LMFDB - Group of Dirichlet characters of modulus 80

Show commands: PariGP / SageMath

sage: H = DirichletGroup(80)

pari: g = idealstar(,80,2)

Character group

sage: G.order() pari: g.no
Order	=	32
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{4}\times C_{4}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{80}(31,\cdot)$, $\chi_{80}(21,\cdot)$, $\chi_{80}(17,\cdot)$

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	$-1$	$1$	$3$	$7$	$9$	$11$	$13$	$17$	$19$	$21$	$23$	$27$
$\chi_{80}(1,\cdot)$	80.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{80}(3,\cdot)$	80.s	4	yes	$1$	$1$	$1$	$-i$	$1$	$i$	$-1$	$-i$	$i$	$-i$	$i$	$1$
$\chi_{80}(7,\cdot)$	80.o	4	no	$1$	$1$	$-i$	$-i$	$-1$	$1$	$i$	$i$	$-1$	$-1$	$i$	$i$
$\chi_{80}(9,\cdot)$	80.f	2	no	$1$	$1$	$1$	$-1$	$1$	$-1$	$1$	$-1$	$-1$	$-1$	$-1$	$1$
$\chi_{80}(11,\cdot)$	80.r	4	no	$-1$	$1$	$i$	$1$	$-1$	$-i$	$-i$	$1$	$i$	$i$	$1$	$-i$
$\chi_{80}(13,\cdot)$	80.i	4	yes	$-1$	$1$	$-1$	$i$	$1$	$-i$	$-1$	$-i$	$-i$	$-i$	$-i$	$-1$
$\chi_{80}(17,\cdot)$	80.p	4	no	$-1$	$1$	$-i$	$i$	$-1$	$1$	$-i$	$i$	$-1$	$1$	$-i$	$i$
$\chi_{80}(19,\cdot)$	80.k	4	yes	$-1$	$1$	$i$	$-1$	$-1$	$i$	$-i$	$-1$	$-i$	$-i$	$-1$	$-i$
$\chi_{80}(21,\cdot)$	80.l	4	no	$1$	$1$	$-i$	$-1$	$-1$	$i$	$-i$	$1$	$-i$	$i$	$-1$	$i$
$\chi_{80}(23,\cdot)$	80.o	4	no	$1$	$1$	$i$	$i$	$-1$	$1$	$-i$	$-i$	$-1$	$-1$	$-i$	$-i$
$\chi_{80}(27,\cdot)$	80.s	4	yes	$1$	$1$	$1$	$i$	$1$	$-i$	$-1$	$i$	$-i$	$i$	$-i$	$1$
$\chi_{80}(29,\cdot)$	80.q	4	yes	$1$	$1$	$-i$	$1$	$-1$	$-i$	$-i$	$-1$	$i$	$-i$	$1$	$i$
$\chi_{80}(31,\cdot)$	80.b	2	no	$-1$	$1$	$-1$	$-1$	$1$	$-1$	$1$	$1$	$-1$	$1$	$-1$	$-1$
$\chi_{80}(33,\cdot)$	80.p	4	no	$-1$	$1$	$i$	$-i$	$-1$	$1$	$i$	$-i$	$-1$	$1$	$i$	$-i$
$\chi_{80}(37,\cdot)$	80.i	4	yes	$-1$	$1$	$-1$	$-i$	$1$	$i$	$-1$	$i$	$i$	$i$	$i$	$-1$
$\chi_{80}(39,\cdot)$	80.e	2	no	$-1$	$1$	$-1$	$1$	$1$	$1$	$1$	$-1$	$1$	$-1$	$1$	$-1$
$\chi_{80}(41,\cdot)$	80.d	2	no	$1$	$1$	$-1$	$1$	$1$	$-1$	$-1$	$1$	$-1$	$-1$	$1$	$-1$
$\chi_{80}(43,\cdot)$	80.j	4	yes	$1$	$1$	$-1$	$-i$	$1$	$-i$	$1$	$-i$	$-i$	$i$	$i$	$-1$
$\chi_{80}(47,\cdot)$	80.n	4	no	$1$	$1$	$i$	$-i$	$-1$	$-1$	$-i$	$i$	$1$	$1$	$i$	$-i$
$\chi_{80}(49,\cdot)$	80.c	2	no	$1$	$1$	$-1$	$-1$	$1$	$1$	$-1$	$-1$	$1$	$1$	$-1$	$-1$
$\chi_{80}(51,\cdot)$	80.r	4	no	$-1$	$1$	$-i$	$1$	$-1$	$i$	$i$	$1$	$-i$	$-i$	$1$	$i$
$\chi_{80}(53,\cdot)$	80.t	4	yes	$-1$	$1$	$1$	$i$	$1$	$i$	$1$	$-i$	$i$	$i$	$-i$	$1$
$\chi_{80}(57,\cdot)$	80.m	4	no	$-1$	$1$	$i$	$i$	$-1$	$-1$	$i$	$i$	$1$	$-1$	$-i$	$-i$
$\chi_{80}(59,\cdot)$	80.k	4	yes	$-1$	$1$	$-i$	$-1$	$-1$	$-i$	$i$	$-1$	$i$	$i$	$-1$	$i$
$\chi_{80}(61,\cdot)$	80.l	4	no	$1$	$1$	$i$	$-1$	$-1$	$-i$	$i$	$1$	$i$	$-i$	$-1$	$-i$
$\chi_{80}(63,\cdot)$	80.n	4	no	$1$	$1$	$-i$	$i$	$-1$	$-1$	$i$	$-i$	$1$	$1$	$-i$	$i$
$\chi_{80}(67,\cdot)$	80.j	4	yes	$1$	$1$	$-1$	$i$	$1$	$i$	$1$	$i$	$i$	$-i$	$-i$	$-1$
$\chi_{80}(69,\cdot)$	80.q	4	yes	$1$	$1$	$i$	$1$	$-1$	$i$	$i$	$-1$	$-i$	$i$	$1$	$-i$
$\chi_{80}(71,\cdot)$	80.g	2	no	$-1$	$1$	$1$	$-1$	$1$	$1$	$-1$	$1$	$1$	$-1$	$-1$	$1$
$\chi_{80}(73,\cdot)$	80.m	4	no	$-1$	$1$	$-i$	$-i$	$-1$	$-1$	$-i$	$-i$	$1$	$-1$	$i$	$i$
$\chi_{80}(77,\cdot)$	80.t	4	yes	$-1$	$1$	$1$	$-i$	$1$	$-i$	$1$	$i$	$-i$	$-i$	$i$	$1$
$\chi_{80}(79,\cdot)$	80.h	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 $\F_{q}$

