LMFDB - Group of Dirichlet characters of modulus 305760

sage:H = DirichletGroup(305760)

pari:g = idealstar(,305760,2)

Character group

sage:G.order() pari:g.no
Order	=	64512
sage:H.invariants() pari:g.cyc
Structure	=	$C_{2}\times C_{2}\times C_{2}\times C_{4}\times C_{12}\times C_{168}$
sage:H.gens() pari:g.gen
Generators	=	$\chi_{305760}(95551,\cdot)$, $\chi_{305760}(114661,\cdot)$, $\chi_{305760}(101921,\cdot)$, $\chi_{305760}(183457,\cdot)$, $\chi_{305760}(18721,\cdot)$, $\chi_{305760}(211681,\cdot)$

First 32 of 64512 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	$-1$	$1$	$11$	$17$	$19$	$23$	$29$	$31$	$37$	$41$	$43$	$47$
$\chi_{305760}(1,\cdot)$	305760.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{305760}(11,\cdot)$	305760.fmx	168	no	$-1$	$1$	$e\left(\frac{17}{56}\right)$	$e\left(\frac{41}{42}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{65}{84}\right)$	$e\left(\frac{143}{168}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{31}{168}\right)$	$e\left(\frac{5}{42}\right)$	$e\left(\frac{85}{168}\right)$	$e\left(\frac{1}{84}\right)$
$\chi_{305760}(17,\cdot)$	305760.eew	84	no	$-1$	$1$	$e\left(\frac{41}{42}\right)$	$e\left(\frac{27}{28}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{37}{42}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{27}{28}\right)$	$e\left(\frac{25}{42}\right)$	$e\left(\frac{13}{84}\right)$	$e\left(\frac{19}{84}\right)$
$\chi_{305760}(19,\cdot)$	305760.cof	24	no	$-1$	$1$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{11}{12}\right)$
$\chi_{305760}(23,\cdot)$	305760.erg	84	no	$-1$	$1$	$e\left(\frac{65}{84}\right)$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{73}{84}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{17}{42}\right)$	$e\left(\frac{25}{42}\right)$	$e\left(\frac{65}{84}\right)$
$\chi_{305760}(29,\cdot)$	305760.fpd	168	yes	$-1$	$1$	$e\left(\frac{143}{168}\right)$	$e\left(\frac{37}{42}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{73}{84}\right)$	$e\left(\frac{113}{168}\right)$	$1$	$e\left(\frac{155}{168}\right)$	$e\left(\frac{43}{84}\right)$	$e\left(\frac{103}{168}\right)$	$e\left(\frac{9}{14}\right)$
$\chi_{305760}(31,\cdot)$	305760.bkg	12	no	$-1$	$1$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{3}\right)$	$1$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{7}{12}\right)$	$i$	$1$	$e\left(\frac{7}{12}\right)$
$\chi_{305760}(37,\cdot)$	305760.fpw	168	no	$1$	$1$	$e\left(\frac{31}{168}\right)$	$e\left(\frac{27}{28}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{155}{168}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{47}{56}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{19}{168}\right)$	$e\left(\frac{13}{42}\right)$
$\chi_{305760}(41,\cdot)$	305760.eel	84	no	$-1$	$1$	$e\left(\frac{5}{42}\right)$	$e\left(\frac{25}{42}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{17}{42}\right)$	$e\left(\frac{43}{84}\right)$	$i$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{37}{84}\right)$	$e\left(\frac{5}{84}\right)$	$e\left(\frac{15}{28}\right)$
$\chi_{305760}(43,\cdot)$	305760.fua	168	no	$1$	$1$	$e\left(\frac{85}{168}\right)$	$e\left(\frac{13}{84}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{25}{42}\right)$	$e\left(\frac{103}{168}\right)$	$1$	$e\left(\frac{19}{168}\right)$	$e\left(\frac{5}{84}\right)$	$e\left(\frac{11}{168}\right)$	$e\left(\frac{27}{28}\right)$
$\chi_{305760}(47,\cdot)$	305760.exn	84	no	$-1$	$1$	$e\left(\frac{1}{84}\right)$	$e\left(\frac{19}{84}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{65}{84}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{27}{28}\right)$	$e\left(\frac{25}{42}\right)$
$\chi_{305760}(53,\cdot)$	305760.frd	168	no	$1$	$1$	$e\left(\frac{25}{168}\right)$	$e\left(\frac{59}{84}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{23}{42}\right)$	$e\left(\frac{9}{56}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{167}{168}\right)$	$e\left(\frac{23}{28}\right)$	$e\left(\frac{45}{56}\right)$	$e\left(\frac{79}{84}\right)$
