LMFDB - Group of Dirichlet characters of modulus 260

Show commands: Magma / Pari/GP / SageMath

comment:Define the Dirichlet group

sage:G = DirichletGroup(260)

gp:g = idealstar(,260,2)

magma:G = FullDirichletGroup(260);

Character group

Order	=	96	comment:Order sage:G.order() gp:g.no magma:Order(G);
Structure	=	$C_{2}\times C_{4}\times C_{12}$	comment:Group structure sage:sorted(g.order() for g in G.gens()) gp:g.cyc magma:PrimaryInvariants(G);
Generators	=	$\chi_{260}(131,\cdot)$, $\chi_{260}(157,\cdot)$, $\chi_{260}(41,\cdot)$	comment:Generators sage:G.gens() gp:g.gen magma:Generators(G);

First 32 of 96 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	$-1$	$1$	$3$	$7$	$9$	$11$	$17$	$19$	$21$	$23$	$27$	$29$
$\chi_{260}(1,\cdot)$	260.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{260}(3,\cdot)$	260.bj	12	yes	$1$	$1$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{2}{3}\right)$	$1$	$e\left(\frac{1}{12}\right)$	$i$	$e\left(\frac{5}{6}\right)$
$\chi_{260}(7,\cdot)$	260.bl	12	yes	$-1$	$1$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{7}{12}\right)$	$-i$	$e\left(\frac{5}{12}\right)$	$-i$	$e\left(\frac{1}{6}\right)$
$\chi_{260}(9,\cdot)$	260.ba	6	no	$1$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{3}\right)$	$1$	$e\left(\frac{1}{6}\right)$	$-1$	$e\left(\frac{2}{3}\right)$
$\chi_{260}(11,\cdot)$	260.bn	12	no	$1$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{12}\right)$	$-i$	$e\left(\frac{1}{3}\right)$	$-1$	$e\left(\frac{1}{3}\right)$
$\chi_{260}(17,\cdot)$	260.bi	12	no	$-1$	$1$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{3}\right)$	$-1$	$e\left(\frac{5}{12}\right)$	$i$	$e\left(\frac{1}{6}\right)$
$\chi_{260}(19,\cdot)$	260.bc	12	yes	$1$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{7}{12}\right)$	$i$	$e\left(\frac{1}{6}\right)$	$1$	$e\left(\frac{2}{3}\right)$
$\chi_{260}(21,\cdot)$	260.t	4	no	$-1$	$1$	$1$	$-i$	$1$	$-i$	$-1$	$i$	$-i$	$-1$	$1$	$1$
$\chi_{260}(23,\cdot)$	260.bg	12	yes	$1$	$1$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{6}\right)$	$-1$	$e\left(\frac{1}{12}\right)$	$i$	$e\left(\frac{5}{6}\right)$
$\chi_{260}(27,\cdot)$	260.o	4	no	$1$	$1$	$i$	$-i$	$-1$	$-1$	$i$	$1$	$1$	$i$	$-i$	$-1$
$\chi_{260}(29,\cdot)$	260.ba	6	no	$1$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{3}\right)$	$1$	$e\left(\frac{5}{6}\right)$	$-1$	$e\left(\frac{1}{3}\right)$
$\chi_{260}(31,\cdot)$	260.j	4	no	$1$	$1$	$-1$	$-i$	$1$	$-i$	$-1$	$i$	$i$	$1$	$-1$	$1$
$\chi_{260}(33,\cdot)$	260.bk	12	no	$1$	$1$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{12}\right)$	$-i$	$e\left(\frac{5}{12}\right)$	$-i$	$e\left(\frac{1}{6}\right)$
