LMFDB - Group of Dirichlet characters of modulus 7350

Show commands: PariGP / SageMath

sage: H = DirichletGroup(7350)

pari: g = idealstar(,7350,2)

Character group

sage: G.order() pari: g.no
Order	=	1680
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{2}\times C_{420}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{7350}(4901,\cdot)$, $\chi_{7350}(1177,\cdot)$, $\chi_{7350}(2551,\cdot)$

First 32 of 1680 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	$-1$	$1$	$11$	$13$	$17$	$19$	$23$	$29$	$31$	$37$	$41$	$43$
$\chi_{7350}(1,\cdot)$	7350.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{7350}(11,\cdot)$	7350.dn	210	no	$-1$	$1$	$e\left(\frac{83}{210}\right)$	$e\left(\frac{22}{35}\right)$	$e\left(\frac{149}{210}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{103}{210}\right)$	$e\left(\frac{17}{70}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{71}{105}\right)$	$e\left(\frac{69}{70}\right)$	$e\left(\frac{5}{7}\right)$
$\chi_{7350}(13,\cdot)$	7350.df	140	no	$1$	$1$	$e\left(\frac{22}{35}\right)$	$e\left(\frac{137}{140}\right)$	$e\left(\frac{139}{140}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{43}{140}\right)$	$e\left(\frac{3}{70}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{97}{140}\right)$	$e\left(\frac{41}{70}\right)$	$e\left(\frac{27}{28}\right)$
$\chi_{7350}(17,\cdot)$	7350.dr	420	no	$-1$	$1$	$e\left(\frac{149}{210}\right)$	$e\left(\frac{139}{140}\right)$	$e\left(\frac{349}{420}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{113}{420}\right)$	$e\left(\frac{18}{35}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{377}{420}\right)$	$e\left(\frac{1}{35}\right)$	$e\left(\frac{9}{28}\right)$
$\chi_{7350}(19,\cdot)$	7350.cc	30	no	$-1$	$1$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{1}{10}\right)$	$-1$
$\chi_{7350}(23,\cdot)$	7350.dq	420	no	$1$	$1$	$e\left(\frac{103}{210}\right)$	$e\left(\frac{43}{140}\right)$	$e\left(\frac{113}{420}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{391}{420}\right)$	$e\left(\frac{31}{35}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{379}{420}\right)$	$e\left(\frac{19}{70}\right)$	$e\left(\frac{19}{28}\right)$
$\chi_{7350}(29,\cdot)$	7350.cr	70	no	$-1$	$1$	$e\left(\frac{17}{70}\right)$	$e\left(\frac{3}{70}\right)$	$e\left(\frac{18}{35}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{31}{35}\right)$	$e\left(\frac{29}{70}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{43}{70}\right)$	$e\left(\frac{23}{70}\right)$	$e\left(\frac{1}{14}\right)$
$\chi_{7350}(31,\cdot)$	7350.cd	30	no	$-1$	$1$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{1}{10}\right)$	$1$
$\chi_{7350}(37,\cdot)$	7350.do	420	no	$-1$	$1$	$e\left(\frac{71}{105}\right)$	$e\left(\frac{97}{140}\right)$	$e\left(\frac{377}{420}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{379}{420}\right)$	$e\left(\frac{43}{70}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{181}{420}\right)$	$e\left(\frac{8}{35}\right)$	$e\left(\frac{9}{28}\right)$
$\chi_{7350}(41,\cdot)$	7350.cs	70	no	$1$	$1$	$e\left(\frac{69}{70}\right)$	$e\left(\frac{41}{70}\right)$	$e\left(\frac{1}{35}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{19}{70}\right)$	$e\left(\frac{23}{70}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{8}{35}\right)$	$e\left(\frac{23}{35}\right)$	$e\left(\frac{1}{7}\right)$
$\chi_{7350}(43,\cdot)$	7350.bu	28	no	$-1$	$1$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{27}{28}\right)$	$e\left(\frac{9}{28}\right)$	$-1$	$e\left(\frac{19}{28}\right)$	$e\left(\frac{1}{14}\right)$	$1$	$e\left(\frac{9}{28}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{3}{28}\right)$
