LMFDB - Group of Dirichlet characters of modulus 1470

Show commands: PariGP / SageMath

sage: H = DirichletGroup(1470)

pari: g = idealstar(,1470,2)

Character group

sage: G.order() pari: g.no
Order	=	336
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{2}\times C_{84}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{1470}(491,\cdot)$, $\chi_{1470}(1177,\cdot)$, $\chi_{1470}(1081,\cdot)$

First 32 of 336 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	$-1$	$1$	$11$	$13$	$17$	$19$	$23$	$29$	$31$	$37$	$41$	$43$
$\chi_{1470}(1,\cdot)$	1470.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{1470}(11,\cdot)$	1470.bl	42	no	$-1$	$1$	$e\left(\frac{25}{42}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{29}{42}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{5}{7}\right)$
$\chi_{1470}(13,\cdot)$	1470.bi	28	no	$1$	$1$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{5}{28}\right)$	$e\left(\frac{11}{28}\right)$	$1$	$e\left(\frac{3}{28}\right)$	$e\left(\frac{9}{14}\right)$	$-1$	$e\left(\frac{25}{28}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{27}{28}\right)$
$\chi_{1470}(17,\cdot)$	1470.bs	84	no	$-1$	$1$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{11}{28}\right)$	$e\left(\frac{53}{84}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{73}{84}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{25}{84}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{9}{28}\right)$
$\chi_{1470}(19,\cdot)$	1470.p	6	no	$-1$	$1$	$e\left(\frac{1}{3}\right)$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{6}\right)$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$	$-1$	$-1$
$\chi_{1470}(23,\cdot)$	1470.bt	84	no	$1$	$1$	$e\left(\frac{29}{42}\right)$	$e\left(\frac{3}{28}\right)$	$e\left(\frac{73}{84}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{11}{84}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{59}{84}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{19}{28}\right)$
$\chi_{1470}(29,\cdot)$	1470.bf	14	no	$-1$	$1$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{5}{7}\right)$	$1$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{3}{14}\right)$	$1$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{1}{14}\right)$
$\chi_{1470}(31,\cdot)$	1470.o	6	no	$-1$	$1$	$e\left(\frac{2}{3}\right)$	$-1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{3}\right)$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$	$-1$	$1$
$\chi_{1470}(37,\cdot)$	1470.bv	84	no	$-1$	$1$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{25}{28}\right)$	$e\left(\frac{25}{84}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{59}{84}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{53}{84}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{9}{28}\right)$
$\chi_{1470}(41,\cdot)$	1470.be	14	no	$1$	$1$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{3}{7}\right)$	$-1$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{13}{14}\right)$	$-1$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{1}{7}\right)$
$\chi_{1470}(43,\cdot)$	1470.bh	28	no	$-1$	$1$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{27}{28}\right)$	$e\left(\frac{9}{28}\right)$	$-1$	$e\left(\frac{19}{28}\right)$	$e\left(\frac{1}{14}\right)$	$1$	$e\left(\frac{9}{28}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{3}{28}\right)$
$\chi_{1470}(47,\cdot)$	1470.bs	84	no	$-1$	$1$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{19}{28}\right)$	$e\left(\frac{61}{84}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{65}{84}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{84}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{13}{28}\right)$
$\chi_{1470}(53,\cdot)$	1470.bt	84	no	$1$	$1$	$e\left(\frac{1}{42}\right)$	$e\left(\frac{3}{28}\right)$	$e\left(\frac{17}{84}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{67}{84}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{31}{84}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{19}{28}\right)$
$\chi_{1470}(59,\cdot)$	1470.bm	42	no	$1$	$1$	$e\left(\frac{37}{42}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{31}{42}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{17}{42}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{5}{14}\right)$
$\chi_{1470}(61,\cdot)$	1470.br	42	no	$-1$	$1$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{23}{42}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{4}{7}\right)$