$\chi_{305760}(59,\cdot)$	305760.gdk	168	yes	$1$	$1$	$e\left(\frac{71}{168}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{5}{28}\right)$	$e\left(\frac{19}{168}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{53}{56}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{53}{168}\right)$	$e\left(\frac{25}{84}\right)$
$\chi_{305760}(61,\cdot)$	305760.gck	168	no	$-1$	$1$	$e\left(\frac{1}{56}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{73}{84}\right)$	$e\left(\frac{85}{168}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{71}{168}\right)$	$e\left(\frac{71}{84}\right)$	$e\left(\frac{131}{168}\right)$	$e\left(\frac{17}{21}\right)$
$\chi_{305760}(67,\cdot)$	305760.csr	24	no	$-1$	$1$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{305760}(71,\cdot)$	305760.eim	84	no	$-1$	$1$	$e\left(\frac{1}{42}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{17}{84}\right)$	$i$	$e\left(\frac{19}{42}\right)$	$e\left(\frac{83}{84}\right)$	$e\left(\frac{1}{84}\right)$	$e\left(\frac{3}{28}\right)$
$\chi_{305760}(73,\cdot)$	305760.ehu	84	no	$-1$	$1$	$e\left(\frac{31}{42}\right)$	$e\left(\frac{23}{84}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{61}{84}\right)$	$e\left(\frac{17}{28}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{37}{84}\right)$	$e\left(\frac{27}{28}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{19}{21}\right)$
$\chi_{305760}(79,\cdot)$	305760.oh	6	no	$-1$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$	$-1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$	$1$	$-1$	$e\left(\frac{2}{3}\right)$
$\chi_{305760}(83,\cdot)$	305760.dyo	56	yes	$-1$	$1$	$e\left(\frac{11}{56}\right)$	$e\left(\frac{17}{28}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{27}{56}\right)$	$-i$	$e\left(\frac{41}{56}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{51}{56}\right)$	$e\left(\frac{4}{7}\right)$
$\chi_{305760}(89,\cdot)$	305760.edw	84	no	$-1$	$1$	$e\left(\frac{31}{42}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{37}{84}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{67}{84}\right)$	$e\left(\frac{17}{84}\right)$	$e\left(\frac{41}{84}\right)$
$\chi_{305760}(97,\cdot)$	305760.bvb	12	no	$-1$	$1$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{6}\right)$	$i$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{7}{12}\right)$	$1$
$\chi_{305760}(101,\cdot)$	305760.fmj	168	no	$1$	$1$	$e\left(\frac{51}{56}\right)$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{41}{84}\right)$	$e\left(\frac{107}{168}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{121}{168}\right)$	$e\left(\frac{37}{84}\right)$	$e\left(\frac{73}{168}\right)$	$e\left(\frac{13}{21}\right)$
$\chi_{305760}(103,\cdot)$	305760.etx	84	no	$-1$	$1$	$e\left(\frac{73}{84}\right)$	$e\left(\frac{1}{84}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{41}{84}\right)$	$e\left(\frac{19}{28}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{25}{42}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{17}{84}\right)$
$\chi_{305760}(107,\cdot)$	305760.fyw	168	yes	$-1$	$1$	$e\left(\frac{61}{168}\right)$	$e\left(\frac{3}{28}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{11}{168}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{41}{56}\right)$	$e\left(\frac{25}{84}\right)$	$e\left(\frac{55}{168}\right)$	$e\left(\frac{83}{84}\right)$
$\chi_{305760}(109,\cdot)$	305760.fms	168	no	$-1$	$1$	$e\left(\frac{121}{168}\right)$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{37}{84}\right)$	$e\left(\frac{43}{56}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{17}{168}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{5}{56}\right)$	$e\left(\frac{1}{84}\right)$
$\chi_{305760}(113,\cdot)$	305760.feg	84	no	$1$	$1$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{37}{84}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{47}{84}\right)$	$e\left(\frac{1}{42}\right)$	$1$	$e\left(\frac{65}{84}\right)$	$e\left(\frac{37}{42}\right)$	$e\left(\frac{31}{84}\right)$	$e\left(\frac{23}{28}\right)$
$\chi_{305760}(121,\cdot)$	305760.ezc	84	no	$1$	$1$	$e\left(\frac{17}{28}\right)$	$e\left(\frac{20}{21}\right)$	$i$	$e\left(\frac{23}{42}\right)$	$e\left(\frac{59}{84}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{31}{84}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{1}{84}\right)$	$e\left(\frac{1}{42}\right)$
