LMFDB - Group of Dirichlet characters of modulus 96

sage:H = DirichletGroup(96)

pari:g = idealstar(,96,2)

Character group

sage:G.order() pari:g.no
Order	=	32
sage:H.invariants() pari:g.cyc
Structure	=	$C_{2}\times C_{2}\times C_{8}$
sage:H.gens() pari:g.gen
Generators	=	$\chi_{96}(31,\cdot)$, $\chi_{96}(37,\cdot)$, $\chi_{96}(65,\cdot)$

First 32 of 32 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	$-1$	$1$	$5$	$7$	$11$	$13$	$17$	$19$	$23$	$25$	$29$	$31$
$\chi_{96}(1,\cdot)$	96.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{96}(5,\cdot)$	96.p	8	yes	$-1$	$1$	$e\left(\frac{5}{8}\right)$	$i$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{7}{8}\right)$	$1$	$e\left(\frac{7}{8}\right)$	$i$	$i$	$e\left(\frac{7}{8}\right)$	$1$
$\chi_{96}(7,\cdot)$	96.l	4	no	$-1$	$1$	$i$	$1$	$-i$	$-i$	$1$	$i$	$1$	$-1$	$-i$	$-1$
$\chi_{96}(11,\cdot)$	96.o	8	yes	$1$	$1$	$e\left(\frac{1}{8}\right)$	$-i$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{3}{8}\right)$	$1$	$e\left(\frac{7}{8}\right)$	$-i$	$i$	$e\left(\frac{3}{8}\right)$	$-1$
$\chi_{96}(13,\cdot)$	96.n	8	no	$1$	$1$	$e\left(\frac{7}{8}\right)$	$-i$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{1}{8}\right)$	$-1$	$e\left(\frac{1}{8}\right)$	$i$	$-i$	$e\left(\frac{5}{8}\right)$	$1$
$\chi_{96}(17,\cdot)$	96.h	2	no	$-1$	$1$	$1$	$1$	$1$	$-1$	$-1$	$-1$	$-1$	$1$	$1$	$1$
$\chi_{96}(19,\cdot)$	96.m	8	no	$-1$	$1$	$e\left(\frac{7}{8}\right)$	$i$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{1}{8}\right)$	$-1$	$e\left(\frac{5}{8}\right)$	$-i$	$-i$	$e\left(\frac{5}{8}\right)$	$-1$
$\chi_{96}(23,\cdot)$	96.k	4	no	$1$	$1$	$i$	$1$	$-i$	$i$	$-1$	$-i$	$-1$	$-1$	$-i$	$-1$
$\chi_{96}(25,\cdot)$	96.j	4	no	$1$	$1$	$i$	$-1$	$i$	$-i$	$1$	$-i$	$-1$	$-1$	$-i$	$1$
$\chi_{96}(29,\cdot)$	96.p	8	yes	$-1$	$1$	$e\left(\frac{7}{8}\right)$	$-i$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{5}{8}\right)$	$1$	$e\left(\frac{5}{8}\right)$	$-i$	$-i$	$e\left(\frac{5}{8}\right)$	$1$
$\chi_{96}(31,\cdot)$	96.g	2	no	$-1$	$1$	$1$	$-1$	$-1$	$1$	$1$	$-1$	$-1$	$1$	$1$	$-1$
$\chi_{96}(35,\cdot)$	96.o	8	yes	$1$	$1$	$e\left(\frac{7}{8}\right)$	$i$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{5}{8}\right)$	$1$	$e\left(\frac{1}{8}\right)$	$i$	$-i$	$e\left(\frac{5}{8}\right)$	$-1$
$\chi_{96}(37,\cdot)$	96.n	8	no	$1$	$1$	$e\left(\frac{1}{8}\right)$	$i$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{7}{8}\right)$	$-1$	$e\left(\frac{7}{8}\right)$	$-i$	$i$	$e\left(\frac{3}{8}\right)$	$1$
$\chi_{96}(41,\cdot)$	96.i	4	no	$-1$	$1$	$i$	$-1$	$i$	$i$	$-1$	$i$	$1$	$-1$	$-i$	$1$
$\chi_{96}(43,\cdot)$	96.m	8	no	$-1$	$1$	$e\left(\frac{5}{8}\right)$	$-i$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{3}{8}\right)$	$-1$	$e\left(\frac{7}{8}\right)$	$i$	$i$	$e\left(\frac{7}{8}\right)$	$-1$
