LMFDB - Group of Dirichlet characters of modulus 1920

Show commands: PariGP / SageMath

sage: H = DirichletGroup(1920)

pari: g = idealstar(,1920,2)

Character group

sage: G.order() pari: g.no
Order	=	512
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{2}\times C_{4}\times C_{32}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{1920}(511,\cdot)$, $\chi_{1920}(901,\cdot)$, $\chi_{1920}(641,\cdot)$, $\chi_{1920}(1537,\cdot)$

First 32 of 512 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	$-1$	$1$	$7$	$11$	$13$	$17$	$19$	$23$	$29$	$31$	$37$	$41$
$\chi_{1920}(1,\cdot)$	1920.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{1920}(7,\cdot)$	1920.cs	16	no	$1$	$1$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{7}{16}\right)$	$1$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{15}{16}\right)$	$1$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{3}{8}\right)$
$\chi_{1920}(11,\cdot)$	1920.cy	32	no	$1$	$1$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{25}{32}\right)$	$e\left(\frac{27}{32}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{19}{32}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{7}{32}\right)$	$-i$	$e\left(\frac{13}{32}\right)$	$e\left(\frac{3}{16}\right)$
$\chi_{1920}(13,\cdot)$	1920.cu	32	no	$-1$	$1$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{27}{32}\right)$	$e\left(\frac{9}{32}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{9}{32}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{5}{32}\right)$	$-i$	$e\left(\frac{15}{32}\right)$	$e\left(\frac{1}{16}\right)$
$\chi_{1920}(17,\cdot)$	1920.cb	8	no	$1$	$1$	$1$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{7}{8}\right)$	$i$	$e\left(\frac{5}{8}\right)$	$-1$	$e\left(\frac{5}{8}\right)$	$1$	$e\left(\frac{1}{8}\right)$	$-i$
$\chi_{1920}(19,\cdot)$	1920.df	32	no	$-1$	$1$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{19}{32}\right)$	$e\left(\frac{9}{32}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{1}{32}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{13}{32}\right)$	$i$	$e\left(\frac{15}{32}\right)$	$e\left(\frac{9}{16}\right)$
$\chi_{1920}(23,\cdot)$	1920.ch	16	no	$-1$	$1$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{13}{16}\right)$	$-1$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{13}{16}\right)$	$1$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{5}{8}\right)$
$\chi_{1920}(29,\cdot)$	1920.db	32	yes	$-1$	$1$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{7}{32}\right)$	$e\left(\frac{5}{32}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{13}{32}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{9}{32}\right)$	$-i$	$e\left(\frac{19}{32}\right)$	$e\left(\frac{13}{16}\right)$
$\chi_{1920}(31,\cdot)$	1920.bn	4	no	$-1$	$1$	$1$	$-i$	$-i$	$1$	$i$	$1$	$-i$	$-1$	$i$	$-1$
$\chi_{1920}(37,\cdot)$	1920.cu	32	no	$-1$	$1$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{13}{32}\right)$	$e\left(\frac{15}{32}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{15}{32}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{19}{32}\right)$	$i$	$e\left(\frac{25}{32}\right)$	$e\left(\frac{7}{16}\right)$
$\chi_{1920}(41,\cdot)$	1920.cj	16	no	$-1$	$1$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{1}{16}\right)$	$-i$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{13}{16}\right)$	$-1$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{5}{8}\right)$
$\chi_{1920}(43,\cdot)$	1920.di	32	no	$1$	$1$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{17}{32}\right)$	$e\left(\frac{27}{32}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{27}{32}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{31}{32}\right)$	$-i$	$e\left(\frac{13}{32}\right)$	$e\left(\frac{3}{16}\right)$
$\chi_{1920}(47,\cdot)$	1920.bq	8	no	$-1$	$1$	$-1$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{3}{8}\right)$	$i$	$e\left(\frac{5}{8}\right)$	$1$	$e\left(\frac{1}{8}\right)$	$-1$	$e\left(\frac{5}{8}\right)$	$-i$
$\chi_{1920}(49,\cdot)$	1920.by	8	no	$1$	$1$	$-i$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{7}{8}\right)$	$1$	$e\left(\frac{3}{8}\right)$	$i$	$e\left(\frac{7}{8}\right)$	$1$	$e\left(\frac{1}{8}\right)$	$-i$
$\chi_{1920}(53,\cdot)$	1920.dj	32	yes	$1$	$1$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{25}{32}\right)$	$e\left(\frac{19}{32}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{3}{32}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{7}{32}\right)$	$i$	$e\left(\frac{21}{32}\right)$	$e\left(\frac{3}{16}\right)$
