LMFDB - Group of Dirichlet characters of modulus 21168

Show commands: PariGP / SageMath

sage: H = DirichletGroup(21168)

pari: g = idealstar(,21168,2)

Character group

sage: G.order() pari: g.no
Order	=	6048
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{2}\times C_{6}\times C_{252}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{21168}(13231,\cdot)$, $\chi_{21168}(15877,\cdot)$, $\chi_{21168}(785,\cdot)$, $\chi_{21168}(11665,\cdot)$

First 32 of 6048 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	$-1$	$1$	$5$	$11$	$13$	$17$	$19$	$23$	$25$	$29$	$31$	$37$
$\chi_{21168}(1,\cdot)$	21168.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{21168}(5,\cdot)$	21168.nx	252	yes	$1$	$1$	$e\left(\frac{167}{252}\right)$	$e\left(\frac{121}{252}\right)$	$e\left(\frac{191}{252}\right)$	$e\left(\frac{3}{7}\right)$	$i$	$e\left(\frac{50}{63}\right)$	$e\left(\frac{41}{126}\right)$	$e\left(\frac{115}{252}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{1}{84}\right)$
$\chi_{21168}(11,\cdot)$	21168.oq	252	yes	$1$	$1$	$e\left(\frac{121}{252}\right)$	$e\left(\frac{59}{252}\right)$	$e\left(\frac{241}{252}\right)$	$e\left(\frac{9}{14}\right)$	$i$	$e\left(\frac{17}{126}\right)$	$e\left(\frac{121}{126}\right)$	$e\left(\frac{155}{252}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{5}{84}\right)$
$\chi_{21168}(13,\cdot)$	21168.oc	252	yes	$-1$	$1$	$e\left(\frac{191}{252}\right)$	$e\left(\frac{241}{252}\right)$	$e\left(\frac{185}{252}\right)$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{31}{126}\right)$	$e\left(\frac{65}{126}\right)$	$e\left(\frac{211}{252}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{47}{84}\right)$
$\chi_{21168}(17,\cdot)$	21168.iq	42	no	$1$	$1$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{23}{42}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{21}\right)$
$\chi_{21168}(19,\cdot)$	21168.eo	12	no	$1$	$1$	$i$	$i$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{11}{12}\right)$	$1$	$-1$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{12}\right)$
$\chi_{21168}(23,\cdot)$	21168.nt	126	no	$1$	$1$	$e\left(\frac{50}{63}\right)$	$e\left(\frac{17}{126}\right)$	$e\left(\frac{31}{126}\right)$	$e\left(\frac{11}{14}\right)$	$1$	$e\left(\frac{38}{63}\right)$	$e\left(\frac{37}{63}\right)$	$e\left(\frac{25}{63}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{5}{42}\right)$
$\chi_{21168}(25,\cdot)$	21168.md	126	no	$1$	$1$	$e\left(\frac{41}{126}\right)$	$e\left(\frac{121}{126}\right)$	$e\left(\frac{65}{126}\right)$	$e\left(\frac{6}{7}\right)$	$-1$	$e\left(\frac{37}{63}\right)$	$e\left(\frac{41}{63}\right)$	$e\left(\frac{115}{126}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{1}{42}\right)$
$\chi_{21168}(29,\cdot)$	21168.of	252	yes	$-1$	$1$	$e\left(\frac{115}{252}\right)$	$e\left(\frac{155}{252}\right)$	$e\left(\frac{211}{252}\right)$	$e\left(\frac{23}{42}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{25}{63}\right)$	$e\left(\frac{115}{126}\right)$	$e\left(\frac{5}{252}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{67}{84}\right)$
$\chi_{21168}(31,\cdot)$	21168.gl	18	no	$1$	$1$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{8}{9}\right)$	$1$
$\chi_{21168}(37,\cdot)$	21168.lr	84	no	$1$	$1$	$e\left(\frac{1}{84}\right)$	$e\left(\frac{5}{84}\right)$	$e\left(\frac{47}{84}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{5}{42}\right)$	$e\left(\frac{1}{42}\right)$	$e\left(\frac{67}{84}\right)$	$1$	$e\left(\frac{53}{84}\right)$
$\chi_{21168}(41,\cdot)$	21168.nb	126	no	$1$	$1$	$e\left(\frac{73}{126}\right)$	$e\left(\frac{4}{63}\right)$	$e\left(\frac{53}{63}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{121}{126}\right)$	$e\left(\frac{10}{63}\right)$	$e\left(\frac{55}{63}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{25}{42}\right)$
