LMFDB - Group of Dirichlet characters of modulus 1323

Show commands: PariGP / SageMath

sage: H = DirichletGroup(1323)

pari: g = idealstar(,1323,2)

Character group

sage: G.order() pari: g.no
Order	=	756
sage: H.invariants() pari: g.cyc
Structure	=	$C_{6}\times C_{126}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{1323}(785,\cdot)$, $\chi_{1323}(1081,\cdot)$

First 32 of 756 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	$-1$	$1$	$2$	$4$	$5$	$8$	$10$	$11$	$13$	$16$	$17$	$19$
$\chi_{1323}(1,\cdot)$	1323.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{1323}(2,\cdot)$	1323.cg	126	yes	$-1$	$1$	$e\left(\frac{19}{126}\right)$	$e\left(\frac{19}{63}\right)$	$e\left(\frac{29}{126}\right)$	$e\left(\frac{19}{42}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{61}{126}\right)$	$e\left(\frac{55}{63}\right)$	$e\left(\frac{38}{63}\right)$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{1323}(4,\cdot)$	1323.cc	63	yes	$1$	$1$	$e\left(\frac{19}{63}\right)$	$e\left(\frac{38}{63}\right)$	$e\left(\frac{29}{63}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{61}{63}\right)$	$e\left(\frac{47}{63}\right)$	$e\left(\frac{13}{63}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{1323}(5,\cdot)$	1323.ci	126	yes	$1$	$1$	$e\left(\frac{29}{126}\right)$	$e\left(\frac{29}{63}\right)$	$e\left(\frac{26}{63}\right)$	$e\left(\frac{29}{42}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{29}{126}\right)$	$e\left(\frac{1}{126}\right)$	$e\left(\frac{58}{63}\right)$	$e\left(\frac{3}{7}\right)$	$-1$
$\chi_{1323}(8,\cdot)$	1323.bq	42	no	$-1$	$1$	$e\left(\frac{19}{42}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{29}{42}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{19}{42}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{13}{14}\right)$	$1$
$\chi_{1323}(10,\cdot)$	1323.bx	42	no	$-1$	$1$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{1}{42}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{37}{42}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{31}{42}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{1323}(11,\cdot)$	1323.cd	126	yes	$-1$	$1$	$e\left(\frac{61}{126}\right)$	$e\left(\frac{61}{63}\right)$	$e\left(\frac{29}{126}\right)$	$e\left(\frac{19}{42}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{61}{126}\right)$	$e\left(\frac{13}{63}\right)$	$e\left(\frac{59}{63}\right)$	$e\left(\frac{9}{14}\right)$	$1$
$\chi_{1323}(13,\cdot)$	1323.ck	126	yes	$-1$	$1$	$e\left(\frac{55}{63}\right)$	$e\left(\frac{47}{63}\right)$	$e\left(\frac{1}{126}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{37}{42}\right)$	$e\left(\frac{13}{63}\right)$	$e\left(\frac{61}{126}\right)$	$e\left(\frac{31}{63}\right)$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{1323}(16,\cdot)$	1323.cc	63	yes	$1$	$1$	$e\left(\frac{38}{63}\right)$	$e\left(\frac{13}{63}\right)$	$e\left(\frac{58}{63}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{59}{63}\right)$	$e\left(\frac{31}{63}\right)$	$e\left(\frac{26}{63}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{1323}(17,\cdot)$	1323.bp	42	no	$1$	$1$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{31}{42}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{1323}(19,\cdot)$	1323.k	6	no	$-1$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$-1$	$1$	$e\left(\frac{5}{6}\right)$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$
$\chi_{1323}(20,\cdot)$	1323.ce	126	yes	$1$	$1$	$e\left(\frac{67}{126}\right)$	$e\left(\frac{4}{63}\right)$	$e\left(\frac{55}{63}\right)$	$e\left(\frac{25}{42}\right)$	$e\left(\frac{17}{42}\right)$	$e\left(\frac{25}{126}\right)$	$e\left(\frac{95}{126}\right)$	$e\left(\frac{8}{63}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{1}{6}\right)$
