LMFDB - Group of Dirichlet characters of modulus 5424

Show commands: PariGP / SageMath

sage: H = DirichletGroup(5424)

pari: g = idealstar(,5424,2)

Character group

sage: G.order() pari: g.no
Order	=	1792
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{2}\times C_{4}\times C_{112}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{5424}(3391,\cdot)$, $\chi_{5424}(4069,\cdot)$, $\chi_{5424}(3617,\cdot)$, $\chi_{5424}(1585,\cdot)$

First 32 of 1792 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	$-1$	$1$	$5$	$7$	$11$	$13$	$17$	$19$	$23$	$25$	$29$	$31$
$\chi_{5424}(1,\cdot)$	5424.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{5424}(5,\cdot)$	5424.ez	112	yes	$1$	$1$	$e\left(\frac{29}{112}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{33}{56}\right)$	$e\left(\frac{3}{56}\right)$	$e\left(\frac{23}{112}\right)$	$e\left(\frac{13}{112}\right)$	$e\left(\frac{43}{112}\right)$	$e\left(\frac{29}{56}\right)$	$e\left(\frac{23}{112}\right)$	$e\left(\frac{3}{56}\right)$
$\chi_{5424}(7,\cdot)$	5424.cj	14	no	$-1$	$1$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{1}{14}\right)$
$\chi_{5424}(11,\cdot)$	5424.ei	56	yes	$1$	$1$	$e\left(\frac{33}{56}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{45}{56}\right)$	$e\left(\frac{37}{56}\right)$	$e\left(\frac{33}{56}\right)$	$e\left(\frac{5}{28}\right)$	$e\left(\frac{3}{56}\right)$	$e\left(\frac{15}{28}\right)$
$\chi_{5424}(13,\cdot)$	5424.eq	56	no	$1$	$1$	$e\left(\frac{3}{56}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{55}{56}\right)$	$e\left(\frac{39}{56}\right)$	$e\left(\frac{31}{56}\right)$	$e\left(\frac{3}{28}\right)$	$e\left(\frac{41}{56}\right)$	$e\left(\frac{23}{28}\right)$
$\chi_{5424}(17,\cdot)$	5424.fj	112	no	$1$	$1$	$e\left(\frac{23}{112}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{45}{56}\right)$	$e\left(\frac{55}{56}\right)$	$e\left(\frac{81}{112}\right)$	$e\left(\frac{47}{112}\right)$	$e\left(\frac{37}{112}\right)$	$e\left(\frac{23}{56}\right)$	$e\left(\frac{53}{112}\right)$	$e\left(\frac{13}{56}\right)$
$\chi_{5424}(19,\cdot)$	5424.fh	112	no	$1$	$1$	$e\left(\frac{13}{112}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{37}{56}\right)$	$e\left(\frac{39}{56}\right)$	$e\left(\frac{47}{112}\right)$	$e\left(\frac{29}{112}\right)$	$e\left(\frac{27}{112}\right)$	$e\left(\frac{13}{56}\right)$	$e\left(\frac{103}{112}\right)$	$e\left(\frac{39}{56}\right)$
$\chi_{5424}(23,\cdot)$	5424.fa	112	no	$-1$	$1$	$e\left(\frac{43}{112}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{33}{56}\right)$	$e\left(\frac{31}{56}\right)$	$e\left(\frac{37}{112}\right)$	$e\left(\frac{27}{112}\right)$	$e\left(\frac{1}{112}\right)$	$e\left(\frac{43}{56}\right)$	$e\left(\frac{65}{112}\right)$	$e\left(\frac{45}{56}\right)$
$\chi_{5424}(25,\cdot)$	5424.el	56	no	$1$	$1$	$e\left(\frac{29}{56}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{5}{28}\right)$	$e\left(\frac{3}{28}\right)$	$e\left(\frac{23}{56}\right)$	$e\left(\frac{13}{56}\right)$	$e\left(\frac{43}{56}\right)$	$e\left(\frac{1}{28}\right)$	$e\left(\frac{23}{56}\right)$	$e\left(\frac{3}{28}\right)$
