LMFDB - Group of Dirichlet characters of modulus 1015

Show commands: PariGP / SageMath

sage: H = DirichletGroup(1015)

pari: g = idealstar(,1015,2)

Character group

sage: G.order() pari: g.no
Order	=	672
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{4}\times C_{84}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{1015}(407,\cdot)$, $\chi_{1015}(871,\cdot)$, $\chi_{1015}(176,\cdot)$

First 32 of 672 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	$-1$	$1$	$2$	$3$	$4$	$6$	$8$	$9$	$11$	$12$	$13$	$16$
$\chi_{1015}(1,\cdot)$	1015.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{1015}(2,\cdot)$	1015.da	84	yes	$1$	$1$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{19}{84}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{11}{28}\right)$	$e\left(\frac{17}{21}\right)$
$\chi_{1015}(3,\cdot)$	1015.cq	84	yes	$-1$	$1$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{11}{84}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{27}{28}\right)$	$e\left(\frac{1}{21}\right)$
$\chi_{1015}(4,\cdot)$	1015.cp	42	yes	$1$	$1$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{19}{42}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{13}{21}\right)$
$\chi_{1015}(6,\cdot)$	1015.bt	14	no	$-1$	$1$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{5}{14}\right)$	$1$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{6}{7}\right)$
$\chi_{1015}(8,\cdot)$	1015.by	28	no	$1$	$1$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{19}{28}\right)$	$-1$	$e\left(\frac{5}{28}\right)$	$e\left(\frac{3}{7}\right)$
$\chi_{1015}(9,\cdot)$	1015.cp	42	yes	$1$	$1$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{2}{21}\right)$
$\chi_{1015}(11,\cdot)$	1015.cy	84	no	$-1$	$1$	$e\left(\frac{19}{84}\right)$	$e\left(\frac{11}{84}\right)$	$e\left(\frac{19}{42}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{19}{28}\right)$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{83}{84}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{19}{21}\right)$
$\chi_{1015}(12,\cdot)$	1015.bo	12	yes	$-1$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{3}\right)$	$1$	$-1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{6}\right)$	$-i$	$e\left(\frac{2}{3}\right)$
$\chi_{1015}(13,\cdot)$	1015.cg	28	yes	$1$	$1$	$e\left(\frac{11}{28}\right)$	$e\left(\frac{27}{28}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{5}{28}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{1}{14}\right)$	$-i$	$e\left(\frac{9}{28}\right)$	$e\left(\frac{4}{7}\right)$
$\chi_{1015}(16,\cdot)$	1015.bw	21	no	$1$	$1$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{5}{21}\right)$
$\chi_{1015}(17,\cdot)$	1015.bd	12	yes	$-1$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$	$1$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{3}\right)$	$-i$	$e\left(\frac{1}{3}\right)$
$\chi_{1015}(18,\cdot)$	1015.da	84	yes	$1$	$1$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{37}{42}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{41}{84}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{9}{28}\right)$	$e\left(\frac{19}{21}\right)$
$\chi_{1015}(19,\cdot)$	1015.cu	84	yes	$1$	$1$	$e\left(\frac{41}{84}\right)$	$e\left(\frac{79}{84}\right)$	$e\left(\frac{41}{42}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{37}{42}\right)$	$e\left(\frac{31}{84}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{20}{21}\right)$
$\chi_{1015}(22,\cdot)$	1015.cc	28	no	$-1$	$1$	$e\left(\frac{5}{28}\right)$	$e\left(\frac{11}{28}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{3}{14}\right)$	$-i$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{5}{7}\right)$
$\chi_{1015}(23,\cdot)$	1015.cv	84	yes	$-1$	$1$	$e\left(\frac{11}{84}\right)$	$e\left(\frac{13}{84}\right)$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{11}{28}\right)$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{3}{28}\right)$	$e\left(\frac{11}{21}\right)$
