LMFDB - Group of Dirichlet characters of modulus 1344

Show commands for: Pari/GP / SageMath

sage: H = DirichletGroup(1344)

pari: g = idealstar(,1344,2)

Character group

sage: G.order() pari: g.no
Order	=	384
sage: H.invariants() pari: g.cyc
Structure	=	$C_{48}\times C_{2}\times C_{2}\times C_{2}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{1344}(127,\cdot)$, $\chi_{1344}(1093,\cdot)$, $\chi_{1344}(449,\cdot)$, $\chi_{1344}(577,\cdot)$

First 32 of 384 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	$-1$	$1$	$5$	$11$	$13$	$17$	$19$	$23$	$25$	$29$	$31$	$37$
$\chi_{1344}(1,\cdot)$	1344.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{1344}(5,\cdot)$	1344.cw	48	yes	$1$	$1$	$e\left(\frac{35}{48}\right)$	$e\left(\frac{7}{48}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{29}{48}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{11}{48}\right)$
$\chi_{1344}(11,\cdot)$	1344.cx	48	yes	$1$	$1$	$e\left(\frac{7}{48}\right)$	$e\left(\frac{11}{48}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{48}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{7}{48}\right)$
$\chi_{1344}(13,\cdot)$	1344.ck	16	no	$-1$	$1$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{9}{16}\right)$	$-i$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{5}{16}\right)$	$1$	$e\left(\frac{7}{16}\right)$
$\chi_{1344}(17,\cdot)$	1344.bw	12	no	$1$	$1$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{11}{12}\right)$	$-i$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$	$-i$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{12}\right)$
$\chi_{1344}(19,\cdot)$	1344.cy	48	no	$1$	$1$	$e\left(\frac{29}{48}\right)$	$e\left(\frac{1}{48}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{35}{48}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{29}{48}\right)$
$\chi_{1344}(23,\cdot)$	1344.cp	24	no	$1$	$1$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{13}{24}\right)$
$\chi_{1344}(25,\cdot)$	1344.cr	24	no	$1$	$1$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{11}{24}\right)$
$\chi_{1344}(29,\cdot)$	1344.cf	16	no	$-1$	$1$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{5}{16}\right)$	$-i$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{1}{16}\right)$	$-1$	$e\left(\frac{3}{16}\right)$
$\chi_{1344}(31,\cdot)$	1344.bb	6	no	$1$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$	$-1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{1344}(37,\cdot)$	1344.cz	48	no	$1$	$1$	$e\left(\frac{11}{48}\right)$	$e\left(\frac{7}{48}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{29}{48}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{35}{48}\right)$
$\chi_{1344}(41,\cdot)$	1344.bo	8	no	$1$	$1$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{5}{8}\right)$	$-1$	$e\left(\frac{5}{8}\right)$	$-i$	$-i$	$e\left(\frac{1}{8}\right)$	$-1$	$e\left(\frac{7}{8}\right)$
$\chi_{1344}(43,\cdot)$	1344.cl	16	no	$-1$	$1$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{3}{16}\right)$	$-i$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{15}{16}\right)$	$1$	$e\left(\frac{5}{16}\right)$
$\chi_{1344}(47,\cdot)$	1344.bz	12	no	$-1$	$1$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{12}\right)$	$-i$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$	$-i$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{12}\right)$