$\chi_{5424}(29,\cdot)$	5424.ez	112	yes	$1$	$1$	$e\left(\frac{23}{112}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{3}{56}\right)$	$e\left(\frac{41}{56}\right)$	$e\left(\frac{53}{112}\right)$	$e\left(\frac{103}{112}\right)$	$e\left(\frac{65}{112}\right)$	$e\left(\frac{23}{56}\right)$	$e\left(\frac{53}{112}\right)$	$e\left(\frac{41}{56}\right)$
$\chi_{5424}(31,\cdot)$	5424.eu	56	no	$-1$	$1$	$e\left(\frac{3}{56}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{23}{28}\right)$	$e\left(\frac{13}{56}\right)$	$e\left(\frac{39}{56}\right)$	$e\left(\frac{45}{56}\right)$	$e\left(\frac{3}{28}\right)$	$e\left(\frac{41}{56}\right)$	$e\left(\frac{23}{28}\right)$
$\chi_{5424}(35,\cdot)$	5424.cu	16	yes	$-1$	$1$	$e\left(\frac{11}{16}\right)$	$-1$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{1}{8}\right)$
$\chi_{5424}(37,\cdot)$	5424.ff	112	no	$-1$	$1$	$e\left(\frac{101}{112}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{29}{56}\right)$	$e\left(\frac{51}{56}\right)$	$e\left(\frac{111}{112}\right)$	$e\left(\frac{109}{112}\right)$	$e\left(\frac{3}{112}\right)$	$e\left(\frac{45}{56}\right)$	$e\left(\frac{111}{112}\right)$	$e\left(\frac{51}{56}\right)$
$\chi_{5424}(41,\cdot)$	5424.en	56	no	$-1$	$1$	$e\left(\frac{37}{56}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{3}{28}\right)$	$e\left(\frac{27}{28}\right)$	$e\left(\frac{39}{56}\right)$	$e\left(\frac{33}{56}\right)$	$e\left(\frac{51}{56}\right)$	$e\left(\frac{9}{28}\right)$	$e\left(\frac{39}{56}\right)$	$e\left(\frac{27}{28}\right)$
$\chi_{5424}(43,\cdot)$	5424.fm	112	no	$1$	$1$	$e\left(\frac{9}{112}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{45}{56}\right)$	$e\left(\frac{55}{56}\right)$	$e\left(\frac{11}{112}\right)$	$e\left(\frac{89}{112}\right)$	$e\left(\frac{23}{112}\right)$	$e\left(\frac{9}{56}\right)$	$e\left(\frac{11}{112}\right)$	$e\left(\frac{27}{56}\right)$
$\chi_{5424}(47,\cdot)$	5424.fd	112	no	$-1$	$1$	$e\left(\frac{53}{112}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{27}{56}\right)$	$e\left(\frac{5}{56}\right)$	$e\left(\frac{99}{112}\right)$	$e\left(\frac{101}{112}\right)$	$e\left(\frac{39}{112}\right)$	$e\left(\frac{53}{56}\right)$	$e\left(\frac{15}{112}\right)$	$e\left(\frac{19}{56}\right)$
$\chi_{5424}(49,\cdot)$	5424.bo	7	no	$1$	$1$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{1}{7}\right)$
$\chi_{5424}(53,\cdot)$	5424.dm	28	yes	$-1$	$1$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{3}{28}\right)$	$e\left(\frac{27}{28}\right)$	$e\left(\frac{23}{28}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{1}{28}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{3}{14}\right)$
$\chi_{5424}(55,\cdot)$	5424.fc	112	no	$1$	$1$	$e\left(\frac{95}{112}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{41}{56}\right)$	$e\left(\frac{19}{56}\right)$	$e\left(\frac{1}{112}\right)$	$e\left(\frac{87}{112}\right)$	$e\left(\frac{109}{112}\right)$	$e\left(\frac{39}{56}\right)$	$e\left(\frac{29}{112}\right)$	$e\left(\frac{33}{56}\right)$
$\chi_{5424}(59,\cdot)$	5424.fg	112	yes	$-1$	$1$	$e\left(\frac{41}{112}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{9}{56}\right)$	$e\left(\frac{39}{56}\right)$	$e\left(\frac{75}{112}\right)$	$e\left(\frac{1}{112}\right)$	$e\left(\frac{55}{112}\right)$	$e\left(\frac{41}{56}\right)$	$e\left(\frac{75}{112}\right)$	$e\left(\frac{11}{56}\right)$