$\chi_{1470}(67,\cdot)$	1470.w	12	no	$-1$	$1$	$e\left(\frac{2}{3}\right)$	$-i$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{12}\right)$	$-1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{7}{12}\right)$	$1$	$-i$
$\chi_{1470}(71,\cdot)$	1470.bd	14	no	$-1$	$1$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{11}{14}\right)$	$1$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{11}{14}\right)$	$1$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{3}{7}\right)$
$\chi_{1470}(73,\cdot)$	1470.bu	84	no	$1$	$1$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{9}{28}\right)$	$e\left(\frac{65}{84}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{61}{84}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{79}{84}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{15}{28}\right)$
$\chi_{1470}(79,\cdot)$	1470.n	6	no	$1$	$1$	$e\left(\frac{1}{3}\right)$	$-1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{6}\right)$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$	$1$	$-1$
$\chi_{1470}(83,\cdot)$	1470.bk	28	no	$-1$	$1$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{9}{28}\right)$	$e\left(\frac{17}{28}\right)$	$1$	$e\left(\frac{25}{28}\right)$	$e\left(\frac{6}{7}\right)$	$-1$	$e\left(\frac{17}{28}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{15}{28}\right)$
$\chi_{1470}(89,\cdot)$	1470.bm	42	no	$1$	$1$	$e\left(\frac{17}{42}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{29}{42}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{42}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{11}{14}\right)$
$\chi_{1470}(97,\cdot)$	1470.m	4	no	$1$	$1$	$1$	$i$	$-i$	$1$	$-i$	$-1$	$-1$	$i$	$-1$	$-i$
$\chi_{1470}(101,\cdot)$	1470.bo	42	no	$1$	$1$	$e\left(\frac{19}{42}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{17}{42}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{1}{7}\right)$
$\chi_{1470}(103,\cdot)$	1470.bu	84	no	$1$	$1$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{1}{28}\right)$	$e\left(\frac{1}{84}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{41}{84}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{71}{84}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{11}{28}\right)$
$\chi_{1470}(107,\cdot)$	1470.bt	84	no	$1$	$1$	$e\left(\frac{17}{42}\right)$	$e\left(\frac{9}{28}\right)$	$e\left(\frac{79}{84}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{84}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{65}{84}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{1}{28}\right)$
$\chi_{1470}(109,\cdot)$	1470.bq	42	no	$1$	$1$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{29}{42}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{41}{42}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{3}{14}\right)$
$\chi_{1470}(113,\cdot)$	1470.bj	28	no	$1$	$1$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{23}{28}\right)$	$e\left(\frac{3}{28}\right)$	$-1$	$e\left(\frac{25}{28}\right)$	$e\left(\frac{6}{7}\right)$	$1$	$e\left(\frac{17}{28}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{15}{28}\right)$
$\chi_{1470}(121,\cdot)$	1470.bg	21	no	$1$	$1$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{3}{7}\right)$
$\chi_{1470}(127,\cdot)$	1470.bh	28	no	$-1$	$1$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{25}{28}\right)$	$e\left(\frac{27}{28}\right)$	$-1$	$e\left(\frac{1}{28}\right)$	$e\left(\frac{3}{14}\right)$	$1$	$e\left(\frac{27}{28}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{9}{28}\right)$
$\chi_{1470}(131,\cdot)$	1470.bo	42	no	$1$	$1$	$e\left(\frac{23}{42}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{25}{42}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{6}{7}\right)$
$\chi_{1470}(137,\cdot)$	1470.bt	84	no	$1$	$1$	$e\left(\frac{37}{42}\right)$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{83}{84}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{84}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{13}{84}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{17}{28}\right)$
$\chi_{1470}(139,\cdot)$	1470.z	14	no	$-1$	$1$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{3}{7}\right)$	$-1$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{3}{7}\right)$	$-1$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{9}{14}\right)$