$\chi_{1323}(22,\cdot)$	1323.cb	63	yes	$1$	$1$	$e\left(\frac{40}{63}\right)$	$e\left(\frac{17}{63}\right)$	$e\left(\frac{29}{63}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{61}{63}\right)$	$e\left(\frac{5}{63}\right)$	$e\left(\frac{34}{63}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{1323}(23,\cdot)$	1323.cd	126	yes	$-1$	$1$	$e\left(\frac{17}{126}\right)$	$e\left(\frac{17}{63}\right)$	$e\left(\frac{37}{126}\right)$	$e\left(\frac{17}{42}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{17}{126}\right)$	$e\left(\frac{47}{63}\right)$	$e\left(\frac{34}{63}\right)$	$e\left(\frac{11}{14}\right)$	$1$
$\chi_{1323}(25,\cdot)$	1323.ca	63	yes	$1$	$1$	$e\left(\frac{29}{63}\right)$	$e\left(\frac{58}{63}\right)$	$e\left(\frac{52}{63}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{29}{63}\right)$	$e\left(\frac{1}{63}\right)$	$e\left(\frac{53}{63}\right)$	$e\left(\frac{6}{7}\right)$	$1$
$\chi_{1323}(26,\cdot)$	1323.bs	42	no	$1$	$1$	$e\left(\frac{1}{42}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{29}{42}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{1}{6}\right)$
$\chi_{1323}(29,\cdot)$	1323.ch	126	yes	$-1$	$1$	$e\left(\frac{25}{126}\right)$	$e\left(\frac{25}{63}\right)$	$e\left(\frac{89}{126}\right)$	$e\left(\frac{25}{42}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{109}{126}\right)$	$e\left(\frac{37}{63}\right)$	$e\left(\frac{50}{63}\right)$	$e\left(\frac{23}{42}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{1323}(31,\cdot)$	1323.bd	18	no	$-1$	$1$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$
$\chi_{1323}(32,\cdot)$	1323.cg	126	yes	$-1$	$1$	$e\left(\frac{95}{126}\right)$	$e\left(\frac{32}{63}\right)$	$e\left(\frac{19}{126}\right)$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{53}{126}\right)$	$e\left(\frac{23}{63}\right)$	$e\left(\frac{1}{63}\right)$	$e\left(\frac{23}{42}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{1323}(34,\cdot)$	1323.ck	126	yes	$-1$	$1$	$e\left(\frac{29}{63}\right)$	$e\left(\frac{58}{63}\right)$	$e\left(\frac{83}{126}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{5}{42}\right)$	$e\left(\frac{8}{63}\right)$	$e\left(\frac{23}{126}\right)$	$e\left(\frac{53}{63}\right)$	$e\left(\frac{29}{42}\right)$	$e\left(\frac{1}{6}\right)$
$\chi_{1323}(37,\cdot)$	1323.bk	21	no	$1$	$1$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{1323}(38,\cdot)$	1323.ci	126	yes	$1$	$1$	$e\left(\frac{61}{126}\right)$	$e\left(\frac{61}{63}\right)$	$e\left(\frac{46}{63}\right)$	$e\left(\frac{19}{42}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{61}{126}\right)$	$e\left(\frac{89}{126}\right)$	$e\left(\frac{59}{63}\right)$	$e\left(\frac{1}{7}\right)$	$-1$
$\chi_{1323}(40,\cdot)$	1323.cl	126	yes	$-1$	$1$	$e\left(\frac{43}{63}\right)$	$e\left(\frac{23}{63}\right)$	$e\left(\frac{13}{126}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{43}{63}\right)$	$e\left(\frac{79}{126}\right)$	$e\left(\frac{46}{63}\right)$	$e\left(\frac{5}{14}\right)$	$-1$