$\chi_{21168}(43,\cdot)$	21168.oj	252	yes	$-1$	$1$	$e\left(\frac{127}{252}\right)$	$e\left(\frac{89}{252}\right)$	$e\left(\frac{61}{252}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{55}{63}\right)$	$e\left(\frac{1}{126}\right)$	$e\left(\frac{137}{252}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{13}{84}\right)$
$\chi_{21168}(47,\cdot)$	21168.na	126	no	$-1$	$1$	$e\left(\frac{25}{63}\right)$	$e\left(\frac{20}{63}\right)$	$e\left(\frac{5}{126}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{19}{63}\right)$	$e\left(\frac{50}{63}\right)$	$e\left(\frac{67}{126}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{1}{7}\right)$
$\chi_{21168}(53,\cdot)$	21168.lh	84	no	$-1$	$1$	$e\left(\frac{55}{84}\right)$	$e\left(\frac{23}{84}\right)$	$e\left(\frac{17}{28}\right)$	$e\left(\frac{19}{42}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{73}{84}\right)$
$\chi_{21168}(55,\cdot)$	21168.eu	14	no	$1$	$1$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{1}{14}\right)$	$-1$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{1}{14}\right)$	$1$	$e\left(\frac{1}{14}\right)$
$\chi_{21168}(59,\cdot)$	21168.om	252	yes	$-1$	$1$	$e\left(\frac{155}{252}\right)$	$e\left(\frac{187}{252}\right)$	$e\left(\frac{47}{252}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{103}{126}\right)$	$e\left(\frac{29}{126}\right)$	$e\left(\frac{151}{252}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{23}{28}\right)$
$\chi_{21168}(61,\cdot)$	21168.oa	252	yes	$-1$	$1$	$e\left(\frac{199}{252}\right)$	$e\left(\frac{197}{252}\right)$	$e\left(\frac{1}{252}\right)$	$e\left(\frac{37}{42}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{29}{126}\right)$	$e\left(\frac{73}{126}\right)$	$e\left(\frac{215}{252}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{13}{28}\right)$
$\chi_{21168}(65,\cdot)$	21168.mk	126	no	$-1$	$1$	$e\left(\frac{53}{126}\right)$	$e\left(\frac{55}{126}\right)$	$e\left(\frac{31}{63}\right)$	$e\left(\frac{31}{42}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{126}\right)$	$e\left(\frac{53}{63}\right)$	$e\left(\frac{37}{126}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{4}{7}\right)$
$\chi_{21168}(67,\cdot)$	21168.hw	36	no	$-1$	$1$	$e\left(\frac{11}{36}\right)$	$e\left(\frac{25}{36}\right)$	$e\left(\frac{29}{36}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{25}{36}\right)$	$e\left(\frac{1}{18}\right)$	$-i$
$\chi_{21168}(71,\cdot)$	21168.jw	42	no	$1$	$1$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{29}{42}\right)$	$e\left(\frac{1}{42}\right)$	$e\left(\frac{11}{14}\right)$	$1$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{11}{14}\right)$
$\chi_{21168}(73,\cdot)$	21168.jy	42	no	$-1$	$1$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{17}{42}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{1}{42}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{1}{42}\right)$	$-1$	$e\left(\frac{29}{42}\right)$
$\chi_{21168}(79,\cdot)$	21168.gd	18	no	$-1$	$1$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{17}{18}\right)$	$1$
$\chi_{21168}(83,\cdot)$	21168.oo	252	yes	$-1$	$1$	$e\left(\frac{61}{252}\right)$	$e\left(\frac{137}{252}\right)$	$e\left(\frac{193}{252}\right)$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{95}{126}\right)$	$e\left(\frac{61}{126}\right)$	$e\left(\frac{41}{252}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{79}{84}\right)$
$\chi_{21168}(85,\cdot)$	21168.on	252	yes	$1$	$1$	$e\left(\frac{23}{252}\right)$	$e\left(\frac{31}{252}\right)$	$e\left(\frac{17}{252}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{73}{126}\right)$	$e\left(\frac{23}{126}\right)$	$e\left(\frac{1}{252}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{5}{84}\right)$
$\chi_{21168}(89,\cdot)$	21168.kp	42	no	$1$	$1$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{42}\right)$