$\chi_{5424}(61,\cdot)$	5424.eq	56	no	$1$	$1$	$e\left(\frac{19}{56}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{31}{56}\right)$	$e\left(\frac{23}{56}\right)$	$e\left(\frac{47}{56}\right)$	$e\left(\frac{19}{28}\right)$	$e\left(\frac{17}{56}\right)$	$e\left(\frac{15}{28}\right)$
$\chi_{5424}(65,\cdot)$	5424.cy	16	no	$1$	$1$	$e\left(\frac{5}{16}\right)$	$-1$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{7}{8}\right)$
$\chi_{5424}(67,\cdot)$	5424.fm	112	no	$1$	$1$	$e\left(\frac{59}{112}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{15}{56}\right)$	$e\left(\frac{37}{56}\right)$	$e\left(\frac{97}{112}\right)$	$e\left(\frac{11}{112}\right)$	$e\left(\frac{101}{112}\right)$	$e\left(\frac{3}{56}\right)$	$e\left(\frac{97}{112}\right)$	$e\left(\frac{9}{56}\right)$
$\chi_{5424}(71,\cdot)$	5424.dh	16	no	$-1$	$1$	$e\left(\frac{1}{16}\right)$	$1$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{7}{8}\right)$
$\chi_{5424}(73,\cdot)$	5424.cz	16	no	$-1$	$1$	$e\left(\frac{3}{16}\right)$	$-1$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{1}{8}\right)$
$\chi_{5424}(77,\cdot)$	5424.er	56	yes	$-1$	$1$	$e\left(\frac{1}{56}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{9}{56}\right)$	$e\left(\frac{41}{56}\right)$	$e\left(\frac{1}{56}\right)$	$e\left(\frac{1}{28}\right)$	$e\left(\frac{51}{56}\right)$	$e\left(\frac{17}{28}\right)$
$\chi_{5424}(79,\cdot)$	5424.fb	112	no	$1$	$1$	$e\left(\frac{11}{112}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{41}{56}\right)$	$e\left(\frac{19}{56}\right)$	$e\left(\frac{29}{112}\right)$	$e\left(\frac{3}{112}\right)$	$e\left(\frac{25}{112}\right)$	$e\left(\frac{11}{56}\right)$	$e\left(\frac{1}{112}\right)$	$e\left(\frac{5}{56}\right)$
$\chi_{5424}(83,\cdot)$	5424.dq	28	yes	$1$	$1$	$e\left(\frac{25}{28}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{5}{28}\right)$	$e\left(\frac{3}{28}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{3}{28}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{5}{14}\right)$
$\chi_{5424}(85,\cdot)$	5424.eb	28	no	$1$	$1$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{11}{28}\right)$	$e\left(\frac{1}{28}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{19}{28}\right)$	$e\left(\frac{2}{7}\right)$
$\chi_{5424}(89,\cdot)$	5424.fk	112	no	$1$	$1$	$e\left(\frac{103}{112}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{25}{56}\right)$	$e\left(\frac{43}{56}\right)$	$e\left(\frac{73}{112}\right)$	$e\left(\frac{79}{112}\right)$	$e\left(\frac{61}{112}\right)$	$e\left(\frac{47}{56}\right)$	$e\left(\frac{101}{112}\right)$	$e\left(\frac{29}{56}\right)$
$\chi_{5424}(91,\cdot)$	5424.ej	56	no	$-1$	$1$	$e\left(\frac{27}{56}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{19}{56}\right)$	$e\left(\frac{43}{56}\right)$	$e\left(\frac{55}{56}\right)$	$e\left(\frac{27}{28}\right)$	$e\left(\frac{33}{56}\right)$	$e\left(\frac{25}{28}\right)$
$\chi_{5424}(95,\cdot)$	5424.bu	8	no	$1$	$1$	$e\left(\frac{3}{8}\right)$	$-1$	$i$	$-i$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{5}{8}\right)$	$-i$	$e\left(\frac{1}{8}\right)$	$-i$

Click here to search among the remaining 1760 characters.

