LMFDB - Group of Dirichlet characters of modulus 47040

Show commands: PariGP / SageMath

sage: H = DirichletGroup(47040)

pari: g = idealstar(,47040,2)

Character group

sage: G.order() pari: g.no
Order	=	10752
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{2}\times C_{2}\times C_{4}\times C_{336}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{47040}(1471,\cdot)$, $\chi_{47040}(44101,\cdot)$, $\chi_{47040}(31361,\cdot)$, $\chi_{47040}(18817,\cdot)$, $\chi_{47040}(42241,\cdot)$

First 32 of 10752 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	$-1$	$1$	$11$	$13$	$17$	$19$	$23$	$29$	$31$	$37$	$41$	$43$
$\chi_{47040}(1,\cdot)$	47040.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{47040}(11,\cdot)$	47040.vj	336	no	$1$	$1$	$e\left(\frac{221}{336}\right)$	$e\left(\frac{13}{112}\right)$	$e\left(\frac{5}{84}\right)$	$e\left(\frac{1}{48}\right)$	$e\left(\frac{95}{168}\right)$	$e\left(\frac{9}{112}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{97}{336}\right)$	$e\left(\frac{9}{56}\right)$	$e\left(\frac{31}{112}\right)$
$\chi_{47040}(13,\cdot)$	47040.tq	112	no	$1$	$1$	$e\left(\frac{13}{112}\right)$	$e\left(\frac{27}{112}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{13}{56}\right)$	$e\left(\frac{107}{112}\right)$	$1$	$e\left(\frac{37}{112}\right)$	$e\left(\frac{51}{56}\right)$	$e\left(\frac{17}{112}\right)$
$\chi_{47040}(17,\cdot)$	47040.sd	84	no	$-1$	$1$	$e\left(\frac{5}{84}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{53}{84}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{31}{84}\right)$	$e\left(\frac{27}{28}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{1}{14}\right)$
$\chi_{47040}(19,\cdot)$	47040.ox	48	no	$1$	$1$	$e\left(\frac{1}{48}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{35}{48}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{48}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{11}{16}\right)$
$\chi_{47040}(23,\cdot)$	47040.uf	168	no	$-1$	$1$	$e\left(\frac{95}{168}\right)$	$e\left(\frac{13}{56}\right)$	$e\left(\frac{31}{84}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{37}{42}\right)$	$e\left(\frac{51}{56}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{97}{168}\right)$	$e\left(\frac{9}{28}\right)$	$e\left(\frac{31}{56}\right)$
$\chi_{47040}(29,\cdot)$	47040.tb	112	yes	$-1$	$1$	$e\left(\frac{9}{112}\right)$	$e\left(\frac{107}{112}\right)$	$e\left(\frac{27}{28}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{51}{56}\right)$	$e\left(\frac{87}{112}\right)$	$-1$	$e\left(\frac{45}{112}\right)$	$e\left(\frac{31}{56}\right)$	$e\left(\frac{1}{112}\right)$
$\chi_{47040}(31,\cdot)$	47040.dr	6	no	$1$	$1$	$e\left(\frac{2}{3}\right)$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{6}\right)$	$-1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{6}\right)$	$-1$	$1$
$\chi_{47040}(37,\cdot)$	47040.wd	336	no	$-1$	$1$	$e\left(\frac{97}{336}\right)$	$e\left(\frac{37}{112}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{5}{48}\right)$	$e\left(\frac{97}{168}\right)$	$e\left(\frac{45}{112}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{233}{336}\right)$	$e\left(\frac{17}{56}\right)$	$e\left(\frac{71}{112}\right)$
$\chi_{47040}(41,\cdot)$	47040.qk	56	no	$1$	$1$	$e\left(\frac{9}{56}\right)$	$e\left(\frac{51}{56}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{9}{28}\right)$	$e\left(\frac{31}{56}\right)$	$-1$	$e\left(\frac{17}{56}\right)$	$e\left(\frac{3}{28}\right)$	$e\left(\frac{29}{56}\right)$