$\chi_{1344}(53,\cdot)$	1344.da	48	yes	$-1$	$1$	$e\left(\frac{7}{48}\right)$	$e\left(\frac{35}{48}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{25}{48}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{7}{48}\right)$
$\chi_{1344}(55,\cdot)$	1344.bu	8	no	$1$	$1$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{1}{8}\right)$	$1$	$e\left(\frac{5}{8}\right)$	$-i$	$-i$	$e\left(\frac{1}{8}\right)$	$1$	$e\left(\frac{3}{8}\right)$
$\chi_{1344}(59,\cdot)$	1344.db	48	yes	$-1$	$1$	$e\left(\frac{19}{48}\right)$	$e\left(\frac{47}{48}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{37}{48}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{43}{48}\right)$
$\chi_{1344}(61,\cdot)$	1344.cv	48	no	$-1$	$1$	$e\left(\frac{17}{48}\right)$	$e\left(\frac{13}{48}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{23}{48}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{17}{48}\right)$
$\chi_{1344}(65,\cdot)$	1344.bn	6	no	$-1$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$	$-1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{1344}(67,\cdot)$	1344.cu	48	no	$-1$	$1$	$e\left(\frac{25}{48}\right)$	$e\left(\frac{5}{48}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{7}{48}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{48}\right)$
$\chi_{1344}(71,\cdot)$	1344.bs	8	no	$1$	$1$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{3}{8}\right)$	$1$	$e\left(\frac{7}{8}\right)$	$-i$	$i$	$e\left(\frac{3}{8}\right)$	$-1$	$e\left(\frac{5}{8}\right)$
$\chi_{1344}(73,\cdot)$	1344.co	24	no	$-1$	$1$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{17}{24}\right)$
$\chi_{1344}(79,\cdot)$	1344.bx	12	no	$-1$	$1$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{12}\right)$	$-i$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{6}\right)$	$-i$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{11}{12}\right)$
$\chi_{1344}(83,\cdot)$	1344.ce	16	yes	$-1$	$1$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{1}{16}\right)$	$i$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{5}{16}\right)$	$-1$	$e\left(\frac{15}{16}\right)$
$\chi_{1344}(85,\cdot)$	1344.cg	16	no	$1$	$1$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{3}{16}\right)$	$-i$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{15}{16}\right)$	$-1$	$e\left(\frac{5}{16}\right)$
$\chi_{1344}(89,\cdot)$	1344.ct	24	no	$1$	$1$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{19}{24}\right)$
$\chi_{1344}(95,\cdot)$	1344.bd	6	no	$1$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$	$-1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{1344}(97,\cdot)$	1344.l	2	no	$-1$	$1$	$1$	$-1$	$1$	$-1$	$1$	$1$	$1$	$-1$	$-1$	$-1$
$\chi_{1344}(101,\cdot)$	1344.cw	48	yes	$1$	$1$	$e\left(\frac{43}{48}\right)$	$e\left(\frac{47}{48}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{37}{48}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{19}{48}\right)$
$\chi_{1344}(103,\cdot)$	1344.cn	24	no	$1$	$1$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{19}{24}\right)$
$\chi_{1344}(107,\cdot)$	1344.cx	48	yes	$1$	$1$	$e\left(\frac{47}{48}\right)$	$e\left(\frac{19}{48}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{41}{48}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{47}{48}\right)$
$\chi_{1344}(109,\cdot)$	1344.cz	48	no	$1$	$1$	$e\left(\frac{37}{48}\right)$	$e\left(\frac{41}{48}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{19}{48}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{13}{48}\right)$