$\chi_{7350}(47,\cdot)$	7350.dr	420	no	$-1$	$1$	$e\left(\frac{181}{210}\right)$	$e\left(\frac{11}{140}\right)$	$e\left(\frac{221}{420}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{157}{420}\right)$	$e\left(\frac{12}{35}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{193}{420}\right)$	$e\left(\frac{24}{35}\right)$	$e\left(\frac{13}{28}\right)$
$\chi_{7350}(53,\cdot)$	7350.dq	420	no	$1$	$1$	$e\left(\frac{131}{210}\right)$	$e\left(\frac{71}{140}\right)$	$e\left(\frac{1}{420}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{167}{420}\right)$	$e\left(\frac{17}{35}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{323}{420}\right)$	$e\left(\frac{33}{70}\right)$	$e\left(\frac{19}{28}\right)$
$\chi_{7350}(59,\cdot)$	7350.dm	210	no	$1$	$1$	$e\left(\frac{17}{210}\right)$	$e\left(\frac{18}{35}\right)$	$e\left(\frac{71}{210}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{101}{105}\right)$	$e\left(\frac{33}{70}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{43}{210}\right)$	$e\left(\frac{33}{35}\right)$	$e\left(\frac{5}{14}\right)$
$\chi_{7350}(61,\cdot)$	7350.dh	210	no	$-1$	$1$	$e\left(\frac{29}{105}\right)$	$e\left(\frac{59}{70}\right)$	$e\left(\frac{199}{210}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{79}{105}\right)$	$e\left(\frac{11}{35}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{61}{105}\right)$	$e\left(\frac{9}{70}\right)$	$e\left(\frac{4}{7}\right)$
$\chi_{7350}(67,\cdot)$	7350.cp	60	no	$-1$	$1$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{7}{60}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{29}{60}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{11}{60}\right)$	$e\left(\frac{3}{5}\right)$	$-i$
$\chi_{7350}(71,\cdot)$	7350.ct	70	no	$-1$	$1$	$e\left(\frac{67}{70}\right)$	$e\left(\frac{9}{35}\right)$	$e\left(\frac{41}{70}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{57}{70}\right)$	$e\left(\frac{69}{70}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{24}{35}\right)$	$e\left(\frac{33}{70}\right)$	$e\left(\frac{3}{7}\right)$
$\chi_{7350}(73,\cdot)$	7350.dp	420	no	$1$	$1$	$e\left(\frac{4}{105}\right)$	$e\left(\frac{73}{140}\right)$	$e\left(\frac{73}{420}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{221}{420}\right)$	$e\left(\frac{67}{70}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{59}{420}\right)$	$e\left(\frac{29}{70}\right)$	$e\left(\frac{15}{28}\right)$
$\chi_{7350}(79,\cdot)$	7350.ce	30	no	$1$	$1$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{2}{5}\right)$	$-1$
$\chi_{7350}(83,\cdot)$	7350.dd	140	no	$-1$	$1$	$e\left(\frac{33}{70}\right)$	$e\left(\frac{129}{140}\right)$	$e\left(\frac{113}{140}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{41}{140}\right)$	$e\left(\frac{23}{35}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{29}{140}\right)$	$e\left(\frac{11}{35}\right)$	$e\left(\frac{15}{28}\right)$
$\chi_{7350}(89,\cdot)$	7350.dm	210	no	$1$	$1$	$e\left(\frac{43}{210}\right)$	$e\left(\frac{27}{35}\right)$	$e\left(\frac{19}{210}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{64}{105}\right)$	$e\left(\frac{67}{70}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{47}{210}\right)$	$e\left(\frac{32}{35}\right)$	$e\left(\frac{11}{14}\right)$
$\chi_{7350}(97,\cdot)$	7350.bp	20	no	$1$	$1$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{9}{10}\right)$	$-i$