$\chi_{1015}(24,\cdot)$	1015.cm	42	yes	$-1$	$1$	$e\left(\frac{5}{42}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{10}{21}\right)$
$\chi_{1015}(26,\cdot)$	1015.ct	84	no	$1$	$1$	$e\left(\frac{29}{84}\right)$	$e\left(\frac{19}{84}\right)$	$e\left(\frac{29}{42}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{1}{28}\right)$	$e\left(\frac{19}{42}\right)$	$e\left(\frac{25}{84}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{8}{21}\right)$
$\chi_{1015}(27,\cdot)$	1015.ci	28	yes	$-1$	$1$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{11}{28}\right)$	$-1$	$e\left(\frac{25}{28}\right)$	$e\left(\frac{1}{7}\right)$
$\chi_{1015}(31,\cdot)$	1015.ct	84	no	$1$	$1$	$e\left(\frac{31}{84}\right)$	$e\left(\frac{29}{84}\right)$	$e\left(\frac{31}{42}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{3}{28}\right)$	$e\left(\frac{29}{42}\right)$	$e\left(\frac{47}{84}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{10}{21}\right)$
$\chi_{1015}(32,\cdot)$	1015.da	84	yes	$1$	$1$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{11}{84}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{27}{28}\right)$	$e\left(\frac{1}{21}\right)$
$\chi_{1015}(33,\cdot)$	1015.cw	84	yes	$1$	$1$	$e\left(\frac{41}{84}\right)$	$e\left(\frac{37}{84}\right)$	$e\left(\frac{41}{42}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{37}{42}\right)$	$e\left(\frac{5}{42}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{28}\right)$	$e\left(\frac{20}{21}\right)$
$\chi_{1015}(34,\cdot)$	1015.br	14	yes	$-1$	$1$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{9}{14}\right)$	$-1$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{1}{7}\right)$
$\chi_{1015}(36,\cdot)$	1015.bc	7	no	$1$	$1$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{5}{7}\right)$	$1$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{5}{7}\right)$
$\chi_{1015}(37,\cdot)$	1015.cr	84	yes	$1$	$1$	$e\left(\frac{1}{42}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{1}{84}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{19}{28}\right)$	$e\left(\frac{2}{21}\right)$
$\chi_{1015}(38,\cdot)$	1015.cw	84	yes	$1$	$1$	$e\left(\frac{37}{84}\right)$	$e\left(\frac{17}{84}\right)$	$e\left(\frac{37}{42}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{9}{28}\right)$	$e\left(\frac{17}{42}\right)$	$e\left(\frac{25}{42}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{5}{28}\right)$	$e\left(\frac{16}{21}\right)$
$\chi_{1015}(39,\cdot)$	1015.cx	84	yes	$-1$	$1$	$e\left(\frac{55}{84}\right)$	$e\left(\frac{23}{84}\right)$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{27}{28}\right)$	$e\left(\frac{23}{42}\right)$	$e\left(\frac{17}{84}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{13}{21}\right)$
$\chi_{1015}(41,\cdot)$	1015.r	4	no	$1$	$1$	$i$	$-i$	$-1$	$1$	$-i$	$-1$	$i$	$i$	$1$	$1$
$\chi_{1015}(43,\cdot)$	1015.ch	28	no	$1$	$1$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{17}{28}\right)$	$1$	$e\left(\frac{17}{28}\right)$	$e\left(\frac{6}{7}\right)$
$\chi_{1015}(44,\cdot)$	1015.cx	84	yes	$-1$	$1$	$e\left(\frac{11}{84}\right)$	$e\left(\frac{55}{84}\right)$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{11}{28}\right)$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{37}{84}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{11}{21}\right)$
$\chi_{1015}(46,\cdot)$	1015.bg	12	no	$-1$	$1$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{6}\right)$	$-1$	$i$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{7}{12}\right)$	$-1$	$e\left(\frac{1}{3}\right)$
$\chi_{1015}(47,\cdot)$	1015.cq	84	yes	$-1$	$1$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{23}{42}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{13}{84}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{9}{28}\right)$	$e\left(\frac{5}{21}\right)$

