LMFDB - Group of Dirichlet characters of modulus 283920

Show commands: PariGP / SageMath

sage: H = DirichletGroup(283920)

pari: g = idealstar(,283920,2)

Character group

sage: G.order() pari: g.no
Order	=	59904
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{2}\times C_{2}\times C_{4}\times C_{12}\times C_{156}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{283920}(248431,\cdot)$, $\chi_{283920}(70981,\cdot)$, $\chi_{283920}(189281,\cdot)$, $\chi_{283920}(227137,\cdot)$, $\chi_{283920}(40561,\cdot)$, $\chi_{283920}(255361,\cdot)$

First 32 of 59904 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	$-1$	$1$	$11$	$17$	$19$	$23$	$29$	$31$	$37$	$41$	$43$	$47$
$\chi_{283920}(1,\cdot)$	283920.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{283920}(11,\cdot)$	283920.czx	156	no	$-1$	$1$	$e\left(\frac{12}{13}\right)$	$e\left(\frac{22}{39}\right)$	$-1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{103}{156}\right)$	$e\left(\frac{5}{156}\right)$	$e\left(\frac{11}{39}\right)$	$e\left(\frac{19}{156}\right)$	$e\left(\frac{47}{156}\right)$	$e\left(\frac{145}{156}\right)$
$\chi_{283920}(17,\cdot)$	283920.eds	156	no	$-1$	$1$	$e\left(\frac{22}{39}\right)$	$e\left(\frac{29}{52}\right)$	$e\left(\frac{1}{6}\right)$	$i$	$e\left(\frac{17}{39}\right)$	$e\left(\frac{32}{39}\right)$	$e\left(\frac{47}{52}\right)$	$e\left(\frac{43}{78}\right)$	$e\left(\frac{145}{156}\right)$	$e\left(\frac{85}{156}\right)$
$\chi_{283920}(19,\cdot)$	283920.wq	12	no	$-1$	$1$	$-1$	$e\left(\frac{1}{6}\right)$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{5}{12}\right)$
$\chi_{283920}(23,\cdot)$	283920.ze	12	no	$-1$	$1$	$e\left(\frac{2}{3}\right)$	$i$	$e\left(\frac{1}{3}\right)$	$i$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{3}\right)$	$-i$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{11}{12}\right)$
$\chi_{283920}(29,\cdot)$	283920.dww	156	no	$-1$	$1$	$e\left(\frac{103}{156}\right)$	$e\left(\frac{17}{39}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{156}\right)$	$e\left(\frac{5}{13}\right)$	$e\left(\frac{151}{156}\right)$	$e\left(\frac{31}{39}\right)$	$e\left(\frac{83}{156}\right)$	$e\left(\frac{2}{13}\right)$
$\chi_{283920}(31,\cdot)$	283920.duo	156	no	$-1$	$1$	$e\left(\frac{5}{156}\right)$	$e\left(\frac{32}{39}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{13}\right)$	$e\left(\frac{77}{156}\right)$	$e\left(\frac{103}{156}\right)$	$e\left(\frac{49}{52}\right)$	$e\left(\frac{12}{13}\right)$	$e\left(\frac{127}{156}\right)$
$\chi_{283920}(37,\cdot)$	283920.ecz	156	no	$1$	$1$	$e\left(\frac{11}{39}\right)$	$e\left(\frac{47}{52}\right)$	$e\left(\frac{5}{6}\right)$	$-i$	$e\left(\frac{151}{156}\right)$	$e\left(\frac{103}{156}\right)$	$e\left(\frac{17}{52}\right)$	$e\left(\frac{121}{156}\right)$	$e\left(\frac{7}{78}\right)$	$e\left(\frac{35}{39}\right)$
$\chi_{283920}(41,\cdot)$	283920.dii	156	no	$-1$	$1$	$e\left(\frac{19}{156}\right)$	$e\left(\frac{43}{78}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{31}{39}\right)$	$e\left(\frac{49}{52}\right)$	$e\left(\frac{121}{156}\right)$	$e\left(\frac{49}{156}\right)$	$e\left(\frac{38}{39}\right)$	$e\left(\frac{17}{52}\right)$
