LMFDB - Group of Dirichlet characters of modulus 7497

Show commands: PariGP / SageMath

sage: H = DirichletGroup(7497)

pari: g = idealstar(,7497,2)

Character group

sage: G.order() pari: g.no
Order	=	4032
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{6}\times C_{336}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{7497}(1667,\cdot)$, $\chi_{7497}(5050,\cdot)$, $\chi_{7497}(6616,\cdot)$

First 32 of 4032 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	$-1$	$1$	$2$	$4$	$5$	$8$	$10$	$11$	$13$	$16$	$19$	$20$
$\chi_{7497}(1,\cdot)$	7497.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{7497}(2,\cdot)$	7497.go	168	yes	$-1$	$1$	$e\left(\frac{43}{84}\right)$	$e\left(\frac{1}{42}\right)$	$e\left(\frac{9}{56}\right)$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{113}{168}\right)$	$e\left(\frac{3}{56}\right)$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{31}{168}\right)$
$\chi_{7497}(4,\cdot)$	7497.fy	84	yes	$1$	$1$	$e\left(\frac{1}{42}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{9}{28}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{29}{84}\right)$	$e\left(\frac{3}{28}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{31}{84}\right)$
$\chi_{7497}(5,\cdot)$	7497.ho	336	yes	$-1$	$1$	$e\left(\frac{9}{56}\right)$	$e\left(\frac{9}{28}\right)$	$e\left(\frac{253}{336}\right)$	$e\left(\frac{27}{56}\right)$	$e\left(\frac{307}{336}\right)$	$e\left(\frac{215}{336}\right)$	$e\left(\frac{59}{84}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{25}{336}\right)$
$\chi_{7497}(8,\cdot)$	7497.fq	56	no	$-1$	$1$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{27}{56}\right)$	$e\left(\frac{17}{28}\right)$	$e\left(\frac{1}{56}\right)$	$e\left(\frac{9}{56}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{1}{7}\right)$	$-i$	$e\left(\frac{31}{56}\right)$
$\chi_{7497}(10,\cdot)$	7497.hc	336	no	$1$	$1$	$e\left(\frac{113}{168}\right)$	$e\left(\frac{29}{84}\right)$	$e\left(\frac{307}{336}\right)$	$e\left(\frac{1}{56}\right)$	$e\left(\frac{197}{336}\right)$	$e\left(\frac{233}{336}\right)$	$e\left(\frac{27}{28}\right)$	$e\left(\frac{29}{42}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{29}{112}\right)$
$\chi_{7497}(11,\cdot)$	7497.hp	336	yes	$1$	$1$	$e\left(\frac{3}{56}\right)$	$e\left(\frac{3}{28}\right)$	$e\left(\frac{215}{336}\right)$	$e\left(\frac{9}{56}\right)$	$e\left(\frac{233}{336}\right)$	$e\left(\frac{109}{336}\right)$	$e\left(\frac{43}{84}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{251}{336}\right)$
$\chi_{7497}(13,\cdot)$	7497.fw	84	yes	$-1$	$1$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{59}{84}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{27}{28}\right)$	$e\left(\frac{43}{84}\right)$	$e\left(\frac{25}{42}\right)$	$e\left(\frac{1}{21}\right)$	$1$	$e\left(\frac{19}{84}\right)$
$\chi_{7497}(16,\cdot)$	7497.et	42	yes	$1$	$1$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{29}{42}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{31}{42}\right)$
$\chi_{7497}(19,\cdot)$	7497.dq	24	no	$-1$	$1$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{13}{24}\right)$	$-i$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{11}{24}\right)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{3}{8}\right)$
