LMFDB - Group of Dirichlet characters of modulus 432

sage:H = DirichletGroup(432)

pari:g = idealstar(,432,2)

Character group

sage:G.order() pari:g.no
Order	=	144
sage:H.invariants() pari:g.cyc
Structure	=	$C_{2}\times C_{2}\times C_{36}$
sage:H.gens() pari:g.gen
Generators	=	$\chi_{432}(271,\cdot)$, $\chi_{432}(325,\cdot)$, $\chi_{432}(353,\cdot)$

First 32 of 144 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	$-1$	$1$	$5$	$7$	$11$	$13$	$17$	$19$	$23$	$25$	$29$	$31$
$\chi_{432}(1,\cdot)$	432.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{432}(5,\cdot)$	432.bi	36	yes	$-1$	$1$	$e\left(\frac{23}{36}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{31}{36}\right)$	$e\left(\frac{35}{36}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{1}{36}\right)$	$e\left(\frac{5}{9}\right)$
$\chi_{432}(7,\cdot)$	432.z	18	no	$-1$	$1$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{5}{18}\right)$
$\chi_{432}(11,\cdot)$	432.bj	36	yes	$1$	$1$	$e\left(\frac{31}{36}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{5}{36}\right)$	$e\left(\frac{19}{36}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{17}{36}\right)$	$e\left(\frac{17}{18}\right)$
$\chi_{432}(13,\cdot)$	432.bg	36	yes	$1$	$1$	$e\left(\frac{35}{36}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{19}{36}\right)$	$e\left(\frac{29}{36}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{25}{36}\right)$	$e\left(\frac{8}{9}\right)$
$\chi_{432}(17,\cdot)$	432.q	6	no	$-1$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$	$-1$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{432}(19,\cdot)$	432.w	12	no	$-1$	$1$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{7}{12}\right)$	$1$	$-i$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{432}(23,\cdot)$	432.bd	18	no	$1$	$1$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{13}{18}\right)$
$\chi_{432}(25,\cdot)$	432.bb	18	no	$1$	$1$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{1}{9}\right)$
$\chi_{432}(29,\cdot)$	432.bi	36	yes	$-1$	$1$	$e\left(\frac{1}{36}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{17}{36}\right)$	$e\left(\frac{25}{36}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{11}{36}\right)$	$e\left(\frac{1}{9}\right)$
$\chi_{432}(31,\cdot)$	432.ba	18	no	$-1$	$1$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{13}{18}\right)$
$\chi_{432}(35,\cdot)$	432.v	12	no	$1$	$1$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{7}{12}\right)$	$-1$	$-i$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{432}(37,\cdot)$	432.y	12	no	$1$	$1$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{5}{12}\right)$	$1$	$-i$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{432}(41,\cdot)$	432.bf	18	no	$-1$	$1$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{8}{9}\right)$
$\chi_{432}(43,\cdot)$	432.bh	36	yes	$-1$	$1$	$e\left(\frac{13}{36}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{23}{36}\right)$	$e\left(\frac{19}{36}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{35}{36}\right)$	$e\left(\frac{17}{18}\right)$
$\chi_{432}(47,\cdot)$	432.be	18	no	$1$	$1$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{5}{18}\right)$
$\chi_{432}(49,\cdot)$	432.u	9	no	$1$	$1$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{5}{9}\right)$
$\chi_{432}(53,\cdot)$	432.j	4	no	$-1$	$1$	$-i$	$-1$	$-i$	$-i$	$-1$	$-i$	$1$	$-1$	$i$	$1$
$\chi_{432}(55,\cdot)$	432.b	2	no	$-1$	$1$	$-1$	$-1$	$1$	$-1$	$1$	$1$	$-1$	$1$	$-1$	$-1$
$\chi_{432}(59,\cdot)$	432.bj	36	yes	$1$	$1$	$e\left(\frac{23}{36}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{13}{36}\right)$	$e\left(\frac{35}{36}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{1}{36}\right)$	$e\left(\frac{1}{18}\right)$
$\chi_{432}(61,\cdot)$	432.bg	36	yes	$1$	$1$	$e\left(\frac{7}{36}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{11}{36}\right)$	$e\left(\frac{13}{36}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{5}{36}\right)$	$e\left(\frac{7}{9}\right)$
$\chi_{432}(65,\cdot)$	432.bc	18	no	$-1$	$1$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{4}{9}\right)$
$\chi_{432}(67,\cdot)$	432.bh	36	yes	$-1$	$1$	$e\left(\frac{35}{36}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{1}{36}\right)$	$e\left(\frac{29}{36}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{25}{36}\right)$	$e\left(\frac{7}{18}\right)$
$\chi_{432}(71,\cdot)$	432.p	6	no	$1$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$	$-1$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$
$\chi_{432}(73,\cdot)$	432.r	6	no	$1$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$	$1$	$-1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{432}(77,\cdot)$	432.bi	36	yes	$-1$	$1$	$e\left(\frac{29}{36}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{25}{36}\right)$	$e\left(\frac{5}{36}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{31}{36}\right)$	$e\left(\frac{2}{9}\right)$
$\chi_{432}(79,\cdot)$	432.ba	18	no	$-1$	$1$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{11}{18}\right)$
$\chi_{432}(83,\cdot)$	432.bj	36	yes	$1$	$1$	$e\left(\frac{1}{36}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{35}{36}\right)$	$e\left(\frac{25}{36}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{11}{36}\right)$	$e\left(\frac{11}{18}\right)$
$\chi_{432}(85,\cdot)$	432.bg	36	yes	$1$	$1$	$e\left(\frac{29}{36}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{25}{36}\right)$	$e\left(\frac{23}{36}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{31}{36}\right)$	$e\left(\frac{2}{9}\right)$
$\chi_{432}(89,\cdot)$	432.n	6	no	$-1$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{6}\right)$	$-1$	$-1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{432}(91,\cdot)$	432.w	12	no	$-1$	$1$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{5}{12}\right)$	$1$	$i$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{6}\right)$
$\chi_{432}(95,\cdot)$	432.be	18	no	$1$	$1$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{7}{18}\right)$

