LMFDB - Group of Dirichlet characters of modulus 3040

Show commands: PariGP / SageMath

sage: H = DirichletGroup(3040)

pari: g = idealstar(,3040,2)

Character group

sage: G.order() pari: g.no
Order	=	1152
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{2}\times C_{4}\times C_{72}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{3040}(191,\cdot)$, $\chi_{3040}(2661,\cdot)$, $\chi_{3040}(1217,\cdot)$, $\chi_{3040}(1921,\cdot)$

First 32 of 1152 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	$-1$	$1$	$3$	$7$	$9$	$11$	$13$	$17$	$21$	$23$	$27$	$29$
$\chi_{3040}(1,\cdot)$	3040.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{3040}(3,\cdot)$	3040.fw	72	yes	$-1$	$1$	$e\left(\frac{19}{72}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{19}{36}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{35}{72}\right)$	$e\left(\frac{17}{36}\right)$	$e\left(\frac{43}{72}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{65}{72}\right)$
$\chi_{3040}(7,\cdot)$	3040.cx	12	no	$1$	$1$	$e\left(\frac{1}{3}\right)$	$i$	$e\left(\frac{2}{3}\right)$	$-i$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{5}{12}\right)$	$1$	$e\left(\frac{11}{12}\right)$
$\chi_{3040}(9,\cdot)$	3040.ey	36	no	$1$	$1$	$e\left(\frac{19}{36}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{35}{36}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{7}{36}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{29}{36}\right)$
$\chi_{3040}(11,\cdot)$	3040.eq	24	no	$-1$	$1$	$e\left(\frac{1}{24}\right)$	$-i$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{5}{24}\right)$
$\chi_{3040}(13,\cdot)$	3040.gl	72	yes	$1$	$1$	$e\left(\frac{35}{72}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{35}{36}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{55}{72}\right)$	$e\left(\frac{1}{36}\right)$	$e\left(\frac{47}{72}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{61}{72}\right)$
$\chi_{3040}(17,\cdot)$	3040.fo	36	no	$-1$	$1$	$e\left(\frac{17}{36}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{36}\right)$	$e\left(\frac{29}{36}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{31}{36}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{4}{9}\right)$
$\chi_{3040}(21,\cdot)$	3040.gg	72	no	$-1$	$1$	$e\left(\frac{43}{72}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{7}{36}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{47}{72}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{13}{72}\right)$	$e\left(\frac{31}{36}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{59}{72}\right)$
$\chi_{3040}(23,\cdot)$	3040.fi	36	no	$1$	$1$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{31}{36}\right)$	$e\left(\frac{31}{36}\right)$	$e\left(\frac{17}{36}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{23}{36}\right)$
$\chi_{3040}(27,\cdot)$	3040.ex	24	yes	$-1$	$1$	$e\left(\frac{19}{24}\right)$	$1$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{17}{24}\right)$
$\chi_{3040}(29,\cdot)$	3040.ge	72	yes	$-1$	$1$	$e\left(\frac{65}{72}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{29}{36}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{61}{72}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{59}{72}\right)$	$e\left(\frac{23}{36}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{13}{72}\right)$
$\chi_{3040}(31,\cdot)$	3040.bq	6	no	$1$	$1$	$e\left(\frac{1}{3}\right)$	$-1$	$e\left(\frac{2}{3}\right)$	$-1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$	$1$	$e\left(\frac{1}{6}\right)$
$\chi_{3040}(33,\cdot)$	3040.fe	36	no	$1$	$1$	$e\left(\frac{11}{36}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{7}{36}\right)$	$e\left(\frac{23}{36}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{1}{36}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{9}\right)$
$\chi_{3040}(37,\cdot)$	3040.ce	8	yes	$1$	$1$	$e\left(\frac{5}{8}\right)$	$-1$	$i$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{1}{8}\right)$	$-i$	$e\left(\frac{1}{8}\right)$	$-1$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{3}{8}\right)$
$\chi_{3040}(39,\cdot)$	3040.v	4	no	$-1$	$1$	$-i$	$-1$	$-1$	$-i$	$i$	$-1$	$i$	$-1$	$i$	$-i$
