LMFDB - Group of Dirichlet characters of modulus 1755

Show commands: Magma / Pari/GP / SageMath

comment:Define the Dirichlet group

sage:G = DirichletGroup(1755)

gp:g = idealstar(,1755,2)

magma:G = FullDirichletGroup(1755);

Character group

Order	=	864	comment:Order sage:G.order() gp:g.no magma:Order(G);
Structure	=	$C_{2}\times C_{12}\times C_{36}$	comment:Group structure sage:sorted(g.order() for g in G.gens()) gp:g.cyc magma:PrimaryInvariants(G);
Generators	=	$\chi_{1755}(326,\cdot)$, $\chi_{1755}(352,\cdot)$, $\chi_{1755}(1081,\cdot)$	comment:Generators sage:G.gens() gp:g.gen magma:Generators(G);

First 32 of 864 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	$-1$	$1$	$2$	$4$	$7$	$8$	$11$	$14$	$16$	$17$	$19$	$22$
$\chi_{1755}(1,\cdot)$	1755.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{1755}(2,\cdot)$	1755.gc	36	yes	$-1$	$1$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{11}{36}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{5}{9}\right)$	$i$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{25}{36}\right)$
$\chi_{1755}(4,\cdot)$	1755.dz	18	yes	$1$	$1$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{1}{9}\right)$	$-1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{7}{18}\right)$
$\chi_{1755}(7,\cdot)$	1755.ga	36	yes	$1$	$1$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{35}{36}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{5}{12}\right)$	$-i$	$e\left(\frac{1}{36}\right)$
$\chi_{1755}(8,\cdot)$	1755.du	12	no	$-1$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$	$-1$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$-i$	$-i$	$e\left(\frac{1}{12}\right)$
$\chi_{1755}(11,\cdot)$	1755.fx	36	no	$1$	$1$	$e\left(\frac{11}{36}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{35}{36}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{17}{36}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{2}{9}\right)$	$1$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{7}{9}\right)$
$\chi_{1755}(14,\cdot)$	1755.eb	18	no	$-1$	$1$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{13}{18}\right)$
$\chi_{1755}(16,\cdot)$	1755.cc	9	no	$1$	$1$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{2}{9}\right)$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{7}{9}\right)$
$\chi_{1755}(17,\cdot)$	1755.cr	12	no	$1$	$1$	$i$	$-1$	$e\left(\frac{5}{12}\right)$	$-i$	$1$	$e\left(\frac{2}{3}\right)$	$1$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{3}\right)$	$i$
$\chi_{1755}(19,\cdot)$	1755.dc	12	no	$-1$	$1$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{6}\right)$	$-i$	$-i$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{6}\right)$
$\chi_{1755}(22,\cdot)$	1755.fp	36	yes	$-1$	$1$	$e\left(\frac{25}{36}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{1}{36}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{7}{9}\right)$	$i$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{17}{36}\right)$
$\chi_{1755}(23,\cdot)$	1755.fr	36	yes	$1$	$1$	$e\left(\frac{7}{36}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{25}{36}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{7}{12}\right)$	$1$	$e\left(\frac{35}{36}\right)$
$\chi_{1755}(28,\cdot)$	1755.ds	12	no	$1$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$	$-1$	$e\left(\frac{7}{12}\right)$	$-1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{5}{12}\right)$
$\chi_{1755}(29,\cdot)$	1755.eh	18	yes	$-1$	$1$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{5}{9}\right)$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{17}{18}\right)$
