LMFDB - Group of Dirichlet characters of modulus 51984

Show commands: PariGP / SageMath

sage: H = DirichletGroup(51984)

pari: g = idealstar(,51984,2)

Character group

sage: G.order() pari: g.no
Order	=	16416
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{2}\times C_{6}\times C_{684}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{51984}(45487,\cdot)$, $\chi_{51984}(12997,\cdot)$, $\chi_{51984}(23105,\cdot)$, $\chi_{51984}(25633,\cdot)$

First 32 of 16416 characters

Each row describes a character. When available, the columns show the orbit label, order of the character, whether the character is primitive, and several values of the character.

Character	Orbit	Order	Primitive	$-1$	$1$	$5$	$7$	$11$	$13$	$17$	$23$	$25$	$29$	$31$	$35$
$\chi_{51984}(1,\cdot)$	51984.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{51984}(5,\cdot)$	51984.ob	684	yes	$-1$	$1$	$e\left(\frac{545}{684}\right)$	$e\left(\frac{67}{114}\right)$	$e\left(\frac{21}{76}\right)$	$e\left(\frac{409}{684}\right)$	$e\left(\frac{277}{342}\right)$	$e\left(\frac{121}{171}\right)$	$e\left(\frac{203}{342}\right)$	$e\left(\frac{79}{684}\right)$	$e\left(\frac{4}{19}\right)$	$e\left(\frac{263}{684}\right)$
$\chi_{51984}(7,\cdot)$	51984.je	114	no	$-1$	$1$	$e\left(\frac{67}{114}\right)$	$e\left(\frac{109}{114}\right)$	$e\left(\frac{23}{57}\right)$	$e\left(\frac{5}{38}\right)$	$e\left(\frac{7}{57}\right)$	$e\left(\frac{33}{38}\right)$	$e\left(\frac{10}{57}\right)$	$e\left(\frac{71}{114}\right)$	$e\left(\frac{83}{114}\right)$	$e\left(\frac{31}{57}\right)$
$\chi_{51984}(11,\cdot)$	51984.lp	228	yes	$1$	$1$	$e\left(\frac{21}{76}\right)$	$e\left(\frac{23}{57}\right)$	$e\left(\frac{77}{228}\right)$	$e\left(\frac{47}{228}\right)$	$e\left(\frac{103}{114}\right)$	$e\left(\frac{43}{114}\right)$	$e\left(\frac{21}{38}\right)$	$e\left(\frac{75}{76}\right)$	$e\left(\frac{23}{114}\right)$	$e\left(\frac{155}{228}\right)$
$\chi_{51984}(13,\cdot)$	51984.oq	684	yes	$-1$	$1$	$e\left(\frac{409}{684}\right)$	$e\left(\frac{5}{38}\right)$	$e\left(\frac{47}{228}\right)$	$e\left(\frac{281}{684}\right)$	$e\left(\frac{70}{171}\right)$	$e\left(\frac{211}{342}\right)$	$e\left(\frac{67}{342}\right)$	$e\left(\frac{641}{684}\right)$	$e\left(\frac{17}{114}\right)$	$e\left(\frac{499}{684}\right)$
$\chi_{51984}(17,\cdot)$	51984.nf	342	no	$-1$	$1$	$e\left(\frac{277}{342}\right)$	$e\left(\frac{7}{57}\right)$	$e\left(\frac{103}{114}\right)$	$e\left(\frac{70}{171}\right)$	$e\left(\frac{289}{342}\right)$	$e\left(\frac{335}{342}\right)$	$e\left(\frac{106}{171}\right)$	$e\left(\frac{251}{342}\right)$	$e\left(\frac{13}{57}\right)$	$e\left(\frac{319}{342}\right)$
$\chi_{51984}(23,\cdot)$	51984.np	342	no	$1$	$1$	$e\left(\frac{121}{171}\right)$	$e\left(\frac{33}{38}\right)$	$e\left(\frac{43}{114}\right)$	$e\left(\frac{211}{342}\right)$	$e\left(\frac{335}{342}\right)$	$e\left(\frac{170}{171}\right)$	$e\left(\frac{71}{171}\right)$	$e\left(\frac{101}{171}\right)$	$e\left(\frac{59}{114}\right)$	$e\left(\frac{197}{342}\right)$