$\chi_{305760}(127,\cdot)$	305760.fgc	84	no	$1$	$1$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{53}{84}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{73}{84}\right)$	$e\left(\frac{23}{42}\right)$	$1$	$e\left(\frac{67}{84}\right)$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{41}{84}\right)$	$e\left(\frac{11}{28}\right)$
$\chi_{305760}(131,\cdot)$	305760.fme	168	no	$-1$	$1$	$e\left(\frac{155}{168}\right)$	$e\left(\frac{17}{42}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{29}{84}\right)$	$e\left(\frac{11}{56}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{103}{168}\right)$	$e\left(\frac{11}{28}\right)$	$e\left(\frac{13}{56}\right)$	$e\left(\frac{8}{21}\right)$
$\chi_{305760}(137,\cdot)$	305760.fex	84	no	$-1$	$1$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{23}{28}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{19}{28}\right)$	$e\left(\frac{41}{84}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{9}{28}\right)$	$e\left(\frac{5}{84}\right)$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{23}{42}\right)$
$\chi_{305760}(139,\cdot)$	305760.fpa	168	no	$1$	$1$	$e\left(\frac{97}{168}\right)$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{83}{84}\right)$	$e\left(\frac{163}{168}\right)$	$1$	$e\left(\frac{37}{168}\right)$	$e\left(\frac{65}{84}\right)$	$e\left(\frac{101}{168}\right)$	$e\left(\frac{2}{7}\right)$
$\chi_{305760}(149,\cdot)$	305760.gbb	168	yes	$1$	$1$	$e\left(\frac{17}{56}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{37}{84}\right)$	$e\left(\frac{31}{168}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{143}{168}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{29}{168}\right)$	$e\left(\frac{71}{84}\right)$

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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 $\F_{q}$
Belyi maps

Modulus	$305760$
Structure	\(C_{2}\times C_{2}\times C_{2}\times C_{4}\times C_{12}\times C_{168}\)
Order	$64512$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(11\)	\(17\)	\(19\)	\(23\)	\(29\)	\(31\)	\(37\)	\(41\)	\(43\)	\(47\)
\(\chi_{305760}(1,\cdot)\)	305760.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{305760}(11,\cdot)\)	305760.fmx	168	no	\(-1\)	\(1\)	\(e\left(\frac{17}{56}\right)\)	\(e\left(\frac{41}{42}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{65}{84}\right)\)	\(e\left(\frac{143}{168}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{31}{168}\right)\)	\(e\left(\frac{5}{42}\right)\)	\(e\left(\frac{85}{168}\right)\)	\(e\left(\frac{1}{84}\right)\)
\(\chi_{305760}(17,\cdot)\)	305760.eew	84	no	\(-1\)	\(1\)	\(e\left(\frac{41}{42}\right)\)	\(e\left(\frac{27}{28}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{15}{28}\right)\)	\(e\left(\frac{37}{42}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{27}{28}\right)\)	\(e\left(\frac{25}{42}\right)\)	\(e\left(\frac{13}{84}\right)\)	\(e\left(\frac{19}{84}\right)\)
\(\chi_{305760}(19,\cdot)\)	305760.cof	24	no	\(-1\)	\(1\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{11}{12}\right)\)
\(\chi_{305760}(23,\cdot)\)	305760.erg	84	no	\(-1\)	\(1\)	\(e\left(\frac{65}{84}\right)\)	\(e\left(\frac{15}{28}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{13}{28}\right)\)	\(e\left(\frac{73}{84}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{17}{42}\right)\)	\(e\left(\frac{25}{42}\right)\)	\(e\left(\frac{65}{84}\right)\)
\(\chi_{305760}(29,\cdot)\)	305760.fpd	168	yes	\(-1\)	\(1\)	\(e\left(\frac{143}{168}\right)\)	\(e\left(\frac{37}{42}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{73}{84}\right)\)	\(e\left(\frac{113}{168}\right)\)	\(1\)	\(e\left(\frac{155}{168}\right)\)	\(e\left(\frac{43}{84}\right)\)	\(e\left(\frac{103}{168}\right)\)	\(e\left(\frac{9}{14}\right)\)
\(\chi_{305760}(31,\cdot)\)	305760.bkg	12	no	\(-1\)	\(1\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(1\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(i\)	\(1\)	\(e\left(\frac{7}{12}\right)\)