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	$5424$
Structure	\(C_{2}\times C_{2}\times C_{4}\times C_{112}\)
Order	$1792$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(5\)	\(7\)	\(11\)	\(13\)	\(17\)	\(19\)	\(23\)	\(25\)	\(29\)	\(31\)
\(\chi_{5424}(1,\cdot)\)	5424.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{5424}(5,\cdot)\)	5424.ez	112	yes	\(1\)	\(1\)	\(e\left(\frac{29}{112}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{33}{56}\right)\)	\(e\left(\frac{3}{56}\right)\)	\(e\left(\frac{23}{112}\right)\)	\(e\left(\frac{13}{112}\right)\)	\(e\left(\frac{43}{112}\right)\)	\(e\left(\frac{29}{56}\right)\)	\(e\left(\frac{23}{112}\right)\)	\(e\left(\frac{3}{56}\right)\)
\(\chi_{5424}(7,\cdot)\)	5424.cj	14	no	\(-1\)	\(1\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{1}{14}\right)\)
\(\chi_{5424}(11,\cdot)\)	5424.ei	56	yes	\(1\)	\(1\)	\(e\left(\frac{33}{56}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{45}{56}\right)\)	\(e\left(\frac{37}{56}\right)\)	\(e\left(\frac{33}{56}\right)\)	\(e\left(\frac{5}{28}\right)\)	\(e\left(\frac{3}{56}\right)\)	\(e\left(\frac{15}{28}\right)\)
\(\chi_{5424}(13,\cdot)\)	5424.eq	56	no	\(1\)	\(1\)	\(e\left(\frac{3}{56}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{55}{56}\right)\)	\(e\left(\frac{39}{56}\right)\)	\(e\left(\frac{31}{56}\right)\)	\(e\left(\frac{3}{28}\right)\)	\(e\left(\frac{41}{56}\right)\)	\(e\left(\frac{23}{28}\right)\)
\(\chi_{5424}(17,\cdot)\)	5424.fj	112	no	\(1\)	\(1\)	\(e\left(\frac{23}{112}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{45}{56}\right)\)	\(e\left(\frac{55}{56}\right)\)	\(e\left(\frac{81}{112}\right)\)	\(e\left(\frac{47}{112}\right)\)	\(e\left(\frac{37}{112}\right)\)	\(e\left(\frac{23}{56}\right)\)	\(e\left(\frac{53}{112}\right)\)	\(e\left(\frac{13}{56}\right)\)
\(\chi_{5424}(19,\cdot)\)	5424.fh	112	no	\(1\)	\(1\)	\(e\left(\frac{13}{112}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{37}{56}\right)\)	\(e\left(\frac{39}{56}\right)\)	\(e\left(\frac{47}{112}\right)\)	\(e\left(\frac{29}{112}\right)\)	\(e\left(\frac{27}{112}\right)\)	\(e\left(\frac{13}{56}\right)\)	\(e\left(\frac{103}{112}\right)\)	\(e\left(\frac{39}{56}\right)\)
\(\chi_{5424}(23,\cdot)\)	5424.fa	112	no	\(-1\)	\(1\)	\(e\left(\frac{43}{112}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{33}{56}\right)\)	\(e\left(\frac{31}{56}\right)\)	\(e\left(\frac{37}{112}\right)\)	\(e\left(\frac{27}{112}\right)\)	\(e\left(\frac{1}{112}\right)\)	\(e\left(\frac{43}{56}\right)\)	\(e\left(\frac{65}{112}\right)\)	\(e\left(\frac{45}{56}\right)\)
\(\chi_{5424}(25,\cdot)\)	5424.el	56	no	\(1\)	\(1\)	\(e\left(\frac{29}{56}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{5}{28}\right)\)	\(e\left(\frac{3}{28}\right)\)	\(e\left(\frac{23}{56}\right)\)	\(e\left(\frac{13}{56}\right)\)	\(e\left(\frac{43}{56}\right)\)	\(e\left(\frac{1}{28}\right)\)	\(e\left(\frac{23}{56}\right)\)	\(e\left(\frac{3}{28}\right)\)
\(\chi_{5424}(29,\cdot)\)	5424.ez	112	yes	\(1\)	\(1\)	\(e\left(\frac{23}{112}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{3}{56}\right)\)	\(e\left(\frac{41}{56}\right)\)	\(e\left(\frac{53}{112}\right)\)	\(e\left(\frac{103}{112}\right)\)	\(e\left(\frac{65}{112}\right)\)	\(e\left(\frac{23}{56}\right)\)	\(e\left(\frac{53}{112}\right)\)	\(e\left(\frac{41}{56}\right)\)