$\chi_{96}(47,\cdot)$	96.f	2	no	$1$	$1$	$1$	$-1$	$-1$	$-1$	$-1$	$1$	$1$	$1$	$1$	$-1$
$\chi_{96}(49,\cdot)$	96.d	2	no	$1$	$1$	$-1$	$1$	$-1$	$-1$	$1$	$-1$	$1$	$1$	$-1$	$1$
$\chi_{96}(53,\cdot)$	96.p	8	yes	$-1$	$1$	$e\left(\frac{1}{8}\right)$	$i$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{3}{8}\right)$	$1$	$e\left(\frac{3}{8}\right)$	$i$	$i$	$e\left(\frac{3}{8}\right)$	$1$
$\chi_{96}(55,\cdot)$	96.l	4	no	$-1$	$1$	$-i$	$1$	$i$	$i$	$1$	$-i$	$1$	$-1$	$i$	$-1$
$\chi_{96}(59,\cdot)$	96.o	8	yes	$1$	$1$	$e\left(\frac{5}{8}\right)$	$-i$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{7}{8}\right)$	$1$	$e\left(\frac{3}{8}\right)$	$-i$	$i$	$e\left(\frac{7}{8}\right)$	$-1$
$\chi_{96}(61,\cdot)$	96.n	8	no	$1$	$1$	$e\left(\frac{3}{8}\right)$	$-i$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{5}{8}\right)$	$-1$	$e\left(\frac{5}{8}\right)$	$i$	$-i$	$e\left(\frac{1}{8}\right)$	$1$
$\chi_{96}(65,\cdot)$	96.e	2	no	$-1$	$1$	$-1$	$1$	$-1$	$1$	$-1$	$1$	$-1$	$1$	$-1$	$1$
$\chi_{96}(67,\cdot)$	96.m	8	no	$-1$	$1$	$e\left(\frac{3}{8}\right)$	$i$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{5}{8}\right)$	$-1$	$e\left(\frac{1}{8}\right)$	$-i$	$-i$	$e\left(\frac{1}{8}\right)$	$-1$
$\chi_{96}(71,\cdot)$	96.k	4	no	$1$	$1$	$-i$	$1$	$i$	$-i$	$-1$	$i$	$-1$	$-1$	$i$	$-1$
$\chi_{96}(73,\cdot)$	96.j	4	no	$1$	$1$	$-i$	$-1$	$-i$	$i$	$1$	$i$	$-1$	$-1$	$i$	$1$
$\chi_{96}(77,\cdot)$	96.p	8	yes	$-1$	$1$	$e\left(\frac{3}{8}\right)$	$-i$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{1}{8}\right)$	$1$	$e\left(\frac{1}{8}\right)$	$-i$	$-i$	$e\left(\frac{1}{8}\right)$	$1$
$\chi_{96}(79,\cdot)$	96.b	2	no	$-1$	$1$	$-1$	$-1$	$1$	$-1$	$1$	$1$	$-1$	$1$	$-1$	$-1$
$\chi_{96}(83,\cdot)$	96.o	8	yes	$1$	$1$	$e\left(\frac{3}{8}\right)$	$i$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{1}{8}\right)$	$1$	$e\left(\frac{5}{8}\right)$	$i$	$-i$	$e\left(\frac{1}{8}\right)$	$-1$
$\chi_{96}(85,\cdot)$	96.n	8	no	$1$	$1$	$e\left(\frac{5}{8}\right)$	$i$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{3}{8}\right)$	$-1$	$e\left(\frac{3}{8}\right)$	$-i$	$i$	$e\left(\frac{7}{8}\right)$	$1$
$\chi_{96}(89,\cdot)$	96.i	4	no	$-1$	$1$	$-i$	$-1$	$-i$	$-i$	$-1$	$-i$	$1$	$-1$	$i$	$1$
$\chi_{96}(91,\cdot)$	96.m	8	no	$-1$	$1$	$e\left(\frac{1}{8}\right)$	$-i$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{7}{8}\right)$	$-1$	$e\left(\frac{3}{8}\right)$	$i$	$i$	$e\left(\frac{3}{8}\right)$	$-1$
$\chi_{96}(95,\cdot)$	96.c	2	no	$1$	$1$	$-1$	$-1$	$1$	$1$	$-1$	$-1$	$1$	$1$	$-1$	$-1$

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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 $\F_{q}$
Belyi maps

