LMFDB - Group of Dirichlet characters of modulus 344

Show commands for: Pari/GP / SageMath

sage: H = DirichletGroup(344)

pari: g = idealstar(,344,2)

Character group

sage: G.order() pari: g.no
Order	=	168
sage: H.invariants() pari: g.cyc
Structure	=	$C_{42}\times C_{2}\times C_{2}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{344}(87,\cdot)$, $\chi_{344}(173,\cdot)$, $\chi_{344}(89,\cdot)$

First 32 of 168 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	$-1$	$1$	$3$	$5$	$7$	$9$	$11$	$13$	$15$	$17$	$19$	$21$
$\chi_{344}(1,\cdot)$	344.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{344}(3,\cdot)$	344.bb	42	yes	$1$	$1$	$e\left(\frac{1}{42}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{5}{42}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{19}{42}\right)$	$e\left(\frac{5}{14}\right)$
$\chi_{344}(5,\cdot)$	344.bf	42	yes	$-1$	$1$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{23}{42}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{13}{14}\right)$
$\chi_{344}(7,\cdot)$	344.k	6	no	$1$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$	$-1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$1$
$\chi_{344}(9,\cdot)$	344.y	21	no	$1$	$1$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{5}{7}\right)$
$\chi_{344}(11,\cdot)$	344.s	14	yes	$-1$	$1$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{5}{14}\right)$	$-1$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{3}{14}\right)$
$\chi_{344}(13,\cdot)$	344.z	42	yes	$1$	$1$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{23}{42}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{37}{42}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{41}{42}\right)$	$e\left(\frac{13}{14}\right)$
$\chi_{344}(15,\cdot)$	344.bc	42	no	$-1$	$1$	$e\left(\frac{5}{42}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{25}{42}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{2}{7}\right)$
$\chi_{344}(17,\cdot)$	344.y	21	no	$1$	$1$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{4}{7}\right)$
$\chi_{344}(19,\cdot)$	344.bb	42	yes	$1$	$1$	$e\left(\frac{19}{42}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{41}{42}\right)$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{25}{42}\right)$	$e\left(\frac{11}{14}\right)$
$\chi_{344}(21,\cdot)$	344.x	14	yes	$1$	$1$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{13}{14}\right)$	$1$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{5}{14}\right)$
$\chi_{344}(23,\cdot)$	344.bc	42	no	$-1$	$1$	$e\left(\frac{37}{42}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{17}{42}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{31}{42}\right)$	$e\left(\frac{5}{7}\right)$
$\chi_{344}(25,\cdot)$	344.y	21	no	$1$	$1$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{6}{7}\right)$
$\chi_{344}(27,\cdot)$	344.v	14	yes	$1$	$1$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{2}{7}\right)$	$1$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{1}{14}\right)$
$\chi_{344}(29,\cdot)$	344.bf	42	yes	$-1$	$1$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{31}{42}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{9}{14}\right)$
$\chi_{344}(31,\cdot)$	344.bc	42	no	$-1$	$1$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{23}{42}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{37}{42}\right)$	$e\left(\frac{1}{7}\right)$
$\chi_{344}(33,\cdot)$	344.ba	42	no	$-1$	$1$	$e\left(\frac{31}{42}\right)$	$e\left(\frac{19}{42}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{1}{42}\right)$	$e\left(\frac{4}{7}\right)$
$\chi_{344}(35,\cdot)$	344.s	14	yes	$-1$	$1$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{3}{14}\right)$	$-1$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{13}{14}\right)$
$\chi_{344}(37,\cdot)$	344.j	6	yes	$-1$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{3}\right)$	$-1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$-1$
$\chi_{344}(39,\cdot)$	344.t	14	no	$1$	$1$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{9}{14}\right)$	$1$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{2}{7}\right)$
$\chi_{344}(41,\cdot)$	344.q	7	no	$1$	$1$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{4}{7}\right)$	$1$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{1}{7}\right)$
$\chi_{344}(45,\cdot)$	344.r	14	yes	$-1$	$1$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{4}{7}\right)$	$-1$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{9}{14}\right)$
$\chi_{344}(47,\cdot)$	344.u	14	no	$-1$	$1$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{1}{7}\right)$	$-1$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{2}{7}\right)$
$\chi_{344}(49,\cdot)$	344.i	3	no	$1$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$1$
$\chi_{344}(51,\cdot)$	344.v	14	yes	$1$	$1$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{5}{7}\right)$	$1$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{13}{14}\right)$
$\chi_{344}(53,\cdot)$	344.z	42	yes	$1$	$1$	$e\left(\frac{31}{42}\right)$	$e\left(\frac{19}{42}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{5}{42}\right)$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{1}{42}\right)$	$e\left(\frac{1}{14}\right)$
$\chi_{344}(55,\cdot)$	344.bd	42	no	$1$	$1$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{31}{42}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{23}{42}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{1}{7}\right)$
$\chi_{344}(57,\cdot)$	344.y	21	no	$1$	$1$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{1}{7}\right)$
$\chi_{344}(59,\cdot)$	344.s	14	yes	$-1$	$1$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{11}{14}\right)$	$-1$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{1}{14}\right)$
$\chi_{344}(61,\cdot)$	344.bf	42	yes	$-1$	$1$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{25}{42}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{5}{14}\right)$
$\chi_{344}(63,\cdot)$	344.bd	42	no	$1$	$1$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{1}{42}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{17}{42}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{5}{7}\right)$
$\chi_{344}(65,\cdot)$	344.w	14	no	$-1$	$1$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{13}{14}\right)$	$-1$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{6}{7}\right)$

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	$344$
Structure	\(C_{42}\times C_{2}\times C_{2}\)
Order	$168$

