LMFDB - Group of Dirichlet characters of modulus 162240

Show commands: PariGP / SageMath

sage: H = DirichletGroup(162240)

pari: g = idealstar(,162240,2)

Character group

sage: G.order() pari: g.no
Order	=	39936
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{2}\times C_{4}\times C_{4}\times C_{624}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{162240}(45631,\cdot)$, $\chi_{162240}(70981,\cdot)$, $\chi_{162240}(108161,\cdot)$, $\chi_{162240}(64897,\cdot)$, $\chi_{162240}(93121,\cdot)$

First 32 of 39936 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	$-1$	$1$	$7$	$11$	$17$	$19$	$23$	$29$	$31$	$37$	$41$	$43$
$\chi_{162240}(1,\cdot)$	162240.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{162240}(7,\cdot)$	162240.bmj	312	no	$-1$	$1$	$e\left(\frac{61}{156}\right)$	$e\left(\frac{85}{312}\right)$	$e\left(\frac{139}{156}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{253}{312}\right)$	$e\left(\frac{47}{52}\right)$	$e\left(\frac{139}{312}\right)$	$e\left(\frac{2}{39}\right)$	$e\left(\frac{17}{312}\right)$
$\chi_{162240}(11,\cdot)$	162240.bov	624	no	$-1$	$1$	$e\left(\frac{85}{312}\right)$	$e\left(\frac{355}{624}\right)$	$e\left(\frac{101}{156}\right)$	$e\left(\frac{29}{48}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{217}{624}\right)$	$e\left(\frac{45}{52}\right)$	$e\left(\frac{319}{624}\right)$	$e\left(\frac{311}{312}\right)$	$e\left(\frac{71}{624}\right)$
$\chi_{162240}(17,\cdot)$	162240.bgj	156	no	$1$	$1$	$e\left(\frac{139}{156}\right)$	$e\left(\frac{101}{156}\right)$	$e\left(\frac{61}{156}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{107}{156}\right)$	$e\left(\frac{17}{26}\right)$	$e\left(\frac{25}{78}\right)$	$e\left(\frac{43}{78}\right)$	$e\left(\frac{53}{78}\right)$
$\chi_{162240}(19,\cdot)$	162240.ux	48	no	$1$	$1$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{29}{48}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{31}{48}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{23}{48}\right)$	$-i$	$e\left(\frac{17}{48}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{25}{48}\right)$
$\chi_{162240}(23,\cdot)$	162240.si	24	no	$-1$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{23}{24}\right)$	$1$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{19}{24}\right)$
$\chi_{162240}(29,\cdot)$	162240.bpd	624	yes	$-1$	$1$	$e\left(\frac{253}{312}\right)$	$e\left(\frac{217}{624}\right)$	$e\left(\frac{107}{156}\right)$	$e\left(\frac{23}{48}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{199}{624}\right)$	$e\left(\frac{23}{26}\right)$	$e\left(\frac{253}{624}\right)$	$e\left(\frac{287}{312}\right)$	$e\left(\frac{449}{624}\right)$
$\chi_{162240}(31,\cdot)$	162240.yy	52	no	$1$	$1$	$e\left(\frac{47}{52}\right)$	$e\left(\frac{45}{52}\right)$	$e\left(\frac{17}{26}\right)$	$-i$	$1$	$e\left(\frac{23}{26}\right)$	$e\left(\frac{17}{52}\right)$	$e\left(\frac{43}{52}\right)$	$e\left(\frac{23}{52}\right)$	$e\left(\frac{11}{26}\right)$
$\chi_{162240}(37,\cdot)$	162240.bns	624	no	$1$	$1$	$e\left(\frac{139}{312}\right)$	$e\left(\frac{319}{624}\right)$	$e\left(\frac{25}{78}\right)$	$e\left(\frac{17}{48}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{253}{624}\right)$	$e\left(\frac{43}{52}\right)$	$e\left(\frac{295}{624}\right)$	$e\left(\frac{47}{312}\right)$	$e\left(\frac{95}{624}\right)$