$\chi_{1920}(59,\cdot)$	1920.dd	32	yes	$1$	$1$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{5}{32}\right)$	$e\left(\frac{15}{32}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{23}{32}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{27}{32}\right)$	$-i$	$e\left(\frac{25}{32}\right)$	$e\left(\frac{7}{16}\right)$
$\chi_{1920}(61,\cdot)$	1920.dc	32	no	$1$	$1$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{15}{32}\right)$	$e\left(\frac{29}{32}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{21}{32}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{1}{32}\right)$	$-i$	$e\left(\frac{27}{32}\right)$	$e\left(\frac{13}{16}\right)$
$\chi_{1920}(67,\cdot)$	1920.di	32	no	$1$	$1$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{31}{32}\right)$	$e\left(\frac{21}{32}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{21}{32}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{17}{32}\right)$	$i$	$e\left(\frac{3}{32}\right)$	$e\left(\frac{13}{16}\right)$
$\chi_{1920}(71,\cdot)$	1920.cn	16	no	$1$	$1$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{3}{16}\right)$	$i$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{7}{16}\right)$	$1$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{7}{8}\right)$
$\chi_{1920}(73,\cdot)$	1920.cq	16	no	$-1$	$1$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{9}{16}\right)$	$1$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{1}{16}\right)$	$-1$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{5}{8}\right)$
$\chi_{1920}(77,\cdot)$	1920.dj	32	yes	$1$	$1$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{27}{32}\right)$	$e\left(\frac{9}{32}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{25}{32}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{5}{32}\right)$	$-i$	$e\left(\frac{15}{32}\right)$	$e\left(\frac{9}{16}\right)$
$\chi_{1920}(79,\cdot)$	1920.bw	8	no	$-1$	$1$	$i$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{7}{8}\right)$	$1$	$e\left(\frac{7}{8}\right)$	$-i$	$e\left(\frac{7}{8}\right)$	$-1$	$e\left(\frac{1}{8}\right)$	$-i$
$\chi_{1920}(83,\cdot)$	1920.cv	32	yes	$-1$	$1$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{19}{32}\right)$	$e\left(\frac{17}{32}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{1}{32}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{29}{32}\right)$	$i$	$e\left(\frac{7}{32}\right)$	$e\left(\frac{1}{16}\right)$
$\chi_{1920}(89,\cdot)$	1920.cl	16	no	$-1$	$1$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{15}{16}\right)$	$-i$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{11}{16}\right)$	$-1$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{3}{8}\right)$
$\chi_{1920}(91,\cdot)$	1920.da	32	no	$-1$	$1$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{29}{32}\right)$	$e\left(\frac{23}{32}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{15}{32}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{3}{32}\right)$	$-i$	$e\left(\frac{17}{32}\right)$	$e\left(\frac{7}{16}\right)$
$\chi_{1920}(97,\cdot)$	1920.ba	4	no	$-1$	$1$	$-i$	$i$	$-1$	$i$	$i$	$i$	$i$	$1$	$-1$	$-1$
$\chi_{1920}(101,\cdot)$	1920.de	32	no	$-1$	$1$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{13}{32}\right)$	$e\left(\frac{7}{32}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{15}{32}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{3}{32}\right)$	$i$	$e\left(\frac{1}{32}\right)$	$e\left(\frac{15}{16}\right)$
$\chi_{1920}(103,\cdot)$	1920.cg	16	no	$1$	$1$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{3}{16}\right)$	$-1$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{3}{16}\right)$	$1$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{7}{8}\right)$
$\chi_{1920}(107,\cdot)$	1920.cv	32	yes	$-1$	$1$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{17}{32}\right)$	$e\left(\frac{27}{32}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{11}{32}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{31}{32}\right)$	$-i$	$e\left(\frac{13}{32}\right)$	$e\left(\frac{11}{16}\right)$
$\chi_{1920}(109,\cdot)$	1920.cz	32	no	$1$	$1$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{3}{32}\right)$	$e\left(\frac{9}{32}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{17}{32}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{13}{32}\right)$	$-i$	$e\left(\frac{15}{32}\right)$	$e\left(\frac{9}{16}\right)$
$\chi_{1920}(113,\cdot)$	1920.cb	8	no	$1$	$1$	$1$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{1}{8}\right)$	$-i$	$e\left(\frac{3}{8}\right)$	$-1$	$e\left(\frac{3}{8}\right)$	$1$	$e\left(\frac{7}{8}\right)$	$i$
$\chi_{1920}(119,\cdot)$	1920.cp	16	no	$1$	$1$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{5}{16}\right)$	$i$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{9}{16}\right)$	$1$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{1}{8}\right)$