\(\chi_{305760}(37,\cdot)\)	305760.fpw	168	no	\(1\)	\(1\)	\(e\left(\frac{31}{168}\right)\)	\(e\left(\frac{27}{28}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{155}{168}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{47}{56}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{19}{168}\right)\)	\(e\left(\frac{13}{42}\right)\)
\(\chi_{305760}(41,\cdot)\)	305760.eel	84	no	\(-1\)	\(1\)	\(e\left(\frac{5}{42}\right)\)	\(e\left(\frac{25}{42}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{17}{42}\right)\)	\(e\left(\frac{43}{84}\right)\)	\(i\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{37}{84}\right)\)	\(e\left(\frac{5}{84}\right)\)	\(e\left(\frac{15}{28}\right)\)
\(\chi_{305760}(43,\cdot)\)	305760.fua	168	no	\(1\)	\(1\)	\(e\left(\frac{85}{168}\right)\)	\(e\left(\frac{13}{84}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{25}{42}\right)\)	\(e\left(\frac{103}{168}\right)\)	\(1\)	\(e\left(\frac{19}{168}\right)\)	\(e\left(\frac{5}{84}\right)\)	\(e\left(\frac{11}{168}\right)\)	\(e\left(\frac{27}{28}\right)\)
\(\chi_{305760}(47,\cdot)\)	305760.exn	84	no	\(-1\)	\(1\)	\(e\left(\frac{1}{84}\right)\)	\(e\left(\frac{19}{84}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{65}{84}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{13}{42}\right)\)	\(e\left(\frac{15}{28}\right)\)	\(e\left(\frac{27}{28}\right)\)	\(e\left(\frac{25}{42}\right)\)
\(\chi_{305760}(53,\cdot)\)	305760.frd	168	no	\(1\)	\(1\)	\(e\left(\frac{25}{168}\right)\)	\(e\left(\frac{59}{84}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{23}{42}\right)\)	\(e\left(\frac{9}{56}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{167}{168}\right)\)	\(e\left(\frac{23}{28}\right)\)	\(e\left(\frac{45}{56}\right)\)	\(e\left(\frac{79}{84}\right)\)
\(\chi_{305760}(59,\cdot)\)	305760.gdk	168	yes	\(1\)	\(1\)	\(e\left(\frac{71}{168}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{5}{28}\right)\)	\(e\left(\frac{19}{168}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{53}{56}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{53}{168}\right)\)	\(e\left(\frac{25}{84}\right)\)
\(\chi_{305760}(61,\cdot)\)	305760.gck	168	no	\(-1\)	\(1\)	\(e\left(\frac{1}{56}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{73}{84}\right)\)	\(e\left(\frac{85}{168}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{71}{168}\right)\)	\(e\left(\frac{71}{84}\right)\)	\(e\left(\frac{131}{168}\right)\)	\(e\left(\frac{17}{21}\right)\)
\(\chi_{305760}(67,\cdot)\)	305760.csr	24	no	\(-1\)	\(1\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{305760}(71,\cdot)\)	305760.eim	84	no	\(-1\)	\(1\)	\(e\left(\frac{1}{42}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{17}{84}\right)\)	\(i\)	\(e\left(\frac{19}{42}\right)\)	\(e\left(\frac{83}{84}\right)\)	\(e\left(\frac{1}{84}\right)\)	\(e\left(\frac{3}{28}\right)\)
\(\chi_{305760}(73,\cdot)\)	305760.ehu	84	no	\(-1\)	\(1\)	\(e\left(\frac{31}{42}\right)\)	\(e\left(\frac{23}{84}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{61}{84}\right)\)	\(e\left(\frac{17}{28}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{37}{84}\right)\)	\(e\left(\frac{27}{28}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{19}{21}\right)\)
\(\chi_{305760}(79,\cdot)\)	305760.oh	6	no	\(-1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(-1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(1\)	\(-1\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{305760}(83,\cdot)\)	305760.dyo	56	yes	\(-1\)	\(1\)	\(e\left(\frac{11}{56}\right)\)	\(e\left(\frac{17}{28}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{27}{56}\right)\)	\(-i\)	\(e\left(\frac{41}{56}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{51}{56}\right)\)	\(e\left(\frac{4}{7}\right)\)
\(\chi_{305760}(89,\cdot)\)	305760.edw	84	no	\(-1\)	\(1\)	\(e\left(\frac{31}{42}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{37}{84}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{67}{84}\right)\)	\(e\left(\frac{17}{84}\right)\)	\(e\left(\frac{41}{84}\right)\)
\(\chi_{305760}(97,\cdot)\)	305760.bvb	12	no	\(-1\)	\(1\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(i\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(1\)