Modulus	$96$
Structure	\(C_{2}\times C_{2}\times C_{8}\)
Order	$32$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(5\)	\(7\)	\(11\)	\(13\)	\(17\)	\(19\)	\(23\)	\(25\)	\(29\)	\(31\)
\(\chi_{96}(1,\cdot)\)	96.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{96}(5,\cdot)\)	96.p	8	yes	\(-1\)	\(1\)	\(e\left(\frac{5}{8}\right)\)	\(i\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(1\)	\(e\left(\frac{7}{8}\right)\)	\(i\)	\(i\)	\(e\left(\frac{7}{8}\right)\)	\(1\)
\(\chi_{96}(7,\cdot)\)	96.l	4	no	\(-1\)	\(1\)	\(i\)	\(1\)	\(-i\)	\(-i\)	\(1\)	\(i\)	\(1\)	\(-1\)	\(-i\)	\(-1\)
\(\chi_{96}(11,\cdot)\)	96.o	8	yes	\(1\)	\(1\)	\(e\left(\frac{1}{8}\right)\)	\(-i\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(1\)	\(e\left(\frac{7}{8}\right)\)	\(-i\)	\(i\)	\(e\left(\frac{3}{8}\right)\)	\(-1\)
\(\chi_{96}(13,\cdot)\)	96.n	8	no	\(1\)	\(1\)	\(e\left(\frac{7}{8}\right)\)	\(-i\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(-1\)	\(e\left(\frac{1}{8}\right)\)	\(i\)	\(-i\)	\(e\left(\frac{5}{8}\right)\)	\(1\)
\(\chi_{96}(17,\cdot)\)	96.h	2	no	\(-1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(-1\)	\(-1\)	\(-1\)	\(-1\)	\(1\)	\(1\)	\(1\)
\(\chi_{96}(19,\cdot)\)	96.m	8	no	\(-1\)	\(1\)	\(e\left(\frac{7}{8}\right)\)	\(i\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(-1\)	\(e\left(\frac{5}{8}\right)\)	\(-i\)	\(-i\)	\(e\left(\frac{5}{8}\right)\)	\(-1\)
\(\chi_{96}(23,\cdot)\)	96.k	4	no	\(1\)	\(1\)	\(i\)	\(1\)	\(-i\)	\(i\)	\(-1\)	\(-i\)	\(-1\)	\(-1\)	\(-i\)	\(-1\)
\(\chi_{96}(25,\cdot)\)	96.j	4	no	\(1\)	\(1\)	\(i\)	\(-1\)	\(i\)	\(-i\)	\(1\)	\(-i\)	\(-1\)	\(-1\)	\(-i\)	\(1\)
\(\chi_{96}(29,\cdot)\)	96.p	8	yes	\(-1\)	\(1\)	\(e\left(\frac{7}{8}\right)\)	\(-i\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(1\)	\(e\left(\frac{5}{8}\right)\)	\(-i\)	\(-i\)	\(e\left(\frac{5}{8}\right)\)	\(1\)
\(\chi_{96}(31,\cdot)\)	96.g	2	no	\(-1\)	\(1\)	\(1\)	\(-1\)	\(-1\)	\(1\)	\(1\)	\(-1\)	\(-1\)	\(1\)	\(1\)	\(-1\)
\(\chi_{96}(35,\cdot)\)	96.o	8	yes	\(1\)	\(1\)	\(e\left(\frac{7}{8}\right)\)	\(i\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(1\)	\(e\left(\frac{1}{8}\right)\)	\(i\)	\(-i\)	\(e\left(\frac{5}{8}\right)\)	\(-1\)
\(\chi_{96}(37,\cdot)\)	96.n	8	no	\(1\)	\(1\)	\(e\left(\frac{1}{8}\right)\)	\(i\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(-1\)	\(e\left(\frac{7}{8}\right)\)	\(-i\)	\(i\)	\(e\left(\frac{3}{8}\right)\)	\(1\)
\(\chi_{96}(41,\cdot)\)	96.i	4	no	\(-1\)	\(1\)	\(i\)	\(-1\)	\(i\)	\(i\)	\(-1\)	\(i\)	\(1\)	\(-1\)	\(-i\)	\(1\)
\(\chi_{96}(43,\cdot)\)	96.m	8	no	\(-1\)	\(1\)	\(e\left(\frac{5}{8}\right)\)	\(-i\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(-1\)	\(e\left(\frac{7}{8}\right)\)	\(i\)	\(i\)	\(e\left(\frac{7}{8}\right)\)	\(-1\)
\(\chi_{96}(47,\cdot)\)	96.f	2	no	\(1\)	\(1\)	\(1\)	\(-1\)	\(-1\)	\(-1\)	\(-1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(-1\)