$\chi_{7350}(101,\cdot)$	7350.cj	42	no	$1$	$1$	$e\left(\frac{19}{42}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{17}{42}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{1}{7}\right)$
$\chi_{7350}(103,\cdot)$	7350.dp	420	no	$1$	$1$	$e\left(\frac{23}{105}\right)$	$e\left(\frac{61}{140}\right)$	$e\left(\frac{341}{420}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{37}{420}\right)$	$e\left(\frac{9}{70}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{103}{420}\right)$	$e\left(\frac{53}{70}\right)$	$e\left(\frac{11}{28}\right)$
$\chi_{7350}(107,\cdot)$	7350.cz	84	no	$1$	$1$	$e\left(\frac{17}{42}\right)$	$e\left(\frac{9}{28}\right)$	$e\left(\frac{79}{84}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{84}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{65}{84}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{1}{28}\right)$
$\chi_{7350}(109,\cdot)$	7350.di	210	no	$1$	$1$	$e\left(\frac{31}{105}\right)$	$e\left(\frac{51}{70}\right)$	$e\left(\frac{191}{210}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{187}{210}\right)$	$e\left(\frac{19}{35}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{163}{210}\right)$	$e\left(\frac{3}{35}\right)$	$e\left(\frac{3}{14}\right)$
$\chi_{7350}(113,\cdot)$	7350.de	140	no	$1$	$1$	$e\left(\frac{19}{70}\right)$	$e\left(\frac{87}{140}\right)$	$e\left(\frac{99}{140}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{13}{140}\right)$	$e\left(\frac{9}{35}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{57}{140}\right)$	$e\left(\frac{1}{70}\right)$	$e\left(\frac{15}{28}\right)$
$\chi_{7350}(121,\cdot)$	7350.dc	105	no	$1$	$1$	$e\left(\frac{83}{105}\right)$	$e\left(\frac{9}{35}\right)$	$e\left(\frac{44}{105}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{103}{105}\right)$	$e\left(\frac{17}{35}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{37}{105}\right)$	$e\left(\frac{34}{35}\right)$	$e\left(\frac{3}{7}\right)$
$\chi_{7350}(127,\cdot)$	7350.dg	140	no	$-1$	$1$	$e\left(\frac{33}{35}\right)$	$e\left(\frac{13}{140}\right)$	$e\left(\frac{51}{140}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{117}{140}\right)$	$e\left(\frac{57}{70}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{23}{140}\right)$	$e\left(\frac{22}{35}\right)$	$e\left(\frac{9}{28}\right)$
$\chi_{7350}(131,\cdot)$	7350.dk	210	no	$1$	$1$	$e\left(\frac{199}{210}\right)$	$e\left(\frac{57}{70}\right)$	$e\left(\frac{11}{105}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{209}{210}\right)$	$e\left(\frac{61}{70}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{88}{105}\right)$	$e\left(\frac{26}{35}\right)$	$e\left(\frac{6}{7}\right)$
$\chi_{7350}(137,\cdot)$	7350.dq	420	no	$1$	$1$	$e\left(\frac{17}{210}\right)$	$e\left(\frac{37}{140}\right)$	$e\left(\frac{247}{420}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{89}{420}\right)$	$e\left(\frac{34}{35}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{401}{420}\right)$	$e\left(\frac{31}{70}\right)$	$e\left(\frac{17}{28}\right)$
$\chi_{7350}(139,\cdot)$	7350.cx	70	no	$-1$	$1$	$e\left(\frac{3}{35}\right)$	$e\left(\frac{17}{35}\right)$	$e\left(\frac{29}{35}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{61}{70}\right)$	$e\left(\frac{1}{35}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{9}{70}\right)$	$e\left(\frac{39}{70}\right)$	$e\left(\frac{9}{14}\right)$

Click here to search among the remaining 1648 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	$7350$
Structure	\(C_{2}\times C_{2}\times C_{420}\)