$\chi_{51984}(25,\cdot)$	51984.nl	342	no	$1$	$1$	$e\left(\frac{203}{342}\right)$	$e\left(\frac{10}{57}\right)$	$e\left(\frac{21}{38}\right)$	$e\left(\frac{67}{342}\right)$	$e\left(\frac{106}{171}\right)$	$e\left(\frac{71}{171}\right)$	$e\left(\frac{32}{171}\right)$	$e\left(\frac{79}{342}\right)$	$e\left(\frac{8}{19}\right)$	$e\left(\frac{263}{342}\right)$
$\chi_{51984}(29,\cdot)$	51984.og	684	yes	$1$	$1$	$e\left(\frac{79}{684}\right)$	$e\left(\frac{71}{114}\right)$	$e\left(\frac{75}{76}\right)$	$e\left(\frac{641}{684}\right)$	$e\left(\frac{251}{342}\right)$	$e\left(\frac{101}{171}\right)$	$e\left(\frac{79}{342}\right)$	$e\left(\frac{179}{684}\right)$	$e\left(\frac{15}{38}\right)$	$e\left(\frac{505}{684}\right)$
$\chi_{51984}(31,\cdot)$	51984.in	114	no	$1$	$1$	$e\left(\frac{4}{19}\right)$	$e\left(\frac{83}{114}\right)$	$e\left(\frac{23}{114}\right)$	$e\left(\frac{17}{114}\right)$	$e\left(\frac{13}{57}\right)$	$e\left(\frac{59}{114}\right)$	$e\left(\frac{8}{19}\right)$	$e\left(\frac{15}{38}\right)$	$e\left(\frac{35}{57}\right)$	$e\left(\frac{107}{114}\right)$
$\chi_{51984}(35,\cdot)$	51984.ok	684	no	$1$	$1$	$e\left(\frac{263}{684}\right)$	$e\left(\frac{31}{57}\right)$	$e\left(\frac{155}{228}\right)$	$e\left(\frac{499}{684}\right)$	$e\left(\frac{319}{342}\right)$	$e\left(\frac{197}{342}\right)$	$e\left(\frac{263}{342}\right)$	$e\left(\frac{505}{684}\right)$	$e\left(\frac{107}{114}\right)$	$e\left(\frac{635}{684}\right)$
$\chi_{51984}(37,\cdot)$	51984.ij	76	no	$-1$	$1$	$e\left(\frac{59}{76}\right)$	$e\left(\frac{9}{38}\right)$	$e\left(\frac{51}{76}\right)$	$e\left(\frac{3}{76}\right)$	$e\left(\frac{14}{19}\right)$	$e\left(\frac{27}{38}\right)$	$e\left(\frac{21}{38}\right)$	$e\left(\frac{75}{76}\right)$	$e\left(\frac{33}{38}\right)$	$e\left(\frac{1}{76}\right)$
$\chi_{51984}(41,\cdot)$	51984.nb	342	no	$1$	$1$	$e\left(\frac{20}{171}\right)$	$e\left(\frac{41}{57}\right)$	$e\left(\frac{6}{19}\right)$	$e\left(\frac{106}{171}\right)$	$e\left(\frac{265}{342}\right)$	$e\left(\frac{263}{342}\right)$	$e\left(\frac{40}{171}\right)$	$e\left(\frac{227}{342}\right)$	$e\left(\frac{1}{38}\right)$	$e\left(\frac{143}{171}\right)$
$\chi_{51984}(43,\cdot)$	51984.nx	684	yes	$-1$	$1$	$e\left(\frac{587}{684}\right)$	$e\left(\frac{9}{19}\right)$	$e\left(\frac{211}{228}\right)$	$e\left(\frac{73}{684}\right)$	$e\left(\frac{62}{171}\right)$	$e\left(\frac{91}{171}\right)$	$e\left(\frac{245}{342}\right)$	$e\left(\frac{1}{684}\right)$	$e\left(\frac{103}{114}\right)$	$e\left(\frac{227}{684}\right)$
$\chi_{51984}(47,\cdot)$	51984.mm	342	no	$1$	$1$	$e\left(\frac{161}{342}\right)$	$e\left(\frac{65}{114}\right)$	$e\left(\frac{8}{19}\right)$	$e\left(\frac{59}{171}\right)$	$e\left(\frac{233}{342}\right)$	$e\left(\frac{74}{171}\right)$	$e\left(\frac{161}{171}\right)$	$e\left(\frac{157}{342}\right)$	$e\left(\frac{33}{38}\right)$	$e\left(\frac{7}{171}\right)$