\(\chi_{5424}(31,\cdot)\)	5424.eu	56	no	\(-1\)	\(1\)	\(e\left(\frac{3}{56}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{15}{28}\right)\)	\(e\left(\frac{23}{28}\right)\)	\(e\left(\frac{13}{56}\right)\)	\(e\left(\frac{39}{56}\right)\)	\(e\left(\frac{45}{56}\right)\)	\(e\left(\frac{3}{28}\right)\)	\(e\left(\frac{41}{56}\right)\)	\(e\left(\frac{23}{28}\right)\)
\(\chi_{5424}(35,\cdot)\)	5424.cu	16	yes	\(-1\)	\(1\)	\(e\left(\frac{11}{16}\right)\)	\(-1\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{1}{8}\right)\)
\(\chi_{5424}(37,\cdot)\)	5424.ff	112	no	\(-1\)	\(1\)	\(e\left(\frac{101}{112}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{29}{56}\right)\)	\(e\left(\frac{51}{56}\right)\)	\(e\left(\frac{111}{112}\right)\)	\(e\left(\frac{109}{112}\right)\)	\(e\left(\frac{3}{112}\right)\)	\(e\left(\frac{45}{56}\right)\)	\(e\left(\frac{111}{112}\right)\)	\(e\left(\frac{51}{56}\right)\)
\(\chi_{5424}(41,\cdot)\)	5424.en	56	no	\(-1\)	\(1\)	\(e\left(\frac{37}{56}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{3}{28}\right)\)	\(e\left(\frac{27}{28}\right)\)	\(e\left(\frac{39}{56}\right)\)	\(e\left(\frac{33}{56}\right)\)	\(e\left(\frac{51}{56}\right)\)	\(e\left(\frac{9}{28}\right)\)	\(e\left(\frac{39}{56}\right)\)	\(e\left(\frac{27}{28}\right)\)
\(\chi_{5424}(43,\cdot)\)	5424.fm	112	no	\(1\)	\(1\)	\(e\left(\frac{9}{112}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{45}{56}\right)\)	\(e\left(\frac{55}{56}\right)\)	\(e\left(\frac{11}{112}\right)\)	\(e\left(\frac{89}{112}\right)\)	\(e\left(\frac{23}{112}\right)\)	\(e\left(\frac{9}{56}\right)\)	\(e\left(\frac{11}{112}\right)\)	\(e\left(\frac{27}{56}\right)\)
\(\chi_{5424}(47,\cdot)\)	5424.fd	112	no	\(-1\)	\(1\)	\(e\left(\frac{53}{112}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{27}{56}\right)\)	\(e\left(\frac{5}{56}\right)\)	\(e\left(\frac{99}{112}\right)\)	\(e\left(\frac{101}{112}\right)\)	\(e\left(\frac{39}{112}\right)\)	\(e\left(\frac{53}{56}\right)\)	\(e\left(\frac{15}{112}\right)\)	\(e\left(\frac{19}{56}\right)\)
\(\chi_{5424}(49,\cdot)\)	5424.bo	7	no	\(1\)	\(1\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{1}{7}\right)\)
\(\chi_{5424}(53,\cdot)\)	5424.dm	28	yes	\(-1\)	\(1\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{3}{28}\right)\)	\(e\left(\frac{27}{28}\right)\)	\(e\left(\frac{23}{28}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{1}{28}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{3}{14}\right)\)
\(\chi_{5424}(55,\cdot)\)	5424.fc	112	no	\(1\)	\(1\)	\(e\left(\frac{95}{112}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{41}{56}\right)\)	\(e\left(\frac{19}{56}\right)\)	\(e\left(\frac{1}{112}\right)\)	\(e\left(\frac{87}{112}\right)\)	\(e\left(\frac{109}{112}\right)\)	\(e\left(\frac{39}{56}\right)\)	\(e\left(\frac{29}{112}\right)\)	\(e\left(\frac{33}{56}\right)\)
\(\chi_{5424}(59,\cdot)\)	5424.fg	112	yes	\(-1\)	\(1\)	\(e\left(\frac{41}{112}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{9}{56}\right)\)	\(e\left(\frac{39}{56}\right)\)	\(e\left(\frac{75}{112}\right)\)	\(e\left(\frac{1}{112}\right)\)	\(e\left(\frac{55}{112}\right)\)	\(e\left(\frac{41}{56}\right)\)	\(e\left(\frac{75}{112}\right)\)	\(e\left(\frac{11}{56}\right)\)
\(\chi_{5424}(61,\cdot)\)	5424.eq	56	no	\(1\)	\(1\)	\(e\left(\frac{19}{56}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{31}{56}\right)\)	\(e\left(\frac{23}{56}\right)\)	\(e\left(\frac{47}{56}\right)\)	\(e\left(\frac{19}{28}\right)\)	\(e\left(\frac{17}{56}\right)\)	\(e\left(\frac{15}{28}\right)\)