$\chi_{1323}(41,\cdot)$	1323.ce	126	yes	$1$	$1$	$e\left(\frac{29}{126}\right)$	$e\left(\frac{29}{63}\right)$	$e\left(\frac{5}{63}\right)$	$e\left(\frac{29}{42}\right)$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{71}{126}\right)$	$e\left(\frac{43}{126}\right)$	$e\left(\frac{58}{63}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{1323}(43,\cdot)$	1323.cb	63	yes	$1$	$1$	$e\left(\frac{59}{63}\right)$	$e\left(\frac{55}{63}\right)$	$e\left(\frac{16}{63}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{38}{63}\right)$	$e\left(\frac{31}{63}\right)$	$e\left(\frac{47}{63}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{1323}(44,\cdot)$	1323.by	42	no	$-1$	$1$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{29}{42}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{19}{42}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{1323}(46,\cdot)$	1323.bk	21	no	$1$	$1$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{1323}(47,\cdot)$	1323.cf	126	yes	$1$	$1$	$e\left(\frac{61}{126}\right)$	$e\left(\frac{61}{63}\right)$	$e\left(\frac{25}{63}\right)$	$e\left(\frac{19}{42}\right)$	$e\left(\frac{37}{42}\right)$	$e\left(\frac{103}{126}\right)$	$e\left(\frac{5}{126}\right)$	$e\left(\frac{59}{63}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{1323}(50,\cdot)$	1323.bf	18	no	$-1$	$1$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{1323}(52,\cdot)$	1323.cl	126	yes	$-1$	$1$	$e\left(\frac{11}{63}\right)$	$e\left(\frac{22}{63}\right)$	$e\left(\frac{59}{126}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{11}{63}\right)$	$e\left(\frac{29}{126}\right)$	$e\left(\frac{44}{63}\right)$	$e\left(\frac{13}{14}\right)$	$-1$
$\chi_{1323}(53,\cdot)$	1323.br	42	no	$-1$	$1$	$e\left(\frac{29}{42}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{17}{42}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{1}{42}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{19}{42}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{1323}(55,\cdot)$	1323.y	14	no	$-1$	$1$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{1}{14}\right)$	$-1$

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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	$1323$
Structure	\(C_{6}\times C_{126}\)
Order	$756$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(4\)	\(5\)	\(8\)	\(10\)	\(11\)	\(13\)	\(16\)	\(17\)	\(19\)
\(\chi_{1323}(1,\cdot)\)	1323.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{1323}(2,\cdot)\)	1323.cg	126	yes	\(-1\)	\(1\)	\(e\left(\frac{19}{126}\right)\)	\(e\left(\frac{19}{63}\right)\)	\(e\left(\frac{29}{126}\right)\)	\(e\left(\frac{19}{42}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{61}{126}\right)\)	\(e\left(\frac{55}{63}\right)\)	\(e\left(\frac{38}{63}\right)\)	\(e\left(\frac{13}{42}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{1323}(4,\cdot)\)	1323.cc	63	yes	\(1\)	\(1\)	\(e\left(\frac{19}{63}\right)\)	\(e\left(\frac{38}{63}\right)\)	\(e\left(\frac{29}{63}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{61}{63}\right)\)	\(e\left(\frac{47}{63}\right)\)	\(e\left(\frac{13}{63}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{1323}(5,\cdot)\)	1323.ci	126	yes	\(1\)	\(1\)	\(e\left(\frac{29}{126}\right)\)	\(e\left(\frac{29}{63}\right)\)	\(e\left(\frac{26}{63}\right)\)	\(e\left(\frac{29}{42}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{29}{126}\right)\)	\(e\left(\frac{1}{126}\right)\)	\(e\left(\frac{58}{63}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(-1\)
\(\chi_{1323}(8,\cdot)\)	1323.bq	42	no	\(-1\)	\(1\)	\(e\left(\frac{19}{42}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{29}{42}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{19}{42}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(1\)
\(\chi_{1323}(10,\cdot)\)	1323.bx	42	no	\(-1\)	\(1\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{1}{42}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{37}{42}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{31}{42}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{1323}(11,\cdot)\)	1323.cd	126	yes	\(-1\)	\(1\)	\(e\left(\frac{61}{126}\right)\)	\(e\left(\frac{61}{63}\right)\)	\(e\left(\frac{29}{126}\right)\)	\(e\left(\frac{19}{42}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{61}{126}\right)\)	\(e\left(\frac{13}{63}\right)\)	\(e\left(\frac{59}{63}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(1\)