$\chi_{3040}(41,\cdot)$	3040.fu	36	no	$-1$	$1$	$e\left(\frac{23}{36}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{31}{36}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{17}{36}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{19}{36}\right)$
$\chi_{3040}(43,\cdot)$	3040.gk	72	yes	$1$	$1$	$e\left(\frac{13}{72}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{13}{36}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{5}{72}\right)$	$e\left(\frac{5}{36}\right)$	$e\left(\frac{1}{72}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{35}{72}\right)$
$\chi_{3040}(47,\cdot)$	3040.ff	36	no	$1$	$1$	$e\left(\frac{19}{36}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{17}{36}\right)$	$e\left(\frac{25}{36}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{5}{36}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{5}{9}\right)$
$\chi_{3040}(49,\cdot)$	3040.bp	6	no	$1$	$1$	$e\left(\frac{2}{3}\right)$	$-1$	$e\left(\frac{1}{3}\right)$	$-1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$	$1$	$e\left(\frac{5}{6}\right)$
$\chi_{3040}(51,\cdot)$	3040.gd	72	no	$1$	$1$	$e\left(\frac{53}{72}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{17}{36}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{37}{72}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{47}{72}\right)$	$e\left(\frac{11}{36}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{25}{72}\right)$
$\chi_{3040}(53,\cdot)$	3040.fy	72	yes	$1$	$1$	$e\left(\frac{5}{72}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{36}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{49}{72}\right)$	$e\left(\frac{13}{36}\right)$	$e\left(\frac{53}{72}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{55}{72}\right)$
$\chi_{3040}(59,\cdot)$	3040.gb	72	yes	$1$	$1$	$e\left(\frac{7}{72}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{7}{36}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{47}{72}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{49}{72}\right)$	$e\left(\frac{31}{36}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{23}{72}\right)$
$\chi_{3040}(61,\cdot)$	3040.ga	72	no	$1$	$1$	$e\left(\frac{41}{72}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{5}{36}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{13}{72}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{71}{72}\right)$	$e\left(\frac{17}{36}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{1}{72}\right)$
$\chi_{3040}(63,\cdot)$	3040.fr	36	no	$1$	$1$	$e\left(\frac{31}{36}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{36}\right)$	$e\left(\frac{19}{36}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{11}{36}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{13}{18}\right)$
$\chi_{3040}(67,\cdot)$	3040.gj	72	yes	$-1$	$1$	$e\left(\frac{47}{72}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{11}{36}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{7}{72}\right)$	$e\left(\frac{7}{36}\right)$	$e\left(\frac{59}{72}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{49}{72}\right)$
$\chi_{3040}(69,\cdot)$	3040.em	24	yes	$-1$	$1$	$e\left(\frac{17}{24}\right)$	$-i$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{13}{24}\right)$
$\chi_{3040}(71,\cdot)$	3040.ez	36	no	$1$	$1$	$e\left(\frac{11}{36}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{25}{36}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{23}{36}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{13}{36}\right)$
$\chi_{3040}(73,\cdot)$	3040.fk	36	no	$-1$	$1$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{35}{36}\right)$	$e\left(\frac{35}{36}\right)$	$e\left(\frac{7}{36}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{19}{36}\right)$
$\chi_{3040}(77,\cdot)$	3040.ct	8	no	$-1$	$1$	$e\left(\frac{3}{8}\right)$	$1$	$-i$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{7}{8}\right)$	$-i$	$e\left(\frac{3}{8}\right)$	$1$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{1}{8}\right)$
$\chi_{3040}(79,\cdot)$	3040.dt	18	no	$1$	$1$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{7}{9}\right)$
$\chi_{3040}(81,\cdot)$	3040.dy	18	no	$1$	$1$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{11}{18}\right)$
$\chi_{3040}(83,\cdot)$	3040.ev	24	yes	$1$	$1$	$e\left(\frac{17}{24}\right)$	$1$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{19}{24}\right)$