Click here to search among the remaining 112 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 $\F_{q}$
Belyi maps

Modulus	$432$
Structure	\(C_{2}\times C_{2}\times C_{36}\)
Order	$144$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(5\)	\(7\)	\(11\)	\(13\)	\(17\)	\(19\)	\(23\)	\(25\)	\(29\)	\(31\)
\(\chi_{432}(1,\cdot)\)	432.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{432}(5,\cdot)\)	432.bi	36	yes	\(-1\)	\(1\)	\(e\left(\frac{23}{36}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{31}{36}\right)\)	\(e\left(\frac{35}{36}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{1}{36}\right)\)	\(e\left(\frac{5}{9}\right)\)
\(\chi_{432}(7,\cdot)\)	432.z	18	no	\(-1\)	\(1\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{5}{18}\right)\)
\(\chi_{432}(11,\cdot)\)	432.bj	36	yes	\(1\)	\(1\)	\(e\left(\frac{31}{36}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{5}{36}\right)\)	\(e\left(\frac{19}{36}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{17}{36}\right)\)	\(e\left(\frac{17}{18}\right)\)
\(\chi_{432}(13,\cdot)\)	432.bg	36	yes	\(1\)	\(1\)	\(e\left(\frac{35}{36}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{19}{36}\right)\)	\(e\left(\frac{29}{36}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{25}{36}\right)\)	\(e\left(\frac{8}{9}\right)\)
\(\chi_{432}(17,\cdot)\)	432.q	6	no	\(-1\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(-1\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{432}(19,\cdot)\)	432.w	12	no	\(-1\)	\(1\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(1\)	\(-i\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{432}(23,\cdot)\)	432.bd	18	no	\(1\)	\(1\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{13}{18}\right)\)
\(\chi_{432}(25,\cdot)\)	432.bb	18	no	\(1\)	\(1\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{1}{9}\right)\)
\(\chi_{432}(29,\cdot)\)	432.bi	36	yes	\(-1\)	\(1\)	\(e\left(\frac{1}{36}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{17}{36}\right)\)	\(e\left(\frac{25}{36}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{11}{36}\right)\)	\(e\left(\frac{1}{9}\right)\)
\(\chi_{432}(31,\cdot)\)	432.ba	18	no	\(-1\)	\(1\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{13}{18}\right)\)
\(\chi_{432}(35,\cdot)\)	432.v	12	no	\(1\)	\(1\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(-1\)	\(-i\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{432}(37,\cdot)\)	432.y	12	no	\(1\)	\(1\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(1\)	\(-i\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{432}(41,\cdot)\)	432.bf	18	no	\(-1\)	\(1\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{8}{9}\right)\)
\(\chi_{432}(43,\cdot)\)	432.bh	36	yes	\(-1\)	\(1\)	\(e\left(\frac{13}{36}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{23}{36}\right)\)	\(e\left(\frac{19}{36}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{35}{36}\right)\)	\(e\left(\frac{17}{18}\right)\)
\(\chi_{432}(47,\cdot)\)	432.be	18	no	\(1\)	\(1\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{5}{18}\right)\)