$\chi_{162240}(41,\cdot)$	162240.bmu	312	no	$1$	$1$	$e\left(\frac{2}{39}\right)$	$e\left(\frac{311}{312}\right)$	$e\left(\frac{43}{78}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{287}{312}\right)$	$e\left(\frac{23}{52}\right)$	$e\left(\frac{47}{312}\right)$	$e\left(\frac{5}{78}\right)$	$e\left(\frac{265}{312}\right)$
$\chi_{162240}(43,\cdot)$	162240.bnw	624	no	$1$	$1$	$e\left(\frac{17}{312}\right)$	$e\left(\frac{71}{624}\right)$	$e\left(\frac{53}{78}\right)$	$e\left(\frac{25}{48}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{449}{624}\right)$	$e\left(\frac{11}{26}\right)$	$e\left(\frac{95}{624}\right)$	$e\left(\frac{265}{312}\right)$	$e\left(\frac{451}{624}\right)$
$\chi_{162240}(47,\cdot)$	162240.xa	52	no	$1$	$1$	$e\left(\frac{6}{13}\right)$	$e\left(\frac{9}{26}\right)$	$e\left(\frac{37}{52}\right)$	$-1$	$-i$	$e\left(\frac{21}{52}\right)$	$e\left(\frac{51}{52}\right)$	$e\left(\frac{51}{52}\right)$	$e\left(\frac{17}{52}\right)$	$e\left(\frac{7}{26}\right)$
$\chi_{162240}(49,\cdot)$	162240.bej	156	no	$1$	$1$	$e\left(\frac{61}{78}\right)$	$e\left(\frac{85}{156}\right)$	$e\left(\frac{61}{78}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{97}{156}\right)$	$e\left(\frac{21}{26}\right)$	$e\left(\frac{139}{156}\right)$	$e\left(\frac{4}{39}\right)$	$e\left(\frac{17}{156}\right)$
$\chi_{162240}(53,\cdot)$	162240.biy	208	yes	$1$	$1$	$e\left(\frac{19}{104}\right)$	$e\left(\frac{61}{208}\right)$	$e\left(\frac{4}{13}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{43}{208}\right)$	$e\left(\frac{17}{26}\right)$	$e\left(\frac{149}{208}\right)$	$e\left(\frac{27}{104}\right)$	$e\left(\frac{33}{208}\right)$
$\chi_{162240}(59,\cdot)$	162240.boj	624	yes	$-1$	$1$	$e\left(\frac{197}{312}\right)$	$e\left(\frac{263}{624}\right)$	$e\left(\frac{79}{156}\right)$	$e\left(\frac{25}{48}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{101}{624}\right)$	$e\left(\frac{37}{52}\right)$	$e\left(\frac{587}{624}\right)$	$e\left(\frac{139}{312}\right)$	$e\left(\frac{115}{624}\right)$
$\chi_{162240}(61,\cdot)$	162240.bpa	624	no	$1$	$1$	$e\left(\frac{281}{312}\right)$	$e\left(\frac{233}{624}\right)$	$e\left(\frac{43}{156}\right)$	$e\left(\frac{31}{48}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{599}{624}\right)$	$e\left(\frac{9}{26}\right)$	$e\left(\frac{125}{624}\right)$	$e\left(\frac{283}{312}\right)$	$e\left(\frac{577}{624}\right)$
$\chi_{162240}(67,\cdot)$	162240.bpm	624	no	$-1$	$1$	$e\left(\frac{1}{312}\right)$	$e\left(\frac{541}{624}\right)$	$e\left(\frac{5}{39}\right)$	$e\left(\frac{35}{48}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{31}{624}\right)$	$e\left(\frac{51}{52}\right)$	$e\left(\frac{469}{624}\right)$	$e\left(\frac{245}{312}\right)$	$e\left(\frac{389}{624}\right)$
$\chi_{162240}(71,\cdot)$	162240.bmx	312	no	$-1$	$1$	$e\left(\frac{28}{39}\right)$	$e\left(\frac{181}{312}\right)$	$e\left(\frac{17}{78}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{157}{312}\right)$	$e\left(\frac{49}{52}\right)$	$e\left(\frac{73}{312}\right)$	$e\left(\frac{35}{39}\right)$	$e\left(\frac{239}{312}\right)$