$\chi_{260}(37,\cdot)$	260.bf	12	no	$1$	$1$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{5}{12}\right)$	$-i$	$e\left(\frac{7}{12}\right)$	$i$	$e\left(\frac{5}{6}\right)$
$\chi_{260}(41,\cdot)$	260.bd	12	no	$-1$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{12}\right)$	$i$	$e\left(\frac{5}{6}\right)$	$1$	$e\left(\frac{1}{3}\right)$
$\chi_{260}(43,\cdot)$	260.bg	12	yes	$1$	$1$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{5}{6}\right)$	$-1$	$e\left(\frac{5}{12}\right)$	$i$	$e\left(\frac{1}{6}\right)$
$\chi_{260}(47,\cdot)$	260.l	4	yes	$-1$	$1$	$i$	$-1$	$-1$	$i$	$-i$	$i$	$-i$	$-i$	$-i$	$-1$
$\chi_{260}(49,\cdot)$	260.z	6	no	$1$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{6}\right)$	$-1$	$e\left(\frac{5}{6}\right)$	$-1$	$e\left(\frac{1}{3}\right)$
$\chi_{260}(51,\cdot)$	260.e	2	no	$-1$	$1$	$-1$	$1$	$1$	$1$	$1$	$1$	$-1$	$-1$	$-1$	$1$
$\chi_{260}(53,\cdot)$	260.q	4	no	$-1$	$1$	$i$	$-i$	$-1$	$1$	$-i$	$-1$	$1$	$i$	$-i$	$-1$
$\chi_{260}(57,\cdot)$	260.m	4	no	$1$	$1$	$-i$	$-1$	$-1$	$i$	$-i$	$i$	$i$	$i$	$i$	$-1$
$\chi_{260}(59,\cdot)$	260.bc	12	yes	$1$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{12}\right)$	$-i$	$e\left(\frac{1}{6}\right)$	$1$	$e\left(\frac{2}{3}\right)$
$\chi_{260}(61,\cdot)$	260.i	3	no	$1$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$	$1$	$e\left(\frac{2}{3}\right)$	$1$	$e\left(\frac{2}{3}\right)$
$\chi_{260}(63,\cdot)$	260.be	12	yes	$-1$	$1$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{11}{12}\right)$	$-i$	$e\left(\frac{7}{12}\right)$	$i$	$e\left(\frac{5}{6}\right)$
$\chi_{260}(67,\cdot)$	260.be	12	yes	$-1$	$1$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{5}{12}\right)$	$i$	$e\left(\frac{1}{12}\right)$	$-i$	$e\left(\frac{5}{6}\right)$
$\chi_{260}(69,\cdot)$	260.z	6	no	$1$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{6}\right)$	$-1$	$e\left(\frac{1}{6}\right)$	$-1$	$e\left(\frac{2}{3}\right)$
$\chi_{260}(71,\cdot)$	260.bn	12	no	$1$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{7}{12}\right)$	$i$	$e\left(\frac{2}{3}\right)$	$-1$	$e\left(\frac{2}{3}\right)$
$\chi_{260}(73,\cdot)$	260.m	4	no	$1$	$1$	$i$	$-1$	$-1$	$-i$	$i$	$-i$	$-i$	$-i$	$-i$	$-1$
$\chi_{260}(77,\cdot)$	260.n	4	no	$-1$	$1$	$-i$	$-i$	$-1$	$-1$	$i$	$1$	$-1$	$-i$	$i$	$-1$
$\chi_{260}(79,\cdot)$	260.h	2	no	$-1$	$1$	$1$	$1$	$1$	$-1$	$-1$	$-1$	$1$	$1$	$1$	$1$
$\chi_{260}(81,\cdot)$	260.i	3	no	$1$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$	$1$	$e\left(\frac{1}{3}\right)$	$1$	$e\left(\frac{1}{3}\right)$
$\chi_{260}(83,\cdot)$	260.l	4	yes	$-1$	$1$	$-i$	$-1$	$-1$	$-i$	$i$	$-i$	$i$	$i$	$i$	$-1$