$\chi_{51984}(49,\cdot)$	51984.ic	57	no	$1$	$1$	$e\left(\frac{10}{57}\right)$	$e\left(\frac{52}{57}\right)$	$e\left(\frac{46}{57}\right)$	$e\left(\frac{5}{19}\right)$	$e\left(\frac{14}{57}\right)$	$e\left(\frac{14}{19}\right)$	$e\left(\frac{20}{57}\right)$	$e\left(\frac{14}{57}\right)$	$e\left(\frac{26}{57}\right)$	$e\left(\frac{5}{57}\right)$
$\chi_{51984}(53,\cdot)$	51984.od	684	no	$1$	$1$	$e\left(\frac{37}{684}\right)$	$e\left(\frac{103}{114}\right)$	$e\left(\frac{115}{228}\right)$	$e\left(\frac{407}{684}\right)$	$e\left(\frac{119}{342}\right)$	$e\left(\frac{74}{171}\right)$	$e\left(\frac{37}{342}\right)$	$e\left(\frac{257}{684}\right)$	$e\left(\frac{61}{114}\right)$	$e\left(\frac{655}{684}\right)$
$\chi_{51984}(55,\cdot)$	51984.mt	342	no	$-1$	$1$	$e\left(\frac{25}{342}\right)$	$e\left(\frac{113}{114}\right)$	$e\left(\frac{35}{57}\right)$	$e\left(\frac{275}{342}\right)$	$e\left(\frac{122}{171}\right)$	$e\left(\frac{29}{342}\right)$	$e\left(\frac{25}{171}\right)$	$e\left(\frac{35}{342}\right)$	$e\left(\frac{47}{114}\right)$	$e\left(\frac{11}{171}\right)$
$\chi_{51984}(59,\cdot)$	51984.oi	684	yes	$-1$	$1$	$e\left(\frac{137}{684}\right)$	$e\left(\frac{41}{57}\right)$	$e\left(\frac{43}{76}\right)$	$e\left(\frac{367}{684}\right)$	$e\left(\frac{37}{342}\right)$	$e\left(\frac{149}{342}\right)$	$e\left(\frac{137}{342}\right)$	$e\left(\frac{397}{684}\right)$	$e\left(\frac{10}{19}\right)$	$e\left(\frac{629}{684}\right)$
$\chi_{51984}(61,\cdot)$	51984.oa	684	yes	$1$	$1$	$e\left(\frac{337}{684}\right)$	$e\left(\frac{59}{114}\right)$	$e\left(\frac{65}{76}\right)$	$e\left(\frac{59}{684}\right)$	$e\left(\frac{136}{171}\right)$	$e\left(\frac{37}{342}\right)$	$e\left(\frac{337}{342}\right)$	$e\left(\frac{335}{684}\right)$	$e\left(\frac{16}{19}\right)$	$e\left(\frac{7}{684}\right)$
$\chi_{51984}(65,\cdot)$	51984.kq	114	no	$1$	$1$	$e\left(\frac{15}{38}\right)$	$e\left(\frac{41}{57}\right)$	$e\left(\frac{55}{114}\right)$	$e\left(\frac{1}{114}\right)$	$e\left(\frac{25}{114}\right)$	$e\left(\frac{37}{114}\right)$	$e\left(\frac{15}{19}\right)$	$e\left(\frac{1}{19}\right)$	$e\left(\frac{41}{114}\right)$	$e\left(\frac{13}{114}\right)$
$\chi_{51984}(67,\cdot)$	51984.ny	684	yes	$1$	$1$	$e\left(\frac{613}{684}\right)$	$e\left(\frac{6}{19}\right)$	$e\left(\frac{185}{228}\right)$	$e\left(\frac{473}{684}\right)$	$e\left(\frac{130}{171}\right)$	$e\left(\frac{86}{171}\right)$	$e\left(\frac{271}{342}\right)$	$e\left(\frac{653}{684}\right)$	$e\left(\frac{28}{57}\right)$	$e\left(\frac{145}{684}\right)$
$\chi_{51984}(71,\cdot)$	51984.mq	342	no	$-1$	$1$	$e\left(\frac{101}{171}\right)$	$e\left(\frac{17}{114}\right)$	$e\left(\frac{7}{114}\right)$	$e\left(\frac{85}{171}\right)$	$e\left(\frac{241}{342}\right)$	$e\left(\frac{124}{171}\right)$	$e\left(\frac{31}{171}\right)$	$e\left(\frac{317}{342}\right)$	$e\left(\frac{28}{57}\right)$	$e\left(\frac{253}{342}\right)$
$\chi_{51984}(73,\cdot)$	51984.ng	342	no	$1$	$1$	$e\left(\frac{163}{342}\right)$	$e\left(\frac{7}{57}\right)$	$e\left(\frac{103}{114}\right)$	$e\left(\frac{83}{342}\right)$	$e\left(\frac{2}{171}\right)$	$e\left(\frac{139}{171}\right)$	$e\left(\frac{163}{171}\right)$	$e\left(\frac{23}{342}\right)$	$e\left(\frac{13}{57}\right)$	$e\left(\frac{205}{342}\right)$