Order	$1680$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(11\)	\(13\)	\(17\)	\(19\)	\(23\)	\(29\)	\(31\)	\(37\)	\(41\)	\(43\)
\(\chi_{7350}(1,\cdot)\)	7350.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{7350}(11,\cdot)\)	7350.dn	210	no	\(-1\)	\(1\)	\(e\left(\frac{83}{210}\right)\)	\(e\left(\frac{22}{35}\right)\)	\(e\left(\frac{149}{210}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{103}{210}\right)\)	\(e\left(\frac{17}{70}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{71}{105}\right)\)	\(e\left(\frac{69}{70}\right)\)	\(e\left(\frac{5}{7}\right)\)
\(\chi_{7350}(13,\cdot)\)	7350.df	140	no	\(1\)	\(1\)	\(e\left(\frac{22}{35}\right)\)	\(e\left(\frac{137}{140}\right)\)	\(e\left(\frac{139}{140}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{43}{140}\right)\)	\(e\left(\frac{3}{70}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{97}{140}\right)\)	\(e\left(\frac{41}{70}\right)\)	\(e\left(\frac{27}{28}\right)\)
\(\chi_{7350}(17,\cdot)\)	7350.dr	420	no	\(-1\)	\(1\)	\(e\left(\frac{149}{210}\right)\)	\(e\left(\frac{139}{140}\right)\)	\(e\left(\frac{349}{420}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{113}{420}\right)\)	\(e\left(\frac{18}{35}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{377}{420}\right)\)	\(e\left(\frac{1}{35}\right)\)	\(e\left(\frac{9}{28}\right)\)
\(\chi_{7350}(19,\cdot)\)	7350.cc	30	no	\(-1\)	\(1\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(-1\)
\(\chi_{7350}(23,\cdot)\)	7350.dq	420	no	\(1\)	\(1\)	\(e\left(\frac{103}{210}\right)\)	\(e\left(\frac{43}{140}\right)\)	\(e\left(\frac{113}{420}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{391}{420}\right)\)	\(e\left(\frac{31}{35}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{379}{420}\right)\)	\(e\left(\frac{19}{70}\right)\)	\(e\left(\frac{19}{28}\right)\)
\(\chi_{7350}(29,\cdot)\)	7350.cr	70	no	\(-1\)	\(1\)	\(e\left(\frac{17}{70}\right)\)	\(e\left(\frac{3}{70}\right)\)	\(e\left(\frac{18}{35}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{31}{35}\right)\)	\(e\left(\frac{29}{70}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{43}{70}\right)\)	\(e\left(\frac{23}{70}\right)\)	\(e\left(\frac{1}{14}\right)\)
\(\chi_{7350}(31,\cdot)\)	7350.cd	30	no	\(-1\)	\(1\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(1\)
\(\chi_{7350}(37,\cdot)\)	7350.do	420	no	\(-1\)	\(1\)	\(e\left(\frac{71}{105}\right)\)	\(e\left(\frac{97}{140}\right)\)	\(e\left(\frac{377}{420}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{379}{420}\right)\)	\(e\left(\frac{43}{70}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{181}{420}\right)\)	\(e\left(\frac{8}{35}\right)\)	\(e\left(\frac{9}{28}\right)\)
\(\chi_{7350}(41,\cdot)\)	7350.cs	70	no	\(1\)	\(1\)	\(e\left(\frac{69}{70}\right)\)	\(e\left(\frac{41}{70}\right)\)	\(e\left(\frac{1}{35}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{19}{70}\right)\)	\(e\left(\frac{23}{70}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{8}{35}\right)\)	\(e\left(\frac{23}{35}\right)\)	\(e\left(\frac{1}{7}\right)\)
\(\chi_{7350}(43,\cdot)\)	7350.bu	28	no	\(-1\)	\(1\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{27}{28}\right)\)	\(e\left(\frac{9}{28}\right)\)	\(-1\)	\(e\left(\frac{19}{28}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(1\)	\(e\left(\frac{9}{28}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{3}{28}\right)\)
