LMFDB - Group of Dirichlet characters of modulus 312

Show commands: PariGP / SageMath

sage: H = DirichletGroup(312)

pari: g = idealstar(,312,2)

Character group

sage: G.order() pari: g.no
Order	=	96
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{2}\times C_{2}\times C_{12}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{312}(79,\cdot)$, $\chi_{312}(157,\cdot)$, $\chi_{312}(209,\cdot)$, $\chi_{312}(145,\cdot)$

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	$-1$	$1$	$5$	$7$	$11$	$17$	$19$	$23$	$25$	$29$	$31$	$35$
$\chi_{312}(1,\cdot)$	312.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{312}(5,\cdot)$	312.y	4	yes	$1$	$1$	$-i$	$i$	$i$	$1$	$i$	$1$	$-1$	$1$	$-i$	$1$
$\chi_{312}(7,\cdot)$	312.bs	12	no	$1$	$1$	$i$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{2}{3}\right)$	$-1$	$e\left(\frac{2}{3}\right)$	$-i$	$e\left(\frac{5}{6}\right)$
$\chi_{312}(11,\cdot)$	312.bq	12	yes	$-1$	$1$	$i$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{5}{6}\right)$	$-1$	$e\left(\frac{1}{3}\right)$	$-i$	$e\left(\frac{1}{6}\right)$
$\chi_{312}(17,\cdot)$	312.bl	6	no	$-1$	$1$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$	$1$	$e\left(\frac{1}{6}\right)$	$-1$	$e\left(\frac{5}{6}\right)$
$\chi_{312}(19,\cdot)$	312.bt	12	no	$1$	$1$	$i$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{2}{3}\right)$	$-1$	$e\left(\frac{1}{6}\right)$	$i$	$e\left(\frac{1}{3}\right)$
$\chi_{312}(23,\cdot)$	312.bj	6	no	$1$	$1$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$1$	$e\left(\frac{5}{6}\right)$	$1$	$e\left(\frac{2}{3}\right)$
$\chi_{312}(25,\cdot)$	312.c	2	no	$1$	$1$	$-1$	$-1$	$-1$	$1$	$-1$	$1$	$1$	$1$	$-1$	$1$
$\chi_{312}(29,\cdot)$	312.bh	6	yes	$-1$	$1$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$	$1$	$e\left(\frac{1}{3}\right)$	$1$	$e\left(\frac{2}{3}\right)$
$\chi_{312}(31,\cdot)$	312.u	4	no	$1$	$1$	$-i$	$-i$	$-i$	$-1$	$i$	$1$	$-1$	$1$	$i$	$-1$
$\chi_{312}(35,\cdot)$	312.bn	6	yes	$1$	$1$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$1$	$e\left(\frac{2}{3}\right)$	$-1$	$e\left(\frac{5}{6}\right)$
$\chi_{312}(37,\cdot)$	312.bv	12	no	$-1$	$1$	$-i$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{5}{6}\right)$	$-1$	$e\left(\frac{5}{6}\right)$	$i$	$e\left(\frac{1}{6}\right)$
$\chi_{312}(41,\cdot)$	312.bp	12	no	$1$	$1$	$i$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{3}\right)$	$-1$	$e\left(\frac{5}{6}\right)$	$-i$	$e\left(\frac{1}{6}\right)$
$\chi_{312}(43,\cdot)$	312.bi	6	no	$-1$	$1$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$	$1$	$e\left(\frac{1}{6}\right)$	$1$	$e\left(\frac{1}{3}\right)$
$\chi_{312}(47,\cdot)$	312.v	4	no	$-1$	$1$	$-i$	$i$	$-i$	$1$	$-i$	$-1$	$-1$	$-1$	$-i$	$1$
$\chi_{312}(49,\cdot)$	312.bf	6	no	$1$	$1$	$-1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$	$1$	$e\left(\frac{1}{3}\right)$	$-1$	$e\left(\frac{2}{3}\right)$
$\chi_{312}(53,\cdot)$	312.p	2	no	$-1$	$1$	$1$	$1$	$1$	$-1$	$-1$	$-1$	$1$	$1$	$1$	$1$
$\chi_{312}(55,\cdot)$	312.bm	6	no	$-1$	$1$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$	$1$	$e\left(\frac{1}{3}\right)$	$-1$	$e\left(\frac{1}{6}\right)$
$\chi_{312}(59,\cdot)$	312.bq	12	yes	$-1$	$1$	$i$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{6}\right)$	$-1$	$e\left(\frac{2}{3}\right)$	$-i$	$e\left(\frac{5}{6}\right)$
$\chi_{312}(61,\cdot)$	312.bb	6	no	$1$	$1$	$-1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$	$1$	$e\left(\frac{1}{6}\right)$	$1$	$e\left(\frac{5}{6}\right)$