$\chi_{283920}(43,\cdot)$	283920.dni	156	no	$1$	$1$	$e\left(\frac{47}{156}\right)$	$e\left(\frac{145}{156}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{83}{156}\right)$	$e\left(\frac{12}{13}\right)$	$e\left(\frac{7}{78}\right)$	$e\left(\frac{38}{39}\right)$	$e\left(\frac{16}{39}\right)$	$e\left(\frac{27}{52}\right)$
$\chi_{283920}(47,\cdot)$	283920.dkz	156	no	$-1$	$1$	$e\left(\frac{145}{156}\right)$	$e\left(\frac{85}{156}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{2}{13}\right)$	$e\left(\frac{127}{156}\right)$	$e\left(\frac{35}{39}\right)$	$e\left(\frac{17}{52}\right)$	$e\left(\frac{27}{52}\right)$	$e\left(\frac{67}{78}\right)$
$\chi_{283920}(53,\cdot)$	283920.dqo	156	yes	$1$	$1$	$e\left(\frac{101}{156}\right)$	$e\left(\frac{35}{156}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{27}{52}\right)$	$e\left(\frac{32}{39}\right)$	$e\left(\frac{19}{39}\right)$	$e\left(\frac{5}{13}\right)$	$e\left(\frac{9}{26}\right)$	$e\left(\frac{7}{156}\right)$
$\chi_{283920}(59,\cdot)$	283920.dzl	156	yes	$1$	$1$	$e\left(\frac{1}{39}\right)$	$e\left(\frac{12}{13}\right)$	$e\left(\frac{2}{3}\right)$	$-1$	$e\left(\frac{35}{156}\right)$	$e\left(\frac{59}{156}\right)$	$e\left(\frac{25}{26}\right)$	$e\left(\frac{89}{156}\right)$	$e\left(\frac{97}{156}\right)$	$e\left(\frac{73}{156}\right)$
$\chi_{283920}(61,\cdot)$	283920.djo	156	no	$-1$	$1$	$e\left(\frac{27}{52}\right)$	$e\left(\frac{67}{78}\right)$	$-i$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{23}{156}\right)$	$e\left(\frac{53}{78}\right)$	$e\left(\frac{145}{156}\right)$	$e\left(\frac{11}{39}\right)$	$e\left(\frac{37}{156}\right)$	$e\left(\frac{55}{78}\right)$
$\chi_{283920}(67,\cdot)$	283920.egd	156	no	$-1$	$1$	$e\left(\frac{9}{26}\right)$	$e\left(\frac{85}{156}\right)$	$1$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{37}{156}\right)$	$e\left(\frac{23}{156}\right)$	$e\left(\frac{23}{156}\right)$	$e\left(\frac{103}{156}\right)$	$e\left(\frac{73}{78}\right)$	$e\left(\frac{1}{39}\right)$
$\chi_{283920}(71,\cdot)$	283920.dxt	156	no	$-1$	$1$	$e\left(\frac{149}{156}\right)$	$e\left(\frac{28}{39}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{39}\right)$	$e\left(\frac{49}{52}\right)$	$e\left(\frac{17}{156}\right)$	$e\left(\frac{23}{156}\right)$	$e\left(\frac{11}{78}\right)$	$e\left(\frac{17}{52}\right)$
$\chi_{283920}(73,\cdot)$	283920.dle	156	no	$-1$	$1$	$e\left(\frac{131}{156}\right)$	$e\left(\frac{101}{156}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{13}\right)$	$e\left(\frac{5}{156}\right)$	$e\left(\frac{37}{39}\right)$	$e\left(\frac{15}{52}\right)$	$e\left(\frac{33}{52}\right)$	$e\left(\frac{7}{39}\right)$
$\chi_{283920}(79,\cdot)$	283920.crb	78	no	$-1$	$1$	$e\left(\frac{53}{78}\right)$	$e\left(\frac{23}{78}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{13}\right)$	$e\left(\frac{5}{78}\right)$	$e\left(\frac{31}{78}\right)$	$e\left(\frac{1}{13}\right)$	$e\left(\frac{10}{13}\right)$	$e\left(\frac{14}{39}\right)$