\(\chi_{7350}(47,\cdot)\)	7350.dr	420	no	\(-1\)	\(1\)	\(e\left(\frac{181}{210}\right)\)	\(e\left(\frac{11}{140}\right)\)	\(e\left(\frac{221}{420}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{157}{420}\right)\)	\(e\left(\frac{12}{35}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{193}{420}\right)\)	\(e\left(\frac{24}{35}\right)\)	\(e\left(\frac{13}{28}\right)\)
\(\chi_{7350}(53,\cdot)\)	7350.dq	420	no	\(1\)	\(1\)	\(e\left(\frac{131}{210}\right)\)	\(e\left(\frac{71}{140}\right)\)	\(e\left(\frac{1}{420}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{167}{420}\right)\)	\(e\left(\frac{17}{35}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{323}{420}\right)\)	\(e\left(\frac{33}{70}\right)\)	\(e\left(\frac{19}{28}\right)\)
\(\chi_{7350}(59,\cdot)\)	7350.dm	210	no	\(1\)	\(1\)	\(e\left(\frac{17}{210}\right)\)	\(e\left(\frac{18}{35}\right)\)	\(e\left(\frac{71}{210}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{101}{105}\right)\)	\(e\left(\frac{33}{70}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{43}{210}\right)\)	\(e\left(\frac{33}{35}\right)\)	\(e\left(\frac{5}{14}\right)\)
\(\chi_{7350}(61,\cdot)\)	7350.dh	210	no	\(-1\)	\(1\)	\(e\left(\frac{29}{105}\right)\)	\(e\left(\frac{59}{70}\right)\)	\(e\left(\frac{199}{210}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{79}{105}\right)\)	\(e\left(\frac{11}{35}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{61}{105}\right)\)	\(e\left(\frac{9}{70}\right)\)	\(e\left(\frac{4}{7}\right)\)
\(\chi_{7350}(67,\cdot)\)	7350.cp	60	no	\(-1\)	\(1\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{7}{60}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{29}{60}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{11}{60}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(-i\)
\(\chi_{7350}(71,\cdot)\)	7350.ct	70	no	\(-1\)	\(1\)	\(e\left(\frac{67}{70}\right)\)	\(e\left(\frac{9}{35}\right)\)	\(e\left(\frac{41}{70}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{57}{70}\right)\)	\(e\left(\frac{69}{70}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{24}{35}\right)\)	\(e\left(\frac{33}{70}\right)\)	\(e\left(\frac{3}{7}\right)\)
\(\chi_{7350}(73,\cdot)\)	7350.dp	420	no	\(1\)	\(1\)	\(e\left(\frac{4}{105}\right)\)	\(e\left(\frac{73}{140}\right)\)	\(e\left(\frac{73}{420}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{221}{420}\right)\)	\(e\left(\frac{67}{70}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{59}{420}\right)\)	\(e\left(\frac{29}{70}\right)\)	\(e\left(\frac{15}{28}\right)\)
\(\chi_{7350}(79,\cdot)\)	7350.ce	30	no	\(1\)	\(1\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(-1\)
\(\chi_{7350}(83,\cdot)\)	7350.dd	140	no	\(-1\)	\(1\)	\(e\left(\frac{33}{70}\right)\)	\(e\left(\frac{129}{140}\right)\)	\(e\left(\frac{113}{140}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{41}{140}\right)\)	\(e\left(\frac{23}{35}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{29}{140}\right)\)	\(e\left(\frac{11}{35}\right)\)	\(e\left(\frac{15}{28}\right)\)
\(\chi_{7350}(89,\cdot)\)	7350.dm	210	no	\(1\)	\(1\)	\(e\left(\frac{43}{210}\right)\)	\(e\left(\frac{27}{35}\right)\)	\(e\left(\frac{19}{210}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{64}{105}\right)\)	\(e\left(\frac{67}{70}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{47}{210}\right)\)	\(e\left(\frac{32}{35}\right)\)	\(e\left(\frac{11}{14}\right)\)
\(\chi_{7350}(97,\cdot)\)	7350.bp	20	no	\(1\)	\(1\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(-i\)
\(\chi_{7350}(101,\cdot)\)	7350.cj	42	no	\(1\)	\(1\)	\(e\left(\frac{19}{42}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{17}{42}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{1}{7}\right)\)
