LMFDB - Group of Dirichlet Characters of Modulus 189

Show commands for: Pari/GP / SageMath

sage: from dirichlet_conrey import DirichletGroup_conrey # requires nonstandard Sage package to be installed

sage: H = DirichletGroup_conrey(189)

pari: g = idealstar(,189,2)

Character group

sage: G.order() pari: g.no
Order	=	108
sage: H.invariants() pari: g.cyc
Structure	=	$C_{18}\times C_{6}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{189}(29,\cdot)$, $\chi_{189}(136,\cdot)$

First 32 of 108 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.

	orbit label	order	primitive	-1	1	2	4	5	8	10	11	13	16	17	19
$\chi_{189}(1,\cdot)$	189.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{189}(2,\cdot)$	189.bc	18	yes	$-1$	$1$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{189}(4,\cdot)$	189.u	9	yes	$1$	$1$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{189}(5,\cdot)$	189.ba	18	yes	$1$	$1$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{5}{6}\right)$	$-1$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{7}{9}\right)$	$1$	$-1$
$\chi_{189}(8,\cdot)$	189.r	6	no	$-1$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{6}\right)$	$-1$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$-1$	$1$
$\chi_{189}(10,\cdot)$	189.k	6	no	$-1$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$-1$	$1$	$e\left(\frac{1}{6}\right)$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{189}(11,\cdot)$	189.bf	18	yes	$-1$	$1$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{1}{6}\right)$	$1$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{2}{9}\right)$	$-1$	$1$
$\chi_{189}(13,\cdot)$	189.y	18	yes	$-1$	$1$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{189}(16,\cdot)$	189.u	9	yes	$1$	$1$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{189}(17,\cdot)$	189.s	6	no	$1$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$	$1$	$-1$	$e\left(\frac{1}{6}\right)$	$-1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{189}(19,\cdot)$	189.k	6	no	$-1$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$-1$	$1$	$e\left(\frac{5}{6}\right)$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$
$\chi_{189}(20,\cdot)$	189.be	18	yes	$1$	$1$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$
$\chi_{189}(22,\cdot)$	189.v	9	no	$1$	$1$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{189}(23,\cdot)$	189.bf	18	yes	$-1$	$1$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{5}{6}\right)$	$1$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{1}{9}\right)$	$-1$	$1$
$\chi_{189}(25,\cdot)$	189.w	9	yes	$1$	$1$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{2}{3}\right)$	$1$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{5}{9}\right)$	$1$	$1$
$\chi_{189}(26,\cdot)$	189.p	6	no	$1$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$-1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{6}\right)$	$-1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$
$\chi_{189}(29,\cdot)$	189.bb	18	no	$-1$	$1$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{189}(31,\cdot)$	189.z	18	yes	$-1$	$1$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$
$\chi_{189}(32,\cdot)$	189.bc	18	yes	$-1$	$1$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{189}(34,\cdot)$	189.y	18	yes	$-1$	$1$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$
$\chi_{189}(37,\cdot)$	189.h	3	no	$1$	$1$	$1$	$1$	$e\left(\frac{1}{3}\right)$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{189}(38,\cdot)$	189.ba	18	yes	$1$	$1$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{1}{6}\right)$	$-1$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{2}{9}\right)$	$1$	$-1$
$\chi_{189}(40,\cdot)$	189.x	18	yes	$-1$	$1$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{1}{3}\right)$	$-1$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{4}{9}\right)$	$-1$	$-1$
$\chi_{189}(41,\cdot)$	189.be	18	yes	$1$	$1$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{189}(43,\cdot)$	189.v	9	no	$1$	$1$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{189}(44,\cdot)$	189.j	6	no	$-1$	$1$	$-1$	$1$	$e\left(\frac{5}{6}\right)$	$-1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{3}\right)$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{189}(46,\cdot)$	189.h	3	no	$1$	$1$	$1$	$1$	$e\left(\frac{2}{3}\right)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{189}(47,\cdot)$	189.bd	18	yes	$1$	$1$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{189}(50,\cdot)$	189.bb	18	no	$-1$	$1$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{189}(52,\cdot)$	189.x	18	yes	$-1$	$1$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{2}{3}\right)$	$-1$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{5}{9}\right)$	$-1$	$-1$
$\chi_{189}(53,\cdot)$	189.q	6	no	$-1$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{6}\right)$	$-1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{6}\right)$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{189}(55,\cdot)$	189.d	2	no	$-1$	$1$	$1$	$1$	$-1$	$1$	$-1$	$1$	$-1$	$1$	$-1$	$-1$