$\chi_{47040}(43,\cdot)$	47040.tp	112	no	$1$	$1$	$e\left(\frac{31}{112}\right)$	$e\left(\frac{17}{112}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{31}{56}\right)$	$e\left(\frac{1}{112}\right)$	$1$	$e\left(\frac{71}{112}\right)$	$e\left(\frac{29}{56}\right)$	$e\left(\frac{19}{112}\right)$
$\chi_{47040}(47,\cdot)$	47040.rz	84	no	$1$	$1$	$e\left(\frac{43}{84}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{61}{84}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{65}{84}\right)$	$e\left(\frac{11}{28}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{5}{7}\right)$
$\chi_{47040}(53,\cdot)$	47040.wc	336	yes	$1$	$1$	$e\left(\frac{197}{336}\right)$	$e\left(\frac{89}{112}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{1}{48}\right)$	$e\left(\frac{29}{168}\right)$	$e\left(\frac{81}{112}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{61}{336}\right)$	$e\left(\frac{25}{56}\right)$	$e\left(\frac{83}{112}\right)$
$\chi_{47040}(59,\cdot)$	47040.vq	336	yes	$-1$	$1$	$e\left(\frac{233}{336}\right)$	$e\left(\frac{73}{112}\right)$	$e\left(\frac{41}{84}\right)$	$e\left(\frac{37}{48}\right)$	$e\left(\frac{23}{168}\right)$	$e\left(\frac{85}{112}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{325}{336}\right)$	$e\left(\frac{1}{56}\right)$	$e\left(\frac{75}{112}\right)$
$\chi_{47040}(61,\cdot)$	47040.vn	336	no	$-1$	$1$	$e\left(\frac{139}{336}\right)$	$e\left(\frac{51}{112}\right)$	$e\left(\frac{67}{84}\right)$	$e\left(\frac{23}{48}\right)$	$e\left(\frac{97}{168}\right)$	$e\left(\frac{87}{112}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{23}{336}\right)$	$e\left(\frac{31}{56}\right)$	$e\left(\frac{1}{112}\right)$
$\chi_{47040}(67,\cdot)$	47040.pd	48	no	$1$	$1$	$e\left(\frac{5}{48}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{31}{48}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{13}{48}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{11}{16}\right)$
$\chi_{47040}(71,\cdot)$	47040.pn	56	no	$1$	$1$	$e\left(\frac{55}{56}\right)$	$e\left(\frac{13}{56}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{37}{56}\right)$	$-1$	$e\left(\frac{51}{56}\right)$	$e\left(\frac{23}{28}\right)$	$e\left(\frac{3}{56}\right)$
$\chi_{47040}(73,\cdot)$	47040.ug	168	no	$1$	$1$	$e\left(\frac{19}{168}\right)$	$e\left(\frac{53}{56}\right)$	$e\left(\frac{23}{84}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{41}{42}\right)$	$e\left(\frac{27}{56}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{53}{168}\right)$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{23}{56}\right)$
$\chi_{47040}(79,\cdot)$	47040.gr	12	no	$-1$	$1$	$e\left(\frac{1}{12}\right)$	$i$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{6}\right)$	$-i$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{12}\right)$	$-1$	$i$
$\chi_{47040}(83,\cdot)$	47040.so	112	yes	$1$	$1$	$e\left(\frac{85}{112}\right)$	$e\left(\frac{99}{112}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{29}{56}\right)$	$e\left(\frac{75}{112}\right)$	$-1$	$e\left(\frac{61}{112}\right)$	$e\left(\frac{47}{56}\right)$	$e\left(\frac{81}{112}\right)$
$\chi_{47040}(89,\cdot)$	47040.ux	168	no	$1$	$1$	$e\left(\frac{5}{168}\right)$	$e\left(\frac{25}{56}\right)$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{47}{84}\right)$	$e\left(\frac{41}{56}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{25}{168}\right)$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{23}{56}\right)$
$\chi_{47040}(97,\cdot)$	47040.bj	4	no	$1$	$1$	$-1$	$-i$	$-i$	$-1$	$-i$	$1$	$-1$	$-i$	$-1$	$i$