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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	$1920$
Structure	\(C_{2}\times C_{2}\times C_{4}\times C_{32}\)
Order	$512$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(7\)	\(11\)	\(13\)	\(17\)	\(19\)	\(23\)	\(29\)	\(31\)	\(37\)	\(41\)
\(\chi_{1920}(1,\cdot)\)	1920.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{1920}(7,\cdot)\)	1920.cs	16	no	\(1\)	\(1\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(1\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(1\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{3}{8}\right)\)
\(\chi_{1920}(11,\cdot)\)	1920.cy	32	no	\(1\)	\(1\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{25}{32}\right)\)	\(e\left(\frac{27}{32}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{19}{32}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{7}{32}\right)\)	\(-i\)	\(e\left(\frac{13}{32}\right)\)	\(e\left(\frac{3}{16}\right)\)
\(\chi_{1920}(13,\cdot)\)	1920.cu	32	no	\(-1\)	\(1\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{27}{32}\right)\)	\(e\left(\frac{9}{32}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{9}{32}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{5}{32}\right)\)	\(-i\)	\(e\left(\frac{15}{32}\right)\)	\(e\left(\frac{1}{16}\right)\)
\(\chi_{1920}(17,\cdot)\)	1920.cb	8	no	\(1\)	\(1\)	\(1\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(i\)	\(e\left(\frac{5}{8}\right)\)	\(-1\)	\(e\left(\frac{5}{8}\right)\)	\(1\)	\(e\left(\frac{1}{8}\right)\)	\(-i\)
\(\chi_{1920}(19,\cdot)\)	1920.df	32	no	\(-1\)	\(1\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{19}{32}\right)\)	\(e\left(\frac{9}{32}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{1}{32}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{13}{32}\right)\)	\(i\)	\(e\left(\frac{15}{32}\right)\)	\(e\left(\frac{9}{16}\right)\)
\(\chi_{1920}(23,\cdot)\)	1920.ch	16	no	\(-1\)	\(1\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(-1\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(1\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{5}{8}\right)\)
\(\chi_{1920}(29,\cdot)\)	1920.db	32	yes	\(-1\)	\(1\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{7}{32}\right)\)	\(e\left(\frac{5}{32}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{13}{32}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{9}{32}\right)\)	\(-i\)	\(e\left(\frac{19}{32}\right)\)	\(e\left(\frac{13}{16}\right)\)
\(\chi_{1920}(31,\cdot)\)	1920.bn	4	no	\(-1\)	\(1\)	\(1\)	\(-i\)	\(-i\)	\(1\)	\(i\)	\(1\)	\(-i\)	\(-1\)	\(i\)	\(-1\)
\(\chi_{1920}(37,\cdot)\)	1920.cu	32	no	\(-1\)	\(1\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{13}{32}\right)\)	\(e\left(\frac{15}{32}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{15}{32}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{19}{32}\right)\)	\(i\)	\(e\left(\frac{25}{32}\right)\)	\(e\left(\frac{7}{16}\right)\)
\(\chi_{1920}(41,\cdot)\)	1920.cj	16	no	\(-1\)	\(1\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(-i\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(-1\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{5}{8}\right)\)
\(\chi_{1920}(43,\cdot)\)	1920.di	32	no	\(1\)	\(1\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{17}{32}\right)\)	\(e\left(\frac{27}{32}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{27}{32}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{31}{32}\right)\)	\(-i\)	\(e\left(\frac{13}{32}\right)\)	\(e\left(\frac{3}{16}\right)\)
\(\chi_{1920}(47,\cdot)\)	1920.bq	8	no	\(-1\)	\(1\)	\(-1\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(i\)	\(e\left(\frac{5}{8}\right)\)	\(1\)	\(e\left(\frac{1}{8}\right)\)	\(-1\)	\(e\left(\frac{5}{8}\right)\)	\(-i\)
\(\chi_{1920}(49,\cdot)\)	1920.by	8	no	\(1\)	\(1\)	\(-i\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(1\)	\(e\left(\frac{3}{8}\right)\)	\(i\)	\(e\left(\frac{7}{8}\right)\)	\(1\)	\(e\left(\frac{1}{8}\right)\)	\(-i\)
\(\chi_{1920}(53,\cdot)\)	1920.dj	32	yes	\(1\)	\(1\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{25}{32}\right)\)	\(e\left(\frac{19}{32}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{3}{32}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{7}{32}\right)\)	\(i\)	\(e\left(\frac{21}{32}\right)\)	\(e\left(\frac{3}{16}\right)\)
\(\chi_{1920}(59,\cdot)\)	1920.dd	32	yes	\(1\)	\(1\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{5}{32}\right)\)	\(e\left(\frac{15}{32}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{23}{32}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{27}{32}\right)\)	\(-i\)	\(e\left(\frac{25}{32}\right)\)	\(e\left(\frac{7}{16}\right)\)