$\chi_{1755}(31,\cdot)$	1755.fs	36	no	$-1$	$1$	$e\left(\frac{31}{36}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{1}{36}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{25}{36}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{5}{9}\right)$
$\chi_{1755}(32,\cdot)$	1755.gc	36	yes	$-1$	$1$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{19}{36}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{7}{9}\right)$	$i$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{17}{36}\right)$
$\chi_{1755}(34,\cdot)$	1755.ff	36	yes	$-1$	$1$	$e\left(\frac{23}{36}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{17}{36}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{11}{36}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{17}{18}\right)$
$\chi_{1755}(37,\cdot)$	1755.dw	12	no	$1$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$	$1$	$-1$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{7}{12}\right)$
$\chi_{1755}(38,\cdot)$	1755.fk	36	yes	$1$	$1$	$e\left(\frac{35}{36}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{29}{36}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{31}{36}\right)$
$\chi_{1755}(41,\cdot)$	1755.fe	36	no	$1$	$1$	$e\left(\frac{1}{36}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{1}{36}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{31}{36}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{1}{3}\right)$	$-i$	$e\left(\frac{8}{9}\right)$
$\chi_{1755}(43,\cdot)$	1755.fq	36	yes	$-1$	$1$	$e\left(\frac{5}{36}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{5}{36}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{5}{12}\right)$	$1$	$e\left(\frac{7}{36}\right)$
$\chi_{1755}(44,\cdot)$	1755.df	12	no	$1$	$1$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{12}\right)$	$i$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$	$-1$	$-i$	$e\left(\frac{1}{6}\right)$
$\chi_{1755}(46,\cdot)$	1755.dd	12	no	$-1$	$1$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{6}\right)$	$-i$	$-i$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{1755}(47,\cdot)$	1755.ez	36	yes	$-1$	$1$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{29}{36}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{25}{36}\right)$
$\chi_{1755}(49,\cdot)$	1755.ed	18	yes	$1$	$1$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{5}{6}\right)$	$-1$	$e\left(\frac{1}{18}\right)$
$\chi_{1755}(53,\cdot)$	1755.p	4	no	$1$	$1$	$i$	$-1$	$-i$	$-i$	$-1$	$1$	$1$	$i$	$-1$	$-i$
$\chi_{1755}(56,\cdot)$	1755.ee	18	no	$-1$	$1$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{1}{6}\right)$	$-1$	$e\left(\frac{1}{9}\right)$
$\chi_{1755}(58,\cdot)$	1755.fz	36	yes	$1$	$1$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{13}{36}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{1}{9}\right)$	$i$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{23}{36}\right)$
$\chi_{1755}(59,\cdot)$	1755.fa	36	yes	$1$	$1$	$e\left(\frac{25}{36}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{1}{36}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{36}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{7}{9}\right)$	$-1$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{13}{18}\right)$
$\chi_{1755}(61,\cdot)$	1755.cb	9	no	$1$	$1$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{2}{3}\right)$	$1$	$e\left(\frac{7}{9}\right)$
$\chi_{1755}(62,\cdot)$	1755.cr	12	no	$1$	$1$	$i$	$-1$	$e\left(\frac{1}{12}\right)$	$-i$	$1$	$e\left(\frac{1}{3}\right)$	$1$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{2}{3}\right)$	$i$
$\chi_{1755}(64,\cdot)$	1755.be	6	no	$1$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$-1$	$-1$	$e\left(\frac{1}{6}\right)$