$\chi_{47040}(101,\cdot)$	47040.vl	336	no	$1$	$1$	$e\left(\frac{89}{336}\right)$	$e\left(\frac{25}{112}\right)$	$e\left(\frac{71}{84}\right)$	$e\left(\frac{37}{48}\right)$	$e\left(\frac{47}{168}\right)$	$e\left(\frac{13}{112}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{277}{336}\right)$	$e\left(\frac{41}{56}\right)$	$e\left(\frac{51}{112}\right)$
$\chi_{47040}(103,\cdot)$	47040.ub	168	no	$-1$	$1$	$e\left(\frac{125}{168}\right)$	$e\left(\frac{51}{56}\right)$	$e\left(\frac{43}{84}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{31}{42}\right)$	$e\left(\frac{17}{56}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{163}{168}\right)$	$e\left(\frac{3}{28}\right)$	$e\left(\frac{29}{56}\right)$
$\chi_{47040}(107,\cdot)$	47040.vb	336	yes	$-1$	$1$	$e\left(\frac{325}{336}\right)$	$e\left(\frac{57}{112}\right)$	$e\left(\frac{29}{42}\right)$	$e\left(\frac{17}{48}\right)$	$e\left(\frac{157}{168}\right)$	$e\left(\frac{89}{112}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{29}{336}\right)$	$e\left(\frac{33}{56}\right)$	$e\left(\frac{11}{112}\right)$
$\chi_{47040}(109,\cdot)$	47040.vu	336	no	$1$	$1$	$e\left(\frac{95}{336}\right)$	$e\left(\frac{55}{112}\right)$	$e\left(\frac{47}{84}\right)$	$e\left(\frac{19}{48}\right)$	$e\left(\frac{137}{168}\right)$	$e\left(\frac{107}{112}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{307}{336}\right)$	$e\left(\frac{23}{56}\right)$	$e\left(\frac{101}{112}\right)$
$\chi_{47040}(113,\cdot)$	47040.lp	28	no	$1$	$1$	$e\left(\frac{9}{28}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{3}{28}\right)$	$i$	$e\left(\frac{11}{28}\right)$	$e\left(\frac{17}{28}\right)$	$1$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{11}{14}\right)$
$\chi_{47040}(121,\cdot)$	47040.tt	168	no	$1$	$1$	$e\left(\frac{53}{168}\right)$	$e\left(\frac{13}{56}\right)$	$e\left(\frac{5}{42}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{11}{84}\right)$	$e\left(\frac{9}{56}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{97}{168}\right)$	$e\left(\frac{9}{28}\right)$	$e\left(\frac{31}{56}\right)$
$\chi_{47040}(127,\cdot)$	47040.mx	28	no	$1$	$1$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{25}{28}\right)$	$e\left(\frac{27}{28}\right)$	$1$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{3}{14}\right)$	$-1$	$e\left(\frac{27}{28}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{23}{28}\right)$
$\chi_{47040}(131,\cdot)$	47040.vv	336	no	$-1$	$1$	$e\left(\frac{331}{336}\right)$	$e\left(\frac{3}{112}\right)$	$e\left(\frac{13}{84}\right)$	$e\left(\frac{47}{48}\right)$	$e\left(\frac{121}{168}\right)$	$e\left(\frac{15}{112}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{311}{336}\right)$	$e\left(\frac{43}{56}\right)$	$e\left(\frac{89}{112}\right)$
$\chi_{47040}(137,\cdot)$	47040.uc	168	no	$1$	$1$	$e\left(\frac{127}{168}\right)$	$e\left(\frac{5}{56}\right)$	$e\left(\frac{41}{84}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{39}{56}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{89}{168}\right)$	$e\left(\frac{25}{28}\right)$	$e\left(\frac{27}{56}\right)$
$\chi_{47040}(139,\cdot)$	47040.sx	112	no	$1$	$1$	$e\left(\frac{39}{112}\right)$	$e\left(\frac{109}{112}\right)$	$e\left(\frac{5}{28}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{53}{56}\right)$	$e\left(\frac{97}{112}\right)$	$-1$	$e\left(\frac{83}{112}\right)$	$e\left(\frac{41}{56}\right)$	$e\left(\frac{23}{112}\right)$

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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	$47040$
Structure	\(C_{2}\times C_{2}\times C_{2}\times C_{4}\times C_{336}\)
