LMFDB - Group of Dirichlet characters of modulus 208

Show commands: PariGP / SageMath

sage: H = DirichletGroup(208)

pari: g = idealstar(,208,2)

Character group

sage: G.order() pari: g.no
Order	=	96
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{4}\times C_{12}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{208}(79,\cdot)$, $\chi_{208}(53,\cdot)$, $\chi_{208}(145,\cdot)$

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	$-1$	$1$	$3$	$5$	$7$	$9$	$11$	$15$	$17$	$19$	$21$	$23$
$\chi_{208}(1,\cdot)$	208.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{208}(3,\cdot)$	208.bg	12	yes	$-1$	$1$	$e\left(\frac{1}{12}\right)$	$-i$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{12}\right)$	$-i$	$e\left(\frac{1}{3}\right)$
$\chi_{208}(5,\cdot)$	208.r	4	yes	$-1$	$1$	$-i$	$1$	$-i$	$-1$	$-1$	$-i$	$-1$	$-1$	$-1$	$1$
$\chi_{208}(7,\cdot)$	208.bc	12	no	$1$	$1$	$e\left(\frac{2}{3}\right)$	$-i$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{7}{12}\right)$	$i$	$e\left(\frac{2}{3}\right)$
$\chi_{208}(9,\cdot)$	208.z	6	no	$1$	$1$	$e\left(\frac{1}{6}\right)$	$-1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{6}\right)$	$-1$	$e\left(\frac{2}{3}\right)$
$\chi_{208}(11,\cdot)$	208.bf	12	yes	$1$	$1$	$e\left(\frac{7}{12}\right)$	$-1$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{6}\right)$	$1$	$e\left(\frac{5}{6}\right)$
$\chi_{208}(15,\cdot)$	208.bm	12	no	$1$	$1$	$e\left(\frac{5}{6}\right)$	$-i$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{11}{12}\right)$	$i$	$e\left(\frac{1}{3}\right)$
$\chi_{208}(17,\cdot)$	208.w	6	no	$1$	$1$	$e\left(\frac{2}{3}\right)$	$-1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{6}\right)$	$-1$	$e\left(\frac{2}{3}\right)$
$\chi_{208}(19,\cdot)$	208.bf	12	yes	$1$	$1$	$e\left(\frac{5}{12}\right)$	$-1$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{6}\right)$	$1$	$e\left(\frac{1}{6}\right)$
$\chi_{208}(21,\cdot)$	208.m	4	yes	$-1$	$1$	$-i$	$-1$	$i$	$-1$	$1$	$i$	$-1$	$1$	$1$	$1$
$\chi_{208}(23,\cdot)$	208.x	6	no	$-1$	$1$	$e\left(\frac{1}{3}\right)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{6}\right)$	$1$	$e\left(\frac{5}{6}\right)$
$\chi_{208}(25,\cdot)$	208.e	2	no	$1$	$1$	$-1$	$1$	$-1$	$1$	$1$	$-1$	$1$	$1$	$1$	$1$
$\chi_{208}(27,\cdot)$	208.q	4	no	$-1$	$1$	$i$	$i$	$1$	$-1$	$-i$	$-1$	$1$	$i$	$i$	$1$
$\chi_{208}(29,\cdot)$	208.bj	12	yes	$1$	$1$	$e\left(\frac{7}{12}\right)$	$-i$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{11}{12}\right)$	$-i$	$e\left(\frac{5}{6}\right)$
$\chi_{208}(31,\cdot)$	208.k	4	no	$1$	$1$	$-1$	$-i$	$-i$	$1$	$-i$	$i$	$-1$	$i$	$i$	$1$
