LMFDB - Group of Dirichlet characters of modulus 65

Show commands: PariGP / SageMath

sage: H = DirichletGroup(65)

pari: g = idealstar(,65,2)

Character group

sage: G.order() pari: g.no
Order	=	48
sage: H.invariants() pari: g.cyc
Structure	=	$C_{4}\times C_{12}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{65}(27,\cdot)$, $\chi_{65}(41,\cdot)$

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	$-1$	$1$	$2$	$3$	$4$	$6$	$7$	$8$	$9$	$11$	$12$	$14$
$\chi_{65}(1,\cdot)$	65.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{65}(2,\cdot)$	65.o	12	yes	$1$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{6}\right)$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{7}{12}\right)$	$-i$	$-1$
$\chi_{65}(3,\cdot)$	65.q	12	yes	$-1$	$1$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{12}\right)$	$i$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$	$-i$	$-1$
$\chi_{65}(4,\cdot)$	65.l	6	yes	$1$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{3}\right)$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$	$-1$	$1$
$\chi_{65}(6,\cdot)$	65.p	12	no	$-1$	$1$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{7}{12}\right)$	$i$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{11}{12}\right)$	$-1$	$1$
$\chi_{65}(7,\cdot)$	65.t	12	yes	$1$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{3}\right)$	$-1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{12}\right)$	$-i$	$-1$
$\chi_{65}(8,\cdot)$	65.k	4	yes	$1$	$1$	$1$	$i$	$1$	$i$	$-1$	$1$	$-1$	$-i$	$i$	$-1$
$\chi_{65}(9,\cdot)$	65.n	6	yes	$1$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{6}\right)$	$-1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$-1$	$1$
$\chi_{65}(11,\cdot)$	65.p	12	no	$-1$	$1$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{5}{12}\right)$	$-i$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{12}\right)$	$-1$	$1$
$\chi_{65}(12,\cdot)$	65.h	4	yes	$-1$	$1$	$-i$	$-i$	$-1$	$-1$	$-i$	$i$	$-1$	$-1$	$i$	$-1$
$\chi_{65}(14,\cdot)$	65.b	2	no	$1$	$1$	$-1$	$-1$	$1$	$1$	$-1$	$-1$	$1$	$1$	$-1$	$1$
$\chi_{65}(16,\cdot)$	65.e	3	no	$1$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$1$	$1$
$\chi_{65}(17,\cdot)$	65.r	12	yes	$-1$	$1$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{12}\right)$	$i$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$	$i$	$-1$
$\chi_{65}(18,\cdot)$	65.f	4	yes	$1$	$1$	$-1$	$i$	$1$	$-i$	$1$	$-1$	$-1$	$i$	$i$	$-1$
$\chi_{65}(19,\cdot)$	65.s	12	yes	$-1$	$1$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{12}\right)$	$-i$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{11}{12}\right)$	$1$	$1$
$\chi_{65}(21,\cdot)$	65.j	4	no	$-1$	$1$	$i$	$1$	$-1$	$i$	$-i$	$-i$	$1$	$-i$	$-1$	$1$
$\chi_{65}(22,\cdot)$	65.q	12	yes	$-1$	$1$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{7}{12}\right)$	$-i$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$	$i$	$-1$
$\chi_{65}(23,\cdot)$	65.r	12	yes	$-1$	$1$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{11}{12}\right)$	$-i$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$	$-i$	$-1$
$\chi_{65}(24,\cdot)$	65.s	12	yes	$-1$	$1$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{11}{12}\right)$	$i$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{12}\right)$	$1$	$1$
$\chi_{65}(27,\cdot)$	65.i	4	no	$-1$	$1$	$i$	$-i$	$-1$	$1$	$i$	$-i$	$-1$	$1$	$i$	$-1$
$\chi_{65}(28,\cdot)$	65.t	12	yes	$1$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{2}{3}\right)$	$-1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{7}{12}\right)$	$i$	$-1$
$\chi_{65}(29,\cdot)$	65.n	6	yes	$1$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{6}\right)$	$-1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$-1$	$1$
$\chi_{65}(31,\cdot)$	65.j	4	no	$-1$	$1$	$-i$	$1$	$-1$	$-i$	$i$	$i$	$1$	$i$	$-1$	$1$
$\chi_{65}(32,\cdot)$	65.o	12	yes	$1$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{5}{6}\right)$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{11}{12}\right)$	$-i$	$-1$
$\chi_{65}(33,\cdot)$	65.o	12	yes	$1$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{5}{6}\right)$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{12}\right)$	$i$	$-1$
$\chi_{65}(34,\cdot)$	65.g	4	yes	$-1$	$1$	$-i$	$-1$	$-1$	$i$	$i$	$i$	$1$	$-i$	$1$	$1$
$\chi_{65}(36,\cdot)$	65.m	6	no	$1$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{6}\right)$	$-1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{6}\right)$	$1$	$1$
$\chi_{65}(37,\cdot)$	65.t	12	yes	$1$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{2}{3}\right)$	$-1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{12}\right)$	$-i$	$-1$
$\chi_{65}(38,\cdot)$	65.h	4	yes	$-1$	$1$	$i$	$i$	$-1$	$-1$	$i$	$-i$	$-1$	$-1$	$-i$	$-1$
$\chi_{65}(41,\cdot)$	65.p	12	no	$-1$	$1$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{11}{12}\right)$	$i$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{7}{12}\right)$	$-1$	$1$
$\chi_{65}(42,\cdot)$	65.q	12	yes	$-1$	$1$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{11}{12}\right)$	$-i$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$	$i$	$-1$
$\chi_{65}(43,\cdot)$	65.r	12	yes	$-1$	$1$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{7}{12}\right)$	$-i$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$	$-i$	$-1$

