LMFDB - Group of Dirichlet characters of modulus 105

Show commands: PariGP / SageMath

sage: H = DirichletGroup(105)

pari: g = idealstar(,105,2)

Character group

sage: G.order() pari: g.no
Order	=	48
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{2}\times C_{12}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{105}(71,\cdot)$, $\chi_{105}(22,\cdot)$, $\chi_{105}(31,\cdot)$

First 32 of 48 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	$-1$	$1$	$2$	$4$	$8$	$11$	$13$	$16$	$17$	$19$	$22$	$23$
$\chi_{105}(1,\cdot)$	105.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{105}(2,\cdot)$	105.x	12	yes	$1$	$1$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{5}{6}\right)$	$i$	$e\left(\frac{5}{6}\right)$	$-i$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{6}\right)$	$i$	$e\left(\frac{11}{12}\right)$
$\chi_{105}(4,\cdot)$	105.q	6	no	$1$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$	$-1$	$e\left(\frac{2}{3}\right)$	$-1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$	$-1$	$e\left(\frac{5}{6}\right)$
$\chi_{105}(8,\cdot)$	105.j	4	no	$1$	$1$	$i$	$-1$	$-i$	$-1$	$i$	$1$	$i$	$-1$	$-i$	$-i$
$\chi_{105}(11,\cdot)$	105.t	6	no	$-1$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$	$-1$	$e\left(\frac{1}{6}\right)$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$	$1$	$e\left(\frac{5}{6}\right)$
$\chi_{105}(13,\cdot)$	105.m	4	no	$1$	$1$	$-i$	$-1$	$i$	$1$	$-i$	$1$	$i$	$1$	$-i$	$i$
$\chi_{105}(16,\cdot)$	105.i	3	no	$1$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$1$	$e\left(\frac{1}{3}\right)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$1$	$e\left(\frac{2}{3}\right)$
$\chi_{105}(17,\cdot)$	105.w	12	yes	$-1$	$1$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{6}\right)$	$i$	$e\left(\frac{1}{6}\right)$	$i$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{3}\right)$	$i$	$e\left(\frac{7}{12}\right)$
$\chi_{105}(19,\cdot)$	105.r	6	no	$-1$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$	$-1$	$e\left(\frac{1}{3}\right)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$	$-1$	$e\left(\frac{1}{6}\right)$
$\chi_{105}(22,\cdot)$	105.l	4	no	$-1$	$1$	$i$	$-1$	$-i$	$1$	$-i$	$1$	$i$	$-1$	$i$	$-i$
$\chi_{105}(23,\cdot)$	105.x	12	yes	$1$	$1$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{5}{6}\right)$	$-i$	$e\left(\frac{5}{6}\right)$	$i$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{6}\right)$	$-i$	$e\left(\frac{5}{12}\right)$
$\chi_{105}(26,\cdot)$	105.s	6	no	$1$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$	$-1$	$e\left(\frac{5}{6}\right)$	$-1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$	$1$	$e\left(\frac{1}{6}\right)$
$\chi_{105}(29,\cdot)$	105.f	2	no	$-1$	$1$	$1$	$1$	$1$	$-1$	$-1$	$1$	$1$	$1$	$-1$	$1$
$\chi_{105}(31,\cdot)$	105.n	6	no	$-1$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$1$	$e\left(\frac{2}{3}\right)$	$-1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$	$1$	$e\left(\frac{1}{3}\right)$
$\chi_{105}(32,\cdot)$	105.x	12	yes	$1$	$1$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{6}\right)$	$i$	$e\left(\frac{1}{6}\right)$	$-i$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{5}{6}\right)$	$i$	$e\left(\frac{7}{12}\right)$