$\chi_{208}(33,\cdot)$	208.bd	12	no	$-1$	$1$	$e\left(\frac{2}{3}\right)$	$i$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{7}{12}\right)$	$-i$	$e\left(\frac{1}{6}\right)$
$\chi_{208}(35,\cdot)$	208.bg	12	yes	$-1$	$1$	$e\left(\frac{5}{12}\right)$	$-i$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{12}\right)$	$-i$	$e\left(\frac{2}{3}\right)$
$\chi_{208}(37,\cdot)$	208.be	12	yes	$-1$	$1$	$e\left(\frac{1}{12}\right)$	$-1$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{3}\right)$	$1$	$e\left(\frac{1}{3}\right)$
$\chi_{208}(41,\cdot)$	208.bn	12	no	$-1$	$1$	$e\left(\frac{5}{6}\right)$	$i$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{11}{12}\right)$	$-i$	$e\left(\frac{5}{6}\right)$
$\chi_{208}(43,\cdot)$	208.bi	12	yes	$-1$	$1$	$e\left(\frac{11}{12}\right)$	$-i$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{12}\right)$	$-i$	$e\left(\frac{2}{3}\right)$
$\chi_{208}(45,\cdot)$	208.be	12	yes	$-1$	$1$	$e\left(\frac{11}{12}\right)$	$-1$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{3}\right)$	$1$	$e\left(\frac{2}{3}\right)$
$\chi_{208}(47,\cdot)$	208.k	4	no	$1$	$1$	$-1$	$i$	$i$	$1$	$i$	$-i$	$-1$	$-i$	$-i$	$1$
$\chi_{208}(49,\cdot)$	208.w	6	no	$1$	$1$	$e\left(\frac{1}{3}\right)$	$-1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{6}\right)$	$-1$	$e\left(\frac{1}{3}\right)$
$\chi_{208}(51,\cdot)$	208.o	4	yes	$-1$	$1$	$-i$	$i$	$-1$	$-1$	$-i$	$1$	$1$	$i$	$i$	$1$
$\chi_{208}(53,\cdot)$	208.n	4	no	$1$	$1$	$-i$	$i$	$-1$	$-1$	$i$	$1$	$1$	$-i$	$i$	$-1$
$\chi_{208}(55,\cdot)$	208.v	6	no	$-1$	$1$	$e\left(\frac{1}{3}\right)$	$-1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$	$-1$	$e\left(\frac{5}{6}\right)$
$\chi_{208}(57,\cdot)$	208.j	4	no	$-1$	$1$	$-1$	$i$	$i$	$1$	$-i$	$-i$	$-1$	$i$	$-i$	$-1$
$\chi_{208}(59,\cdot)$	208.bf	12	yes	$1$	$1$	$e\left(\frac{11}{12}\right)$	$-1$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{6}\right)$	$1$	$e\left(\frac{1}{6}\right)$
$\chi_{208}(61,\cdot)$	208.bj	12	yes	$1$	$1$	$e\left(\frac{11}{12}\right)$	$-i$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{7}{12}\right)$	$-i$	$e\left(\frac{1}{6}\right)$
$\chi_{208}(63,\cdot)$	208.bm	12	no	$1$	$1$	$e\left(\frac{5}{6}\right)$	$i$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{12}\right)$	$-i$	$e\left(\frac{1}{3}\right)$
$\chi_{208}(67,\cdot)$	208.bf	12	yes	$1$	$1$	$e\left(\frac{1}{12}\right)$	$-1$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{6}\right)$	$1$	$e\left(\frac{5}{6}\right)$
$\chi_{208}(69,\cdot)$	208.bh	12	yes	$1$	$1$	$e\left(\frac{5}{12}\right)$	$-i$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{7}{12}\right)$	$-i$	$e\left(\frac{1}{6}\right)$