$\chi_{283920}(83,\cdot)$	283920.cgo	52	yes	$-1$	$1$	$e\left(\frac{6}{13}\right)$	$e\left(\frac{45}{52}\right)$	$-1$	$i$	$e\left(\frac{41}{52}\right)$	$e\left(\frac{3}{52}\right)$	$e\left(\frac{3}{52}\right)$	$e\left(\frac{1}{52}\right)$	$e\left(\frac{9}{13}\right)$	$e\left(\frac{11}{26}\right)$
$\chi_{283920}(89,\cdot)$	283920.buw	12	no	$-1$	$1$	$e\left(\frac{5}{12}\right)$	$1$	$e\left(\frac{7}{12}\right)$	$-1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{12}\right)$	$-i$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{11}{12}\right)$
$\chi_{283920}(97,\cdot)$	283920.dlp	156	no	$-1$	$1$	$e\left(\frac{35}{156}\right)$	$e\left(\frac{103}{156}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{67}{78}\right)$	$e\left(\frac{41}{52}\right)$	$e\left(\frac{55}{78}\right)$	$e\left(\frac{119}{156}\right)$	$e\left(\frac{7}{156}\right)$	$e\left(\frac{8}{13}\right)$
$\chi_{283920}(101,\cdot)$	283920.dvo	156	no	$1$	$1$	$e\left(\frac{33}{52}\right)$	$e\left(\frac{7}{39}\right)$	$-i$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{31}{156}\right)$	$e\left(\frac{23}{39}\right)$	$e\left(\frac{53}{156}\right)$	$e\left(\frac{25}{39}\right)$	$e\left(\frac{155}{156}\right)$	$e\left(\frac{47}{78}\right)$
$\chi_{283920}(103,\cdot)$	283920.dcy	156	no	$-1$	$1$	$e\left(\frac{29}{78}\right)$	$e\left(\frac{151}{156}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{6}{13}\right)$	$e\left(\frac{41}{78}\right)$	$e\left(\frac{17}{156}\right)$	$e\left(\frac{3}{13}\right)$	$e\left(\frac{29}{52}\right)$	$e\left(\frac{155}{156}\right)$
$\chi_{283920}(107,\cdot)$	283920.dpk	156	yes	$-1$	$1$	$e\left(\frac{95}{156}\right)$	$e\left(\frac{35}{52}\right)$	$e\left(\frac{1}{12}\right)$	$i$	$e\left(\frac{61}{156}\right)$	$e\left(\frac{23}{78}\right)$	$e\left(\frac{25}{26}\right)$	$e\left(\frac{19}{39}\right)$	$e\left(\frac{55}{78}\right)$	$e\left(\frac{47}{156}\right)$
$\chi_{283920}(109,\cdot)$	283920.eeh	156	no	$-1$	$1$	$e\left(\frac{2}{39}\right)$	$e\left(\frac{20}{39}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{45}{52}\right)$	$e\left(\frac{53}{156}\right)$	$e\left(\frac{59}{78}\right)$	$e\left(\frac{29}{52}\right)$	$e\left(\frac{43}{52}\right)$	$e\left(\frac{133}{156}\right)$
$\chi_{283920}(113,\cdot)$	283920.dei	156	no	$1$	$1$	$e\left(\frac{49}{78}\right)$	$e\left(\frac{31}{156}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{8}{39}\right)$	$e\left(\frac{4}{13}\right)$	$e\left(\frac{113}{156}\right)$	$e\left(\frac{73}{78}\right)$	$e\left(\frac{43}{156}\right)$	$e\left(\frac{9}{52}\right)$
$\chi_{283920}(121,\cdot)$	283920.cpo	78	no	$1$	$1$	$e\left(\frac{11}{13}\right)$	$e\left(\frac{5}{39}\right)$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{25}{78}\right)$	$e\left(\frac{5}{78}\right)$	$e\left(\frac{22}{39}\right)$	$e\left(\frac{19}{78}\right)$	$e\left(\frac{47}{78}\right)$	$e\left(\frac{67}{78}\right)$
$\chi_{283920}(127,\cdot)$	283920.eci	156	no	$1$	$1$	$e\left(\frac{7}{39}\right)$	$e\left(\frac{59}{156}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{77}{78}\right)$	$e\left(\frac{3}{13}\right)$	$e\left(\frac{49}{156}\right)$	$e\left(\frac{71}{78}\right)$	$e\left(\frac{107}{156}\right)$	$e\left(\frac{49}{52}\right)$