Order	$10752$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(11\)	\(13\)	\(17\)	\(19\)	\(23\)	\(29\)	\(31\)	\(37\)	\(41\)	\(43\)
\(\chi_{47040}(1,\cdot)\)	47040.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{47040}(11,\cdot)\)	47040.vj	336	no	\(1\)	\(1\)	\(e\left(\frac{221}{336}\right)\)	\(e\left(\frac{13}{112}\right)\)	\(e\left(\frac{5}{84}\right)\)	\(e\left(\frac{1}{48}\right)\)	\(e\left(\frac{95}{168}\right)\)	\(e\left(\frac{9}{112}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{97}{336}\right)\)	\(e\left(\frac{9}{56}\right)\)	\(e\left(\frac{31}{112}\right)\)
\(\chi_{47040}(13,\cdot)\)	47040.tq	112	no	\(1\)	\(1\)	\(e\left(\frac{13}{112}\right)\)	\(e\left(\frac{27}{112}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{13}{56}\right)\)	\(e\left(\frac{107}{112}\right)\)	\(1\)	\(e\left(\frac{37}{112}\right)\)	\(e\left(\frac{51}{56}\right)\)	\(e\left(\frac{17}{112}\right)\)
\(\chi_{47040}(17,\cdot)\)	47040.sd	84	no	\(-1\)	\(1\)	\(e\left(\frac{5}{84}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{53}{84}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{31}{84}\right)\)	\(e\left(\frac{27}{28}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{1}{14}\right)\)
\(\chi_{47040}(19,\cdot)\)	47040.ox	48	no	\(1\)	\(1\)	\(e\left(\frac{1}{48}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{35}{48}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{48}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{11}{16}\right)\)
\(\chi_{47040}(23,\cdot)\)	47040.uf	168	no	\(-1\)	\(1\)	\(e\left(\frac{95}{168}\right)\)	\(e\left(\frac{13}{56}\right)\)	\(e\left(\frac{31}{84}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{37}{42}\right)\)	\(e\left(\frac{51}{56}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{97}{168}\right)\)	\(e\left(\frac{9}{28}\right)\)	\(e\left(\frac{31}{56}\right)\)
\(\chi_{47040}(29,\cdot)\)	47040.tb	112	yes	\(-1\)	\(1\)	\(e\left(\frac{9}{112}\right)\)	\(e\left(\frac{107}{112}\right)\)	\(e\left(\frac{27}{28}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{51}{56}\right)\)	\(e\left(\frac{87}{112}\right)\)	\(-1\)	\(e\left(\frac{45}{112}\right)\)	\(e\left(\frac{31}{56}\right)\)	\(e\left(\frac{1}{112}\right)\)
\(\chi_{47040}(31,\cdot)\)	47040.dr	6	no	\(1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(-1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(-1\)	\(1\)
\(\chi_{47040}(37,\cdot)\)	47040.wd	336	no	\(-1\)	\(1\)	\(e\left(\frac{97}{336}\right)\)	\(e\left(\frac{37}{112}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{5}{48}\right)\)	\(e\left(\frac{97}{168}\right)\)	\(e\left(\frac{45}{112}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{233}{336}\right)\)	\(e\left(\frac{17}{56}\right)\)	\(e\left(\frac{71}{112}\right)\)
\(\chi_{47040}(41,\cdot)\)	47040.qk	56	no	\(1\)	\(1\)	\(e\left(\frac{9}{56}\right)\)	\(e\left(\frac{51}{56}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{9}{28}\right)\)	\(e\left(\frac{31}{56}\right)\)	\(-1\)	\(e\left(\frac{17}{56}\right)\)	\(e\left(\frac{3}{28}\right)\)	\(e\left(\frac{29}{56}\right)\)
\(\chi_{47040}(43,\cdot)\)	47040.tp	112	no	\(1\)	\(1\)	\(e\left(\frac{31}{112}\right)\)	\(e\left(\frac{17}{112}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{31}{56}\right)\)	\(e\left(\frac{1}{112}\right)\)	\(1\)	\(e\left(\frac{71}{112}\right)\)	\(e\left(\frac{29}{56}\right)\)	\(e\left(\frac{19}{112}\right)\)