$\chi_{7497}(20,\cdot)$	7497.hf	336	yes	$-1$	$1$	$e\left(\frac{31}{168}\right)$	$e\left(\frac{31}{84}\right)$	$e\left(\frac{25}{336}\right)$	$e\left(\frac{31}{56}\right)$	$e\left(\frac{29}{112}\right)$	$e\left(\frac{251}{336}\right)$	$e\left(\frac{19}{84}\right)$	$e\left(\frac{31}{42}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{149}{336}\right)$
$\chi_{7497}(22,\cdot)$	7497.hk	336	yes	$-1$	$1$	$e\left(\frac{95}{168}\right)$	$e\left(\frac{11}{84}\right)$	$e\left(\frac{269}{336}\right)$	$e\left(\frac{39}{56}\right)$	$e\left(\frac{41}{112}\right)$	$e\left(\frac{127}{336}\right)$	$e\left(\frac{65}{84}\right)$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{313}{336}\right)$
$\chi_{7497}(23,\cdot)$	7497.hp	336	yes	$1$	$1$	$e\left(\frac{27}{56}\right)$	$e\left(\frac{27}{28}\right)$	$e\left(\frac{31}{336}\right)$	$e\left(\frac{25}{56}\right)$	$e\left(\frac{193}{336}\right)$	$e\left(\frac{197}{336}\right)$	$e\left(\frac{23}{84}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{19}{336}\right)$
$\chi_{7497}(25,\cdot)$	7497.gy	168	yes	$1$	$1$	$e\left(\frac{9}{28}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{85}{168}\right)$	$e\left(\frac{27}{28}\right)$	$e\left(\frac{139}{168}\right)$	$e\left(\frac{47}{168}\right)$	$e\left(\frac{17}{42}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{25}{168}\right)$
$\chi_{7497}(26,\cdot)$	7497.gm	168	no	$1$	$1$	$e\left(\frac{65}{84}\right)$	$e\left(\frac{23}{42}\right)$	$e\left(\frac{145}{168}\right)$	$e\left(\frac{9}{28}\right)$	$e\left(\frac{107}{168}\right)$	$e\left(\frac{95}{168}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{23}{56}\right)$
$\chi_{7497}(29,\cdot)$	7497.hg	336	yes	$1$	$1$	$e\left(\frac{115}{168}\right)$	$e\left(\frac{31}{84}\right)$	$e\left(\frac{109}{336}\right)$	$e\left(\frac{3}{56}\right)$	$e\left(\frac{1}{112}\right)$	$e\left(\frac{335}{336}\right)$	$e\left(\frac{61}{84}\right)$	$e\left(\frac{31}{42}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{233}{336}\right)$
$\chi_{7497}(31,\cdot)$	7497.fi	48	no	$1$	$1$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{41}{48}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{19}{48}\right)$
$\chi_{7497}(32,\cdot)$	7497.go	168	yes	$-1$	$1$	$e\left(\frac{47}{84}\right)$	$e\left(\frac{5}{42}\right)$	$e\left(\frac{45}{56}\right)$	$e\left(\frac{19}{28}\right)$	$e\left(\frac{61}{168}\right)$	$e\left(\frac{15}{56}\right)$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{155}{168}\right)$
$\chi_{7497}(37,\cdot)$	7497.hd	336	no	$-1$	$1$	$e\left(\frac{115}{168}\right)$	$e\left(\frac{31}{84}\right)$	$e\left(\frac{137}{336}\right)$	$e\left(\frac{3}{56}\right)$	$e\left(\frac{31}{336}\right)$	$e\left(\frac{307}{336}\right)$	$e\left(\frac{11}{28}\right)$	$e\left(\frac{31}{42}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{87}{112}\right)$
$\chi_{7497}(38,\cdot)$	7497.fs	84	yes	$1$	$1$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{59}{84}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{11}{84}\right)$	$e\left(\frac{43}{84}\right)$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{47}{84}\right)$
$\chi_{7497}(40,\cdot)$	7497.hq	336	yes	$1$	$1$	$e\left(\frac{39}{56}\right)$	$e\left(\frac{11}{28}\right)$	$e\left(\frac{79}{336}\right)$	$e\left(\frac{5}{56}\right)$	$e\left(\frac{313}{336}\right)$	$e\left(\frac{269}{336}\right)$	$e\left(\frac{41}{84}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{211}{336}\right)$