Click here to search among the remaining 640 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	$1015$
Structure	\(C_{2}\times C_{4}\times C_{84}\)
Order	$672$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(6\)	\(8\)	\(9\)	\(11\)	\(12\)	\(13\)	\(16\)
\(\chi_{1015}(1,\cdot)\)	1015.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{1015}(2,\cdot)\)	1015.da	84	yes	\(1\)	\(1\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{11}{42}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{19}{84}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{11}{28}\right)\)	\(e\left(\frac{17}{21}\right)\)
\(\chi_{1015}(3,\cdot)\)	1015.cq	84	yes	\(-1\)	\(1\)	\(e\left(\frac{11}{42}\right)\)	\(e\left(\frac{13}{42}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{11}{84}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{27}{28}\right)\)	\(e\left(\frac{1}{21}\right)\)
\(\chi_{1015}(4,\cdot)\)	1015.cp	42	yes	\(1\)	\(1\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{19}{42}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{13}{21}\right)\)
\(\chi_{1015}(6,\cdot)\)	1015.bt	14	no	\(-1\)	\(1\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(1\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{6}{7}\right)\)
\(\chi_{1015}(8,\cdot)\)	1015.by	28	no	\(1\)	\(1\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{19}{28}\right)\)	\(-1\)	\(e\left(\frac{5}{28}\right)\)	\(e\left(\frac{3}{7}\right)\)
\(\chi_{1015}(9,\cdot)\)	1015.cp	42	yes	\(1\)	\(1\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{11}{42}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{2}{21}\right)\)
\(\chi_{1015}(11,\cdot)\)	1015.cy	84	no	\(-1\)	\(1\)	\(e\left(\frac{19}{84}\right)\)	\(e\left(\frac{11}{84}\right)\)	\(e\left(\frac{19}{42}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{19}{28}\right)\)	\(e\left(\frac{11}{42}\right)\)	\(e\left(\frac{83}{84}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{19}{21}\right)\)
\(\chi_{1015}(12,\cdot)\)	1015.bo	12	yes	\(-1\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(1\)	\(-1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(-i\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{1015}(13,\cdot)\)	1015.cg	28	yes	\(1\)	\(1\)	\(e\left(\frac{11}{28}\right)\)	\(e\left(\frac{27}{28}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{5}{28}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(-i\)	\(e\left(\frac{9}{28}\right)\)	\(e\left(\frac{4}{7}\right)\)
\(\chi_{1015}(16,\cdot)\)	1015.bw	21	no	\(1\)	\(1\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{5}{21}\right)\)
\(\chi_{1015}(17,\cdot)\)	1015.bd	12	yes	\(-1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(-i\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{1015}(18,\cdot)\)	1015.da	84	yes	\(1\)	\(1\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{37}{42}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{41}{84}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{9}{28}\right)\)	\(e\left(\frac{19}{21}\right)\)
\(\chi_{1015}(19,\cdot)\)	1015.cu	84	yes	\(1\)	\(1\)	\(e\left(\frac{41}{84}\right)\)	\(e\left(\frac{79}{84}\right)\)	\(e\left(\frac{41}{42}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{13}{28}\right)\)	\(e\left(\frac{37}{42}\right)\)	\(e\left(\frac{31}{84}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{20}{21}\right)\)
\(\chi_{1015}(22,\cdot)\)	1015.cc	28	no	\(-1\)	\(1\)	\(e\left(\frac{5}{28}\right)\)	\(e\left(\frac{11}{28}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{15}{28}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(-i\)	\(e\left(\frac{13}{28}\right)\)	\(e\left(\frac{5}{7}\right)\)
\(\chi_{1015}(23,\cdot)\)	1015.cv	84	yes	\(-1\)	\(1\)	\(e\left(\frac{11}{84}\right)\)	\(e\left(\frac{13}{84}\right)\)	\(e\left(\frac{11}{42}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{11}{28}\right)\)	\(e\left(\frac{13}{42}\right)\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{3}{28}\right)\)	\(e\left(\frac{11}{21}\right)\)
\(\chi_{1015}(24,\cdot)\)	1015.cm	42	yes	\(-1\)	\(1\)	\(e\left(\frac{5}{42}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{10}{21}\right)\)