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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 $\F_{q}$

Modulus	$65$
Structure	\(C_{4}\times C_{12}\)
Order	$48$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(6\)	\(7\)	\(8\)	\(9\)	\(11\)	\(12\)	\(14\)
\(\chi_{65}(1,\cdot)\)	65.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{65}(2,\cdot)\)	65.o	12	yes	\(1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(-i\)	\(-1\)
\(\chi_{65}(3,\cdot)\)	65.q	12	yes	\(-1\)	\(1\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(i\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(-i\)	\(-1\)
\(\chi_{65}(4,\cdot)\)	65.l	6	yes	\(1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(-1\)	\(1\)
\(\chi_{65}(6,\cdot)\)	65.p	12	no	\(-1\)	\(1\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(i\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(-1\)	\(1\)
\(\chi_{65}(7,\cdot)\)	65.t	12	yes	\(1\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(-1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(-i\)	\(-1\)
\(\chi_{65}(8,\cdot)\)	65.k	4	yes	\(1\)	\(1\)	\(1\)	\(i\)	\(1\)	\(i\)	\(-1\)	\(1\)	\(-1\)	\(-i\)	\(i\)	\(-1\)
\(\chi_{65}(9,\cdot)\)	65.n	6	yes	\(1\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(-1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(-1\)	\(1\)
\(\chi_{65}(11,\cdot)\)	65.p	12	no	\(-1\)	\(1\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(-i\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(-1\)	\(1\)
\(\chi_{65}(12,\cdot)\)	65.h	4	yes	\(-1\)	\(1\)	\(-i\)	\(-i\)	\(-1\)	\(-1\)	\(-i\)	\(i\)	\(-1\)	\(-1\)	\(i\)	\(-1\)
\(\chi_{65}(14,\cdot)\)	65.b	2	no	\(1\)	\(1\)	\(-1\)	\(-1\)	\(1\)	\(1\)	\(-1\)	\(-1\)	\(1\)	\(1\)	\(-1\)	\(1\)
\(\chi_{65}(16,\cdot)\)	65.e	3	no	\(1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(1\)	\(1\)
\(\chi_{65}(17,\cdot)\)	65.r	12	yes	\(-1\)	\(1\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(i\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(i\)	\(-1\)
\(\chi_{65}(18,\cdot)\)	65.f	4	yes	\(1\)	\(1\)	\(-1\)	\(i\)	\(1\)	\(-i\)	\(1\)	\(-1\)	\(-1\)	\(i\)	\(i\)	\(-1\)
\(\chi_{65}(19,\cdot)\)	65.s	12	yes	\(-1\)	\(1\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(-i\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(1\)	\(1\)
\(\chi_{65}(21,\cdot)\)	65.j	4	no	\(-1\)	\(1\)	\(i\)	\(1\)	\(-1\)	\(i\)	\(-i\)	\(-i\)	\(1\)	\(-i\)	\(-1\)	\(1\)
\(\chi_{65}(22,\cdot)\)	65.q	12	yes	\(-1\)	\(1\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(-i\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(i\)	\(-1\)
\(\chi_{65}(23,\cdot)\)	65.r	12	yes	\(-1\)	\(1\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(-i\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(-i\)	\(-1\)
\(\chi_{65}(24,\cdot)\)	65.s	12	yes	\(-1\)	\(1\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(i\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(1\)	\(1\)
\(\chi_{65}(27,\cdot)\)	65.i	4	no	\(-1\)	\(1\)	\(i\)	\(-i\)	\(-1\)	\(1\)	\(i\)	\(-i\)	\(-1\)	\(1\)	\(i\)	\(-1\)
\(\chi_{65}(28,\cdot)\)	65.t	12	yes	\(1\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(-1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(i\)	\(-1\)
\(\chi_{65}(29,\cdot)\)	65.n	6	yes	\(1\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(-1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(-1\)	\(1\)
\(\chi_{65}(31,\cdot)\)	65.j	4	no	\(-1\)	\(1\)	\(-i\)	\(1\)	\(-1\)	\(-i\)	\(i\)	\(i\)	\(1\)	\(i\)	\(-1\)	\(1\)
\(\chi_{65}(32,\cdot)\)	65.o	12	yes	\(1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(-i\)	\(-1\)
\(\chi_{65}(33,\cdot)\)	65.o	12	yes	\(1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(i\)	\(-1\)
\(\chi_{65}(34,\cdot)\)	65.g	4	yes	\(-1\)	\(1\)	\(-i\)	\(-1\)	\(-1\)	\(i\)	\(i\)	\(i\)	\(1\)	\(-i\)	\(1\)	\(1\)
\(\chi_{65}(36,\cdot)\)	65.m	6	no	\(1\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(-1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(1\)	\(1\)
\(\chi_{65}(37,\cdot)\)	65.t	12	yes	\(1\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(-1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(-i\)	\(-1\)
\(\chi_{65}(38,\cdot)\)	65.h	4	yes	\(-1\)	\(1\)	\(i\)	\(i\)	\(-1\)	\(-1\)	\(i\)	\(-i\)	\(-1\)	\(-1\)	\(-i\)	\(-1\)
\(\chi_{65}(41,\cdot)\)	65.p	12	no	\(-1\)	\(1\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(i\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(-1\)	\(1\)
\(\chi_{65}(42,\cdot)\)	65.q	12	yes	\(-1\)	\(1\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(-i\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(i\)	\(-1\)
\(\chi_{65}(43,\cdot)\)	65.r	12	yes	\(-1\)	\(1\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(-i\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(-i\)	\(-1\)

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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.