\(\chi_{432}(49,\cdot)\)	432.u	9	no	\(1\)	\(1\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{5}{9}\right)\)
\(\chi_{432}(53,\cdot)\)	432.j	4	no	\(-1\)	\(1\)	\(-i\)	\(-1\)	\(-i\)	\(-i\)	\(-1\)	\(-i\)	\(1\)	\(-1\)	\(i\)	\(1\)
\(\chi_{432}(55,\cdot)\)	432.b	2	no	\(-1\)	\(1\)	\(-1\)	\(-1\)	\(1\)	\(-1\)	\(1\)	\(1\)	\(-1\)	\(1\)	\(-1\)	\(-1\)
\(\chi_{432}(59,\cdot)\)	432.bj	36	yes	\(1\)	\(1\)	\(e\left(\frac{23}{36}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{13}{36}\right)\)	\(e\left(\frac{35}{36}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{1}{36}\right)\)	\(e\left(\frac{1}{18}\right)\)
\(\chi_{432}(61,\cdot)\)	432.bg	36	yes	\(1\)	\(1\)	\(e\left(\frac{7}{36}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{11}{36}\right)\)	\(e\left(\frac{13}{36}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{5}{36}\right)\)	\(e\left(\frac{7}{9}\right)\)
\(\chi_{432}(65,\cdot)\)	432.bc	18	no	\(-1\)	\(1\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{4}{9}\right)\)
\(\chi_{432}(67,\cdot)\)	432.bh	36	yes	\(-1\)	\(1\)	\(e\left(\frac{35}{36}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{1}{36}\right)\)	\(e\left(\frac{29}{36}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{25}{36}\right)\)	\(e\left(\frac{7}{18}\right)\)
\(\chi_{432}(71,\cdot)\)	432.p	6	no	\(1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(-1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{432}(73,\cdot)\)	432.r	6	no	\(1\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(1\)	\(-1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{432}(77,\cdot)\)	432.bi	36	yes	\(-1\)	\(1\)	\(e\left(\frac{29}{36}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{25}{36}\right)\)	\(e\left(\frac{5}{36}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{31}{36}\right)\)	\(e\left(\frac{2}{9}\right)\)
\(\chi_{432}(79,\cdot)\)	432.ba	18	no	\(-1\)	\(1\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{11}{18}\right)\)
\(\chi_{432}(83,\cdot)\)	432.bj	36	yes	\(1\)	\(1\)	\(e\left(\frac{1}{36}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{35}{36}\right)\)	\(e\left(\frac{25}{36}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{11}{36}\right)\)	\(e\left(\frac{11}{18}\right)\)
\(\chi_{432}(85,\cdot)\)	432.bg	36	yes	\(1\)	\(1\)	\(e\left(\frac{29}{36}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{25}{36}\right)\)	\(e\left(\frac{23}{36}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{31}{36}\right)\)	\(e\left(\frac{2}{9}\right)\)
\(\chi_{432}(89,\cdot)\)	432.n	6	no	\(-1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(-1\)	\(-1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{432}(91,\cdot)\)	432.w	12	no	\(-1\)	\(1\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(1\)	\(i\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{432}(95,\cdot)\)	432.be	18	no	\(1\)	\(1\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{7}{18}\right)\)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Learn more

Character group

First 32 of 144 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.