LMFDB - Group of Dirichlet characters of modulus 240

Show commands: PariGP / SageMath

sage: H = DirichletGroup(240)

pari: g = idealstar(,240,2)

Character group

sage: G.order() pari: g.no
Order	=	64
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{2}\times C_{4}\times C_{4}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{240}(31,\cdot)$, $\chi_{240}(181,\cdot)$, $\chi_{240}(161,\cdot)$, $\chi_{240}(97,\cdot)$

First 32 of 64 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	$-1$	$1$	$7$	$11$	$13$	$17$	$19$	$23$	$29$	$31$	$37$	$41$
$\chi_{240}(1,\cdot)$	240.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{240}(7,\cdot)$	240.bh	4	no	$1$	$1$	$-i$	$1$	$i$	$i$	$-1$	$i$	$1$	$-1$	$-i$	$1$
$\chi_{240}(11,\cdot)$	240.bk	4	no	$1$	$1$	$1$	$i$	$-i$	$-1$	$i$	$-1$	$i$	$-1$	$i$	$1$
$\chi_{240}(13,\cdot)$	240.ba	4	no	$-1$	$1$	$i$	$-i$	$-1$	$-i$	$-i$	$-i$	$-i$	$1$	$-1$	$-1$
$\chi_{240}(17,\cdot)$	240.v	4	no	$1$	$1$	$i$	$-1$	$-i$	$-i$	$-1$	$i$	$1$	$1$	$i$	$-1$
$\chi_{240}(19,\cdot)$	240.q	4	no	$-1$	$1$	$-1$	$i$	$-i$	$-1$	$-i$	$-1$	$i$	$-1$	$i$	$-1$
$\chi_{240}(23,\cdot)$	240.u	4	no	$-1$	$1$	$i$	$-1$	$-i$	$i$	$-1$	$i$	$-1$	$-1$	$i$	$-1$
$\chi_{240}(29,\cdot)$	240.bm	4	yes	$-1$	$1$	$1$	$i$	$-i$	$1$	$i$	$-1$	$-i$	$1$	$i$	$1$
$\chi_{240}(31,\cdot)$	240.e	2	no	$-1$	$1$	$-1$	$-1$	$1$	$1$	$-1$	$-1$	$1$	$-1$	$1$	$1$
$\chi_{240}(37,\cdot)$	240.ba	4	no	$-1$	$1$	$-i$	$i$	$-1$	$i$	$i$	$i$	$i$	$1$	$-1$	$-1$
$\chi_{240}(41,\cdot)$	240.n	2	no	$-1$	$1$	$1$	$1$	$-1$	$-1$	$-1$	$-1$	$1$	$1$	$-1$	$-1$
$\chi_{240}(43,\cdot)$	240.bc	4	no	$1$	$1$	$-i$	$-i$	$1$	$-i$	$-i$	$i$	$i$	$-1$	$1$	$-1$
$\chi_{240}(47,\cdot)$	240.bj	4	no	$-1$	$1$	$-i$	$1$	$-i$	$-i$	$1$	$-i$	$1$	$-1$	$i$	$-1$
$\chi_{240}(49,\cdot)$	240.f	2	no	$1$	$1$	$-1$	$1$	$-1$	$-1$	$1$	$-1$	$1$	$1$	$-1$	$1$
$\chi_{240}(53,\cdot)$	240.bf	4	yes	$1$	$1$	$i$	$-i$	$1$	$i$	$i$	$i$	$-i$	$1$	$1$	$1$
$\chi_{240}(59,\cdot)$	240.t	4	yes	$1$	$1$	$-1$	$i$	$i$	$1$	$i$	$1$	$i$	$-1$	$-i$	$1$
$\chi_{240}(61,\cdot)$	240.s	4	no	$1$	$1$	$-1$	$-i$	$i$	$1$	$i$	$-1$	$i$	$1$	$-i$	$-1$
$\chi_{240}(67,\cdot)$	240.bc	4	no	$1$	$1$	$i$	$i$	$1$	$i$	$i$	$-i$	$-i$	$-1$	$1$	$-1$
$\chi_{240}(71,\cdot)$	240.b	2	no	$1$	$1$	$-1$	$-1$	$-1$	$-1$	$1$	$1$	$1$	$-1$	$-1$	$-1$
$\chi_{240}(73,\cdot)$	240.x	4	no	$-1$	$1$	$-i$	$-1$	$-i$	$-i$	$1$	$i$	$1$	$1$	$i$	$1$
$\chi_{240}(77,\cdot)$	240.bf	4	yes	$1$	$1$	$-i$	$i$	$1$	$-i$	$-i$	$-i$	$i$	$1$	$1$	$1$
$\chi_{240}(79,\cdot)$	240.j	2	no	$-1$	$1$	$1$	$-1$	$-1$	$-1$	$-1$	$1$	$1$	$-1$	$-1$	$1$