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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	$260$
Structure	\(C_{2}\times C_{4}\times C_{12}\)
Order	$96$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(3\)	\(7\)	\(9\)	\(11\)	\(17\)	\(19\)	\(21\)	\(23\)	\(27\)	\(29\)
\(\chi_{260}(1,\cdot)\)	260.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{260}(3,\cdot)\)	260.bj	12	yes	\(1\)	\(1\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(1\)	\(e\left(\frac{1}{12}\right)\)	\(i\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{260}(7,\cdot)\)	260.bl	12	yes	\(-1\)	\(1\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(-i\)	\(e\left(\frac{5}{12}\right)\)	\(-i\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{260}(9,\cdot)\)	260.ba	6	no	\(1\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(-1\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{260}(11,\cdot)\)	260.bn	12	no	\(1\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(-i\)	\(e\left(\frac{1}{3}\right)\)	\(-1\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{260}(17,\cdot)\)	260.bi	12	no	\(-1\)	\(1\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(-1\)	\(e\left(\frac{5}{12}\right)\)	\(i\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{260}(19,\cdot)\)	260.bc	12	yes	\(1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(i\)	\(e\left(\frac{1}{6}\right)\)	\(1\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{260}(21,\cdot)\)	260.t	4	no	\(-1\)	\(1\)	\(1\)	\(-i\)	\(1\)	\(-i\)	\(-1\)	\(i\)	\(-i\)	\(-1\)	\(1\)	\(1\)
\(\chi_{260}(23,\cdot)\)	260.bg	12	yes	\(1\)	\(1\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(-1\)	\(e\left(\frac{1}{12}\right)\)	\(i\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{260}(27,\cdot)\)	260.o	4	no	\(1\)	\(1\)	\(i\)	\(-i\)	\(-1\)	\(-1\)	\(i\)	\(1\)	\(1\)	\(i\)	\(-i\)	\(-1\)
\(\chi_{260}(29,\cdot)\)	260.ba	6	no	\(1\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(-1\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{260}(31,\cdot)\)	260.j	4	no	\(1\)	\(1\)	\(-1\)	\(-i\)	\(1\)	\(-i\)	\(-1\)	\(i\)	\(i\)	\(1\)	\(-1\)	\(1\)
\(\chi_{260}(33,\cdot)\)	260.bk	12	no	\(1\)	\(1\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(-i\)	\(e\left(\frac{5}{12}\right)\)	\(-i\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{260}(37,\cdot)\)	260.bf	12	no	\(1\)	\(1\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(-i\)	\(e\left(\frac{7}{12}\right)\)	\(i\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{260}(41,\cdot)\)	260.bd	12	no	\(-1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(i\)	\(e\left(\frac{5}{6}\right)\)	\(1\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{260}(43,\cdot)\)	260.bg	12	yes	\(1\)	\(1\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(-1\)	\(e\left(\frac{5}{12}\right)\)	\(i\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{260}(47,\cdot)\)	260.l	4	yes	\(-1\)	\(1\)	\(i\)	\(-1\)	\(-1\)	\(i\)	\(-i\)	\(i\)	\(-i\)	\(-i\)	\(-i\)	\(-1\)
\(\chi_{260}(49,\cdot)\)	260.z	6	no	\(1\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(-1\)	\(e\left(\frac{5}{6}\right)\)	\(-1\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{260}(51,\cdot)\)	260.e	2	no	\(-1\)	\(1\)	\(-1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(-1\)	\(-1\)	\(-1\)	\(1\)
\(\chi_{260}(53,\cdot)\)	260.q	4	no	\(-1\)	\(1\)	\(i\)	\(-i\)	\(-1\)	\(1\)	\(-i\)	\(-1\)	\(1\)	\(i\)	\(-i\)	\(-1\)
\(\chi_{260}(57,\cdot)\)	260.m	4	no	\(1\)	\(1\)	\(-i\)	\(-1\)	\(-1\)	\(i\)	\(-i\)	\(i\)	\(i\)	\(i\)	\(i\)	\(-1\)
\(\chi_{260}(59,\cdot)\)	260.bc	12	yes	\(1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(-i\)	\(e\left(\frac{1}{6}\right)\)	\(1\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{260}(61,\cdot)\)	260.i	3	no	\(1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(1\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{260}(63,\cdot)\)	260.be	12	yes	\(-1\)	\(1\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(-i\)	\(e\left(\frac{7}{12}\right)\)	\(i\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{260}(67,\cdot)\)	260.be	12	yes	\(-1\)	\(1\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(i\)	\(e\left(\frac{1}{12}\right)\)	\(-i\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{260}(69,\cdot)\)	260.z	6	no	\(1\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(-1\)	\(e\left(\frac{1}{6}\right)\)	\(-1\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{260}(71,\cdot)\)	260.bn	12	no	\(1\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(i\)	\(e\left(\frac{2}{3}\right)\)	\(-1\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{260}(73,\cdot)\)	260.m	4	no	\(1\)	\(1\)	\(i\)	\(-1\)	\(-1\)	\(-i\)	\(i\)	\(-i\)	\(-i\)	\(-i\)	\(-i\)	\(-1\)
\(\chi_{260}(77,\cdot)\)	260.n	4	no	\(-1\)	\(1\)	\(-i\)	\(-i\)	\(-1\)	\(-1\)	\(i\)	\(1\)	\(-1\)	\(-i\)	\(i\)	\(-1\)
\(\chi_{260}(79,\cdot)\)	260.h	2	no	\(-1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(-1\)	\(-1\)	\(-1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{260}(81,\cdot)\)	260.i	3	no	\(1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(1\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{260}(83,\cdot)\)	260.l	4	yes	\(-1\)	\(1\)	\(-i\)	\(-1\)	\(-1\)	\(-i\)	\(i\)	\(-i\)	\(i\)	\(i\)	\(i\)	\(-1\)

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L-functions

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This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.