$\chi_{162240}(73,\cdot)$	162240.bdc	104	no	$1$	$1$	$e\left(\frac{25}{52}\right)$	$e\left(\frac{57}{104}\right)$	$e\left(\frac{51}{52}\right)$	$e\left(\frac{3}{8}\right)$	$1$	$e\left(\frac{73}{104}\right)$	$e\left(\frac{45}{52}\right)$	$e\left(\frac{51}{104}\right)$	$e\left(\frac{1}{26}\right)$	$e\left(\frac{1}{104}\right)$
$\chi_{162240}(77,\cdot)$	162240.bio	208	yes	$1$	$1$	$e\left(\frac{69}{104}\right)$	$e\left(\frac{175}{208}\right)$	$e\left(\frac{7}{13}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{33}{208}\right)$	$e\left(\frac{10}{13}\right)$	$e\left(\frac{199}{208}\right)$	$e\left(\frac{5}{104}\right)$	$e\left(\frac{35}{208}\right)$
$\chi_{162240}(79,\cdot)$	162240.bag	52	no	$-1$	$1$	$e\left(\frac{25}{26}\right)$	$e\left(\frac{31}{52}\right)$	$e\left(\frac{25}{26}\right)$	$i$	$-1$	$e\left(\frac{47}{52}\right)$	$e\left(\frac{19}{26}\right)$	$e\left(\frac{51}{52}\right)$	$e\left(\frac{15}{26}\right)$	$e\left(\frac{1}{52}\right)$
$\chi_{162240}(83,\cdot)$	162240.bis	208	yes	$1$	$1$	$e\left(\frac{51}{104}\right)$	$e\left(\frac{187}{208}\right)$	$e\left(\frac{8}{13}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{73}{208}\right)$	$e\left(\frac{3}{52}\right)$	$e\left(\frac{51}{208}\right)$	$e\left(\frac{15}{104}\right)$	$e\left(\frac{131}{208}\right)$
$\chi_{162240}(89,\cdot)$	162240.rz	24	no	$1$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{5}{24}\right)$	$i$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{7}{24}\right)$
$\chi_{162240}(97,\cdot)$	162240.bet	156	no	$1$	$1$	$e\left(\frac{71}{78}\right)$	$e\left(\frac{113}{156}\right)$	$e\left(\frac{25}{156}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{14}{39}\right)$	$e\left(\frac{15}{52}\right)$	$e\left(\frac{8}{39}\right)$	$e\left(\frac{41}{156}\right)$	$e\left(\frac{85}{156}\right)$
$\chi_{162240}(101,\cdot)$	162240.boh	624	no	$-1$	$1$	$e\left(\frac{199}{312}\right)$	$e\left(\frac{331}{624}\right)$	$e\left(\frac{119}{156}\right)$	$e\left(\frac{5}{48}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{397}{624}\right)$	$e\left(\frac{12}{13}\right)$	$e\left(\frac{511}{624}\right)$	$e\left(\frac{161}{312}\right)$	$e\left(\frac{35}{624}\right)$
$\chi_{162240}(103,\cdot)$	162240.bbx	104	no	$1$	$1$	$e\left(\frac{5}{13}\right)$	$e\left(\frac{17}{104}\right)$	$e\left(\frac{33}{52}\right)$	$e\left(\frac{3}{8}\right)$	$-1$	$e\left(\frac{35}{104}\right)$	$e\left(\frac{9}{13}\right)$	$e\left(\frac{7}{104}\right)$	$e\left(\frac{25}{52}\right)$	$e\left(\frac{71}{104}\right)$
$\chi_{162240}(107,\cdot)$	162240.bnl	624	yes	$-1$	$1$	$e\left(\frac{145}{312}\right)$	$e\left(\frac{55}{624}\right)$	$e\left(\frac{7}{78}\right)$	$e\left(\frac{17}{48}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{361}{624}\right)$	$e\left(\frac{6}{13}\right)$	$e\left(\frac{223}{624}\right)$	$e\left(\frac{113}{312}\right)$	$e\left(\frac{11}{624}\right)$
$\chi_{162240}(109,\cdot)$	162240.bjn	208	no	$-1$	$1$	$e\left(\frac{101}{104}\right)$	$e\left(\frac{171}{208}\right)$	$e\left(\frac{5}{52}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{89}{208}\right)$	$e\left(\frac{9}{52}\right)$	$e\left(\frac{127}{208}\right)$	$e\left(\frac{19}{104}\right)$	$e\left(\frac{159}{208}\right)$