$\chi_{51984}(77,\cdot)$	51984.lm	228	yes	$-1$	$1$	$e\left(\frac{197}{228}\right)$	$e\left(\frac{41}{114}\right)$	$e\left(\frac{169}{228}\right)$	$e\left(\frac{77}{228}\right)$	$e\left(\frac{1}{38}\right)$	$e\left(\frac{14}{57}\right)$	$e\left(\frac{83}{114}\right)$	$e\left(\frac{139}{228}\right)$	$e\left(\frac{53}{57}\right)$	$e\left(\frac{17}{76}\right)$
$\chi_{51984}(79,\cdot)$	51984.nr	342	no	$1$	$1$	$e\left(\frac{161}{171}\right)$	$e\left(\frac{37}{38}\right)$	$e\left(\frac{77}{114}\right)$	$e\left(\frac{179}{342}\right)$	$e\left(\frac{119}{171}\right)$	$e\left(\frac{239}{342}\right)$	$e\left(\frac{151}{171}\right)$	$e\left(\frac{143}{342}\right)$	$e\left(\frac{23}{57}\right)$	$e\left(\frac{313}{342}\right)$
$\chi_{51984}(83,\cdot)$	51984.lr	228	yes	$1$	$1$	$e\left(\frac{173}{228}\right)$	$e\left(\frac{14}{57}\right)$	$e\left(\frac{203}{228}\right)$	$e\left(\frac{39}{76}\right)$	$e\left(\frac{47}{114}\right)$	$e\left(\frac{9}{38}\right)$	$e\left(\frac{59}{114}\right)$	$e\left(\frac{151}{228}\right)$	$e\left(\frac{71}{114}\right)$	$e\left(\frac{1}{228}\right)$
$\chi_{51984}(85,\cdot)$	51984.ot	684	yes	$1$	$1$	$e\left(\frac{415}{684}\right)$	$e\left(\frac{27}{38}\right)$	$e\left(\frac{41}{228}\right)$	$e\left(\frac{5}{684}\right)$	$e\left(\frac{112}{171}\right)$	$e\left(\frac{235}{342}\right)$	$e\left(\frac{73}{342}\right)$	$e\left(\frac{581}{684}\right)$	$e\left(\frac{25}{57}\right)$	$e\left(\frac{217}{684}\right)$
$\chi_{51984}(89,\cdot)$	51984.nh	342	no	$1$	$1$	$e\left(\frac{4}{171}\right)$	$e\left(\frac{50}{57}\right)$	$e\left(\frac{34}{57}\right)$	$e\left(\frac{44}{171}\right)$	$e\left(\frac{167}{342}\right)$	$e\left(\frac{235}{342}\right)$	$e\left(\frac{8}{171}\right)$	$e\left(\frac{319}{342}\right)$	$e\left(\frac{31}{114}\right)$	$e\left(\frac{154}{171}\right)$
$\chi_{51984}(91,\cdot)$	51984.om	684	no	$1$	$1$	$e\left(\frac{127}{684}\right)$	$e\left(\frac{5}{57}\right)$	$e\left(\frac{139}{228}\right)$	$e\left(\frac{371}{684}\right)$	$e\left(\frac{91}{171}\right)$	$e\left(\frac{83}{171}\right)$	$e\left(\frac{127}{342}\right)$	$e\left(\frac{383}{684}\right)$	$e\left(\frac{50}{57}\right)$	$e\left(\frac{187}{684}\right)$
$\chi_{51984}(97,\cdot)$	51984.mi	342	no	$-1$	$1$	$e\left(\frac{146}{171}\right)$	$e\left(\frac{13}{19}\right)$	$e\left(\frac{25}{57}\right)$	$e\left(\frac{191}{342}\right)$	$e\left(\frac{41}{171}\right)$	$e\left(\frac{85}{171}\right)$	$e\left(\frac{121}{171}\right)$	$e\left(\frac{101}{342}\right)$	$e\left(\frac{1}{114}\right)$	$e\left(\frac{92}{171}\right)$
$\chi_{51984}(101,\cdot)$	51984.ob	684	yes	$-1$	$1$	$e\left(\frac{1}{684}\right)$	$e\left(\frac{11}{114}\right)$	$e\left(\frac{25}{76}\right)$	$e\left(\frac{125}{684}\right)$	$e\left(\frac{185}{342}\right)$	$e\left(\frac{116}{171}\right)$	$e\left(\frac{1}{342}\right)$	$e\left(\frac{275}{684}\right)$	$e\left(\frac{12}{19}\right)$	$e\left(\frac{67}{684}\right)$