\(\chi_{1323}(13,\cdot)\)	1323.ck	126	yes	\(-1\)	\(1\)	\(e\left(\frac{55}{63}\right)\)	\(e\left(\frac{47}{63}\right)\)	\(e\left(\frac{1}{126}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{37}{42}\right)\)	\(e\left(\frac{13}{63}\right)\)	\(e\left(\frac{61}{126}\right)\)	\(e\left(\frac{31}{63}\right)\)	\(e\left(\frac{13}{42}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{1323}(16,\cdot)\)	1323.cc	63	yes	\(1\)	\(1\)	\(e\left(\frac{38}{63}\right)\)	\(e\left(\frac{13}{63}\right)\)	\(e\left(\frac{58}{63}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{59}{63}\right)\)	\(e\left(\frac{31}{63}\right)\)	\(e\left(\frac{26}{63}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{1323}(17,\cdot)\)	1323.bp	42	no	\(1\)	\(1\)	\(e\left(\frac{13}{42}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{31}{42}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{13}{42}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{1323}(19,\cdot)\)	1323.k	6	no	\(-1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(-1\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{1323}(20,\cdot)\)	1323.ce	126	yes	\(1\)	\(1\)	\(e\left(\frac{67}{126}\right)\)	\(e\left(\frac{4}{63}\right)\)	\(e\left(\frac{55}{63}\right)\)	\(e\left(\frac{25}{42}\right)\)	\(e\left(\frac{17}{42}\right)\)	\(e\left(\frac{25}{126}\right)\)	\(e\left(\frac{95}{126}\right)\)	\(e\left(\frac{8}{63}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{1323}(22,\cdot)\)	1323.cb	63	yes	\(1\)	\(1\)	\(e\left(\frac{40}{63}\right)\)	\(e\left(\frac{17}{63}\right)\)	\(e\left(\frac{29}{63}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{61}{63}\right)\)	\(e\left(\frac{5}{63}\right)\)	\(e\left(\frac{34}{63}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{1323}(23,\cdot)\)	1323.cd	126	yes	\(-1\)	\(1\)	\(e\left(\frac{17}{126}\right)\)	\(e\left(\frac{17}{63}\right)\)	\(e\left(\frac{37}{126}\right)\)	\(e\left(\frac{17}{42}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{17}{126}\right)\)	\(e\left(\frac{47}{63}\right)\)	\(e\left(\frac{34}{63}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(1\)
\(\chi_{1323}(25,\cdot)\)	1323.ca	63	yes	\(1\)	\(1\)	\(e\left(\frac{29}{63}\right)\)	\(e\left(\frac{58}{63}\right)\)	\(e\left(\frac{52}{63}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{29}{63}\right)\)	\(e\left(\frac{1}{63}\right)\)	\(e\left(\frac{53}{63}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(1\)
\(\chi_{1323}(26,\cdot)\)	1323.bs	42	no	\(1\)	\(1\)	\(e\left(\frac{1}{42}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{11}{42}\right)\)	\(e\left(\frac{29}{42}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{1323}(29,\cdot)\)	1323.ch	126	yes	\(-1\)	\(1\)	\(e\left(\frac{25}{126}\right)\)	\(e\left(\frac{25}{63}\right)\)	\(e\left(\frac{89}{126}\right)\)	\(e\left(\frac{25}{42}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{109}{126}\right)\)	\(e\left(\frac{37}{63}\right)\)	\(e\left(\frac{50}{63}\right)\)	\(e\left(\frac{23}{42}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{1323}(31,\cdot)\)	1323.bd	18	no	\(-1\)	\(1\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{1323}(32,\cdot)\)	1323.cg	126	yes	\(-1\)	\(1\)	\(e\left(\frac{95}{126}\right)\)	\(e\left(\frac{32}{63}\right)\)	\(e\left(\frac{19}{126}\right)\)	\(e\left(\frac{11}{42}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{53}{126}\right)\)	\(e\left(\frac{23}{63}\right)\)	