$\chi_{312}(67,\cdot)$	312.bt	12	no	$1$	$1$	$i$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{3}\right)$	$-1$	$e\left(\frac{5}{6}\right)$	$i$	$e\left(\frac{2}{3}\right)$
$\chi_{312}(71,\cdot)$	312.br	12	no	$-1$	$1$	$i$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{6}\right)$	$-1$	$e\left(\frac{1}{6}\right)$	$i$	$e\left(\frac{1}{3}\right)$
$\chi_{312}(73,\cdot)$	312.s	4	no	$-1$	$1$	$i$	$-i$	$-i$	$-1$	$i$	$-1$	$-1$	$1$	$i$	$1$
$\chi_{312}(77,\cdot)$	312.b	2	yes	$-1$	$1$	$-1$	$-1$	$-1$	$-1$	$1$	$-1$	$1$	$1$	$-1$	$1$
$\chi_{312}(79,\cdot)$	312.k	2	no	$-1$	$1$	$1$	$-1$	$-1$	$1$	$-1$	$-1$	$1$	$1$	$-1$	$-1$
$\chi_{312}(83,\cdot)$	312.w	4	yes	$-1$	$1$	$-i$	$-i$	$-i$	$1$	$-i$	$-1$	$-1$	$1$	$i$	$-1$
$\chi_{312}(85,\cdot)$	312.bv	12	no	$-1$	$1$	$-i$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{6}\right)$	$-1$	$e\left(\frac{1}{6}\right)$	$i$	$e\left(\frac{5}{6}\right)$
$\chi_{312}(89,\cdot)$	312.bp	12	no	$1$	$1$	$-i$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{3}\right)$	$-1$	$e\left(\frac{5}{6}\right)$	$i$	$e\left(\frac{1}{6}\right)$
$\chi_{312}(95,\cdot)$	312.bj	6	no	$1$	$1$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$1$	$e\left(\frac{1}{6}\right)$	$1$	$e\left(\frac{1}{3}\right)$
$\chi_{312}(97,\cdot)$	312.bu	12	no	$-1$	$1$	$-i$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{6}\right)$	$-1$	$e\left(\frac{2}{3}\right)$	$-i$	$e\left(\frac{1}{3}\right)$
$\chi_{312}(101,\cdot)$	312.bg	6	yes	$-1$	$1$	$-1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{6}\right)$	$1$	$e\left(\frac{1}{3}\right)$	$-1$	$e\left(\frac{2}{3}\right)$
$\chi_{312}(103,\cdot)$	312.i	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	$312$
Structure	\(C_{2}\times C_{2}\times C_{2}\times C_{12}\)
Order	$96$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(5\)	\(7\)	\(11\)	\(17\)	\(19\)	\(23\)	\(25\)	\(29\)	\(31\)	\(35\)
\(\chi_{312}(1,\cdot)\)	312.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{312}(5,\cdot)\)	312.y	4	yes	\(1\)	\(1\)	\(-i\)	\(i\)	\(i\)	\(1\)	\(i\)	\(1\)	\(-1\)	\(1\)	\(-i\)	\(1\)
\(\chi_{312}(7,\cdot)\)	312.bs	12	no	\(1\)	\(1\)	\(i\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(-1\)	\(e\left(\frac{2}{3}\right)\)	\(-i\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{312}(11,\cdot)\)	312.bq	12	yes	\(-1\)	\(1\)	\(i\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(-1\)	\(e\left(\frac{1}{3}\right)\)	\(-i\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{312}(17,\cdot)\)	312.bl	6	no	\(-1\)	\(1\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(-1\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{312}(19,\cdot)\)	312.bt	12	no	\(1\)	\(1\)	\(i\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(-1\)	\(e\left(\frac{1}{6}\right)\)	\(i\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{312}(23,\cdot)\)	312.bj	6	no	\(1\)	\(1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(1\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{312}(25,\cdot)\)	312.c	2	no	\(1\)	\(1\)	\(-1\)	\(-1\)	\(-1\)	\(1\)	\(-1\)	\(1\)	\(1\)	\(1\)	\(-1\)	\(1\)
\(\chi_{312}(29,\cdot)\)	312.bh	6	yes	\(-1\)	\(1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(1\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{312}(31,\cdot)\)	312.u	4	no	\(1\)	\(1\)	\(-i\)	\(-i\)	\(-i\)	\(-1\)	\(i\)	\(1\)	\(-1\)	\(1\)	\(i\)	\(-1\)