Click here to search among the remaining 1120 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	$3040$
Structure	\(C_{2}\times C_{2}\times C_{4}\times C_{72}\)
Order	$1152$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(3\)	\(7\)	\(9\)	\(11\)	\(13\)	\(17\)	\(21\)	\(23\)	\(27\)	\(29\)
\(\chi_{3040}(1,\cdot)\)	3040.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{3040}(3,\cdot)\)	3040.fw	72	yes	\(-1\)	\(1\)	\(e\left(\frac{19}{72}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{19}{36}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{35}{72}\right)\)	\(e\left(\frac{17}{36}\right)\)	\(e\left(\frac{43}{72}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{65}{72}\right)\)
\(\chi_{3040}(7,\cdot)\)	3040.cx	12	no	\(1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(i\)	\(e\left(\frac{2}{3}\right)\)	\(-i\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(1\)	\(e\left(\frac{11}{12}\right)\)
\(\chi_{3040}(9,\cdot)\)	3040.ey	36	no	\(1\)	\(1\)	\(e\left(\frac{19}{36}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{35}{36}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{7}{36}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{29}{36}\right)\)
\(\chi_{3040}(11,\cdot)\)	3040.eq	24	no	\(-1\)	\(1\)	\(e\left(\frac{1}{24}\right)\)	\(-i\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{5}{24}\right)\)
\(\chi_{3040}(13,\cdot)\)	3040.gl	72	yes	\(1\)	\(1\)	\(e\left(\frac{35}{72}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{35}{36}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{55}{72}\right)\)	\(e\left(\frac{1}{36}\right)\)	\(e\left(\frac{47}{72}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{61}{72}\right)\)
\(\chi_{3040}(17,\cdot)\)	3040.fo	36	no	\(-1\)	\(1\)	\(e\left(\frac{17}{36}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{36}\right)\)	\(e\left(\frac{29}{36}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{31}{36}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{4}{9}\right)\)
\(\chi_{3040}(21,\cdot)\)	3040.gg	72	no	\(-1\)	\(1\)	\(e\left(\frac{43}{72}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{7}{36}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{47}{72}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{13}{72}\right)\)	\(e\left(\frac{31}{36}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{59}{72}\right)\)
\(\chi_{3040}(23,\cdot)\)	3040.fi	36	no	\(1\)	\(1\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{31}{36}\right)\)	\(e\left(\frac{31}{36}\right)\)	\(e\left(\frac{17}{36}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{23}{36}\right)\)
\(\chi_{3040}(27,\cdot)\)	3040.ex	24	yes	\(-1\)	\(1\)	\(e\left(\frac{19}{24}\right)\)	\(1\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{17}{24}\right)\)
\(\chi_{3040}(29,\cdot)\)	3040.ge	72	yes	\(-1\)	\(1\)	\(e\left(\frac{65}{72}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{29}{36}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{61}{72}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{59}{72}\right)\)	\(e\left(\frac{23}{36}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{13}{72}\right)\)
\(\chi_{3040}(31,\cdot)\)	3040.bq	6	no	\(1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(-1\)	\(e\left(\frac{2}{3}\right)\)	\(-1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(1\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{3040}(33,\cdot)\)	3040.fe	36	no	\(1\)	\(1\)	\(e\left(\frac{11}{36}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{7}{36}\right)\)	\(e\left(\frac{23}{36}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{1}{36}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{1}{9}\right)\)
\(\chi_{3040}(37,\cdot)\)	3040.ce	8	yes	\(1\)	\(1\)	\(e\left(\frac{5}{8}\right)\)	\(-1\)	\(i\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(-i\)	\(e\left(\frac{1}{8}\right)\)	\(-1\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{3}{8}\right)\)
\(\chi_{3040}(39,\cdot)\)	3040.v	4	no	\(-1\)	\(1\)	\(-i\)	\(-1\)	\(-1\)	\(-i\)	\(i\)	\(-1\)	\(i\)	\(-1\)	\(i\)	\(-i\)
\(\chi_{3040}(41,\cdot)\)	3040.fu	36	no	\(-1\)	\(1\)	\(e\left(\frac{23}{36}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{31}{36}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{17}{36}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{19}{36}\right)\)