\(\chi_{96}(49,\cdot)\)	96.d	2	no	\(1\)	\(1\)	\(-1\)	\(1\)	\(-1\)	\(-1\)	\(1\)	\(-1\)	\(1\)	\(1\)	\(-1\)	\(1\)
\(\chi_{96}(53,\cdot)\)	96.p	8	yes	\(-1\)	\(1\)	\(e\left(\frac{1}{8}\right)\)	\(i\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(1\)	\(e\left(\frac{3}{8}\right)\)	\(i\)	\(i\)	\(e\left(\frac{3}{8}\right)\)	\(1\)
\(\chi_{96}(55,\cdot)\)	96.l	4	no	\(-1\)	\(1\)	\(-i\)	\(1\)	\(i\)	\(i\)	\(1\)	\(-i\)	\(1\)	\(-1\)	\(i\)	\(-1\)
\(\chi_{96}(59,\cdot)\)	96.o	8	yes	\(1\)	\(1\)	\(e\left(\frac{5}{8}\right)\)	\(-i\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(1\)	\(e\left(\frac{3}{8}\right)\)	\(-i\)	\(i\)	\(e\left(\frac{7}{8}\right)\)	\(-1\)
\(\chi_{96}(61,\cdot)\)	96.n	8	no	\(1\)	\(1\)	\(e\left(\frac{3}{8}\right)\)	\(-i\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(-1\)	\(e\left(\frac{5}{8}\right)\)	\(i\)	\(-i\)	\(e\left(\frac{1}{8}\right)\)	\(1\)
\(\chi_{96}(65,\cdot)\)	96.e	2	no	\(-1\)	\(1\)	\(-1\)	\(1\)	\(-1\)	\(1\)	\(-1\)	\(1\)	\(-1\)	\(1\)	\(-1\)	\(1\)
\(\chi_{96}(67,\cdot)\)	96.m	8	no	\(-1\)	\(1\)	\(e\left(\frac{3}{8}\right)\)	\(i\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(-1\)	\(e\left(\frac{1}{8}\right)\)	\(-i\)	\(-i\)	\(e\left(\frac{1}{8}\right)\)	\(-1\)
\(\chi_{96}(71,\cdot)\)	96.k	4	no	\(1\)	\(1\)	\(-i\)	\(1\)	\(i\)	\(-i\)	\(-1\)	\(i\)	\(-1\)	\(-1\)	\(i\)	\(-1\)
\(\chi_{96}(73,\cdot)\)	96.j	4	no	\(1\)	\(1\)	\(-i\)	\(-1\)	\(-i\)	\(i\)	\(1\)	\(i\)	\(-1\)	\(-1\)	\(i\)	\(1\)
\(\chi_{96}(77,\cdot)\)	96.p	8	yes	\(-1\)	\(1\)	\(e\left(\frac{3}{8}\right)\)	\(-i\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(1\)	\(e\left(\frac{1}{8}\right)\)	\(-i\)	\(-i\)	\(e\left(\frac{1}{8}\right)\)	\(1\)
\(\chi_{96}(79,\cdot)\)	96.b	2	no	\(-1\)	\(1\)	\(-1\)	\(-1\)	\(1\)	\(-1\)	\(1\)	\(1\)	\(-1\)	\(1\)	\(-1\)	\(-1\)
\(\chi_{96}(83,\cdot)\)	96.o	8	yes	\(1\)	\(1\)	\(e\left(\frac{3}{8}\right)\)	\(i\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(1\)	\(e\left(\frac{5}{8}\right)\)	\(i\)	\(-i\)	\(e\left(\frac{1}{8}\right)\)	\(-1\)
\(\chi_{96}(85,\cdot)\)	96.n	8	no	\(1\)	\(1\)	\(e\left(\frac{5}{8}\right)\)	\(i\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(-1\)	\(e\left(\frac{3}{8}\right)\)	\(-i\)	\(i\)	\(e\left(\frac{7}{8}\right)\)	\(1\)
\(\chi_{96}(89,\cdot)\)	96.i	4	no	\(-1\)	\(1\)	\(-i\)	\(-1\)	\(-i\)	\(-i\)	\(-1\)	\(-i\)	\(1\)	\(-1\)	\(i\)	\(1\)
\(\chi_{96}(91,\cdot)\)	96.m	8	no	\(-1\)	\(1\)	\(e\left(\frac{1}{8}\right)\)	\(-i\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(-1\)	\(e\left(\frac{3}{8}\right)\)	\(i\)	\(i\)	\(e\left(\frac{3}{8}\right)\)	\(-1\)
\(\chi_{96}(95,\cdot)\)	96.c	2	no	\(1\)	\(1\)	\(-1\)	\(-1\)	\(1\)	\(1\)	\(-1\)	\(-1\)	\(1\)	\(1\)	\(-1\)	\(-1\)

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First 32 of 32 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.