$\chi_{7497}(41,\cdot)$	7497.hf	336	yes	$-1$	$1$	$e\left(\frac{125}{168}\right)$	$e\left(\frac{41}{84}\right)$	$e\left(\frac{323}{336}\right)$	$e\left(\frac{13}{56}\right)$	$e\left(\frac{79}{112}\right)$	$e\left(\frac{313}{336}\right)$	$e\left(\frac{17}{84}\right)$	$e\left(\frac{41}{42}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{151}{336}\right)$
$\chi_{7497}(43,\cdot)$	7497.gp	168	yes	$1$	$1$	$e\left(\frac{11}{84}\right)$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{17}{168}\right)$	$e\left(\frac{11}{28}\right)$	$e\left(\frac{13}{56}\right)$	$e\left(\frac{43}{168}\right)$	$e\left(\frac{23}{42}\right)$	$e\left(\frac{11}{21}\right)$	$-i$	$e\left(\frac{61}{168}\right)$
$\chi_{7497}(44,\cdot)$	7497.hn	336	no	$1$	$1$	$e\left(\frac{13}{168}\right)$	$e\left(\frac{13}{84}\right)$	$e\left(\frac{323}{336}\right)$	$e\left(\frac{13}{56}\right)$	$e\left(\frac{13}{336}\right)$	$e\left(\frac{145}{336}\right)$	$e\left(\frac{1}{28}\right)$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{13}{112}\right)$
$\chi_{7497}(46,\cdot)$	7497.hd	336	no	$-1$	$1$	$e\left(\frac{167}{168}\right)$	$e\left(\frac{83}{84}\right)$	$e\left(\frac{85}{336}\right)$	$e\left(\frac{55}{56}\right)$	$e\left(\frac{83}{336}\right)$	$e\left(\frac{215}{336}\right)$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{41}{42}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{27}{112}\right)$
$\chi_{7497}(47,\cdot)$	7497.gb	84	yes	$1$	$1$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{25}{84}\right)$	$e\left(\frac{19}{28}\right)$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{84}\right)$
$\chi_{7497}(50,\cdot)$	7497.bf	6	no	$-1$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$	$-1$	$-1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$1$	$e\left(\frac{1}{3}\right)$
$\chi_{7497}(52,\cdot)$	7497.dx	42	no	$-1$	$1$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{1}{42}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{5}{42}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{25}{42}\right)$
$\chi_{7497}(53,\cdot)$	7497.gx	168	no	$-1$	$1$	$e\left(\frac{79}{84}\right)$	$e\left(\frac{37}{42}\right)$	$e\left(\frac{131}{168}\right)$	$e\left(\frac{23}{28}\right)$	$e\left(\frac{121}{168}\right)$	$e\left(\frac{25}{168}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{37}{56}\right)$
$\chi_{7497}(55,\cdot)$	7497.dv	28	no	$-1$	$1$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{11}{28}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{17}{28}\right)$	$e\left(\frac{27}{28}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{6}{7}\right)$	$1$	$e\left(\frac{23}{28}\right)$
$\chi_{7497}(58,\cdot)$	7497.hr	336	yes	$-1$	$1$	$e\left(\frac{11}{56}\right)$	$e\left(\frac{11}{28}\right)$	$e\left(\frac{163}{336}\right)$	$e\left(\frac{33}{56}\right)$	$e\left(\frac{229}{336}\right)$	$e\left(\frac{17}{336}\right)$	$e\left(\frac{83}{84}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{295}{336}\right)$
$\chi_{7497}(59,\cdot)$	7497.gv	168	yes	$1$	$1$	$e\left(\frac{53}{84}\right)$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{15}{56}\right)$	$e\left(\frac{25}{28}\right)$	$e\left(\frac{151}{168}\right)$	$e\left(\frac{33}{56}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{89}{168}\right)$

Click here to search among the remaining 4000 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	$7497$
Structure	\(C_{2}\times C_{6}\times C_{336}\)
Order	$4032$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(4\)	\(5\)	\(8\)	\(10\)	\(11\)	\(13\)	\(16\)	\(19\)	\(20\)