\(e\left(\frac{1}{63}\right)\)	\(e\left(\frac{23}{42}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{1323}(34,\cdot)\)	1323.ck	126	yes	\(-1\)	\(1\)	\(e\left(\frac{29}{63}\right)\)	\(e\left(\frac{58}{63}\right)\)	\(e\left(\frac{83}{126}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{5}{42}\right)\)	\(e\left(\frac{8}{63}\right)\)	\(e\left(\frac{23}{126}\right)\)	\(e\left(\frac{53}{63}\right)\)	\(e\left(\frac{29}{42}\right)\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{1323}(37,\cdot)\)	1323.bk	21	no	\(1\)	\(1\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{1323}(38,\cdot)\)	1323.ci	126	yes	\(1\)	\(1\)	\(e\left(\frac{61}{126}\right)\)	\(e\left(\frac{61}{63}\right)\)	\(e\left(\frac{46}{63}\right)\)	\(e\left(\frac{19}{42}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{61}{126}\right)\)	\(e\left(\frac{89}{126}\right)\)	\(e\left(\frac{59}{63}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(-1\)
\(\chi_{1323}(40,\cdot)\)	1323.cl	126	yes	\(-1\)	\(1\)	\(e\left(\frac{43}{63}\right)\)	\(e\left(\frac{23}{63}\right)\)	\(e\left(\frac{13}{126}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{43}{63}\right)\)	\(e\left(\frac{79}{126}\right)\)	\(e\left(\frac{46}{63}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(-1\)
\(\chi_{1323}(41,\cdot)\)	1323.ce	126	yes	\(1\)	\(1\)	\(e\left(\frac{29}{126}\right)\)	\(e\left(\frac{29}{63}\right)\)	\(e\left(\frac{5}{63}\right)\)	\(e\left(\frac{29}{42}\right)\)	\(e\left(\frac{13}{42}\right)\)	\(e\left(\frac{71}{126}\right)\)	\(e\left(\frac{43}{126}\right)\)	\(e\left(\frac{58}{63}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{1323}(43,\cdot)\)	1323.cb	63	yes	\(1\)	\(1\)	\(e\left(\frac{59}{63}\right)\)	\(e\left(\frac{55}{63}\right)\)	\(e\left(\frac{16}{63}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{38}{63}\right)\)	\(e\left(\frac{31}{63}\right)\)	\(e\left(\frac{47}{63}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{1323}(44,\cdot)\)	1323.by	42	no	\(-1\)	\(1\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{29}{42}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{19}{42}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{11}{42}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{1323}(46,\cdot)\)	1323.bk	21	no	\(1\)	\(1\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{1323}(47,\cdot)\)	1323.cf	126	yes	\(1\)	\(1\)	\(e\left(\frac{61}{126}\right)\)	\(e\left(\frac{61}{63}\right)\)	\(e\left(\frac{25}{63}\right)\)	\(e\left(\frac{19}{42}\right)\)	\(e\left(\frac{37}{42}\right)\)	\(e\left(\frac{103}{126}\right)\)	\(e\left(\frac{5}{126}\right)\)	\(e\left(\frac{59}{63}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{1323}(50,\cdot)\)	1323.bf	18	no	\(-1\)	\(1\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{1323}(52,\cdot)\)	1323.cl	126	yes	\(-1\)	\(1\)	\(e\left(\frac{11}{63}\right)\)	\(e\left(\frac{22}{63}\right)\)	\(e\left(\frac{59}{126}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{11}{63}\right)\)	\(e\left(\frac{29}{126}\right)\)	\(e\left(\frac{44}{63}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(-1\)
\(\chi_{1323}(53,\cdot)\)	1323.br	42	no	\(-1\)	\(1\)	\(e\left(\frac{29}{42}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{17}{42}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{1}{42}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{19}{42}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{1323}(55,\cdot)\)	1323.y	14	no	\(-1\)	\(1\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(-1\)

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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.