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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	$208$
Structure	\(C_{2}\times C_{4}\times C_{12}\)
Order	$96$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(3\)	\(5\)	\(7\)	\(9\)	\(11\)	\(15\)	\(17\)	\(19\)	\(21\)	\(23\)
\(\chi_{208}(1,\cdot)\)	208.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{208}(3,\cdot)\)	208.bg	12	yes	\(-1\)	\(1\)	\(e\left(\frac{1}{12}\right)\)	\(-i\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(-i\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{208}(5,\cdot)\)	208.r	4	yes	\(-1\)	\(1\)	\(-i\)	\(1\)	\(-i\)	\(-1\)	\(-1\)	\(-i\)	\(-1\)	\(-1\)	\(-1\)	\(1\)
\(\chi_{208}(7,\cdot)\)	208.bc	12	no	\(1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(-i\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(i\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{208}(9,\cdot)\)	208.z	6	no	\(1\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(-1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(-1\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{208}(11,\cdot)\)	208.bf	12	yes	\(1\)	\(1\)	\(e\left(\frac{7}{12}\right)\)	\(-1\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(1\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{208}(15,\cdot)\)	208.bm	12	no	\(1\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(-i\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(i\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{208}(17,\cdot)\)	208.w	6	no	\(1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(-1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(-1\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{208}(19,\cdot)\)	208.bf	12	yes	\(1\)	\(1\)	\(e\left(\frac{5}{12}\right)\)	\(-1\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(1\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{208}(21,\cdot)\)	208.m	4	yes	\(-1\)	\(1\)	\(-i\)	\(-1\)	\(i\)	\(-1\)	\(1\)	\(i\)	\(-1\)	\(1\)	\(1\)	\(1\)
\(\chi_{208}(23,\cdot)\)	208.x	6	no	\(-1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(1\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{208}(25,\cdot)\)	208.e	2	no	\(1\)	\(1\)	\(-1\)	\(1\)	\(-1\)	\(1\)	\(1\)	\(-1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{208}(27,\cdot)\)	208.q	4	no	\(-1\)	\(1\)	\(i\)	\(i\)	\(1\)	\(-1\)	\(-i\)	\(-1\)	\(1\)	\(i\)	\(i\)	\(1\)
\(\chi_{208}(29,\cdot)\)	208.bj	12	yes	\(1\)	\(1\)	\(e\left(\frac{7}{12}\right)\)	\(-i\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(-i\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{208}(31,\cdot)\)	208.k	4	no	\(1\)	\(1\)	\(-1\)	\(-i\)	\(-i\)	\(1\)	\(-i\)	\(i\)	\(-1\)	\(i\)	\(i\)	\(1\)
\(\chi_{208}(33,\cdot)\)	208.bd	12	no	\(-1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(i\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(-i\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{208}(35,\cdot)\)	208.bg	12	yes	\(-1\)	\(1\)	\(e\left(\frac{5}{12}\right)\)	\(-i\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(-i\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{208}(37,\cdot)\)	208.be	12	yes	\(-1\)	\(1\)	\(e\left(\frac{1}{12}\right)\)	\(-1\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(1\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{208}(41,\cdot)\)	208.bn	12	no	\(-1\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(i\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(-i\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{208}(43,\cdot)\)	208.bi	12	yes	\(-1\)	\(1\)	\(e\left(\frac{11}{12}\right)\)	\(-i\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(-i\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{208}(45,\cdot)\)	208.be	12	yes	\(-1\)	\(1\)	\(e\left(\frac{11}{12}\right)\)	\(-1\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(1\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{208}(47,\cdot)\)	208.k	4	no	\(1\)	\(1\)	\(-1\)	\(i\)	\(i\)	\(1\)	\(i\)	\(-i\)	\(-1\)	\(-i\)	\(-i\)	\(1\)
\(\chi_{208}(49,\cdot)\)	208.w	6	no	\(1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(-1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(-1\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{208}(51,\cdot)\)	208.o	4	yes	\(-1\)	\(1\)	\(-i\)	\(i\)	\(-1\)	\(-1\)	\(-i\)	\(1\)	\(1\)	\(i\)	\(i\)	\(1\)
\(\chi_{208}(53,\cdot)\)	208.n	4	no	\(1\)	\(1\)	\(-i\)	\(i\)	\(-1\)	\(-1\)	\(i\)	\(1\)	\(1\)	\(-i\)	\(i\)	\(-1\)
\(\chi_{208}(55,\cdot)\)	208.v	6	no	\(-1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(-1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(-1\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{208}(57,\cdot)\)	208.j	4	no	\(-1\)	\(1\)	\(-1\)	\(i\)	\(i\)	\(1\)	\(-i\)	\(-i\)	\(-1\)	\(i\)	\(-i\)	\(-1\)
\(\chi_{208}(59,\cdot)\)	208.bf	12	yes	\(1\)	\(1\)	\(e\left(\frac{11}{12}\right)\)	\(-1\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(1\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{208}(61,\cdot)\)	208.bj	12	yes	\(1\)	\(1\)	\(e\left(\frac{11}{12}\right)\)	\(-i\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(-i\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{208}(63,\cdot)\)	208.bm	12	no	\(1\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(i\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(-i\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{208}(67,\cdot)\)	208.bf	12	yes	\(1\)	\(1\)	\(e\left(\frac{1}{12}\right)\)	\(-1\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(1\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{208}(69,\cdot)\)	208.bh	12	yes	\(1\)	\(1\)	\(e\left(\frac{5}{12}\right)\)	\(-i\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(-i\)	\(e\left(\frac{1}{6}\right)\)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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Character group

First 32 of 96 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.