\(\chi_{7497}(1,\cdot)\)	7497.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{7497}(2,\cdot)\)	7497.go	168	yes	\(-1\)	\(1\)	\(e\left(\frac{43}{84}\right)\)	\(e\left(\frac{1}{42}\right)\)	\(e\left(\frac{9}{56}\right)\)	\(e\left(\frac{15}{28}\right)\)	\(e\left(\frac{113}{168}\right)\)	\(e\left(\frac{3}{56}\right)\)	\(e\left(\frac{11}{42}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{31}{168}\right)\)
\(\chi_{7497}(4,\cdot)\)	7497.fy	84	yes	\(1\)	\(1\)	\(e\left(\frac{1}{42}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{9}{28}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{29}{84}\right)\)	\(e\left(\frac{3}{28}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{31}{84}\right)\)
\(\chi_{7497}(5,\cdot)\)	7497.ho	336	yes	\(-1\)	\(1\)	\(e\left(\frac{9}{56}\right)\)	\(e\left(\frac{9}{28}\right)\)	\(e\left(\frac{253}{336}\right)\)	\(e\left(\frac{27}{56}\right)\)	\(e\left(\frac{307}{336}\right)\)	\(e\left(\frac{215}{336}\right)\)	\(e\left(\frac{59}{84}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{25}{336}\right)\)
\(\chi_{7497}(8,\cdot)\)	7497.fq	56	no	\(-1\)	\(1\)	\(e\left(\frac{15}{28}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{27}{56}\right)\)	\(e\left(\frac{17}{28}\right)\)	\(e\left(\frac{1}{56}\right)\)	\(e\left(\frac{9}{56}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(-i\)	\(e\left(\frac{31}{56}\right)\)
\(\chi_{7497}(10,\cdot)\)	7497.hc	336	no	\(1\)	\(1\)	\(e\left(\frac{113}{168}\right)\)	\(e\left(\frac{29}{84}\right)\)	\(e\left(\frac{307}{336}\right)\)	\(e\left(\frac{1}{56}\right)\)	\(e\left(\frac{197}{336}\right)\)	\(e\left(\frac{233}{336}\right)\)	\(e\left(\frac{27}{28}\right)\)	\(e\left(\frac{29}{42}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{29}{112}\right)\)
\(\chi_{7497}(11,\cdot)\)	7497.hp	336	yes	\(1\)	\(1\)	\(e\left(\frac{3}{56}\right)\)	\(e\left(\frac{3}{28}\right)\)	\(e\left(\frac{215}{336}\right)\)	\(e\left(\frac{9}{56}\right)\)	\(e\left(\frac{233}{336}\right)\)	\(e\left(\frac{109}{336}\right)\)	\(e\left(\frac{43}{84}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{251}{336}\right)\)
\(\chi_{7497}(13,\cdot)\)	7497.fw	84	yes	\(-1\)	\(1\)	\(e\left(\frac{11}{42}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{59}{84}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{27}{28}\right)\)	\(e\left(\frac{43}{84}\right)\)	\(e\left(\frac{25}{42}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(1\)	\(e\left(\frac{19}{84}\right)\)
\(\chi_{7497}(16,\cdot)\)	7497.et	42	yes	\(1\)	\(1\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{29}{42}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{31}{42}\right)\)
\(\chi_{7497}(19,\cdot)\)	7497.dq	24	no	\(-1\)	\(1\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(-i\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{3}{8}\right)\)
\(\chi_{7497}(20,\cdot)\)	7497.hf	336	yes	\(-1\)	\(1\)	\(e\left(\frac{31}{168}\right)\)	\(e\left(\frac{31}{84}\right)\)	\(e\left(\frac{25}{336}\right)\)	\(e\left(\frac{31}{56}\right)\)	\(e\left(\frac{29}{112}\right)\)	\(e\left(\frac{251}{336}\right)\)	\(e\left(\frac{19}{84}\right)\)	\(e\left(\frac{31}{42}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{149}{336}\right)\)
\(\chi_{7497}(22,\cdot)\)	7497.hk	336	yes	\(-1\)	\(1\)	\(e\left(\frac{95}{168}\right)\)	\(e\left(\frac{11}{84}\right)\)	\(e\left(\frac{269}{336}\right)\)	\(e\left(\frac{39}{56}\right)\)	\(e\left(\frac{41}{112}\right)\)	\(e\left(\frac{127}{336}\right)\)	\(e\left(\frac{65}{84}\right)\)	\(e\left(\frac{11}{42}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{313}{336}\right)\)