Introduction	Features
Universe	News

	orbit label	order	primitive	-1	1	2	4	5	8	10	11	13	16	17	19
\(\chi_{189}(1,\cdot)\)	189.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{189}(2,\cdot)\)	189.bc	18	yes	\(-1\)	\(1\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{189}(4,\cdot)\)	189.u	9	yes	\(1\)	\(1\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{189}(5,\cdot)\)	189.ba	18	yes	\(1\)	\(1\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(-1\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(1\)	\(-1\)
\(\chi_{189}(8,\cdot)\)	189.r	6	no	\(-1\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(-1\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(-1\)	\(1\)
\(\chi_{189}(10,\cdot)\)	189.k	6	no	\(-1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(-1\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{189}(11,\cdot)\)	189.bf	18	yes	\(-1\)	\(1\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(1\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(-1\)	\(1\)
\(\chi_{189}(13,\cdot)\)	189.y	18	yes	\(-1\)	\(1\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{189}(16,\cdot)\)	189.u	9	yes	\(1\)	\(1\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{189}(17,\cdot)\)	189.s	6	no	\(1\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(1\)	\(-1\)	\(e\left(\frac{1}{6}\right)\)	\(-1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{189}(19,\cdot)\)	189.k	6	no	\(-1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(-1\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{189}(20,\cdot)\)	189.be	18	yes	\(1\)	\(1\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{189}(22,\cdot)\)	189.v	9	no	\(1\)	\(1\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{189}(23,\cdot)\)	189.bf	18	yes	\(-1\)	\(1\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(1\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(-1\)	\(1\)
\(\chi_{189}(25,\cdot)\)	189.w	9	yes	\(1\)	\(1\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(1\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(1\)	\(1\)
\(\chi_{189}(26,\cdot)\)	189.p	6	no	\(1\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(-1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(-1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{189}(29,\cdot)\)	189.bb	18	no	\(-1\)	\(1\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{189}(31,\cdot)\)	189.z	18	yes	\(-1\)	\(1\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{189}(32,\cdot)\)	189.bc	18	yes	\(-1\)	\(1\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{189}(34,\cdot)\)	189.y	18	yes	\(-1\)	\(1\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{189}(37,\cdot)\)	189.h	3	no	\(1\)	\(1\)	\(1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{189}(38,\cdot)\)	189.ba	18	yes	\(1\)	\(1\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(-1\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(1\)	\(-1\)
\(\chi_{189}(40,\cdot)\)	189.x	18	yes	\(-1\)	\(1\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(-1\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(-1\)	\(-1\)
\(\chi_{189}(41,\cdot)\)	189.be	18	yes	\(1\)	\(1\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{189}(43,\cdot)\)	189.v	9	no	\(1\)	\(1\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{189}(44,\cdot)\)	189.j	6	no	\(-1\)	\(1\)	\(-1\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(-1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{189}(46,\cdot)\)	189.h	3	no	\(1\)	\(1\)	\(1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{189}(47,\cdot)\)	189.bd	18	yes	\(1\)	\(1\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{189}(50,\cdot)\)	189.bb	18	no	\(-1\)	\(1\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{189}(52,\cdot)\)	189.x	18	yes	\(-1\)	\(1\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(-1\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(-1\)	\(-1\)
\(\chi_{189}(53,\cdot)\)	189.q	6	no	\(-1\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(-1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{189}(55,\cdot)\)	189.d	2	no	\(-1\)	\(1\)	\(1\)	\(1\)	\(-1\)	\(1\)	\(-1\)	\(1\)	\(-1\)	\(1\)	\(-1\)	\(-1\)

Introduction and more

L-functions

Modular Forms

Varieties

Fields

Representations

Groups

Knowledge

Properties

Learn more about

Character group

First 32 of 108 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.