\(\chi_{47040}(47,\cdot)\)	47040.rz	84	no	\(1\)	\(1\)	\(e\left(\frac{43}{84}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{61}{84}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{65}{84}\right)\)	\(e\left(\frac{11}{28}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{5}{7}\right)\)
\(\chi_{47040}(53,\cdot)\)	47040.wc	336	yes	\(1\)	\(1\)	\(e\left(\frac{197}{336}\right)\)	\(e\left(\frac{89}{112}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{1}{48}\right)\)	\(e\left(\frac{29}{168}\right)\)	\(e\left(\frac{81}{112}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{61}{336}\right)\)	\(e\left(\frac{25}{56}\right)\)	\(e\left(\frac{83}{112}\right)\)
\(\chi_{47040}(59,\cdot)\)	47040.vq	336	yes	\(-1\)	\(1\)	\(e\left(\frac{233}{336}\right)\)	\(e\left(\frac{73}{112}\right)\)	\(e\left(\frac{41}{84}\right)\)	\(e\left(\frac{37}{48}\right)\)	\(e\left(\frac{23}{168}\right)\)	\(e\left(\frac{85}{112}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{325}{336}\right)\)	\(e\left(\frac{1}{56}\right)\)	\(e\left(\frac{75}{112}\right)\)
\(\chi_{47040}(61,\cdot)\)	47040.vn	336	no	\(-1\)	\(1\)	\(e\left(\frac{139}{336}\right)\)	\(e\left(\frac{51}{112}\right)\)	\(e\left(\frac{67}{84}\right)\)	\(e\left(\frac{23}{48}\right)\)	\(e\left(\frac{97}{168}\right)\)	\(e\left(\frac{87}{112}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{23}{336}\right)\)	\(e\left(\frac{31}{56}\right)\)	\(e\left(\frac{1}{112}\right)\)
\(\chi_{47040}(67,\cdot)\)	47040.pd	48	no	\(1\)	\(1\)	\(e\left(\frac{5}{48}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{31}{48}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{13}{48}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{11}{16}\right)\)
\(\chi_{47040}(71,\cdot)\)	47040.pn	56	no	\(1\)	\(1\)	\(e\left(\frac{55}{56}\right)\)	\(e\left(\frac{13}{56}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{13}{28}\right)\)	\(e\left(\frac{37}{56}\right)\)	\(-1\)	\(e\left(\frac{51}{56}\right)\)	\(e\left(\frac{23}{28}\right)\)	\(e\left(\frac{3}{56}\right)\)
\(\chi_{47040}(73,\cdot)\)	47040.ug	168	no	\(1\)	\(1\)	\(e\left(\frac{19}{168}\right)\)	\(e\left(\frac{53}{56}\right)\)	\(e\left(\frac{23}{84}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{41}{42}\right)\)	\(e\left(\frac{27}{56}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{53}{168}\right)\)	\(e\left(\frac{13}{28}\right)\)	\(e\left(\frac{23}{56}\right)\)
\(\chi_{47040}(79,\cdot)\)	47040.gr	12	no	\(-1\)	\(1\)	\(e\left(\frac{1}{12}\right)\)	\(i\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(-i\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(-1\)	\(i\)
\(\chi_{47040}(83,\cdot)\)	47040.so	112	yes	\(1\)	\(1\)	\(e\left(\frac{85}{112}\right)\)	\(e\left(\frac{99}{112}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{29}{56}\right)\)	\(e\left(\frac{75}{112}\right)\)	\(-1\)	\(e\left(\frac{61}{112}\right)\)	\(e\left(\frac{47}{56}\right)\)	\(e\left(\frac{81}{112}\right)\)
\(\chi_{47040}(89,\cdot)\)	47040.ux	168	no	\(1\)	\(1\)	\(e\left(\frac{5}{168}\right)\)	\(e\left(\frac{25}{56}\right)\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{47}{84}\right)\)	\(e\left(\frac{41}{56}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{25}{168}\right)\)	\(e\left(\frac{13}{28}\right)\)	\(e\left(\frac{23}{56}\right)\)
\(\chi_{47040}(97,\cdot)\)	47040.bj	4	no	\(1\)	\(1\)	\(-1\)	\(-i\)	\(-i\)	\(-1\)	\(-i\)	\(1\)	\(-1\)	\(-i\)	\(-1\)	\(i\)
\(\chi_{47040}(101,\cdot)\)	47040.vl	336	no	\(1\)	\(1\)	\(e\left(\frac{89}{336}\right)\)	\(e\left(\frac{25}{112}\right)\)	\(e\left(\frac{71}{84}\right)\)	\(e\left(\frac{37}{48}\right)\)	\(e\left(\frac{47}{168}\right)\)	\(e\left(\frac{13}{112}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{277}{336}\right)\)	\(e\left(\frac{41}{56}\right)\)	\(e\left(\frac{51}{112}\right)\)