$\chi_{21168}(95,\cdot)$	21168.ms	126	no	$1$	$1$	$e\left(\frac{115}{126}\right)$	$e\left(\frac{46}{63}\right)$	$e\left(\frac{53}{63}\right)$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{50}{63}\right)$	$e\left(\frac{52}{63}\right)$	$e\left(\frac{47}{126}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{3}{7}\right)$
$\chi_{21168}(97,\cdot)$	21168.gq	18	no	$-1$	$1$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{21168}(101,\cdot)$	21168.nx	252	yes	$1$	$1$	$e\left(\frac{223}{252}\right)$	$e\left(\frac{65}{252}\right)$	$e\left(\frac{163}{252}\right)$	$e\left(\frac{3}{7}\right)$	$i$	$e\left(\frac{43}{63}\right)$	$e\left(\frac{97}{126}\right)$	$e\left(\frac{143}{252}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{29}{84}\right)$
$\chi_{21168}(103,\cdot)$	21168.no	126	no	$1$	$1$	$e\left(\frac{26}{63}\right)$	$e\left(\frac{46}{63}\right)$	$e\left(\frac{32}{63}\right)$	$e\left(\frac{13}{14}\right)$	$-1$	$e\left(\frac{37}{126}\right)$	$e\left(\frac{52}{63}\right)$	$e\left(\frac{89}{126}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{11}{42}\right)$
$\chi_{21168}(107,\cdot)$	21168.lg	84	no	$1$	$1$	$e\left(\frac{11}{84}\right)$	$e\left(\frac{13}{84}\right)$	$e\left(\frac{9}{28}\right)$	$e\left(\frac{29}{42}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{3}{28}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{65}{84}\right)$
$\chi_{21168}(109,\cdot)$	21168.lq	84	no	$1$	$1$	$e\left(\frac{31}{84}\right)$	$e\left(\frac{71}{84}\right)$	$e\left(\frac{19}{28}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{29}{42}\right)$	$e\left(\frac{31}{42}\right)$	$e\left(\frac{11}{28}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{19}{84}\right)$

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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	$21168$
Structure	\(C_{2}\times C_{2}\times C_{6}\times C_{252}\)
Order	$6048$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(5\)	\(11\)	\(13\)	\(17\)	\(19\)	\(23\)	\(25\)	\(29\)	\(31\)	\(37\)
\(\chi_{21168}(1,\cdot)\)	21168.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{21168}(5,\cdot)\)	21168.nx	252	yes	\(1\)	\(1\)	\(e\left(\frac{167}{252}\right)\)	\(e\left(\frac{121}{252}\right)\)	\(e\left(\frac{191}{252}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(i\)	\(e\left(\frac{50}{63}\right)\)	\(e\left(\frac{41}{126}\right)\)	\(e\left(\frac{115}{252}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{1}{84}\right)\)
\(\chi_{21168}(11,\cdot)\)	21168.oq	252	yes	\(1\)	\(1\)	\(e\left(\frac{121}{252}\right)\)	\(e\left(\frac{59}{252}\right)\)	\(e\left(\frac{241}{252}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(i\)	\(e\left(\frac{17}{126}\right)\)	\(e\left(\frac{121}{126}\right)\)	\(e\left(\frac{155}{252}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{5}{84}\right)\)
\(\chi_{21168}(13,\cdot)\)	21168.oc	252	yes	\(-1\)	\(1\)	\(e\left(\frac{191}{252}\right)\)	\(e\left(\frac{241}{252}\right)\)	\(e\left(\frac{185}{252}\right)\)	\(e\left(\frac{13}{42}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{31}{126}\right)\)	\(e\left(\frac{65}{126}\right)\)	\(e\left(\frac{211}{252}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{47}{84}\right)\)
\(\chi_{21168}(17,\cdot)\)	21168.iq	42	no	\(1\)	\(1\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{13}{42}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{23}{42}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{21}\right)\)
\(\chi_{21168}(19,\cdot)\)	21168.eo	12	no	\(1\)	\(1\)	\(i\)	\(i\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(1\)	\(-1\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{12}\right)\)
\(\chi_{21168}(23,\cdot)\)	21168.nt	126	no	\(1\)	\(1\)	\(e\left(\frac{50}{63}\right)\)	\(e\left(\frac{17}{126}\right)\)	\(e\left(\frac{31}{126}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(1\)	\(e\left(\frac{38}{63}\right)\)	\(e\left(\frac{37}{63}\right)\)	\(e\left(\frac{25}{63}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{5}{42}\right)\)