$\chi_{162240}(113,\cdot)$	162240.bgg	156	no	$1$	$1$	$e\left(\frac{31}{156}\right)$	$e\left(\frac{137}{156}\right)$	$e\left(\frac{31}{156}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{149}{156}\right)$	$e\left(\frac{4}{13}\right)$	$e\left(\frac{38}{39}\right)$	$e\left(\frac{17}{39}\right)$	$e\left(\frac{41}{78}\right)$
$\chi_{162240}(119,\cdot)$	162240.bng	312	no	$-1$	$1$	$e\left(\frac{11}{39}\right)$	$e\left(\frac{287}{312}\right)$	$e\left(\frac{11}{39}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{155}{312}\right)$	$e\left(\frac{29}{52}\right)$	$e\left(\frac{239}{312}\right)$	$e\left(\frac{47}{78}\right)$	$e\left(\frac{229}{312}\right)$
$\chi_{162240}(121,\cdot)$	162240.blu	312	no	$1$	$1$	$e\left(\frac{85}{156}\right)$	$e\left(\frac{43}{312}\right)$	$e\left(\frac{23}{78}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{217}{312}\right)$	$e\left(\frac{19}{26}\right)$	$e\left(\frac{7}{312}\right)$	$e\left(\frac{155}{156}\right)$	$e\left(\frac{71}{312}\right)$
$\chi_{162240}(127,\cdot)$	162240.bhg	156	no	$1$	$1$	$e\left(\frac{59}{156}\right)$	$e\left(\frac{7}{39}\right)$	$e\left(\frac{59}{156}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{77}{78}\right)$	$e\left(\frac{3}{13}\right)$	$e\left(\frac{49}{156}\right)$	$e\left(\frac{71}{78}\right)$	$e\left(\frac{107}{156}\right)$

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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	$162240$
Structure	\(C_{2}\times C_{2}\times C_{4}\times C_{4}\times C_{624}\)
Order	$39936$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(7\)	\(11\)	\(17\)	\(19\)	\(23\)	\(29\)	\(31\)	\(37\)	\(41\)	\(43\)
\(\chi_{162240}(1,\cdot)\)	162240.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{162240}(7,\cdot)\)	162240.bmj	312	no	\(-1\)	\(1\)	\(e\left(\frac{61}{156}\right)\)	\(e\left(\frac{85}{312}\right)\)	\(e\left(\frac{139}{156}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{253}{312}\right)\)	\(e\left(\frac{47}{52}\right)\)	\(e\left(\frac{139}{312}\right)\)	\(e\left(\frac{2}{39}\right)\)	\(e\left(\frac{17}{312}\right)\)
\(\chi_{162240}(11,\cdot)\)	162240.bov	624	no	\(-1\)	\(1\)	\(e\left(\frac{85}{312}\right)\)	\(e\left(\frac{355}{624}\right)\)	\(e\left(\frac{101}{156}\right)\)	\(e\left(\frac{29}{48}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{217}{624}\right)\)	\(e\left(\frac{45}{52}\right)\)	\(e\left(\frac{319}{624}\right)\)	\(e\left(\frac{311}{312}\right)\)	\(e\left(\frac{71}{624}\right)\)
\(\chi_{162240}(17,\cdot)\)	162240.bgj	156	no	\(1\)	\(1\)	\(e\left(\frac{139}{156}\right)\)	\(e\left(\frac{101}{156}\right)\)	\(e\left(\frac{61}{156}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{107}{156}\right)\)	\(e\left(\frac{17}{26}\right)\)	\(e\left(\frac{25}{78}\right)\)	\(e\left(\frac{43}{78}\right)\)	\(e\left(\frac{53}{78}\right)\)
\(\chi_{162240}(19,\cdot)\)	162240.ux	48	no	\(1\)	\(1\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{29}{48}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{31}{48}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{23}{48}\right)\)	\(-i\)	\(e\left(\frac{17}{48}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{25}{48}\right)\)