\(\chi_{7497}(23,\cdot)\)	7497.hp	336	yes	\(1\)	\(1\)	\(e\left(\frac{27}{56}\right)\)	\(e\left(\frac{27}{28}\right)\)	\(e\left(\frac{31}{336}\right)\)	\(e\left(\frac{25}{56}\right)\)	\(e\left(\frac{193}{336}\right)\)	\(e\left(\frac{197}{336}\right)\)	\(e\left(\frac{23}{84}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{19}{336}\right)\)
\(\chi_{7497}(25,\cdot)\)	7497.gy	168	yes	\(1\)	\(1\)	\(e\left(\frac{9}{28}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{85}{168}\right)\)	\(e\left(\frac{27}{28}\right)\)	\(e\left(\frac{139}{168}\right)\)	\(e\left(\frac{47}{168}\right)\)	\(e\left(\frac{17}{42}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{25}{168}\right)\)
\(\chi_{7497}(26,\cdot)\)	7497.gm	168	no	\(1\)	\(1\)	\(e\left(\frac{65}{84}\right)\)	\(e\left(\frac{23}{42}\right)\)	\(e\left(\frac{145}{168}\right)\)	\(e\left(\frac{9}{28}\right)\)	\(e\left(\frac{107}{168}\right)\)	\(e\left(\frac{95}{168}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{23}{56}\right)\)
\(\chi_{7497}(29,\cdot)\)	7497.hg	336	yes	\(1\)	\(1\)	\(e\left(\frac{115}{168}\right)\)	\(e\left(\frac{31}{84}\right)\)	\(e\left(\frac{109}{336}\right)\)	\(e\left(\frac{3}{56}\right)\)	\(e\left(\frac{1}{112}\right)\)	\(e\left(\frac{335}{336}\right)\)	\(e\left(\frac{61}{84}\right)\)	\(e\left(\frac{31}{42}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{233}{336}\right)\)
\(\chi_{7497}(31,\cdot)\)	7497.fi	48	no	\(1\)	\(1\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{41}{48}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{19}{48}\right)\)
\(\chi_{7497}(32,\cdot)\)	7497.go	168	yes	\(-1\)	\(1\)	\(e\left(\frac{47}{84}\right)\)	\(e\left(\frac{5}{42}\right)\)	\(e\left(\frac{45}{56}\right)\)	\(e\left(\frac{19}{28}\right)\)	\(e\left(\frac{61}{168}\right)\)	\(e\left(\frac{15}{56}\right)\)	\(e\left(\frac{13}{42}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{155}{168}\right)\)
\(\chi_{7497}(37,\cdot)\)	7497.hd	336	no	\(-1\)	\(1\)	\(e\left(\frac{115}{168}\right)\)	\(e\left(\frac{31}{84}\right)\)	\(e\left(\frac{137}{336}\right)\)	\(e\left(\frac{3}{56}\right)\)	\(e\left(\frac{31}{336}\right)\)	\(e\left(\frac{307}{336}\right)\)	\(e\left(\frac{11}{28}\right)\)	\(e\left(\frac{31}{42}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{87}{112}\right)\)
\(\chi_{7497}(38,\cdot)\)	7497.fs	84	yes	\(1\)	\(1\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{59}{84}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{11}{84}\right)\)	\(e\left(\frac{43}{84}\right)\)	\(e\left(\frac{11}{42}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{47}{84}\right)\)
\(\chi_{7497}(40,\cdot)\)	7497.hq	336	yes	\(1\)	\(1\)	\(e\left(\frac{39}{56}\right)\)	\(e\left(\frac{11}{28}\right)\)	\(e\left(\frac{79}{336}\right)\)	\(e\left(\frac{5}{56}\right)\)	\(e\left(\frac{313}{336}\right)\)	\(e\left(\frac{269}{336}\right)\)	\(e\left(\frac{41}{84}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{211}{336}\right)\)
\(\chi_{7497}(41,\cdot)\)	7497.hf	336	yes	\(-1\)	\(1\)	\(e\left(\frac{125}{168}\right)\)	\(e\left(\frac{41}{84}\right)\)	\(e\left(\frac{323}{336}\right)\)	\(e\left(\frac{13}{56}\right)\)	\(e\left(\frac{79}{112}\right)\)	\(e\left(\frac{313}{336}\right)\)	\(e\left(\frac{17}{84}\right)\)	\(e\left(\frac{41}{42}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{151}{336}\right)\)