Introduction

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Modular forms

Varieties

Fields

Representations

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Properties

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Character group

First 32 of 168 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	\(-1\)	\(1\)	\(3\)	\(5\)	\(7\)	\(9\)	\(11\)	\(13\)	\(15\)	\(17\)	\(19\)	\(21\)
\(\chi_{344}(1,\cdot)\)	344.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{344}(3,\cdot)\)	344.bb	42	yes	\(1\)	\(1\)	\(e\left(\frac{1}{42}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{11}{42}\right)\)	\(e\left(\frac{5}{42}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{19}{42}\right)\)	\(e\left(\frac{5}{14}\right)\)
\(\chi_{344}(5,\cdot)\)	344.bf	42	yes	\(-1\)	\(1\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{23}{42}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{13}{14}\right)\)
\(\chi_{344}(7,\cdot)\)	344.k	6	no	\(1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(-1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(1\)
\(\chi_{344}(9,\cdot)\)	344.y	21	no	\(1\)	\(1\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{5}{7}\right)\)
\(\chi_{344}(11,\cdot)\)	344.s	14	yes	\(-1\)	\(1\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(-1\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{3}{14}\right)\)
\(\chi_{344}(13,\cdot)\)	344.z	42	yes	\(1\)	\(1\)	\(e\left(\frac{11}{42}\right)\)	\(e\left(\frac{23}{42}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{37}{42}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{41}{42}\right)\)	\(e\left(\frac{13}{14}\right)\)
\(\chi_{344}(15,\cdot)\)	344.bc	42	no	\(-1\)	\(1\)	\(e\left(\frac{5}{42}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{25}{42}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{11}{42}\right)\)	\(e\left(\frac{2}{7}\right)\)
\(\chi_{344}(17,\cdot)\)	344.y	21	no	\(1\)	\(1\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{4}{7}\right)\)
\(\chi_{344}(19,\cdot)\)	344.bb	42	yes	\(1\)	\(1\)	\(e\left(\frac{19}{42}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{41}{42}\right)\)	\(e\left(\frac{11}{42}\right)\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{25}{42}\right)\)	\(e\left(\frac{11}{14}\right)\)
\(\chi_{344}(21,\cdot)\)	344.x	14	yes	\(1\)	\(1\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(1\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{5}{14}\right)\)
\(\chi_{344}(23,\cdot)\)	344.bc	42	no	\(-1\)	\(1\)	\(e\left(\frac{37}{42}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{17}{42}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{31}{42}\right)\)	\(e\left(\frac{5}{7}\right)\)
\(\chi_{344}(25,\cdot)\)	344.y	21	no	\(1\)	\(1\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{6}{7}\right)\)
\(\chi_{344}(27,\cdot)\)	344.v	14	yes	\(1\)	\(1\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(1\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{1}{14}\right)\)
\(\chi_{344}(29,\cdot)\)	344.bf	42	yes	\(-1\)	\(1\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{31}{42}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{9}{14}\right)\)
\(\chi_{344}(31,\cdot)\)	344.bc	42	no	\(-1\)	\(1\)	\(e\left(\frac{13}{42}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{23}{42}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{37}{42}\right)\)	\(e\left(\frac{1}{7}\right)\)
\(\chi_{344}(33,\cdot)\)	344.ba	42	no	\(-1\)	\(1\)	\(e\left(\frac{31}{42}\right)\)	\(e\left(\frac{19}{42}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{1}{42}\right)\)	\(e\left(\frac{4}{7}\right)\)
\(\chi_{344}(35,\cdot)\)	344.s	14	yes	\(-1\)	\(1\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(-1\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{13}{14}\right)\)
\(\chi_{344}(37,\cdot)\)	344.j	6	yes	\(-1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(-1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(-1\)
\(\chi_{344}(39,\cdot)\)	344.t	14	no	\(1\)	\(1\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(1\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{2}{7}\right)\)
\(\chi_{344}(41,\cdot)\)	344.q	7	no	\(1\)	\(1\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(1\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{1}{7}\right)\)
\(\chi_{344}(45,\cdot)\)	344.r	14	yes	\(-1\)	\(1\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(-1\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{9}{14}\right)\)
\(\chi_{344}(47,\cdot)\)	344.u	14	no	\(-1\)	\(1\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(-1\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{2}{7}\right)\)
\(\chi_{344}(49,\cdot)\)	344.i	3	no	\(1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(1\)
\(\chi_{344}(51,\cdot)\)	344.v	14	yes	\(1\)	\(1\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(1\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{13}{14}\right)\)
\(\chi_{344}(53,\cdot)\)	344.z	42	yes	\(1\)	\(1\)	\(e\left(\frac{31}{42}\right)\)	\(e\left(\frac{19}{42}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{5}{42}\right)\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{1}{42}\right)\)	\(e\left(\frac{1}{14}\right)\)
\(\chi_{344}(55,\cdot)\)	344.bd	42	no	\(1\)	\(1\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{31}{42}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{23}{42}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{1}{7}\right)\)
\(\chi_{344}(57,\cdot)\)	344.y	21	no	\(1\)	\(1\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{1}{7}\right)\)
\(\chi_{344}(59,\cdot)\)	344.s	14	yes	\(-1\)	\(1\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(-1\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{1}{14}\right)\)
\(\chi_{344}(61,\cdot)\)	344.bf	42	yes	\(-1\)	\(1\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{25}{42}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{5}{14}\right)\)
\(\chi_{344}(63,\cdot)\)	344.bd	42	no	\(1\)	\(1\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{1}{42}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{17}{42}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{5}{7}\right)\)
\(\chi_{344}(65,\cdot)\)	344.w	14	no	\(-1\)	\(1\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(-1\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{6}{7}\right)\)