\(\chi_{162240}(23,\cdot)\)	162240.si	24	no	\(-1\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(1\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{19}{24}\right)\)
\(\chi_{162240}(29,\cdot)\)	162240.bpd	624	yes	\(-1\)	\(1\)	\(e\left(\frac{253}{312}\right)\)	\(e\left(\frac{217}{624}\right)\)	\(e\left(\frac{107}{156}\right)\)	\(e\left(\frac{23}{48}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{199}{624}\right)\)	\(e\left(\frac{23}{26}\right)\)	\(e\left(\frac{253}{624}\right)\)	\(e\left(\frac{287}{312}\right)\)	\(e\left(\frac{449}{624}\right)\)
\(\chi_{162240}(31,\cdot)\)	162240.yy	52	no	\(1\)	\(1\)	\(e\left(\frac{47}{52}\right)\)	\(e\left(\frac{45}{52}\right)\)	\(e\left(\frac{17}{26}\right)\)	\(-i\)	\(1\)	\(e\left(\frac{23}{26}\right)\)	\(e\left(\frac{17}{52}\right)\)	\(e\left(\frac{43}{52}\right)\)	\(e\left(\frac{23}{52}\right)\)	\(e\left(\frac{11}{26}\right)\)
\(\chi_{162240}(37,\cdot)\)	162240.bns	624	no	\(1\)	\(1\)	\(e\left(\frac{139}{312}\right)\)	\(e\left(\frac{319}{624}\right)\)	\(e\left(\frac{25}{78}\right)\)	\(e\left(\frac{17}{48}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{253}{624}\right)\)	\(e\left(\frac{43}{52}\right)\)	\(e\left(\frac{295}{624}\right)\)	\(e\left(\frac{47}{312}\right)\)	\(e\left(\frac{95}{624}\right)\)
\(\chi_{162240}(41,\cdot)\)	162240.bmu	312	no	\(1\)	\(1\)	\(e\left(\frac{2}{39}\right)\)	\(e\left(\frac{311}{312}\right)\)	\(e\left(\frac{43}{78}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{287}{312}\right)\)	\(e\left(\frac{23}{52}\right)\)	\(e\left(\frac{47}{312}\right)\)	\(e\left(\frac{5}{78}\right)\)	\(e\left(\frac{265}{312}\right)\)
\(\chi_{162240}(43,\cdot)\)	162240.bnw	624	no	\(1\)	\(1\)	\(e\left(\frac{17}{312}\right)\)	\(e\left(\frac{71}{624}\right)\)	\(e\left(\frac{53}{78}\right)\)	\(e\left(\frac{25}{48}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{449}{624}\right)\)	\(e\left(\frac{11}{26}\right)\)	\(e\left(\frac{95}{624}\right)\)	\(e\left(\frac{265}{312}\right)\)	\(e\left(\frac{451}{624}\right)\)
\(\chi_{162240}(47,\cdot)\)	162240.xa	52	no	\(1\)	\(1\)	\(e\left(\frac{6}{13}\right)\)	\(e\left(\frac{9}{26}\right)\)	\(e\left(\frac{37}{52}\right)\)	\(-1\)	\(-i\)	\(e\left(\frac{21}{52}\right)\)	\(e\left(\frac{51}{52}\right)\)	\(e\left(\frac{51}{52}\right)\)	\(e\left(\frac{17}{52}\right)\)	\(e\left(\frac{7}{26}\right)\)
\(\chi_{162240}(49,\cdot)\)	162240.bej	156	no	\(1\)	\(1\)	\(e\left(\frac{61}{78}\right)\)	\(e\left(\frac{85}{156}\right)\)	\(e\left(\frac{61}{78}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{97}{156}\right)\)	\(e\left(\frac{21}{26}\right)\)	\(e\left(\frac{139}{156}\right)\)	\(e\left(\frac{4}{39}\right)\)	\(e\left(\frac{17}{156}\right)\)
\(\chi_{162240}(53,\cdot)\)	162240.biy	208	yes	\(1\)	\(1\)	\(e\left(\frac{19}{104}\right)\)	\(e\left(\frac{61}{208}\right)\)	\(e\left(\frac{4}{13}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{43}{208}\right)\)	\(e\left(\frac{17}{26}\right)\)	\(e\left(\frac{149}{208}\right)\)	\(e\left(\frac{27}{104}\right)\)	\(e\left(\frac{33}{208}\right)\)