\(\chi_{1015}(26,\cdot)\)	1015.ct	84	no	\(1\)	\(1\)	\(e\left(\frac{29}{84}\right)\)	\(e\left(\frac{19}{84}\right)\)	\(e\left(\frac{29}{42}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{1}{28}\right)\)	\(e\left(\frac{19}{42}\right)\)	\(e\left(\frac{25}{84}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{8}{21}\right)\)
\(\chi_{1015}(27,\cdot)\)	1015.ci	28	yes	\(-1\)	\(1\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{11}{28}\right)\)	\(-1\)	\(e\left(\frac{25}{28}\right)\)	\(e\left(\frac{1}{7}\right)\)
\(\chi_{1015}(31,\cdot)\)	1015.ct	84	no	\(1\)	\(1\)	\(e\left(\frac{31}{84}\right)\)	\(e\left(\frac{29}{84}\right)\)	\(e\left(\frac{31}{42}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{3}{28}\right)\)	\(e\left(\frac{29}{42}\right)\)	\(e\left(\frac{47}{84}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{10}{21}\right)\)
\(\chi_{1015}(32,\cdot)\)	1015.da	84	yes	\(1\)	\(1\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{13}{42}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{11}{84}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{27}{28}\right)\)	\(e\left(\frac{1}{21}\right)\)
\(\chi_{1015}(33,\cdot)\)	1015.cw	84	yes	\(1\)	\(1\)	\(e\left(\frac{41}{84}\right)\)	\(e\left(\frac{37}{84}\right)\)	\(e\left(\frac{41}{42}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{13}{28}\right)\)	\(e\left(\frac{37}{42}\right)\)	\(e\left(\frac{5}{42}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{1}{28}\right)\)	\(e\left(\frac{20}{21}\right)\)
\(\chi_{1015}(34,\cdot)\)	1015.br	14	yes	\(-1\)	\(1\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(-1\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{1}{7}\right)\)
\(\chi_{1015}(36,\cdot)\)	1015.bc	7	no	\(1\)	\(1\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(1\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{5}{7}\right)\)
\(\chi_{1015}(37,\cdot)\)	1015.cr	84	yes	\(1\)	\(1\)	\(e\left(\frac{1}{42}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{1}{84}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{19}{28}\right)\)	\(e\left(\frac{2}{21}\right)\)
\(\chi_{1015}(38,\cdot)\)	1015.cw	84	yes	\(1\)	\(1\)	\(e\left(\frac{37}{84}\right)\)	\(e\left(\frac{17}{84}\right)\)	\(e\left(\frac{37}{42}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{9}{28}\right)\)	\(e\left(\frac{17}{42}\right)\)	\(e\left(\frac{25}{42}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{5}{28}\right)\)	\(e\left(\frac{16}{21}\right)\)
\(\chi_{1015}(39,\cdot)\)	1015.cx	84	yes	\(-1\)	\(1\)	\(e\left(\frac{55}{84}\right)\)	\(e\left(\frac{23}{84}\right)\)	\(e\left(\frac{13}{42}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{27}{28}\right)\)	\(e\left(\frac{23}{42}\right)\)	\(e\left(\frac{17}{84}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{13}{21}\right)\)
\(\chi_{1015}(41,\cdot)\)	1015.r	4	no	\(1\)	\(1\)	\(i\)	\(-i\)	\(-1\)	\(1\)	\(-i\)	\(-1\)	\(i\)	\(i\)	\(1\)	\(1\)
\(\chi_{1015}(43,\cdot)\)	1015.ch	28	no	\(1\)	\(1\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{17}{28}\right)\)	\(1\)	\(e\left(\frac{17}{28}\right)\)	\(e\left(\frac{6}{7}\right)\)
\(\chi_{1015}(44,\cdot)\)	1015.cx	84	yes	\(-1\)	\(1\)	\(e\left(\frac{11}{84}\right)\)	\(e\left(\frac{55}{84}\right)\)	\(e\left(\frac{11}{42}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{11}{28}\right)\)	\(e\left(\frac{13}{42}\right)\)	\(e\left(\frac{37}{84}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{11}{21}\right)\)
\(\chi_{1015}(46,\cdot)\)	1015.bg	12	no	\(-1\)	\(1\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(-1\)	\(i\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(-1\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{1015}(47,\cdot)\)	1015.cq	84	yes	\(-1\)	\(1\)	\(e\left(\frac{13}{42}\right)\)	\(e\left(\frac{23}{42}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{13}{84}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{9}{28}\right)\)	\(e\left(\frac{5}{21}\right)\)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Learn more

Character group

First 32 of 672 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.