\(\chi_{47040}(103,\cdot)\)	47040.ub	168	no	\(-1\)	\(1\)	\(e\left(\frac{125}{168}\right)\)	\(e\left(\frac{51}{56}\right)\)	\(e\left(\frac{43}{84}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{31}{42}\right)\)	\(e\left(\frac{17}{56}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{163}{168}\right)\)	\(e\left(\frac{3}{28}\right)\)	\(e\left(\frac{29}{56}\right)\)
\(\chi_{47040}(107,\cdot)\)	47040.vb	336	yes	\(-1\)	\(1\)	\(e\left(\frac{325}{336}\right)\)	\(e\left(\frac{57}{112}\right)\)	\(e\left(\frac{29}{42}\right)\)	\(e\left(\frac{17}{48}\right)\)	\(e\left(\frac{157}{168}\right)\)	\(e\left(\frac{89}{112}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{29}{336}\right)\)	\(e\left(\frac{33}{56}\right)\)	\(e\left(\frac{11}{112}\right)\)
\(\chi_{47040}(109,\cdot)\)	47040.vu	336	no	\(1\)	\(1\)	\(e\left(\frac{95}{336}\right)\)	\(e\left(\frac{55}{112}\right)\)	\(e\left(\frac{47}{84}\right)\)	\(e\left(\frac{19}{48}\right)\)	\(e\left(\frac{137}{168}\right)\)	\(e\left(\frac{107}{112}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{307}{336}\right)\)	\(e\left(\frac{23}{56}\right)\)	\(e\left(\frac{101}{112}\right)\)
\(\chi_{47040}(113,\cdot)\)	47040.lp	28	no	\(1\)	\(1\)	\(e\left(\frac{9}{28}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{3}{28}\right)\)	\(i\)	\(e\left(\frac{11}{28}\right)\)	\(e\left(\frac{17}{28}\right)\)	\(1\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{11}{14}\right)\)
\(\chi_{47040}(121,\cdot)\)	47040.tt	168	no	\(1\)	\(1\)	\(e\left(\frac{53}{168}\right)\)	\(e\left(\frac{13}{56}\right)\)	\(e\left(\frac{5}{42}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{11}{84}\right)\)	\(e\left(\frac{9}{56}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{97}{168}\right)\)	\(e\left(\frac{9}{28}\right)\)	\(e\left(\frac{31}{56}\right)\)
\(\chi_{47040}(127,\cdot)\)	47040.mx	28	no	\(1\)	\(1\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{25}{28}\right)\)	\(e\left(\frac{27}{28}\right)\)	\(1\)	\(e\left(\frac{15}{28}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(-1\)	\(e\left(\frac{27}{28}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{23}{28}\right)\)
\(\chi_{47040}(131,\cdot)\)	47040.vv	336	no	\(-1\)	\(1\)	\(e\left(\frac{331}{336}\right)\)	\(e\left(\frac{3}{112}\right)\)	\(e\left(\frac{13}{84}\right)\)	\(e\left(\frac{47}{48}\right)\)	\(e\left(\frac{121}{168}\right)\)	\(e\left(\frac{15}{112}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{311}{336}\right)\)	\(e\left(\frac{43}{56}\right)\)	\(e\left(\frac{89}{112}\right)\)
\(\chi_{47040}(137,\cdot)\)	47040.uc	168	no	\(1\)	\(1\)	\(e\left(\frac{127}{168}\right)\)	\(e\left(\frac{5}{56}\right)\)	\(e\left(\frac{41}{84}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{11}{42}\right)\)	\(e\left(\frac{39}{56}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{89}{168}\right)\)	\(e\left(\frac{25}{28}\right)\)	\(e\left(\frac{27}{56}\right)\)
\(\chi_{47040}(139,\cdot)\)	47040.sx	112	no	\(1\)	\(1\)	\(e\left(\frac{39}{112}\right)\)	\(e\left(\frac{109}{112}\right)\)	\(e\left(\frac{5}{28}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{53}{56}\right)\)	\(e\left(\frac{97}{112}\right)\)	\(-1\)	\(e\left(\frac{83}{112}\right)\)	\(e\left(\frac{41}{56}\right)\)	\(e\left(\frac{23}{112}\right)\)

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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.