$\chi_{105}(34,\cdot)$	105.e	2	no	$-1$	$1$	$-1$	$1$	$-1$	$1$	$1$	$1$	$1$	$-1$	$-1$	$-1$
$\chi_{105}(37,\cdot)$	105.v	12	no	$-1$	$1$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{5}{6}\right)$	$-i$	$e\left(\frac{1}{3}\right)$	$-i$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{6}\right)$	$i$	$e\left(\frac{5}{12}\right)$
$\chi_{105}(38,\cdot)$	105.w	12	yes	$-1$	$1$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{6}\right)$	$-i$	$e\left(\frac{1}{6}\right)$	$-i$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{3}\right)$	$-i$	$e\left(\frac{1}{12}\right)$
$\chi_{105}(41,\cdot)$	105.b	2	no	$1$	$1$	$-1$	$1$	$-1$	$-1$	$-1$	$1$	$1$	$-1$	$1$	$-1$
$\chi_{105}(43,\cdot)$	105.l	4	no	$-1$	$1$	$-i$	$-1$	$i$	$1$	$i$	$1$	$-i$	$-1$	$-i$	$i$
$\chi_{105}(44,\cdot)$	105.o	6	yes	$-1$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$1$	$e\left(\frac{5}{6}\right)$	$-1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$-1$	$e\left(\frac{2}{3}\right)$
$\chi_{105}(46,\cdot)$	105.i	3	no	$1$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$1$	$e\left(\frac{2}{3}\right)$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$1$	$e\left(\frac{1}{3}\right)$
$\chi_{105}(47,\cdot)$	105.w	12	yes	$-1$	$1$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{5}{6}\right)$	$i$	$e\left(\frac{5}{6}\right)$	$i$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{2}{3}\right)$	$i$	$e\left(\frac{11}{12}\right)$
$\chi_{105}(52,\cdot)$	105.u	12	no	$1$	$1$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{6}\right)$	$-i$	$e\left(\frac{2}{3}\right)$	$i$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{3}\right)$	$i$	$e\left(\frac{1}{12}\right)$
$\chi_{105}(53,\cdot)$	105.x	12	yes	$1$	$1$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{6}\right)$	$-i$	$e\left(\frac{1}{6}\right)$	$i$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{5}{6}\right)$	$-i$	$e\left(\frac{1}{12}\right)$
$\chi_{105}(58,\cdot)$	105.v	12	no	$-1$	$1$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{5}{6}\right)$	$i$	$e\left(\frac{1}{3}\right)$	$i$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{6}\right)$	$-i$	$e\left(\frac{11}{12}\right)$
$\chi_{105}(59,\cdot)$	105.p	6	yes	$1$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$1$	$e\left(\frac{1}{6}\right)$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$	$-1$	$e\left(\frac{1}{3}\right)$
$\chi_{105}(61,\cdot)$	105.n	6	no	$-1$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$1$	$e\left(\frac{1}{3}\right)$	$-1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$	$1$	$e\left(\frac{2}{3}\right)$
$\chi_{105}(62,\cdot)$	105.k	4	yes	$-1$	$1$	$-i$	$-1$	$i$	$-1$	$i$	$1$	$i$	$1$	$i$	$i$
$\chi_{105}(64,\cdot)$	105.d	2	no	$1$	$1$	$-1$	$1$	$-1$	$1$	$-1$	$1$	$-1$	$1$	$-1$	$-1$
$\chi_{105}(67,\cdot)$	105.v	12	no	$-1$	$1$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{6}\right)$	$-i$	$e\left(\frac{2}{3}\right)$	$-i$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{5}{6}\right)$	$i$	$e\left(\frac{1}{12}\right)$
$\chi_{105}(68,\cdot)$	105.w	12	yes	$-1$	$1$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{5}{6}\right)$	$-i$	$e\left(\frac{5}{6}\right)$	$-i$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{2}{3}\right)$	$-i$	$e\left(\frac{5}{12}\right)$