Click here to search among the remaining 304 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	$1470$
Structure	\(C_{2}\times C_{2}\times C_{84}\)
Order	$336$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(11\)	\(13\)	\(17\)	\(19\)	\(23\)	\(29\)	\(31\)	\(37\)	\(41\)	\(43\)
\(\chi_{1470}(1,\cdot)\)	1470.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{1470}(11,\cdot)\)	1470.bl	42	no	\(-1\)	\(1\)	\(e\left(\frac{25}{42}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{13}{42}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{29}{42}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{5}{7}\right)\)
\(\chi_{1470}(13,\cdot)\)	1470.bi	28	no	\(1\)	\(1\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{5}{28}\right)\)	\(e\left(\frac{11}{28}\right)\)	\(1\)	\(e\left(\frac{3}{28}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(-1\)	\(e\left(\frac{25}{28}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{27}{28}\right)\)
\(\chi_{1470}(17,\cdot)\)	1470.bs	84	no	\(-1\)	\(1\)	\(e\left(\frac{13}{42}\right)\)	\(e\left(\frac{11}{28}\right)\)	\(e\left(\frac{53}{84}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{73}{84}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{25}{84}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{9}{28}\right)\)
\(\chi_{1470}(19,\cdot)\)	1470.p	6	no	\(-1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(-1\)	\(-1\)
\(\chi_{1470}(23,\cdot)\)	1470.bt	84	no	\(1\)	\(1\)	\(e\left(\frac{29}{42}\right)\)	\(e\left(\frac{3}{28}\right)\)	\(e\left(\frac{73}{84}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{11}{84}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{59}{84}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{19}{28}\right)\)
\(\chi_{1470}(29,\cdot)\)	1470.bf	14	no	\(-1\)	\(1\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(1\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(1\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{1}{14}\right)\)
\(\chi_{1470}(31,\cdot)\)	1470.o	6	no	\(-1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(-1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(-1\)	\(1\)
\(\chi_{1470}(37,\cdot)\)	1470.bv	84	no	\(-1\)	\(1\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{25}{28}\right)\)	\(e\left(\frac{25}{84}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{59}{84}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{53}{84}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{9}{28}\right)\)
\(\chi_{1470}(41,\cdot)\)	1470.be	14	no	\(1\)	\(1\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(-1\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(-1\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{1}{7}\right)\)
\(\chi_{1470}(43,\cdot)\)	1470.bh	28	no	\(-1\)	\(1\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{27}{28}\right)\)	\(e\left(\frac{9}{28}\right)\)	\(-1\)	\(e\left(\frac{19}{28}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(1\)	\(e\left(\frac{9}{28}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{3}{28}\right)\)
\(\chi_{1470}(47,\cdot)\)	1470.bs	84	no	\(-1\)	\(1\)	\(e\left(\frac{11}{42}\right)\)	\(e\left(\frac{19}{28}\right)\)	\(e\left(\frac{61}{84}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{65}{84}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{84}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{13}{28}\right)\)
\(\chi_{1470}(53,\cdot)\)	1470.bt	84	no	\(1\)	\(1\)	\(e\left(\frac{1}{42}\right)\)	\(e\left(\frac{3}{28}\right)\)	\(e\left(\frac{17}{84}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{67}{84}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{31}{84}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{19}{28}\right)\)
\(\chi_{1470}(59,\cdot)\)	1470.bm	42	no	\(1\)	\(1\)	\(e\left(\frac{37}{42}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{31}{42}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{17}{42}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{5}{14}\right)\)
\(\chi_{1470}(61,\cdot)\)	1470.br	42	no	\(-1\)	\(1\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{23}{42}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{4}{7}\right)\)
\(\chi_{1470}(67,\cdot)\)	1470.w	12	no	\(-1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(-i\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(-1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(1\)	\(-i\)
\(\chi_{1470}(71,\cdot)\)	1470.bd	14	no	\(-1\)	\(1\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(1\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(1\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{3}{7}\right)\)
\(\chi_{1470}(73,\cdot)\)	1470.bu	84	no	\(1\)	\(1\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{9}{28}\right)\)	\(e\left(\frac{65}{84}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{61}{84}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{79}{84}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{15}{28}\right)\)
\(\chi_{1470}(79,\cdot)\)	1470.n	6	no	\(1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(-1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(1\)	\(-1\)
\(\chi_{1470}(83,\cdot)\)	1470.bk	28	no	\(-1\)	\(1\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{9}{28}\right)\)	\(e\left(\frac{17}{28}\right)\)	\(1\)	\(e\left(\frac{25}{28}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(-1\)	\(e\left(\frac{17}{28}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{15}{28}\right)\)
\(\chi_{1470}(89,\cdot)\)	1470.bm	42	no	\(1\)	\(1\)	\(e\left(\frac{17}{42}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{29}{42}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{42}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{11}{14}\right)\)
\(\chi_{1470}(97,\cdot)\)	1470.m	4	no	\(1\)	\(1\)	\(1\)	\(i\)	\(-i\)	\(1\)	\(-i\)	\(-1\)	\(-1\)	\(i\)	\(-1\)	\(-i\)
\(\chi_{1470}(101,\cdot)\)	1470.bo	42	no	\(1\)	\(1\)	\(e\left(\frac{19}{42}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{17}{42}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{1}{7}\right)\)
\(\chi_{1470}(103,\cdot)\)	1470.bu	84	no	\(1\)	\(1\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{1}{28}\right)\)	\(e\left(\frac{1}{84}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{41}{84}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{71}{84}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{11}{28}\right)\)
\(\chi_{1470}(107,\cdot)\)	1470.bt	84	no	\(1\)	\(1\)	\(e\left(\frac{17}{42}\right)\)	\(e\left(\frac{9}{28}\right)\)	\(e\left(\frac{79}{84}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{84}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{65}{84}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{1}{28}\right)\)
\(\chi_{1470}(109,\cdot)\)	1470.bq	42	no	\(1\)	\(1\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{13}{42}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{29}{42}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{41}{42}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{3}{14}\right)\)
\(\chi_{1470}(113,\cdot)\)	1470.bj	28	no	\(1\)	\(1\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{23}{28}\right)\)	\(e\left(\frac{3}{28}\right)\)	\(-1\)	\(e\left(\frac{25}{28}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(1\)	\(e\left(\frac{17}{28}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{15}{28}\right)\)
\(\chi_{1470}(121,\cdot)\)	1470.bg	21	no	\(1\)	\(1\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{3}{7}\right)\)
\(\chi_{1470}(127,\cdot)\)	1470.bh	28	no	\(-1\)	\(1\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{25}{28}\right)\)	\(e\left(\frac{27}{28}\right)\)	\(-1\)	\(e\left(\frac{1}{28}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(1\)	\(e\left(\frac{27}{28}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{9}{28}\right)\)
\(\chi_{1470}(131,\cdot)\)	1470.bo	42	no	\(1\)	\(1\)	\(e\left(\frac{23}{42}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{25}{42}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{6}{7}\right)\)
\(\chi_{1470}(137,\cdot)\)	1470.bt	84	no	\(1\)	\(1\)	\(e\left(\frac{37}{42}\right)\)	\(e\left(\frac{13}{28}\right)\)	\(e\left(\frac{83}{84}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{84}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{13}{84}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{17}{28}\right)\)
\(\chi_{1470}(139,\cdot)\)	1470.z	14	no	\(-1\)	\(1\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(-1\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(-1\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{9}{14}\right)\)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Learn more

Character group

First 32 of 336 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.