Click here to search among the remaining 832 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	$1755$
Structure	\(C_{2}\times C_{12}\times C_{36}\)
Order	$864$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(4\)	\(7\)	\(8\)	\(11\)	\(14\)	\(16\)	\(17\)	\(19\)	\(22\)
\(\chi_{1755}(1,\cdot)\)	1755.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{1755}(2,\cdot)\)	1755.gc	36	yes	\(-1\)	\(1\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{11}{36}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(i\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{25}{36}\right)\)
\(\chi_{1755}(4,\cdot)\)	1755.dz	18	yes	\(1\)	\(1\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(-1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{7}{18}\right)\)
\(\chi_{1755}(7,\cdot)\)	1755.ga	36	yes	\(1\)	\(1\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{35}{36}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(-i\)	\(e\left(\frac{1}{36}\right)\)
\(\chi_{1755}(8,\cdot)\)	1755.du	12	no	\(-1\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(-1\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(-i\)	\(-i\)	\(e\left(\frac{1}{12}\right)\)
\(\chi_{1755}(11,\cdot)\)	1755.fx	36	no	\(1\)	\(1\)	\(e\left(\frac{11}{36}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{35}{36}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{17}{36}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(1\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{7}{9}\right)\)
\(\chi_{1755}(14,\cdot)\)	1755.eb	18	no	\(-1\)	\(1\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{13}{18}\right)\)
\(\chi_{1755}(16,\cdot)\)	1755.cc	9	no	\(1\)	\(1\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{7}{9}\right)\)
\(\chi_{1755}(17,\cdot)\)	1755.cr	12	no	\(1\)	\(1\)	\(i\)	\(-1\)	\(e\left(\frac{5}{12}\right)\)	\(-i\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(1\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(i\)
\(\chi_{1755}(19,\cdot)\)	1755.dc	12	no	\(-1\)	\(1\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(-i\)	\(-i\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{1755}(22,\cdot)\)	1755.fp	36	yes	\(-1\)	\(1\)	\(e\left(\frac{25}{36}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{1}{36}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(i\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{17}{36}\right)\)
\(\chi_{1755}(23,\cdot)\)	1755.fr	36	yes	\(1\)	\(1\)	\(e\left(\frac{7}{36}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{25}{36}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(1\)	\(e\left(\frac{35}{36}\right)\)
\(\chi_{1755}(28,\cdot)\)	1755.ds	12	no	\(1\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(-1\)	\(e\left(\frac{7}{12}\right)\)	\(-1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{5}{12}\right)\)
\(\chi_{1755}(29,\cdot)\)	1755.eh	18	yes	\(-1\)	\(1\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{17}{18}\right)\)
\(\chi_{1755}(31,\cdot)\)	1755.fs	36	no	\(-1\)	\(1\)	\(e\left(\frac{31}{36}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{1}{36}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{25}{36}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{5}{9}\right)\)
\(\chi_{1755}(32,\cdot)\)	1755.gc	36	yes	\(-1\)	\(1\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{19}{36}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(i\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{17}{36}\right)\)
\(\chi_{1755}(34,\cdot)\)	1755.ff	36	yes	\(-1\)	\(1\)	\(e\left(\frac{23}{36}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{17}{36}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{11}{36}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{17}{18}\right)\)
\(\chi_{1755}(37,\cdot)\)	1755.dw	12	no	\(1\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(1\)	\(-1\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{7}{12}\right)\)
\(\chi_{1755}(38,\cdot)\)	1755.fk	36	yes	\(1\)	\(1\)	\(e\left(\frac{35}{36}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{29}{36}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{31}{36}\right)\)
\(\chi_{1755}(41,\cdot)\)	1755.fe	36	no	\(1\)	\(1\)	\(e\left(\frac{1}{36}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{1}{36}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{31}{36}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(-i\)	\(e\left(\frac{8}{9}\right)\)
\(\chi_{1755}(43,\cdot)\)	1755.fq	36	yes	\(-1\)	\(1\)	\(e\left(\frac{5}{36}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{5}{36}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(1\)	\(e\left(\frac{7}{36}\right)\)
\(\chi_{1755}(44,\cdot)\)	1755.df	12	no	\(1\)	\(1\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(i\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(-1\)	\(-i\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{1755}(46,\cdot)\)	1755.dd	12	no	\(-1\)	\(1\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(-i\)	\(-i\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{1755}(47,\cdot)\)	1755.ez	36	yes	\(-1\)	\(1\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{29}{36}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{25}{36}\right)\)
\(\chi_{1755}(49,\cdot)\)	1755.ed	18	yes	\(1\)	\(1\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(-1\)	\(e\left(\frac{1}{18}\right)\)
\(\chi_{1755}(53,\cdot)\)	1755.p	4	no	\(1\)	\(1\)	\(i\)	\(-1\)	\(-i\)	\(-i\)	\(-1\)	\(1\)	\(1\)	\(i\)	\(-1\)	\(-i\)
\(\chi_{1755}(56,\cdot)\)	1755.ee	18	no	\(-1\)	\(1\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(-1\)	\(e\left(\frac{1}{9}\right)\)
\(\chi_{1755}(58,\cdot)\)	1755.fz	36	yes	\(1\)	\(1\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{13}{36}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(i\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{23}{36}\right)\)
\(\chi_{1755}(59,\cdot)\)	1755.fa	36	yes	\(1\)	\(1\)	\(e\left(\frac{25}{36}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{1}{36}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{36}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(-1\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{13}{18}\right)\)
\(\chi_{1755}(61,\cdot)\)	1755.cb	9	no	\(1\)	\(1\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(1\)	\(e\left(\frac{7}{9}\right)\)
\(\chi_{1755}(62,\cdot)\)	1755.cr	12	no	\(1\)	\(1\)	\(i\)	\(-1\)	\(e\left(\frac{1}{12}\right)\)	\(-i\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(1\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(i\)
\(\chi_{1755}(64,\cdot)\)	1755.be	6	no	\(1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(-1\)	\(-1\)	\(e\left(\frac{1}{6}\right)\)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Downloads

Learn more

Character group

First 32 of 864 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.