$\chi_{240}(83,\cdot)$	240.z	4	yes	$-1$	$1$	$-i$	$-i$	$-1$	$i$	$i$	$-i$	$i$	$-1$	$-1$	$1$
$\chi_{240}(89,\cdot)$	240.i	2	no	$-1$	$1$	$-1$	$1$	$1$	$1$	$-1$	$1$	$1$	$1$	$1$	$-1$
$\chi_{240}(91,\cdot)$	240.bn	4	no	$-1$	$1$	$1$	$-i$	$-i$	$1$	$i$	$1$	$-i$	$-1$	$i$	$-1$
$\chi_{240}(97,\cdot)$	240.bg	4	no	$-1$	$1$	$i$	$1$	$-i$	$i$	$-1$	$-i$	$-1$	$1$	$i$	$1$
$\chi_{240}(101,\cdot)$	240.r	4	no	$-1$	$1$	$-1$	$-i$	$-i$	$-1$	$-i$	$1$	$i$	$1$	$i$	$1$
$\chi_{240}(103,\cdot)$	240.bh	4	no	$1$	$1$	$i$	$1$	$-i$	$-i$	$-1$	$-i$	$1$	$-1$	$i$	$1$
$\chi_{240}(107,\cdot)$	240.z	4	yes	$-1$	$1$	$i$	$i$	$-1$	$-i$	$-i$	$i$	$-i$	$-1$	$-1$	$1$
$\chi_{240}(109,\cdot)$	240.bl	4	no	$1$	$1$	$1$	$-i$	$-i$	$-1$	$i$	$1$	$i$	$1$	$i$	$-1$
$\chi_{240}(113,\cdot)$	240.v	4	no	$1$	$1$	$-i$	$-1$	$i$	$i$	$-1$	$-i$	$1$	$1$	$-i$	$-1$
$\chi_{240}(119,\cdot)$	240.m	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	$240$
Structure	\(C_{2}\times C_{2}\times C_{4}\times C_{4}\)
Order	$64$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(7\)	\(11\)	\(13\)	\(17\)	\(19\)	\(23\)	\(29\)	\(31\)	\(37\)	\(41\)
\(\chi_{240}(1,\cdot)\)	240.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{240}(7,\cdot)\)	240.bh	4	no	\(1\)	\(1\)	\(-i\)	\(1\)	\(i\)	\(i\)	\(-1\)	\(i\)	\(1\)	\(-1\)	\(-i\)	\(1\)
\(\chi_{240}(11,\cdot)\)	240.bk	4	no	\(1\)	\(1\)	\(1\)	\(i\)	\(-i\)	\(-1\)	\(i\)	\(-1\)	\(i\)	\(-1\)	\(i\)	\(1\)
\(\chi_{240}(13,\cdot)\)	240.ba	4	no	\(-1\)	\(1\)	\(i\)	\(-i\)	\(-1\)	\(-i\)	\(-i\)	\(-i\)	\(-i\)	\(1\)	\(-1\)	\(-1\)
\(\chi_{240}(17,\cdot)\)	240.v	4	no	\(1\)	\(1\)	\(i\)	\(-1\)	\(-i\)	\(-i\)	\(-1\)	\(i\)	\(1\)	\(1\)	\(i\)	\(-1\)
\(\chi_{240}(19,\cdot)\)	240.q	4	no	\(-1\)	\(1\)	\(-1\)	\(i\)	\(-i\)	\(-1\)	\(-i\)	\(-1\)	\(i\)	\(-1\)	\(i\)	\(-1\)
\(\chi_{240}(23,\cdot)\)	240.u	4	no	\(-1\)	\(1\)	\(i\)	\(-1\)	\(-i\)	\(i\)	\(-1\)	\(i\)	\(-1\)	\(-1\)	\(i\)	\(-1\)
\(\chi_{240}(29,\cdot)\)	240.bm	4	yes	\(-1\)	\(1\)	\(1\)	\(i\)	\(-i\)	\(1\)	\(i\)	\(-1\)	\(-i\)	\(1\)	\(i\)	\(1\)
\(\chi_{240}(31,\cdot)\)	240.e	2	no	\(-1\)	\(1\)	\(-1\)	\(-1\)	\(1\)	\(1\)	\(-1\)	\(-1\)	\(1\)	\(-1\)	\(1\)	\(1\)
\(\chi_{240}(37,\cdot)\)	240.ba	4	no	\(-1\)	\(1\)	\(-i\)	\(i\)	\(-1\)	\(i\)	\(i\)	\(i\)	\(i\)	\(1\)	\(-1\)	\(-1\)
\(\chi_{240}(41,\cdot)\)	240.n	2	no	\(-1\)	\(1\)	\(1\)	\(1\)	\(-1\)	\(-1\)	\(-1\)	\(-1\)	\(1\)	\(1\)	\(-1\)	\(-1\)
\(\chi_{240}(43,\cdot)\)	240.bc	4	no	\(1\)	\(1\)	\(-i\)	\(-i\)	\(1\)	\(-i\)	\(-i\)	\(i\)	\(i\)	\(-1\)	\(1\)	\(-1\)