\(\chi_{7350}(103,\cdot)\)	7350.dp	420	no	\(1\)	\(1\)	\(e\left(\frac{23}{105}\right)\)	\(e\left(\frac{61}{140}\right)\)	\(e\left(\frac{341}{420}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{37}{420}\right)\)	\(e\left(\frac{9}{70}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{103}{420}\right)\)	\(e\left(\frac{53}{70}\right)\)	\(e\left(\frac{11}{28}\right)\)
\(\chi_{7350}(107,\cdot)\)	7350.cz	84	no	\(1\)	\(1\)	\(e\left(\frac{17}{42}\right)\)	\(e\left(\frac{9}{28}\right)\)	\(e\left(\frac{79}{84}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{84}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{65}{84}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{1}{28}\right)\)
\(\chi_{7350}(109,\cdot)\)	7350.di	210	no	\(1\)	\(1\)	\(e\left(\frac{31}{105}\right)\)	\(e\left(\frac{51}{70}\right)\)	\(e\left(\frac{191}{210}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{187}{210}\right)\)	\(e\left(\frac{19}{35}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{163}{210}\right)\)	\(e\left(\frac{3}{35}\right)\)	\(e\left(\frac{3}{14}\right)\)
\(\chi_{7350}(113,\cdot)\)	7350.de	140	no	\(1\)	\(1\)	\(e\left(\frac{19}{70}\right)\)	\(e\left(\frac{87}{140}\right)\)	\(e\left(\frac{99}{140}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{13}{140}\right)\)	\(e\left(\frac{9}{35}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{57}{140}\right)\)	\(e\left(\frac{1}{70}\right)\)	\(e\left(\frac{15}{28}\right)\)
\(\chi_{7350}(121,\cdot)\)	7350.dc	105	no	\(1\)	\(1\)	\(e\left(\frac{83}{105}\right)\)	\(e\left(\frac{9}{35}\right)\)	\(e\left(\frac{44}{105}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{103}{105}\right)\)	\(e\left(\frac{17}{35}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{37}{105}\right)\)	\(e\left(\frac{34}{35}\right)\)	\(e\left(\frac{3}{7}\right)\)
\(\chi_{7350}(127,\cdot)\)	7350.dg	140	no	\(-1\)	\(1\)	\(e\left(\frac{33}{35}\right)\)	\(e\left(\frac{13}{140}\right)\)	\(e\left(\frac{51}{140}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{117}{140}\right)\)	\(e\left(\frac{57}{70}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{23}{140}\right)\)	\(e\left(\frac{22}{35}\right)\)	\(e\left(\frac{9}{28}\right)\)
\(\chi_{7350}(131,\cdot)\)	7350.dk	210	no	\(1\)	\(1\)	\(e\left(\frac{199}{210}\right)\)	\(e\left(\frac{57}{70}\right)\)	\(e\left(\frac{11}{105}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{209}{210}\right)\)	\(e\left(\frac{61}{70}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{88}{105}\right)\)	\(e\left(\frac{26}{35}\right)\)	\(e\left(\frac{6}{7}\right)\)
\(\chi_{7350}(137,\cdot)\)	7350.dq	420	no	\(1\)	\(1\)	\(e\left(\frac{17}{210}\right)\)	\(e\left(\frac{37}{140}\right)\)	\(e\left(\frac{247}{420}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{89}{420}\right)\)	\(e\left(\frac{34}{35}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{401}{420}\right)\)	\(e\left(\frac{31}{70}\right)\)	\(e\left(\frac{17}{28}\right)\)
\(\chi_{7350}(139,\cdot)\)	7350.cx	70	no	\(-1\)	\(1\)	\(e\left(\frac{3}{35}\right)\)	\(e\left(\frac{17}{35}\right)\)	\(e\left(\frac{29}{35}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{61}{70}\right)\)	\(e\left(\frac{1}{35}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{9}{70}\right)\)	\(e\left(\frac{39}{70}\right)\)	\(e\left(\frac{9}{14}\right)\)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Learn more

Character group

First 32 of 1680 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.