$\chi_{283920}(131,\cdot)$	283920.dxm	156	no	$-1$	$1$	$e\left(\frac{25}{156}\right)$	$e\left(\frac{4}{39}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{35}{52}\right)$	$e\left(\frac{28}{39}\right)$	$e\left(\frac{125}{156}\right)$	$e\left(\frac{25}{26}\right)$	$e\left(\frac{45}{52}\right)$	$e\left(\frac{25}{78}\right)$
$\chi_{283920}(137,\cdot)$	283920.dmv	156	no	$-1$	$1$	$e\left(\frac{73}{156}\right)$	$e\left(\frac{5}{52}\right)$	$e\left(\frac{11}{12}\right)$	$-i$	$e\left(\frac{61}{78}\right)$	$e\left(\frac{131}{156}\right)$	$e\left(\frac{11}{26}\right)$	$e\left(\frac{113}{156}\right)$	$e\left(\frac{25}{156}\right)$	$e\left(\frac{47}{78}\right)$
$\chi_{283920}(139,\cdot)$	283920.dwx	156	no	$1$	$1$	$e\left(\frac{113}{156}\right)$	$e\left(\frac{16}{39}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{17}{156}\right)$	$e\left(\frac{7}{13}\right)$	$e\left(\frac{149}{156}\right)$	$e\left(\frac{20}{39}\right)$	$e\left(\frac{7}{156}\right)$	$e\left(\frac{3}{26}\right)$
$\chi_{283920}(149,\cdot)$	283920.cyj	156	yes	$1$	$1$	$e\left(\frac{11}{13}\right)$	$e\left(\frac{49}{78}\right)$	$-1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{11}{156}\right)$	$e\left(\frac{49}{156}\right)$	$e\left(\frac{22}{39}\right)$	$e\left(\frac{77}{156}\right)$	$e\left(\frac{55}{156}\right)$	$e\left(\frac{95}{156}\right)$

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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	$283920$
Structure	\(C_{2}\times C_{2}\times C_{2}\times C_{4}\times C_{12}\times C_{156}\)
Order	$59904$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(11\)	\(17\)	\(19\)	\(23\)	\(29\)	\(31\)	\(37\)	\(41\)	\(43\)	\(47\)
\(\chi_{283920}(1,\cdot)\)	283920.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{283920}(11,\cdot)\)	283920.czx	156	no	\(-1\)	\(1\)	\(e\left(\frac{12}{13}\right)\)	\(e\left(\frac{22}{39}\right)\)	\(-1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{103}{156}\right)\)	\(e\left(\frac{5}{156}\right)\)	\(e\left(\frac{11}{39}\right)\)	\(e\left(\frac{19}{156}\right)\)	\(e\left(\frac{47}{156}\right)\)	\(e\left(\frac{145}{156}\right)\)
\(\chi_{283920}(17,\cdot)\)	283920.eds	156	no	\(-1\)	\(1\)	\(e\left(\frac{22}{39}\right)\)	\(e\left(\frac{29}{52}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(i\)	\(e\left(\frac{17}{39}\right)\)	\(e\left(\frac{32}{39}\right)\)	\(e\left(\frac{47}{52}\right)\)	\(e\left(\frac{43}{78}\right)\)	\(e\left(\frac{145}{156}\right)\)	\(e\left(\frac{85}{156}\right)\)
\(\chi_{283920}(19,\cdot)\)	283920.wq	12	no	\(-1\)	\(1\)	\(-1\)	\(e\left(\frac{1}{6}\right)\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{5}{12}\right)\)
\(\chi_{283920}(23,\cdot)\)	283920.ze	12	no	\(-1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(i\)	\(e\left(\frac{1}{3}\right)\)	\(i\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(-i\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{11}{12}\right)\)
\(\chi_{283920}(29,\cdot)\)	283920.dww	156	no	\(-1\)	\(1\)	\(e\left(\frac{103}{156}\right)\)	\(e\left(\frac{17}{39}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{156}\right)\)	\(e\left(\frac{5}{13}\right)\)	\(e\left(\frac{151}{156}\right)\)	\(e\left(\frac{31}{39}\right)\)	\(e\left(\frac{83}{156}\right)\)	\(e\left(\frac{2}{13}\right)\)