\(\chi_{240}(47,\cdot)\)	240.bj	4	no	\(-1\)	\(1\)	\(-i\)	\(1\)	\(-i\)	\(-i\)	\(1\)	\(-i\)	\(1\)	\(-1\)	\(i\)	\(-1\)
\(\chi_{240}(49,\cdot)\)	240.f	2	no	\(1\)	\(1\)	\(-1\)	\(1\)	\(-1\)	\(-1\)	\(1\)	\(-1\)	\(1\)	\(1\)	\(-1\)	\(1\)
\(\chi_{240}(53,\cdot)\)	240.bf	4	yes	\(1\)	\(1\)	\(i\)	\(-i\)	\(1\)	\(i\)	\(i\)	\(i\)	\(-i\)	\(1\)	\(1\)	\(1\)
\(\chi_{240}(59,\cdot)\)	240.t	4	yes	\(1\)	\(1\)	\(-1\)	\(i\)	\(i\)	\(1\)	\(i\)	\(1\)	\(i\)	\(-1\)	\(-i\)	\(1\)
\(\chi_{240}(61,\cdot)\)	240.s	4	no	\(1\)	\(1\)	\(-1\)	\(-i\)	\(i\)	\(1\)	\(i\)	\(-1\)	\(i\)	\(1\)	\(-i\)	\(-1\)
\(\chi_{240}(67,\cdot)\)	240.bc	4	no	\(1\)	\(1\)	\(i\)	\(i\)	\(1\)	\(i\)	\(i\)	\(-i\)	\(-i\)	\(-1\)	\(1\)	\(-1\)
\(\chi_{240}(71,\cdot)\)	240.b	2	no	\(1\)	\(1\)	\(-1\)	\(-1\)	\(-1\)	\(-1\)	\(1\)	\(1\)	\(1\)	\(-1\)	\(-1\)	\(-1\)
\(\chi_{240}(73,\cdot)\)	240.x	4	no	\(-1\)	\(1\)	\(-i\)	\(-1\)	\(-i\)	\(-i\)	\(1\)	\(i\)	\(1\)	\(1\)	\(i\)	\(1\)
\(\chi_{240}(77,\cdot)\)	240.bf	4	yes	\(1\)	\(1\)	\(-i\)	\(i\)	\(1\)	\(-i\)	\(-i\)	\(-i\)	\(i\)	\(1\)	\(1\)	\(1\)
\(\chi_{240}(79,\cdot)\)	240.j	2	no	\(-1\)	\(1\)	\(1\)	\(-1\)	\(-1\)	\(-1\)	\(-1\)	\(1\)	\(1\)	\(-1\)	\(-1\)	\(1\)
\(\chi_{240}(83,\cdot)\)	240.z	4	yes	\(-1\)	\(1\)	\(-i\)	\(-i\)	\(-1\)	\(i\)	\(i\)	\(-i\)	\(i\)	\(-1\)	\(-1\)	\(1\)
\(\chi_{240}(89,\cdot)\)	240.i	2	no	\(-1\)	\(1\)	\(-1\)	\(1\)	\(1\)	\(1\)	\(-1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(-1\)
\(\chi_{240}(91,\cdot)\)	240.bn	4	no	\(-1\)	\(1\)	\(1\)	\(-i\)	\(-i\)	\(1\)	\(i\)	\(1\)	\(-i\)	\(-1\)	\(i\)	\(-1\)
\(\chi_{240}(97,\cdot)\)	240.bg	4	no	\(-1\)	\(1\)	\(i\)	\(1\)	\(-i\)	\(i\)	\(-1\)	\(-i\)	\(-1\)	\(1\)	\(i\)	\(1\)
\(\chi_{240}(101,\cdot)\)	240.r	4	no	\(-1\)	\(1\)	\(-1\)	\(-i\)	\(-i\)	\(-1\)	\(-i\)	\(1\)	\(i\)	\(1\)	\(i\)	\(1\)
\(\chi_{240}(103,\cdot)\)	240.bh	4	no	\(1\)	\(1\)	\(i\)	\(1\)	\(-i\)	\(-i\)	\(-1\)	\(-i\)	\(1\)	\(-1\)	\(i\)	\(1\)
\(\chi_{240}(107,\cdot)\)	240.z	4	yes	\(-1\)	\(1\)	\(i\)	\(i\)	\(-1\)	\(-i\)	\(-i\)	\(i\)	\(-i\)	\(-1\)	\(-1\)	\(1\)
\(\chi_{240}(109,\cdot)\)	240.bl	4	no	\(1\)	\(1\)	\(1\)	\(-i\)	\(-i\)	\(-1\)	\(i\)	\(1\)	\(i\)	\(1\)	\(i\)	\(-1\)
\(\chi_{240}(113,\cdot)\)	240.v	4	no	\(1\)	\(1\)	\(-i\)	\(-1\)	\(i\)	\(i\)	\(-1\)	\(-i\)	\(1\)	\(1\)	\(-i\)	\(-1\)
\(\chi_{240}(119,\cdot)\)	240.m	2	no	\(1\)	\(1\)	\(1\)	\(-1\)	\(1\)	\(1\)	\(1\)	\(-1\)	\(1\)	\(-1\)	\(1\)	\(-1\)

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First 32 of 64 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.