\(\chi_{5424}(65,\cdot)\)	5424.cy	16	no	\(1\)	\(1\)	\(e\left(\frac{5}{16}\right)\)	\(-1\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{7}{8}\right)\)
\(\chi_{5424}(67,\cdot)\)	5424.fm	112	no	\(1\)	\(1\)	\(e\left(\frac{59}{112}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{15}{56}\right)\)	\(e\left(\frac{37}{56}\right)\)	\(e\left(\frac{97}{112}\right)\)	\(e\left(\frac{11}{112}\right)\)	\(e\left(\frac{101}{112}\right)\)	\(e\left(\frac{3}{56}\right)\)	\(e\left(\frac{97}{112}\right)\)	\(e\left(\frac{9}{56}\right)\)
\(\chi_{5424}(71,\cdot)\)	5424.dh	16	no	\(-1\)	\(1\)	\(e\left(\frac{1}{16}\right)\)	\(1\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{7}{8}\right)\)
\(\chi_{5424}(73,\cdot)\)	5424.cz	16	no	\(-1\)	\(1\)	\(e\left(\frac{3}{16}\right)\)	\(-1\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{1}{8}\right)\)
\(\chi_{5424}(77,\cdot)\)	5424.er	56	yes	\(-1\)	\(1\)	\(e\left(\frac{1}{56}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{9}{56}\right)\)	\(e\left(\frac{41}{56}\right)\)	\(e\left(\frac{1}{56}\right)\)	\(e\left(\frac{1}{28}\right)\)	\(e\left(\frac{51}{56}\right)\)	\(e\left(\frac{17}{28}\right)\)
\(\chi_{5424}(79,\cdot)\)	5424.fb	112	no	\(1\)	\(1\)	\(e\left(\frac{11}{112}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{41}{56}\right)\)	\(e\left(\frac{19}{56}\right)\)	\(e\left(\frac{29}{112}\right)\)	\(e\left(\frac{3}{112}\right)\)	\(e\left(\frac{25}{112}\right)\)	\(e\left(\frac{11}{56}\right)\)	\(e\left(\frac{1}{112}\right)\)	\(e\left(\frac{5}{56}\right)\)
\(\chi_{5424}(83,\cdot)\)	5424.dq	28	yes	\(1\)	\(1\)	\(e\left(\frac{25}{28}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{5}{28}\right)\)	\(e\left(\frac{3}{28}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{3}{28}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{15}{28}\right)\)	\(e\left(\frac{5}{14}\right)\)
\(\chi_{5424}(85,\cdot)\)	5424.eb	28	no	\(1\)	\(1\)	\(e\left(\frac{13}{28}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{11}{28}\right)\)	\(e\left(\frac{1}{28}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{15}{28}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{19}{28}\right)\)	\(e\left(\frac{2}{7}\right)\)
\(\chi_{5424}(89,\cdot)\)	5424.fk	112	no	\(1\)	\(1\)	\(e\left(\frac{103}{112}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{25}{56}\right)\)	\(e\left(\frac{43}{56}\right)\)	\(e\left(\frac{73}{112}\right)\)	\(e\left(\frac{79}{112}\right)\)	\(e\left(\frac{61}{112}\right)\)	\(e\left(\frac{47}{56}\right)\)	\(e\left(\frac{101}{112}\right)\)	\(e\left(\frac{29}{56}\right)\)
\(\chi_{5424}(91,\cdot)\)	5424.ej	56	no	\(-1\)	\(1\)	\(e\left(\frac{27}{56}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{19}{56}\right)\)	\(e\left(\frac{43}{56}\right)\)	\(e\left(\frac{55}{56}\right)\)	\(e\left(\frac{27}{28}\right)\)	\(e\left(\frac{33}{56}\right)\)	\(e\left(\frac{25}{28}\right)\)
\(\chi_{5424}(95,\cdot)\)	5424.bu	8	no	\(1\)	\(1\)	\(e\left(\frac{3}{8}\right)\)	\(-1\)	\(i\)	\(-i\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(-i\)	\(e\left(\frac{1}{8}\right)\)	\(-i\)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Learn more

Character group

First 32 of 1792 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.