\(\chi_{7497}(43,\cdot)\)	7497.gp	168	yes	\(1\)	\(1\)	\(e\left(\frac{11}{84}\right)\)	\(e\left(\frac{11}{42}\right)\)	\(e\left(\frac{17}{168}\right)\)	\(e\left(\frac{11}{28}\right)\)	\(e\left(\frac{13}{56}\right)\)	\(e\left(\frac{43}{168}\right)\)	\(e\left(\frac{23}{42}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(-i\)	\(e\left(\frac{61}{168}\right)\)
\(\chi_{7497}(44,\cdot)\)	7497.hn	336	no	\(1\)	\(1\)	\(e\left(\frac{13}{168}\right)\)	\(e\left(\frac{13}{84}\right)\)	\(e\left(\frac{323}{336}\right)\)	\(e\left(\frac{13}{56}\right)\)	\(e\left(\frac{13}{336}\right)\)	\(e\left(\frac{145}{336}\right)\)	\(e\left(\frac{1}{28}\right)\)	\(e\left(\frac{13}{42}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{13}{112}\right)\)
\(\chi_{7497}(46,\cdot)\)	7497.hd	336	no	\(-1\)	\(1\)	\(e\left(\frac{167}{168}\right)\)	\(e\left(\frac{83}{84}\right)\)	\(e\left(\frac{85}{336}\right)\)	\(e\left(\frac{55}{56}\right)\)	\(e\left(\frac{83}{336}\right)\)	\(e\left(\frac{215}{336}\right)\)	\(e\left(\frac{15}{28}\right)\)	\(e\left(\frac{41}{42}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{27}{112}\right)\)
\(\chi_{7497}(47,\cdot)\)	7497.gb	84	yes	\(1\)	\(1\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{15}{28}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{25}{84}\right)\)	\(e\left(\frac{19}{28}\right)\)	\(e\left(\frac{11}{42}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{84}\right)\)
\(\chi_{7497}(50,\cdot)\)	7497.bf	6	no	\(-1\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(-1\)	\(-1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(1\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{7497}(52,\cdot)\)	7497.dx	42	no	\(-1\)	\(1\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{1}{42}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{13}{42}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{5}{42}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{25}{42}\right)\)
\(\chi_{7497}(53,\cdot)\)	7497.gx	168	no	\(-1\)	\(1\)	\(e\left(\frac{79}{84}\right)\)	\(e\left(\frac{37}{42}\right)\)	\(e\left(\frac{131}{168}\right)\)	\(e\left(\frac{23}{28}\right)\)	\(e\left(\frac{121}{168}\right)\)	\(e\left(\frac{25}{168}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{37}{56}\right)\)
\(\chi_{7497}(55,\cdot)\)	7497.dv	28	no	\(-1\)	\(1\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{11}{28}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{17}{28}\right)\)	\(e\left(\frac{27}{28}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(1\)	\(e\left(\frac{23}{28}\right)\)
\(\chi_{7497}(58,\cdot)\)	7497.hr	336	yes	\(-1\)	\(1\)	\(e\left(\frac{11}{56}\right)\)	\(e\left(\frac{11}{28}\right)\)	\(e\left(\frac{163}{336}\right)\)	\(e\left(\frac{33}{56}\right)\)	\(e\left(\frac{229}{336}\right)\)	\(e\left(\frac{17}{336}\right)\)	\(e\left(\frac{83}{84}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{295}{336}\right)\)
\(\chi_{7497}(59,\cdot)\)	7497.gv	168	yes	\(1\)	\(1\)	\(e\left(\frac{53}{84}\right)\)	\(e\left(\frac{11}{42}\right)\)	\(e\left(\frac{15}{56}\right)\)	\(e\left(\frac{25}{28}\right)\)	\(e\left(\frac{151}{168}\right)\)	\(e\left(\frac{33}{56}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{89}{168}\right)\)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Learn more

Character group

First 32 of 4032 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.