Modulus	$80$
Structure	\(C_{2}\times C_{4}\times C_{4}\)
Order	$32$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(3\)	\(7\)	\(9\)	\(11\)	\(13\)	\(17\)	\(19\)	\(21\)	\(23\)	\(27\)
\(\chi_{80}(1,\cdot)\)	80.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{80}(3,\cdot)\)	80.s	4	yes	\(1\)	\(1\)	\(1\)	\(-i\)	\(1\)	\(i\)	\(-1\)	\(-i\)	\(i\)	\(-i\)	\(i\)	\(1\)
\(\chi_{80}(7,\cdot)\)	80.o	4	no	\(1\)	\(1\)	\(-i\)	\(-i\)	\(-1\)	\(1\)	\(i\)	\(i\)	\(-1\)	\(-1\)	\(i\)	\(i\)
\(\chi_{80}(9,\cdot)\)	80.f	2	no	\(1\)	\(1\)	\(1\)	\(-1\)	\(1\)	\(-1\)	\(1\)	\(-1\)	\(-1\)	\(-1\)	\(-1\)	\(1\)
\(\chi_{80}(11,\cdot)\)	80.r	4	no	\(-1\)	\(1\)	\(i\)	\(1\)	\(-1\)	\(-i\)	\(-i\)	\(1\)	\(i\)	\(i\)	\(1\)	\(-i\)
\(\chi_{80}(13,\cdot)\)	80.i	4	yes	\(-1\)	\(1\)	\(-1\)	\(i\)	\(1\)	\(-i\)	\(-1\)	\(-i\)	\(-i\)	\(-i\)	\(-i\)	\(-1\)
\(\chi_{80}(17,\cdot)\)	80.p	4	no	\(-1\)	\(1\)	\(-i\)	\(i\)	\(-1\)	\(1\)	\(-i\)	\(i\)	\(-1\)	\(1\)	\(-i\)	\(i\)
\(\chi_{80}(19,\cdot)\)	80.k	4	yes	\(-1\)	\(1\)	\(i\)	\(-1\)	\(-1\)	\(i\)	\(-i\)	\(-1\)	\(-i\)	\(-i\)	\(-1\)	\(-i\)
\(\chi_{80}(21,\cdot)\)	80.l	4	no	\(1\)	\(1\)	\(-i\)	\(-1\)	\(-1\)	\(i\)	\(-i\)	\(1\)	\(-i\)	\(i\)	\(-1\)	\(i\)
\(\chi_{80}(23,\cdot)\)	80.o	4	no	\(1\)	\(1\)	\(i\)	\(i\)	\(-1\)	\(1\)	\(-i\)	\(-i\)	\(-1\)	\(-1\)	\(-i\)	\(-i\)
\(\chi_{80}(27,\cdot)\)	80.s	4	yes	\(1\)	\(1\)	\(1\)	\(i\)	\(1\)	\(-i\)	\(-1\)	\(i\)	\(-i\)	\(i\)	\(-i\)	\(1\)
\(\chi_{80}(29,\cdot)\)	80.q	4	yes	\(1\)	\(1\)	\(-i\)	\(1\)	\(-1\)	\(-i\)	\(-i\)	\(-1\)	\(i\)	\(-i\)	\(1\)	\(i\)
\(\chi_{80}(31,\cdot)\)	80.b	2	no	\(-1\)	\(1\)	\(-1\)	\(-1\)	\(1\)	\(-1\)	\(1\)	\(1\)	\(-1\)	\(1\)	\(-1\)	\(-1\)
\(\chi_{80}(33,\cdot)\)	80.p	4	no	\(-1\)	\(1\)	\(i\)	\(-i\)	\(-1\)	\(1\)	\(i\)	\(-i\)	\(-1\)	\(1\)	\(i\)	\(-i\)
\(\chi_{80}(37,\cdot)\)	80.i	4	yes	\(-1\)	\(1\)	\(-1\)	\(-i\)	\(1\)	\(i\)	\(-1\)	\(i\)	\(i\)	\(i\)	\(i\)	\(-1\)