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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	$105$
Structure	\(C_{2}\times C_{2}\times C_{12}\)
Order	$48$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(4\)	\(8\)	\(11\)	\(13\)	\(16\)	\(17\)	\(19\)	\(22\)	\(23\)
\(\chi_{105}(1,\cdot)\)	105.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{105}(2,\cdot)\)	105.x	12	yes	\(1\)	\(1\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(i\)	\(e\left(\frac{5}{6}\right)\)	\(-i\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(i\)	\(e\left(\frac{11}{12}\right)\)
\(\chi_{105}(4,\cdot)\)	105.q	6	no	\(1\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(-1\)	\(e\left(\frac{2}{3}\right)\)	\(-1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(-1\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{105}(8,\cdot)\)	105.j	4	no	\(1\)	\(1\)	\(i\)	\(-1\)	\(-i\)	\(-1\)	\(i\)	\(1\)	\(i\)	\(-1\)	\(-i\)	\(-i\)
\(\chi_{105}(11,\cdot)\)	105.t	6	no	\(-1\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(-1\)	\(e\left(\frac{1}{6}\right)\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(1\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{105}(13,\cdot)\)	105.m	4	no	\(1\)	\(1\)	\(-i\)	\(-1\)	\(i\)	\(1\)	\(-i\)	\(1\)	\(i\)	\(1\)	\(-i\)	\(i\)
\(\chi_{105}(16,\cdot)\)	105.i	3	no	\(1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(1\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{105}(17,\cdot)\)	105.w	12	yes	\(-1\)	\(1\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(i\)	\(e\left(\frac{1}{6}\right)\)	\(i\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(i\)	\(e\left(\frac{7}{12}\right)\)
\(\chi_{105}(19,\cdot)\)	105.r	6	no	\(-1\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(-1\)	\(e\left(\frac{1}{3}\right)\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(-1\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{105}(22,\cdot)\)	105.l	4	no	\(-1\)	\(1\)	\(i\)	\(-1\)	\(-i\)	\(1\)	\(-i\)	\(1\)	\(i\)	\(-1\)	\(i\)	\(-i\)
\(\chi_{105}(23,\cdot)\)	105.x	12	yes	\(1\)	\(1\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(-i\)	\(e\left(\frac{5}{6}\right)\)	\(i\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(-i\)	\(e\left(\frac{5}{12}\right)\)
\(\chi_{105}(26,\cdot)\)	105.s	6	no	\(1\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(-1\)	\(e\left(\frac{5}{6}\right)\)	\(-1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(1\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{105}(29,\cdot)\)	105.f	2	no	\(-1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(-1\)	\(-1\)	\(1\)	\(1\)	\(1\)	\(-1\)	\(1\)
\(\chi_{105}(31,\cdot)\)	105.n	6	no	\(-1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(-1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(1\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{105}(32,\cdot)\)	105.x	12	yes	\(1\)	\(1\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(i\)	\(e\left(\frac{1}{6}\right)\)	\(-i\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(i\)	\(e\left(\frac{7}{12}\right)\)
\(\chi_{105}(34,\cdot)\)	105.e	2	no	\(-1\)	\(1\)	\(-1\)	\(1\)	\(-1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(-1\)	\(-1\)	\(-1\)
\(\chi_{105}(37,\cdot)\)	105.v	12	no	\(-1\)	\(1\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(-i\)	\(e\left(\frac{1}{3}\right)\)	\(-i\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(i\)	\(e\left(\frac{5}{12}\right)\)
\(\chi_{105}(38,\cdot)\)	105.w	12	yes	\(-1\)	\(1\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(-i\)	\(e\left(\frac{1}{6}\right)\)	\(-i\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(-i\)	\(e\left(\frac{1}{12}\right)\)
\(\chi_{105}(41,\cdot)\)	105.b	2	no	\(1\)	\(1\)	\(-1\)	\(1\)	\(-1\)	\(-1\)	\(-1\)	\(1\)	\(1\)	\(-1\)	\(1\)	\(-1\)
\(\chi_{105}(43,\cdot)\)	105.l	4	no	\(-1\)	\(1\)	\(-i\)	\(-1\)	\(i\)	\(1\)	\(i\)	\(1\)	\(-i\)	\(-1\)	\(-i\)	\(i\)
\(\chi_{105}(44,\cdot)\)	105.o	6	yes	\(-1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(-1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(-1\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{105}(46,\cdot)\)	105.i	3	no	\(1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(1\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{105}(47,\cdot)\)	105.w	12	yes	\(-1\)	\(1\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(i\)	\(e\left(\frac{5}{6}\right)\)	\(i\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(i\)	\(e\left(\frac{11}{12}\right)\)
\(\chi_{105}(52,\cdot)\)	105.u	12	no	\(1\)	\(1\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(-i\)	\(e\left(\frac{2}{3}\right)\)	\(i\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(i\)	\(e\left(\frac{1}{12}\right)\)
\(\chi_{105}(53,\cdot)\)	105.x	12	yes	\(1\)	\(1\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(-i\)	\(e\left(\frac{1}{6}\right)\)	\(i\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(-i\)	\(e\left(\frac{1}{12}\right)\)
\(\chi_{105}(58,\cdot)\)	105.v	12	no	\(-1\)	\(1\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(i\)	\(e\left(\frac{1}{3}\right)\)	\(i\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(-i\)	\(e\left(\frac{11}{12}\right)\)
\(\chi_{105}(59,\cdot)\)	105.p	6	yes	\(1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(-1\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{105}(61,\cdot)\)	105.n	6	no	\(-1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(-1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(1\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{105}(62,\cdot)\)	105.k	4	yes	\(-1\)	\(1\)	\(-i\)	\(-1\)	\(i\)	\(-1\)	\(i\)	\(1\)	\(i\)	\(1\)	\(i\)	\(i\)
\(\chi_{105}(64,\cdot)\)	105.d	2	no	\(1\)	\(1\)	\(-1\)	\(1\)	\(-1\)	\(1\)	\(-1\)	\(1\)	\(-1\)	\(1\)	\(-1\)	\(-1\)
\(\chi_{105}(67,\cdot)\)	105.v	12	no	\(-1\)	\(1\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(-i\)	\(e\left(\frac{2}{3}\right)\)	\(-i\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(i\)	\(e\left(\frac{1}{12}\right)\)
\(\chi_{105}(68,\cdot)\)	105.w	12	yes	\(-1\)	\(1\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(-i\)	\(e\left(\frac{5}{6}\right)\)	\(-i\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(-i\)	\(e\left(\frac{5}{12}\right)\)

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Character group

First 32 of 48 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.