\(\chi_{305760}(101,\cdot)\)	305760.fmj	168	no	\(1\)	\(1\)	\(e\left(\frac{51}{56}\right)\)	\(e\left(\frac{11}{42}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{41}{84}\right)\)	\(e\left(\frac{107}{168}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{121}{168}\right)\)	\(e\left(\frac{37}{84}\right)\)	\(e\left(\frac{73}{168}\right)\)	\(e\left(\frac{13}{21}\right)\)
\(\chi_{305760}(103,\cdot)\)	305760.etx	84	no	\(-1\)	\(1\)	\(e\left(\frac{73}{84}\right)\)	\(e\left(\frac{1}{84}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{41}{84}\right)\)	\(e\left(\frac{19}{28}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{25}{42}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{17}{84}\right)\)
\(\chi_{305760}(107,\cdot)\)	305760.fyw	168	yes	\(-1\)	\(1\)	\(e\left(\frac{61}{168}\right)\)	\(e\left(\frac{3}{28}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{11}{168}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{41}{56}\right)\)	\(e\left(\frac{25}{84}\right)\)	\(e\left(\frac{55}{168}\right)\)	\(e\left(\frac{83}{84}\right)\)
\(\chi_{305760}(109,\cdot)\)	305760.fms	168	no	\(-1\)	\(1\)	\(e\left(\frac{121}{168}\right)\)	\(e\left(\frac{13}{42}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{37}{84}\right)\)	\(e\left(\frac{43}{56}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{17}{168}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{5}{56}\right)\)	\(e\left(\frac{1}{84}\right)\)
\(\chi_{305760}(113,\cdot)\)	305760.feg	84	no	\(1\)	\(1\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{37}{84}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{47}{84}\right)\)	\(e\left(\frac{1}{42}\right)\)	\(1\)	\(e\left(\frac{65}{84}\right)\)	\(e\left(\frac{37}{42}\right)\)	\(e\left(\frac{31}{84}\right)\)	\(e\left(\frac{23}{28}\right)\)
\(\chi_{305760}(121,\cdot)\)	305760.ezc	84	no	\(1\)	\(1\)	\(e\left(\frac{17}{28}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(i\)	\(e\left(\frac{23}{42}\right)\)	\(e\left(\frac{59}{84}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{31}{84}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{1}{84}\right)\)	\(e\left(\frac{1}{42}\right)\)
\(\chi_{305760}(127,\cdot)\)	305760.fgc	84	no	\(1\)	\(1\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{53}{84}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{73}{84}\right)\)	\(e\left(\frac{23}{42}\right)\)	\(1\)	\(e\left(\frac{67}{84}\right)\)	\(e\left(\frac{11}{42}\right)\)	\(e\left(\frac{41}{84}\right)\)	\(e\left(\frac{11}{28}\right)\)
\(\chi_{305760}(131,\cdot)\)	305760.fme	168	no	\(-1\)	\(1\)	\(e\left(\frac{155}{168}\right)\)	\(e\left(\frac{17}{42}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{29}{84}\right)\)	\(e\left(\frac{11}{56}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{103}{168}\right)\)	\(e\left(\frac{11}{28}\right)\)	\(e\left(\frac{13}{56}\right)\)	\(e\left(\frac{8}{21}\right)\)
\(\chi_{305760}(137,\cdot)\)	305760.fex	84	no	\(-1\)	\(1\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{23}{28}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{19}{28}\right)\)	\(e\left(\frac{41}{84}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{9}{28}\right)\)	\(e\left(\frac{5}{84}\right)\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{23}{42}\right)\)
\(\chi_{305760}(139,\cdot)\)	305760.fpa	168	no	\(1\)	\(1\)	\(e\left(\frac{97}{168}\right)\)	\(e\left(\frac{11}{42}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{83}{84}\right)\)	\(e\left(\frac{163}{168}\right)\)	\(1\)	\(e\left(\frac{37}{168}\right)\)	\(e\left(\frac{65}{84}\right)\)	\(e\left(\frac{101}{168}\right)\)	\(e\left(\frac{2}{7}\right)\)
\(\chi_{305760}(149,\cdot)\)	305760.gbb	168	yes	\(1\)	\(1\)	\(e\left(\frac{17}{56}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{37}{84}\right)\)	\(e\left(\frac{31}{168}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{143}{168}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{29}{168}\right)\)	\(e\left(\frac{71}{84}\right)\)

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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.