\(\chi_{312}(35,\cdot)\)	312.bn	6	yes	\(1\)	\(1\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(-1\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{312}(37,\cdot)\)	312.bv	12	no	\(-1\)	\(1\)	\(-i\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(-1\)	\(e\left(\frac{5}{6}\right)\)	\(i\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{312}(41,\cdot)\)	312.bp	12	no	\(1\)	\(1\)	\(i\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(-1\)	\(e\left(\frac{5}{6}\right)\)	\(-i\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{312}(43,\cdot)\)	312.bi	6	no	\(-1\)	\(1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(1\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{312}(47,\cdot)\)	312.v	4	no	\(-1\)	\(1\)	\(-i\)	\(i\)	\(-i\)	\(1\)	\(-i\)	\(-1\)	\(-1\)	\(-1\)	\(-i\)	\(1\)
\(\chi_{312}(49,\cdot)\)	312.bf	6	no	\(1\)	\(1\)	\(-1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(-1\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{312}(53,\cdot)\)	312.p	2	no	\(-1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(-1\)	\(-1\)	\(-1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{312}(55,\cdot)\)	312.bm	6	no	\(-1\)	\(1\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(-1\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{312}(59,\cdot)\)	312.bq	12	yes	\(-1\)	\(1\)	\(i\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(-1\)	\(e\left(\frac{2}{3}\right)\)	\(-i\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{312}(61,\cdot)\)	312.bb	6	no	\(1\)	\(1\)	\(-1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(1\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{312}(67,\cdot)\)	312.bt	12	no	\(1\)	\(1\)	\(i\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(-1\)	\(e\left(\frac{5}{6}\right)\)	\(i\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{312}(71,\cdot)\)	312.br	12	no	\(-1\)	\(1\)	\(i\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(-1\)	\(e\left(\frac{1}{6}\right)\)	\(i\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{312}(73,\cdot)\)	312.s	4	no	\(-1\)	\(1\)	\(i\)	\(-i\)	\(-i\)	\(-1\)	\(i\)	\(-1\)	\(-1\)	\(1\)	\(i\)	\(1\)
\(\chi_{312}(77,\cdot)\)	312.b	2	yes	\(-1\)	\(1\)	\(-1\)	\(-1\)	\(-1\)	\(-1\)	\(1\)	\(-1\)	\(1\)	\(1\)	\(-1\)	\(1\)
\(\chi_{312}(79,\cdot)\)	312.k	2	no	\(-1\)	\(1\)	\(1\)	\(-1\)	\(-1\)	\(1\)	\(-1\)	\(-1\)	\(1\)	\(1\)	\(-1\)	\(-1\)
\(\chi_{312}(83,\cdot)\)	312.w	4	yes	\(-1\)	\(1\)	\(-i\)	\(-i\)	\(-i\)	\(1\)	\(-i\)	\(-1\)	\(-1\)	\(1\)	\(i\)	\(-1\)
\(\chi_{312}(85,\cdot)\)	312.bv	12	no	\(-1\)	\(1\)	\(-i\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(-1\)	\(e\left(\frac{1}{6}\right)\)	\(i\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{312}(89,\cdot)\)	312.bp	12	no	\(1\)	\(1\)	\(-i\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(-1\)	\(e\left(\frac{5}{6}\right)\)	\(i\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{312}(95,\cdot)\)	312.bj	6	no	\(1\)	\(1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(1\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{312}(97,\cdot)\)	312.bu	12	no	\(-1\)	\(1\)	\(-i\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(-1\)	\(e\left(\frac{2}{3}\right)\)	\(-i\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{312}(101,\cdot)\)	312.bg	6	yes	\(-1\)	\(1\)	\(-1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(-1\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{312}(103,\cdot)\)	312.i	2	no	\(-1\)	\(1\)	\(-1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(-1\)	\(1\)	\(1\)	\(1\)	\(-1\)

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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.