\(\chi_{283920}(31,\cdot)\)	283920.duo	156	no	\(-1\)	\(1\)	\(e\left(\frac{5}{156}\right)\)	\(e\left(\frac{32}{39}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{13}\right)\)	\(e\left(\frac{77}{156}\right)\)	\(e\left(\frac{103}{156}\right)\)	\(e\left(\frac{49}{52}\right)\)	\(e\left(\frac{12}{13}\right)\)	\(e\left(\frac{127}{156}\right)\)
\(\chi_{283920}(37,\cdot)\)	283920.ecz	156	no	\(1\)	\(1\)	\(e\left(\frac{11}{39}\right)\)	\(e\left(\frac{47}{52}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(-i\)	\(e\left(\frac{151}{156}\right)\)	\(e\left(\frac{103}{156}\right)\)	\(e\left(\frac{17}{52}\right)\)	\(e\left(\frac{121}{156}\right)\)	\(e\left(\frac{7}{78}\right)\)	\(e\left(\frac{35}{39}\right)\)
\(\chi_{283920}(41,\cdot)\)	283920.dii	156	no	\(-1\)	\(1\)	\(e\left(\frac{19}{156}\right)\)	\(e\left(\frac{43}{78}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{31}{39}\right)\)	\(e\left(\frac{49}{52}\right)\)	\(e\left(\frac{121}{156}\right)\)	\(e\left(\frac{49}{156}\right)\)	\(e\left(\frac{38}{39}\right)\)	\(e\left(\frac{17}{52}\right)\)
\(\chi_{283920}(43,\cdot)\)	283920.dni	156	no	\(1\)	\(1\)	\(e\left(\frac{47}{156}\right)\)	\(e\left(\frac{145}{156}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{83}{156}\right)\)	\(e\left(\frac{12}{13}\right)\)	\(e\left(\frac{7}{78}\right)\)	\(e\left(\frac{38}{39}\right)\)	\(e\left(\frac{16}{39}\right)\)	\(e\left(\frac{27}{52}\right)\)
\(\chi_{283920}(47,\cdot)\)	283920.dkz	156	no	\(-1\)	\(1\)	\(e\left(\frac{145}{156}\right)\)	\(e\left(\frac{85}{156}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{2}{13}\right)\)	\(e\left(\frac{127}{156}\right)\)	\(e\left(\frac{35}{39}\right)\)	\(e\left(\frac{17}{52}\right)\)	\(e\left(\frac{27}{52}\right)\)	\(e\left(\frac{67}{78}\right)\)
\(\chi_{283920}(53,\cdot)\)	283920.dqo	156	yes	\(1\)	\(1\)	\(e\left(\frac{101}{156}\right)\)	\(e\left(\frac{35}{156}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{27}{52}\right)\)	\(e\left(\frac{32}{39}\right)\)	\(e\left(\frac{19}{39}\right)\)	\(e\left(\frac{5}{13}\right)\)	\(e\left(\frac{9}{26}\right)\)	\(e\left(\frac{7}{156}\right)\)
\(\chi_{283920}(59,\cdot)\)	283920.dzl	156	yes	\(1\)	\(1\)	\(e\left(\frac{1}{39}\right)\)	\(e\left(\frac{12}{13}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(-1\)	\(e\left(\frac{35}{156}\right)\)	\(e\left(\frac{59}{156}\right)\)	\(e\left(\frac{25}{26}\right)\)	\(e\left(\frac{89}{156}\right)\)	\(e\left(\frac{97}{156}\right)\)	\(e\left(\frac{73}{156}\right)\)
\(\chi_{283920}(61,\cdot)\)	283920.djo	156	no	\(-1\)	\(1\)	\(e\left(\frac{27}{52}\right)\)	\(e\left(\frac{67}{78}\right)\)	\(-i\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{23}{156}\right)\)	\(e\left(\frac{53}{78}\right)\)	\(e\left(\frac{145}{156}\right)\)	\(e\left(\frac{11}{39}\right)\)	\(e\left(\frac{37}{156}\right)\)	\(e\left(\frac{55}{78}\right)\)