Overview	Random
Universe	Knowledge

Degree 1	Degree 2
Degree 3	Degree 4
$\zeta$ zeros

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	$1344$
Structure	\(C_{48}\times C_{2}\times C_{2}\times C_{2}\)
Order	$384$

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Properties

Learn more about

Character group

First 32 of 384 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.

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(5\)	\(11\)	\(13\)	\(17\)	\(19\)	\(23\)	\(25\)	\(29\)	\(31\)	\(37\)
\(\chi_{1344}(1,\cdot)\)	1344.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{1344}(5,\cdot)\)	1344.cw	48	yes	\(1\)	\(1\)	\(e\left(\frac{35}{48}\right)\)	\(e\left(\frac{7}{48}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{29}{48}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{11}{48}\right)\)
\(\chi_{1344}(11,\cdot)\)	1344.cx	48	yes	\(1\)	\(1\)	\(e\left(\frac{7}{48}\right)\)	\(e\left(\frac{11}{48}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{1}{48}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{7}{48}\right)\)
\(\chi_{1344}(13,\cdot)\)	1344.ck	16	no	\(-1\)	\(1\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(-i\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(1\)	\(e\left(\frac{7}{16}\right)\)
\(\chi_{1344}(17,\cdot)\)	1344.bw	12	no	\(1\)	\(1\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(-i\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(-i\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{12}\right)\)
\(\chi_{1344}(19,\cdot)\)	1344.cy	48	no	\(1\)	\(1\)	\(e\left(\frac{29}{48}\right)\)	\(e\left(\frac{1}{48}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{35}{48}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{29}{48}\right)\)
\(\chi_{1344}(23,\cdot)\)	1344.cp	24	no	\(1\)	\(1\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{13}{24}\right)\)
\(\chi_{1344}(25,\cdot)\)	1344.cr	24	no	\(1\)	\(1\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{11}{24}\right)\)
\(\chi_{1344}(29,\cdot)\)	1344.cf	16	no	\(-1\)	\(1\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(-i\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(-1\)	\(e\left(\frac{3}{16}\right)\)
\(\chi_{1344}(31,\cdot)\)	1344.bb	6	no	\(1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(-1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{1344}(37,\cdot)\)	1344.cz	48	no	\(1\)	\(1\)	\(e\left(\frac{11}{48}\right)\)	\(e\left(\frac{7}{48}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{29}{48}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{35}{48}\right)\)
\(\chi_{1344}(41,\cdot)\)	1344.bo	8	no	\(1\)	\(1\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(-1\)	\(e\left(\frac{5}{8}\right)\)	\(-i\)	\(-i\)	\(e\left(\frac{1}{8}\right)\)	\(-1\)	\(e\left(\frac{7}{8}\right)\)
\(\chi_{1344}(43,\cdot)\)	1344.cl	16	no	\(-1\)	\(1\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(-i\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(1\)	\(e\left(\frac{5}{16}\right)\)
\(\chi_{1344}(47,\cdot)\)	1344.bz	12	no	\(-1\)	\(1\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(-i\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(-i\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{12}\right)\)
\(\chi_{1344}(53,\cdot)\)	1344.da	48	yes	\(-1\)	\(1\)	\(e\left(\frac{7}{48}\right)\)	\(e\left(\frac{35}{48}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{25}{48}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{7}{48}\right)\)
\(\chi_{1344}(55,\cdot)\)	1344.bu	8	no	\(1\)	\(1\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(1\)	\(e\left(\frac{5}{8}\right)\)	\(-i\)	\(-i\)	\(e\left(\frac{1}{8}\right)\)	\(1\)	\(e\left(\frac{3}{8}\right)\)
\(\chi_{1344}(59,\cdot)\)	1344.db	48	yes	\(-1\)	\(1\)	\(e\left(\frac{19}{48}\right)\)	\(e\left(\frac{47}{48}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{37}{48}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{43}{48}\right)\)
\(\chi_{1344}(61,\cdot)\)	1344.cv	48	no	\(-1\)	\(1\)	\(e\left(\frac{17}{48}\right)\)	\(e\left(\frac{13}{48}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{23}{48}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{17}{48}\right)\)
\(\chi_{1344}(65,\cdot)\)	1344.bn	6	no	\(-1\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(-1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{1344}(67,\cdot)\)	1344.cu	48	no	\(-1\)	\(1\)	\(e\left(\frac{25}{48}\right)\)	\(e\left(\frac{5}{48}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{7}{48}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{48}\right)\)
\(\chi_{1344}(71,\cdot)\)	1344.bs	8	no	\(1\)	\(1\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(1\)	\(e\left(\frac{7}{8}\right)\)	\(-i\)	\(i\)	\(e\left(\frac{3}{8}\right)\)	\(-1\)	\(e\left(\frac{5}{8}\right)\)
\(\chi_{1344}(73,\cdot)\)	1344.co	24	no	\(-1\)	\(1\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{17}{24}\right)\)
\(\chi_{1344}(79,\cdot)\)	1344.bx	12	no	\(-1\)	\(1\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(-i\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(-i\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{11}{12}\right)\)
\(\chi_{1344}(83,\cdot)\)	1344.ce	16	yes	\(-1\)	\(1\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(i\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(-1\)	\(e\left(\frac{15}{16}\right)\)
\(\chi_{1344}(85,\cdot)\)	1344.cg	16	no	\(1\)	\(1\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(-i\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(-1\)	\(e\left(\frac{5}{16}\right)\)
\(\chi_{1344}(89,\cdot)\)	1344.ct	24	no	\(1\)	\(1\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{19}{24}\right)\)
\(\chi_{1344}(95,\cdot)\)	1344.bd	6	no	\(1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(-1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{1344}(97,\cdot)\)	1344.l	2	no	\(-1\)	\(1\)	\(1\)	\(-1\)	\(1\)	\(-1\)	\(1\)	\(1\)	\(1\)	\(-1\)	\(-1\)	\(-1\)
\(\chi_{1344}(101,\cdot)\)	1344.cw	48	yes	\(1\)	\(1\)	\(e\left(\frac{43}{48}\right)\)	\(e\left(\frac{47}{48}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{37}{48}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{19}{48}\right)\)
\(\chi_{1344}(103,\cdot)\)	1344.cn	24	no	\(1\)	\(1\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{19}{24}\right)\)
\(\chi_{1344}(107,\cdot)\)	1344.cx	48	yes	\(1\)	\(1\)	\(e\left(\frac{47}{48}\right)\)	\(e\left(\frac{19}{48}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{41}{48}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{47}{48}\right)\)
\(\chi_{1344}(109,\cdot)\)	1344.cz	48	no	\(1\)	\(1\)	\(e\left(\frac{37}{48}\right)\)	\(e\left(\frac{41}{48}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{19}{48}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{13}{48}\right)\)