\(\chi_{21168}(25,\cdot)\)	21168.md	126	no	\(1\)	\(1\)	\(e\left(\frac{41}{126}\right)\)	\(e\left(\frac{121}{126}\right)\)	\(e\left(\frac{65}{126}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(-1\)	\(e\left(\frac{37}{63}\right)\)	\(e\left(\frac{41}{63}\right)\)	\(e\left(\frac{115}{126}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{1}{42}\right)\)
\(\chi_{21168}(29,\cdot)\)	21168.of	252	yes	\(-1\)	\(1\)	\(e\left(\frac{115}{252}\right)\)	\(e\left(\frac{155}{252}\right)\)	\(e\left(\frac{211}{252}\right)\)	\(e\left(\frac{23}{42}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{25}{63}\right)\)	\(e\left(\frac{115}{126}\right)\)	\(e\left(\frac{5}{252}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{67}{84}\right)\)
\(\chi_{21168}(31,\cdot)\)	21168.gl	18	no	\(1\)	\(1\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(1\)
\(\chi_{21168}(37,\cdot)\)	21168.lr	84	no	\(1\)	\(1\)	\(e\left(\frac{1}{84}\right)\)	\(e\left(\frac{5}{84}\right)\)	\(e\left(\frac{47}{84}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{5}{42}\right)\)	\(e\left(\frac{1}{42}\right)\)	\(e\left(\frac{67}{84}\right)\)	\(1\)	\(e\left(\frac{53}{84}\right)\)
\(\chi_{21168}(41,\cdot)\)	21168.nb	126	no	\(1\)	\(1\)	\(e\left(\frac{73}{126}\right)\)	\(e\left(\frac{4}{63}\right)\)	\(e\left(\frac{53}{63}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{121}{126}\right)\)	\(e\left(\frac{10}{63}\right)\)	\(e\left(\frac{55}{63}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{25}{42}\right)\)
\(\chi_{21168}(43,\cdot)\)	21168.oj	252	yes	\(-1\)	\(1\)	\(e\left(\frac{127}{252}\right)\)	\(e\left(\frac{89}{252}\right)\)	\(e\left(\frac{61}{252}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{55}{63}\right)\)	\(e\left(\frac{1}{126}\right)\)	\(e\left(\frac{137}{252}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{13}{84}\right)\)
\(\chi_{21168}(47,\cdot)\)	21168.na	126	no	\(-1\)	\(1\)	\(e\left(\frac{25}{63}\right)\)	\(e\left(\frac{20}{63}\right)\)	\(e\left(\frac{5}{126}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{19}{63}\right)\)	\(e\left(\frac{50}{63}\right)\)	\(e\left(\frac{67}{126}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{1}{7}\right)\)
\(\chi_{21168}(53,\cdot)\)	21168.lh	84	no	\(-1\)	\(1\)	\(e\left(\frac{55}{84}\right)\)	\(e\left(\frac{23}{84}\right)\)	\(e\left(\frac{17}{28}\right)\)	\(e\left(\frac{19}{42}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{13}{42}\right)\)	\(e\left(\frac{15}{28}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{73}{84}\right)\)
\(\chi_{21168}(55,\cdot)\)	21168.eu	14	no	\(1\)	\(1\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(-1\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(1\)	\(e\left(\frac{1}{14}\right)\)
\(\chi_{21168}(59,\cdot)\)	21168.om	252	yes	\(-1\)	\(1\)	\(e\left(\frac{155}{252}\right)\)	\(e\left(\frac{187}{252}\right)\)	\(e\left(\frac{47}{252}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{103}{126}\right)\)	\(e\left(\frac{29}{126}\right)\)	\(e\left(\frac{151}{252}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{23}{28}\right)\)
\(\chi_{21168}(61,\cdot)\)	21168.oa	252	yes	\(-1\)	\(1\)	\(e\left(\frac{199}{252}\right)\)	\(e\left(\frac{197}{252}\right)\)	\(e\left(\frac{1}{252}\right)\)	\(e\left(\frac{37}{42}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{29}{126}\right)\)	\(e\left(\frac{73}{126}\right)\)	\(e\left(\frac{215}{252}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{13}{28}\right)\)
\(\chi_{21168}(65,\cdot)\)	21168.mk	126	no	\(-1\)	\(1\)	\(e\left(\frac{53}{126}\right)\)	\(e\left(\frac{55}{126}\right)\)	\(e\left(\frac{31}{63}\right)\)	\(e\left(\frac{31}{42}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{126}\right)\)	\(e\left(\frac{53}{63}\right)\)	\(e\left(\frac{37}{126}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{4}{7}\right)\)