\(\chi_{283920}(67,\cdot)\)	283920.egd	156	no	\(-1\)	\(1\)	\(e\left(\frac{9}{26}\right)\)	\(e\left(\frac{85}{156}\right)\)	\(1\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{37}{156}\right)\)	\(e\left(\frac{23}{156}\right)\)	\(e\left(\frac{23}{156}\right)\)	\(e\left(\frac{103}{156}\right)\)	\(e\left(\frac{73}{78}\right)\)	\(e\left(\frac{1}{39}\right)\)
\(\chi_{283920}(71,\cdot)\)	283920.dxt	156	no	\(-1\)	\(1\)	\(e\left(\frac{149}{156}\right)\)	\(e\left(\frac{28}{39}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{39}\right)\)	\(e\left(\frac{49}{52}\right)\)	\(e\left(\frac{17}{156}\right)\)	\(e\left(\frac{23}{156}\right)\)	\(e\left(\frac{11}{78}\right)\)	\(e\left(\frac{17}{52}\right)\)
\(\chi_{283920}(73,\cdot)\)	283920.dle	156	no	\(-1\)	\(1\)	\(e\left(\frac{131}{156}\right)\)	\(e\left(\frac{101}{156}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{13}\right)\)	\(e\left(\frac{5}{156}\right)\)	\(e\left(\frac{37}{39}\right)\)	\(e\left(\frac{15}{52}\right)\)	\(e\left(\frac{33}{52}\right)\)	\(e\left(\frac{7}{39}\right)\)
\(\chi_{283920}(79,\cdot)\)	283920.crb	78	no	\(-1\)	\(1\)	\(e\left(\frac{53}{78}\right)\)	\(e\left(\frac{23}{78}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{2}{13}\right)\)	\(e\left(\frac{5}{78}\right)\)	\(e\left(\frac{31}{78}\right)\)	\(e\left(\frac{1}{13}\right)\)	\(e\left(\frac{10}{13}\right)\)	\(e\left(\frac{14}{39}\right)\)
\(\chi_{283920}(83,\cdot)\)	283920.cgo	52	yes	\(-1\)	\(1\)	\(e\left(\frac{6}{13}\right)\)	\(e\left(\frac{45}{52}\right)\)	\(-1\)	\(i\)	\(e\left(\frac{41}{52}\right)\)	\(e\left(\frac{3}{52}\right)\)	\(e\left(\frac{3}{52}\right)\)	\(e\left(\frac{1}{52}\right)\)	\(e\left(\frac{9}{13}\right)\)	\(e\left(\frac{11}{26}\right)\)
\(\chi_{283920}(89,\cdot)\)	283920.buw	12	no	\(-1\)	\(1\)	\(e\left(\frac{5}{12}\right)\)	\(1\)	\(e\left(\frac{7}{12}\right)\)	\(-1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(-i\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{11}{12}\right)\)
\(\chi_{283920}(97,\cdot)\)	283920.dlp	156	no	\(-1\)	\(1\)	\(e\left(\frac{35}{156}\right)\)	\(e\left(\frac{103}{156}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{67}{78}\right)\)	\(e\left(\frac{41}{52}\right)\)	\(e\left(\frac{55}{78}\right)\)	\(e\left(\frac{119}{156}\right)\)	\(e\left(\frac{7}{156}\right)\)	\(e\left(\frac{8}{13}\right)\)
\(\chi_{283920}(101,\cdot)\)	283920.dvo	156	no	\(1\)	\(1\)	\(e\left(\frac{33}{52}\right)\)	\(e\left(\frac{7}{39}\right)\)	\(-i\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{31}{156}\right)\)	\(e\left(\frac{23}{39}\right)\)	\(e\left(\frac{53}{156}\right)\)	\(e\left(\frac{25}{39}\right)\)	\(e\left(\frac{155}{156}\right)\)	\(e\left(\frac{47}{78}\right)\)
\(\chi_{283920}(103,\cdot)\)	283920.dcy	156	no	\(-1\)	\(1\)	\(e\left(\frac{29}{78}\right)\)	\(e\left(\frac{151}{156}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{6}{13}\right)\)	\(e\left(\frac{41}{78}\right)\)	\(e\left(\frac{17}{156}\right)\)	\(e\left(\frac{3}{13}\right)\)	\(e\left(\frac{29}{52}\right)\)	\(e\left(\frac{155}{156}\right)\)
\(\chi_{283920}(107,\cdot)\)	283920.dpk	156	yes	\(-1\)	\(1\)	\(e\left(\frac{95}{156}\right)\)	\(e\left(\frac{35}{52}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(i\)	\(e\left(\frac{61}{156}\right)\)	\(e\left(\frac{23}{78}\right)\)	\(e\left(\frac{25}{26}\right)\)	\(e\left(\frac{19}{39}\right)\)	\(e\left(\frac{55}{78}\right)\)	\(e\left(\frac{47}{156}\right)\)
