}{66}\right)\)	\(e\left(\frac{125}{132}\right)\)	\(e\left(\frac{23}{66}\right)\)	\(e\left(\frac{39}{44}\right)\)	\(e\left(\frac{47}{66}\right)\)	\(e\left(\frac{65}{132}\right)\)	\(e\left(\frac{13}{22}\right)\)
\(\chi_{7728}(71,\cdot)\)	7728.eg	22	no	\(1\)	\(1\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{13}{22}\right)\)
\(\chi_{7728}(73,\cdot)\)	7728.gg	66	no	\(-1\)	\(1\)	\(e\left(\frac{17}{33}\right)\)	\(e\left(\frac{53}{66}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{29}{66}\right)\)	\(e\left(\frac{2}{33}\right)\)	\(e\left(\frac{1}{33}\right)\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{17}{66}\right)\)	\(e\left(\frac{43}{66}\right)\)	\(e\left(\frac{15}{22}\right)\)
\(\chi_{7728}(79,\cdot)\)	7728.fy	66	no	\(1\)	\(1\)	\(e\left(\frac{53}{66}\right)\)	\(e\left(\frac{2}{33}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{19}{66}\right)\)	\(e\left(\frac{7}{33}\right)\)	\(e\left(\frac{20}{33}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{43}{66}\right)\)	\(e\left(\frac{35}{66}\right)\)	\(e\left(\frac{7}{11}\right)\)
\(\chi_{7728}(83,\cdot)\)	7728.fj	44	yes	\(1\)	\(1\)	\(e\left(\frac{31}{44}\right)\)	\(e\left(\frac{15}{44}\right)\)	\(e\left(\frac{5}{44}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{25}{44}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{41}{44}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{35}{44}\right)\)	\(e\left(\frac{21}{22}\right)\)
\(\chi_{7728}(85,\cdot)\)	7728.fc	44	no	\(1\)	\(1\)	\(e\left(\frac{27}{44}\right)\)	\(e\left(\frac{23}{44}\right)\)	\(e\left(\frac{37}{44}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{9}{44}\right)\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{13}{44}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{39}{44}\right)\)	\(e\left(\frac{19}{22}\right)\)
\(\chi_{7728}(89,\cdot)\)	7728.gf	66	no	\(-1\)	\(1\)	\(e\left(\frac{13}{33}\right)\)	\(e\left(\frac{25}{66}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{61}{66}\right)\)	\(e\left(\frac{5}{66}\right)\)	\(e\left(\frac{26}{33}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{13}{66}\right)\)	\(e\left(\frac{31}{33}\right)\)	\(e\left(\frac{8}{11}\right)\)
\(\chi_{7728}(95,\cdot)\)	7728.fx	66	no	\(1\)	\(1\)	\(e\left(\frac{37}{66}\right)\)	\(e\left(\frac{7}{33}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{17}{66}\right)\)	\(e\left(\frac{49}{66}\right)\)	\(e\left(\frac{4}{33}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{35}{66}\right)\)	\(e\left(\frac{20}{33}\right)\)	\(e\left(\frac{5}{22}\right)\)
\(\chi_{7728}(97,\cdot)\)	7728.ee	22	no	\(1\)	\(1\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{1}{22}\right)\)
\(\chi_{7728}(101,\cdot)\)	7728.he	132	yes	\(1\)	\(1\)	\(e\left(\frac{5}{132}\right)\)	\(e\left(\frac{67}{132}\right)\)	\(e\left(\frac{27}{44}\right)\)	\(e\left(\frac{28}{33}\right)\)	\(e\left(\frac{53}{132}\right)\)	\(e\left(\frac{5}{66}\right)\)	\(e\left(\frac{19}{44}\right)\)	\(e\left(\frac{59}{66}\right)\)	\(e\left(\frac{17}{132}\right)\)	\(e\left(\frac{21}{22}\right)\)
\(\chi_{7728}(103,\cdot)\)	7728.fs	66	no	\(-1\)	\(1\)	\(e\left(\frac{5}{66}\right)\)	\(e\left(\frac{1}{66}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{23}{33}\right)\)	\(e\left(\frac{10}{33}\right)\)	\(e\left(\frac{5}{33}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{26}{33}\right)\)	\(e\left(\frac{25}{33}\right)\)	\(e\left(\frac{9}{22}\right)\)
\(\chi_{7728}(107,\cdot)\)	7728.hc	132	yes	\(-1\)	\(1\)	\(e\left(\frac{25}{132}\right)\)	\(e\left(\frac{71}{132}\right)\)	\(e\left(\frac{25}{44}\right)\)	\(e\left(\frac{8}{33}\right)\)	\(e\left(\frac{67}{132}\right)\)	\(e\left(\frac{25}{66}\right)\)	\(e\left(\frac{7}{44}\right)\)	\(e\left(\frac{31}{66}\right)\)	\(e\left(\frac{19}{132}\right)\)	\(e\left(\frac{3}{11}\right)\)
\(\chi_{7728}(109,\cdot)\)	7728.ha	132	no	\(-1\)	\(1\)	\(e\left(\frac{53}{132}\right)\)	\(e\left(\frac{37}{132}\right)\)	\(e\left(\frac{31}{44}\right)\)	\(e\left(\frac{59}{66}\right)\)	\(e\left(\frac{47}{132}\right)\)	\(e\left(\frac{53}{66}\right)\)	\(e\left(\frac{43}{44}\right)\)	\(e\left(\frac{19}{33}\right)\)	\(e\left(\frac{101}{132}\right)\)	\(e\left(\frac{7}{22}\right)\)
\(\chi_{7728}(113,\cdot)\)	7728.dt	22	no	\(1\)	\(1\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{13}{22}\right)\)

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.