\(\chi_{162240}(59,\cdot)\)	162240.boj	624	yes	\(-1\)	\(1\)	\(e\left(\frac{197}{312}\right)\)	\(e\left(\frac{263}{624}\right)\)	\(e\left(\frac{79}{156}\right)\)	\(e\left(\frac{25}{48}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{101}{624}\right)\)	\(e\left(\frac{37}{52}\right)\)	\(e\left(\frac{587}{624}\right)\)	\(e\left(\frac{139}{312}\right)\)	\(e\left(\frac{115}{624}\right)\)
\(\chi_{162240}(61,\cdot)\)	162240.bpa	624	no	\(1\)	\(1\)	\(e\left(\frac{281}{312}\right)\)	\(e\left(\frac{233}{624}\right)\)	\(e\left(\frac{43}{156}\right)\)	\(e\left(\frac{31}{48}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{599}{624}\right)\)	\(e\left(\frac{9}{26}\right)\)	\(e\left(\frac{125}{624}\right)\)	\(e\left(\frac{283}{312}\right)\)	\(e\left(\frac{577}{624}\right)\)
\(\chi_{162240}(67,\cdot)\)	162240.bpm	624	no	\(-1\)	\(1\)	\(e\left(\frac{1}{312}\right)\)	\(e\left(\frac{541}{624}\right)\)	\(e\left(\frac{5}{39}\right)\)	\(e\left(\frac{35}{48}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{31}{624}\right)\)	\(e\left(\frac{51}{52}\right)\)	\(e\left(\frac{469}{624}\right)\)	\(e\left(\frac{245}{312}\right)\)	\(e\left(\frac{389}{624}\right)\)
\(\chi_{162240}(71,\cdot)\)	162240.bmx	312	no	\(-1\)	\(1\)	\(e\left(\frac{28}{39}\right)\)	\(e\left(\frac{181}{312}\right)\)	\(e\left(\frac{17}{78}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{157}{312}\right)\)	\(e\left(\frac{49}{52}\right)\)	\(e\left(\frac{73}{312}\right)\)	\(e\left(\frac{35}{39}\right)\)	\(e\left(\frac{239}{312}\right)\)
\(\chi_{162240}(73,\cdot)\)	162240.bdc	104	no	\(1\)	\(1\)	\(e\left(\frac{25}{52}\right)\)	\(e\left(\frac{57}{104}\right)\)	\(e\left(\frac{51}{52}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(1\)	\(e\left(\frac{73}{104}\right)\)	\(e\left(\frac{45}{52}\right)\)	\(e\left(\frac{51}{104}\right)\)	\(e\left(\frac{1}{26}\right)\)	\(e\left(\frac{1}{104}\right)\)
\(\chi_{162240}(77,\cdot)\)	162240.bio	208	yes	\(1\)	\(1\)	\(e\left(\frac{69}{104}\right)\)	\(e\left(\frac{175}{208}\right)\)	\(e\left(\frac{7}{13}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{33}{208}\right)\)	\(e\left(\frac{10}{13}\right)\)	\(e\left(\frac{199}{208}\right)\)	\(e\left(\frac{5}{104}\right)\)	\(e\left(\frac{35}{208}\right)\)
\(\chi_{162240}(79,\cdot)\)	162240.bag	52	no	\(-1\)	\(1\)	\(e\left(\frac{25}{26}\right)\)	\(e\left(\frac{31}{52}\right)\)	\(e\left(\frac{25}{26}\right)\)	\(i\)	\(-1\)	\(e\left(\frac{47}{52}\right)\)	\(e\left(\frac{19}{26}\right)\)	\(e\left(\frac{51}{52}\right)\)	\(e\left(\frac{15}{26}\right)\)	\(e\left(\frac{1}{52}\right)\)
\(\chi_{162240}(83,\cdot)\)	162240.bis	208	yes	\(1\)	\(1\)	\(e\left(\frac{51}{104}\right)\)	\(e\left(\frac{187}{208}\right)\)	\(e\left(\frac{8}{13}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{73}{208}\right)\)	\(e\left(\frac{3}{52}\right)\)	\(e\left(\frac{51}{208}\right)\)	\(e\left(\frac{15}{104}\right)\)	\(e\left(\frac{131}{208}\right)\)
\(\chi_{162240}(89,\cdot)\)	162240.rz	24	no	\(1\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(i\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{7}{24}\right)\)
\(\chi_{162240}(97,\cdot)\)	162240.bet	156	no	\(1\)	\(1\)	\(e\left(\frac{71}{78}\right)\)	\(e\left(\frac{113}{156}\right)\)	\(e\left(\frac{25}{156}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{14}{39}\right)\)	\(e\left(\frac{15}{52}\right)\)	\(e\left(\frac{8}{39}\right)\)	\(e\left(\frac{41}{156}\right)\)	\(e\left(\frac{85}{156}\right)\)