\(\chi_{283920}(109,\cdot)\)	283920.eeh	156	no	\(-1\)	\(1\)	\(e\left(\frac{2}{39}\right)\)	\(e\left(\frac{20}{39}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{45}{52}\right)\)	\(e\left(\frac{53}{156}\right)\)	\(e\left(\frac{59}{78}\right)\)	\(e\left(\frac{29}{52}\right)\)	\(e\left(\frac{43}{52}\right)\)	\(e\left(\frac{133}{156}\right)\)
\(\chi_{283920}(113,\cdot)\)	283920.dei	156	no	\(1\)	\(1\)	\(e\left(\frac{49}{78}\right)\)	\(e\left(\frac{31}{156}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{8}{39}\right)\)	\(e\left(\frac{4}{13}\right)\)	\(e\left(\frac{113}{156}\right)\)	\(e\left(\frac{73}{78}\right)\)	\(e\left(\frac{43}{156}\right)\)	\(e\left(\frac{9}{52}\right)\)
\(\chi_{283920}(121,\cdot)\)	283920.cpo	78	no	\(1\)	\(1\)	\(e\left(\frac{11}{13}\right)\)	\(e\left(\frac{5}{39}\right)\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{25}{78}\right)\)	\(e\left(\frac{5}{78}\right)\)	\(e\left(\frac{22}{39}\right)\)	\(e\left(\frac{19}{78}\right)\)	\(e\left(\frac{47}{78}\right)\)	\(e\left(\frac{67}{78}\right)\)
\(\chi_{283920}(127,\cdot)\)	283920.eci	156	no	\(1\)	\(1\)	\(e\left(\frac{7}{39}\right)\)	\(e\left(\frac{59}{156}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{77}{78}\right)\)	\(e\left(\frac{3}{13}\right)\)	\(e\left(\frac{49}{156}\right)\)	\(e\left(\frac{71}{78}\right)\)	\(e\left(\frac{107}{156}\right)\)	\(e\left(\frac{49}{52}\right)\)
\(\chi_{283920}(131,\cdot)\)	283920.dxm	156	no	\(-1\)	\(1\)	\(e\left(\frac{25}{156}\right)\)	\(e\left(\frac{4}{39}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{35}{52}\right)\)	\(e\left(\frac{28}{39}\right)\)	\(e\left(\frac{125}{156}\right)\)	\(e\left(\frac{25}{26}\right)\)	\(e\left(\frac{45}{52}\right)\)	\(e\left(\frac{25}{78}\right)\)
\(\chi_{283920}(137,\cdot)\)	283920.dmv	156	no	\(-1\)	\(1\)	\(e\left(\frac{73}{156}\right)\)	\(e\left(\frac{5}{52}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(-i\)	\(e\left(\frac{61}{78}\right)\)	\(e\left(\frac{131}{156}\right)\)	\(e\left(\frac{11}{26}\right)\)	\(e\left(\frac{113}{156}\right)\)	\(e\left(\frac{25}{156}\right)\)	\(e\left(\frac{47}{78}\right)\)
\(\chi_{283920}(139,\cdot)\)	283920.dwx	156	no	\(1\)	\(1\)	\(e\left(\frac{113}{156}\right)\)	\(e\left(\frac{16}{39}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{17}{156}\right)\)	\(e\left(\frac{7}{13}\right)\)	\(e\left(\frac{149}{156}\right)\)	\(e\left(\frac{20}{39}\right)\)	\(e\left(\frac{7}{156}\right)\)	\(e\left(\frac{3}{26}\right)\)
\(\chi_{283920}(149,\cdot)\)	283920.cyj	156	yes	\(1\)	\(1\)	\(e\left(\frac{11}{13}\right)\)	\(e\left(\frac{49}{78}\right)\)	\(-1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{11}{156}\right)\)	\(e\left(\frac{49}{156}\right)\)	\(e\left(\frac{22}{39}\right)\)	\(e\left(\frac{77}{156}\right)\)	\(e\left(\frac{55}{156}\right)\)	\(e\left(\frac{95}{156}\right)\)

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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.