\(\chi_{21168}(67,\cdot)\)	21168.hw	36	no	\(-1\)	\(1\)	\(e\left(\frac{11}{36}\right)\)	\(e\left(\frac{25}{36}\right)\)	\(e\left(\frac{29}{36}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{25}{36}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(-i\)
\(\chi_{21168}(71,\cdot)\)	21168.jw	42	no	\(1\)	\(1\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{29}{42}\right)\)	\(e\left(\frac{1}{42}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(1\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{11}{14}\right)\)
\(\chi_{21168}(73,\cdot)\)	21168.jy	42	no	\(-1\)	\(1\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{17}{42}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{1}{42}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{1}{42}\right)\)	\(-1\)	\(e\left(\frac{29}{42}\right)\)
\(\chi_{21168}(79,\cdot)\)	21168.gd	18	no	\(-1\)	\(1\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(1\)
\(\chi_{21168}(83,\cdot)\)	21168.oo	252	yes	\(-1\)	\(1\)	\(e\left(\frac{61}{252}\right)\)	\(e\left(\frac{137}{252}\right)\)	\(e\left(\frac{193}{252}\right)\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{95}{126}\right)\)	\(e\left(\frac{61}{126}\right)\)	\(e\left(\frac{41}{252}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{79}{84}\right)\)
\(\chi_{21168}(85,\cdot)\)	21168.on	252	yes	\(1\)	\(1\)	\(e\left(\frac{23}{252}\right)\)	\(e\left(\frac{31}{252}\right)\)	\(e\left(\frac{17}{252}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{73}{126}\right)\)	\(e\left(\frac{23}{126}\right)\)	\(e\left(\frac{1}{252}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{5}{84}\right)\)
\(\chi_{21168}(89,\cdot)\)	21168.kp	42	no	\(1\)	\(1\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{42}\right)\)
\(\chi_{21168}(95,\cdot)\)	21168.ms	126	no	\(1\)	\(1\)	\(e\left(\frac{115}{126}\right)\)	\(e\left(\frac{46}{63}\right)\)	\(e\left(\frac{53}{63}\right)\)	\(e\left(\frac{11}{42}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{50}{63}\right)\)	\(e\left(\frac{52}{63}\right)\)	\(e\left(\frac{47}{126}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{3}{7}\right)\)
\(\chi_{21168}(97,\cdot)\)	21168.gq	18	no	\(-1\)	\(1\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{21168}(101,\cdot)\)	21168.nx	252	yes	\(1\)	\(1\)	\(e\left(\frac{223}{252}\right)\)	\(e\left(\frac{65}{252}\right)\)	\(e\left(\frac{163}{252}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(i\)	\(e\left(\frac{43}{63}\right)\)	\(e\left(\frac{97}{126}\right)\)	\(e\left(\frac{143}{252}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{29}{84}\right)\)
\(\chi_{21168}(103,\cdot)\)	21168.no	126	no	\(1\)	\(1\)	\(e\left(\frac{26}{63}\right)\)	\(e\left(\frac{46}{63}\right)\)	\(e\left(\frac{32}{63}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(-1\)	\(e\left(\frac{37}{126}\right)\)	\(e\left(\frac{52}{63}\right)\)	\(e\left(\frac{89}{126}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{11}{42}\right)\)
\(\chi_{21168}(107,\cdot)\)	21168.lg	84	no	\(1\)	\(1\)	\(e\left(\frac{11}{84}\right)\)	\(e\left(\frac{13}{84}\right)\)	\(e\left(\frac{9}{28}\right)\)	\(e\left(\frac{29}{42}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{13}{42}\right)\)	\(e\left(\frac{11}{42}\right)\)	\(e\left(\frac{3}{28}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{65}{84}\right)\)
\(\chi_{21168}(109,\cdot)\)	21168.lq	84	no	\(1\)	\(1\)	\(e\left(\frac{31}{84}\right)\)	\(e\left(\frac{71}{84}\right)\)	\(e\left(\frac{19}{28}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{29}{42}\right)\)	\(e\left(\frac{31}{42}\right)\)	\(e\left(\frac{11}{28}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{19}{84}\right)\)

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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.