\(\chi_{162240}(101,\cdot)\)	162240.boh	624	no	\(-1\)	\(1\)	\(e\left(\frac{199}{312}\right)\)	\(e\left(\frac{331}{624}\right)\)	\(e\left(\frac{119}{156}\right)\)	\(e\left(\frac{5}{48}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{397}{624}\right)\)	\(e\left(\frac{12}{13}\right)\)	\(e\left(\frac{511}{624}\right)\)	\(e\left(\frac{161}{312}\right)\)	\(e\left(\frac{35}{624}\right)\)
\(\chi_{162240}(103,\cdot)\)	162240.bbx	104	no	\(1\)	\(1\)	\(e\left(\frac{5}{13}\right)\)	\(e\left(\frac{17}{104}\right)\)	\(e\left(\frac{33}{52}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(-1\)	\(e\left(\frac{35}{104}\right)\)	\(e\left(\frac{9}{13}\right)\)	\(e\left(\frac{7}{104}\right)\)	\(e\left(\frac{25}{52}\right)\)	\(e\left(\frac{71}{104}\right)\)
\(\chi_{162240}(107,\cdot)\)	162240.bnl	624	yes	\(-1\)	\(1\)	\(e\left(\frac{145}{312}\right)\)	\(e\left(\frac{55}{624}\right)\)	\(e\left(\frac{7}{78}\right)\)	\(e\left(\frac{17}{48}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{361}{624}\right)\)	\(e\left(\frac{6}{13}\right)\)	\(e\left(\frac{223}{624}\right)\)	\(e\left(\frac{113}{312}\right)\)	\(e\left(\frac{11}{624}\right)\)
\(\chi_{162240}(109,\cdot)\)	162240.bjn	208	no	\(-1\)	\(1\)	\(e\left(\frac{101}{104}\right)\)	\(e\left(\frac{171}{208}\right)\)	\(e\left(\frac{5}{52}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{89}{208}\right)\)	\(e\left(\frac{9}{52}\right)\)	\(e\left(\frac{127}{208}\right)\)	\(e\left(\frac{19}{104}\right)\)	\(e\left(\frac{159}{208}\right)\)
\(\chi_{162240}(113,\cdot)\)	162240.bgg	156	no	\(1\)	\(1\)	\(e\left(\frac{31}{156}\right)\)	\(e\left(\frac{137}{156}\right)\)	\(e\left(\frac{31}{156}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{149}{156}\right)\)	\(e\left(\frac{4}{13}\right)\)	\(e\left(\frac{38}{39}\right)\)	\(e\left(\frac{17}{39}\right)\)	\(e\left(\frac{41}{78}\right)\)
\(\chi_{162240}(119,\cdot)\)	162240.bng	312	no	\(-1\)	\(1\)	\(e\left(\frac{11}{39}\right)\)	\(e\left(\frac{287}{312}\right)\)	\(e\left(\frac{11}{39}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{155}{312}\right)\)	\(e\left(\frac{29}{52}\right)\)	\(e\left(\frac{239}{312}\right)\)	\(e\left(\frac{47}{78}\right)\)	\(e\left(\frac{229}{312}\right)\)
\(\chi_{162240}(121,\cdot)\)	162240.blu	312	no	\(1\)	\(1\)	\(e\left(\frac{85}{156}\right)\)	\(e\left(\frac{43}{312}\right)\)	\(e\left(\frac{23}{78}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{217}{312}\right)\)	\(e\left(\frac{19}{26}\right)\)	\(e\left(\frac{7}{312}\right)\)	\(e\left(\frac{155}{156}\right)\)	\(e\left(\frac{71}{312}\right)\)
\(\chi_{162240}(127,\cdot)\)	162240.bhg	156	no	\(1\)	\(1\)	\(e\left(\frac{59}{156}\right)\)	\(e\left(\frac{7}{39}\right)\)	\(e\left(\frac{59}{156}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{77}{78}\right)\)	\(e\left(\frac{3}{13}\right)\)	\(e\left(\frac{49}{156}\right)\)	\(e\left(\frac{71}{78}\right)\)	\(e\left(\frac{107}{156}\right)\)

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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.