\(\chi_{3040}(43,\cdot)\)	3040.gk	72	yes	\(1\)	\(1\)	\(e\left(\frac{13}{72}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{13}{36}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{5}{72}\right)\)	\(e\left(\frac{5}{36}\right)\)	\(e\left(\frac{1}{72}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{35}{72}\right)\)
\(\chi_{3040}(47,\cdot)\)	3040.ff	36	no	\(1\)	\(1\)	\(e\left(\frac{19}{36}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{17}{36}\right)\)	\(e\left(\frac{25}{36}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{5}{36}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{5}{9}\right)\)
\(\chi_{3040}(49,\cdot)\)	3040.bp	6	no	\(1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(-1\)	\(e\left(\frac{1}{3}\right)\)	\(-1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(1\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{3040}(51,\cdot)\)	3040.gd	72	no	\(1\)	\(1\)	\(e\left(\frac{53}{72}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{17}{36}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{37}{72}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{47}{72}\right)\)	\(e\left(\frac{11}{36}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{25}{72}\right)\)
\(\chi_{3040}(53,\cdot)\)	3040.fy	72	yes	\(1\)	\(1\)	\(e\left(\frac{5}{72}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{36}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{49}{72}\right)\)	\(e\left(\frac{13}{36}\right)\)	\(e\left(\frac{53}{72}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{55}{72}\right)\)
\(\chi_{3040}(59,\cdot)\)	3040.gb	72	yes	\(1\)	\(1\)	\(e\left(\frac{7}{72}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{7}{36}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{47}{72}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{49}{72}\right)\)	\(e\left(\frac{31}{36}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{23}{72}\right)\)
\(\chi_{3040}(61,\cdot)\)	3040.ga	72	no	\(1\)	\(1\)	\(e\left(\frac{41}{72}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{5}{36}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{13}{72}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{71}{72}\right)\)	\(e\left(\frac{17}{36}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{1}{72}\right)\)
\(\chi_{3040}(63,\cdot)\)	3040.fr	36	no	\(1\)	\(1\)	\(e\left(\frac{31}{36}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{36}\right)\)	\(e\left(\frac{19}{36}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{11}{36}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{13}{18}\right)\)
\(\chi_{3040}(67,\cdot)\)	3040.gj	72	yes	\(-1\)	\(1\)	\(e\left(\frac{47}{72}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{11}{36}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{7}{72}\right)\)	\(e\left(\frac{7}{36}\right)\)	\(e\left(\frac{59}{72}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{49}{72}\right)\)
\(\chi_{3040}(69,\cdot)\)	3040.em	24	yes	\(-1\)	\(1\)	\(e\left(\frac{17}{24}\right)\)	\(-i\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{13}{24}\right)\)
\(\chi_{3040}(71,\cdot)\)	3040.ez	36	no	\(1\)	\(1\)	\(e\left(\frac{11}{36}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{25}{36}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{23}{36}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{13}{36}\right)\)
\(\chi_{3040}(73,\cdot)\)	3040.fk	36	no	\(-1\)	\(1\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{35}{36}\right)\)	\(e\left(\frac{35}{36}\right)\)	\(e\left(\frac{7}{36}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{19}{36}\right)\)
\(\chi_{3040}(77,\cdot)\)	3040.ct	8	no	\(-1\)	\(1\)	\(e\left(\frac{3}{8}\right)\)	\(1\)	\(-i\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(-i\)	\(e\left(\frac{3}{8}\right)\)	\(1\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{1}{8}\right)\)
\(\chi_{3040}(79,\cdot)\)	3040.dt	18	no	\(1\)	\(1\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{7}{9}\right)\)
\(\chi_{3040}(81,\cdot)\)	3040.dy	18	no	\(1\)	\(1\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{11}{18}\right)\)
\(\chi_{3040}(83,\cdot)\)	3040.ev	24	yes	\(1\)	\(1\)	\(e\left(\frac{17}{24}\right)\)	\(1\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{19}{24}\right)\)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Learn more

Character group

First 32 of 1152 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.