\(\chi_{80}(39,\cdot)\)	80.e	2	no	\(-1\)	\(1\)	\(-1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(-1\)	\(1\)	\(-1\)	\(1\)	\(-1\)
\(\chi_{80}(41,\cdot)\)	80.d	2	no	\(1\)	\(1\)	\(-1\)	\(1\)	\(1\)	\(-1\)	\(-1\)	\(1\)	\(-1\)	\(-1\)	\(1\)	\(-1\)
\(\chi_{80}(43,\cdot)\)	80.j	4	yes	\(1\)	\(1\)	\(-1\)	\(-i\)	\(1\)	\(-i\)	\(1\)	\(-i\)	\(-i\)	\(i\)	\(i\)	\(-1\)
\(\chi_{80}(47,\cdot)\)	80.n	4	no	\(1\)	\(1\)	\(i\)	\(-i\)	\(-1\)	\(-1\)	\(-i\)	\(i\)	\(1\)	\(1\)	\(i\)	\(-i\)
\(\chi_{80}(49,\cdot)\)	80.c	2	no	\(1\)	\(1\)	\(-1\)	\(-1\)	\(1\)	\(1\)	\(-1\)	\(-1\)	\(1\)	\(1\)	\(-1\)	\(-1\)
\(\chi_{80}(51,\cdot)\)	80.r	4	no	\(-1\)	\(1\)	\(-i\)	\(1\)	\(-1\)	\(i\)	\(i\)	\(1\)	\(-i\)	\(-i\)	\(1\)	\(i\)
\(\chi_{80}(53,\cdot)\)	80.t	4	yes	\(-1\)	\(1\)	\(1\)	\(i\)	\(1\)	\(i\)	\(1\)	\(-i\)	\(i\)	\(i\)	\(-i\)	\(1\)
\(\chi_{80}(57,\cdot)\)	80.m	4	no	\(-1\)	\(1\)	\(i\)	\(i\)	\(-1\)	\(-1\)	\(i\)	\(i\)	\(1\)	\(-1\)	\(-i\)	\(-i\)
\(\chi_{80}(59,\cdot)\)	80.k	4	yes	\(-1\)	\(1\)	\(-i\)	\(-1\)	\(-1\)	\(-i\)	\(i\)	\(-1\)	\(i\)	\(i\)	\(-1\)	\(i\)
\(\chi_{80}(61,\cdot)\)	80.l	4	no	\(1\)	\(1\)	\(i\)	\(-1\)	\(-1\)	\(-i\)	\(i\)	\(1\)	\(i\)	\(-i\)	\(-1\)	\(-i\)
\(\chi_{80}(63,\cdot)\)	80.n	4	no	\(1\)	\(1\)	\(-i\)	\(i\)	\(-1\)	\(-1\)	\(i\)	\(-i\)	\(1\)	\(1\)	\(-i\)	\(i\)
\(\chi_{80}(67,\cdot)\)	80.j	4	yes	\(1\)	\(1\)	\(-1\)	\(i\)	\(1\)	\(i\)	\(1\)	\(i\)	\(i\)	\(-i\)	\(-i\)	\(-1\)
\(\chi_{80}(69,\cdot)\)	80.q	4	yes	\(1\)	\(1\)	\(i\)	\(1\)	\(-1\)	\(i\)	\(i\)	\(-1\)	\(-i\)	\(i\)	\(1\)	\(-i\)
\(\chi_{80}(71,\cdot)\)	80.g	2	no	\(-1\)	\(1\)	\(1\)	\(-1\)	\(1\)	\(1\)	\(-1\)	\(1\)	\(1\)	\(-1\)	\(-1\)	\(1\)
\(\chi_{80}(73,\cdot)\)	80.m	4	no	\(-1\)	\(1\)	\(-i\)	\(-i\)	\(-1\)	\(-1\)	\(-i\)	\(-i\)	\(1\)	\(-1\)	\(i\)	\(i\)
\(\chi_{80}(77,\cdot)\)	80.t	4	yes	\(-1\)	\(1\)	\(1\)	\(-i\)	\(1\)	\(-i\)	\(1\)	\(i\)	\(-i\)	\(-i\)	\(i\)	\(1\)
\(\chi_{80}(79,\cdot)\)	80.h	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.