\(\chi_{1920}(61,\cdot)\)	1920.dc	32	no	\(1\)	\(1\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{15}{32}\right)\)	\(e\left(\frac{29}{32}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{21}{32}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{1}{32}\right)\)	\(-i\)	\(e\left(\frac{27}{32}\right)\)	\(e\left(\frac{13}{16}\right)\)
\(\chi_{1920}(67,\cdot)\)	1920.di	32	no	\(1\)	\(1\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{31}{32}\right)\)	\(e\left(\frac{21}{32}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{21}{32}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{17}{32}\right)\)	\(i\)	\(e\left(\frac{3}{32}\right)\)	\(e\left(\frac{13}{16}\right)\)
\(\chi_{1920}(71,\cdot)\)	1920.cn	16	no	\(1\)	\(1\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(i\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(1\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{7}{8}\right)\)
\(\chi_{1920}(73,\cdot)\)	1920.cq	16	no	\(-1\)	\(1\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(1\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(-1\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{5}{8}\right)\)
\(\chi_{1920}(77,\cdot)\)	1920.dj	32	yes	\(1\)	\(1\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{27}{32}\right)\)	\(e\left(\frac{9}{32}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{25}{32}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{5}{32}\right)\)	\(-i\)	\(e\left(\frac{15}{32}\right)\)	\(e\left(\frac{9}{16}\right)\)
\(\chi_{1920}(79,\cdot)\)	1920.bw	8	no	\(-1\)	\(1\)	\(i\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(1\)	\(e\left(\frac{7}{8}\right)\)	\(-i\)	\(e\left(\frac{7}{8}\right)\)	\(-1\)	\(e\left(\frac{1}{8}\right)\)	\(-i\)
\(\chi_{1920}(83,\cdot)\)	1920.cv	32	yes	\(-1\)	\(1\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{19}{32}\right)\)	\(e\left(\frac{17}{32}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{1}{32}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{29}{32}\right)\)	\(i\)	\(e\left(\frac{7}{32}\right)\)	\(e\left(\frac{1}{16}\right)\)
\(\chi_{1920}(89,\cdot)\)	1920.cl	16	no	\(-1\)	\(1\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(-i\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(-1\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{3}{8}\right)\)
\(\chi_{1920}(91,\cdot)\)	1920.da	32	no	\(-1\)	\(1\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{29}{32}\right)\)	\(e\left(\frac{23}{32}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{15}{32}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{3}{32}\right)\)	\(-i\)	\(e\left(\frac{17}{32}\right)\)	\(e\left(\frac{7}{16}\right)\)
\(\chi_{1920}(97,\cdot)\)	1920.ba	4	no	\(-1\)	\(1\)	\(-i\)	\(i\)	\(-1\)	\(i\)	\(i\)	\(i\)	\(i\)	\(1\)	\(-1\)	\(-1\)
\(\chi_{1920}(101,\cdot)\)	1920.de	32	no	\(-1\)	\(1\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{13}{32}\right)\)	\(e\left(\frac{7}{32}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{15}{32}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{3}{32}\right)\)	\(i\)	\(e\left(\frac{1}{32}\right)\)	\(e\left(\frac{15}{16}\right)\)
\(\chi_{1920}(103,\cdot)\)	1920.cg	16	no	\(1\)	\(1\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(-1\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(1\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{7}{8}\right)\)
\(\chi_{1920}(107,\cdot)\)	1920.cv	32	yes	\(-1\)	\(1\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{17}{32}\right)\)	\(e\left(\frac{27}{32}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{11}{32}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{31}{32}\right)\)	\(-i\)	\(e\left(\frac{13}{32}\right)\)	\(e\left(\frac{11}{16}\right)\)
\(\chi_{1920}(109,\cdot)\)	1920.cz	32	no	\(1\)	\(1\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{3}{32}\right)\)	\(e\left(\frac{9}{32}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{17}{32}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{13}{32}\right)\)	\(-i\)	\(e\left(\frac{15}{32}\right)\)	\(e\left(\frac{9}{16}\right)\)
\(\chi_{1920}(113,\cdot)\)	1920.cb	8	no	\(1\)	\(1\)	\(1\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(-i\)	\(e\left(\frac{3}{8}\right)\)	\(-1\)	\(e\left(\frac{3}{8}\right)\)	\(1\)	\(e\left(\frac{7}{8}\right)\)	\(i\)
\(\chi_{1920}(119,\cdot)\)	1920.cp	16	no	\(1\)	\(1\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(i\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(1\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{1}{8}\right)\)

Introduction

L-functions

Modular forms

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Fields

Representations

Groups

Database

Properties

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Character group

First 32 of 512 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.