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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	$51984$
Structure	\(C_{2}\times C_{2}\times C_{6}\times C_{684}\)
Order	$16416$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(5\)	\(7\)	\(11\)	\(13\)	\(17\)	\(23\)	\(25\)	\(29\)	\(31\)	\(35\)
\(\chi_{51984}(1,\cdot)\)	51984.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{51984}(5,\cdot)\)	51984.ob	684	yes	\(-1\)	\(1\)	\(e\left(\frac{545}{684}\right)\)	\(e\left(\frac{67}{114}\right)\)	\(e\left(\frac{21}{76}\right)\)	\(e\left(\frac{409}{684}\right)\)	\(e\left(\frac{277}{342}\right)\)	\(e\left(\frac{121}{171}\right)\)	\(e\left(\frac{203}{342}\right)\)	\(e\left(\frac{79}{684}\right)\)	\(e\left(\frac{4}{19}\right)\)	\(e\left(\frac{263}{684}\right)\)
\(\chi_{51984}(7,\cdot)\)	51984.je	114	no	\(-1\)	\(1\)	\(e\left(\frac{67}{114}\right)\)	\(e\left(\frac{109}{114}\right)\)	\(e\left(\frac{23}{57}\right)\)	\(e\left(\frac{5}{38}\right)\)	\(e\left(\frac{7}{57}\right)\)	\(e\left(\frac{33}{38}\right)\)	\(e\left(\frac{10}{57}\right)\)	\(e\left(\frac{71}{114}\right)\)	\(e\left(\frac{83}{114}\right)\)	\(e\left(\frac{31}{57}\right)\)
\(\chi_{51984}(11,\cdot)\)	51984.lp	228	yes	\(1\)	\(1\)	\(e\left(\frac{21}{76}\right)\)	\(e\left(\frac{23}{57}\right)\)	\(e\left(\frac{77}{228}\right)\)	\(e\left(\frac{47}{228}\right)\)	\(e\left(\frac{103}{114}\right)\)	\(e\left(\frac{43}{114}\right)\)	\(e\left(\frac{21}{38}\right)\)	\(e\left(\frac{75}{76}\right)\)	\(e\left(\frac{23}{114}\right)\)	\(e\left(\frac{155}{228}\right)\)
\(\chi_{51984}(13,\cdot)\)	51984.oq	684	yes	\(-1\)	\(1\)	\(e\left(\frac{409}{684}\right)\)	\(e\left(\frac{5}{38}\right)\)	\(e\left(\frac{47}{228}\right)\)	\(e\left(\frac{281}{684}\right)\)	\(e\left(\frac{70}{171}\right)\)	\(e\left(\frac{211}{342}\right)\)	\(e\left(\frac{67}{342}\right)\)	\(e\left(\frac{641}{684}\right)\)	\(e\left(\frac{17}{114}\right)\)	\(e\left(\frac{499}{684}\right)\)
\(\chi_{51984}(17,\cdot)\)	51984.nf	342	no	\(-1\)	\(1\)	\(e\left(\frac{277}{342}\right)\)	\(e\left(\frac{7}{57}\right)\)	\(e\left(\frac{103}{114}\right)\)	\(e\left(\frac{70}{171}\right)\)	\(e\left(\frac{289}{342}\right)\)	\(e\left(\frac{335}{342}\right)\)	\(e\left(\frac{106}{171}\right)\)	\(e\left(\frac{251}{342}\right)\)	\(e\left(\frac{13}{57}\right)\)	\(e\left(\frac{319}{342}\right)\)
\(\chi_{51984}(23,\cdot)\)	51984.np	342	no	\(1\)	\(1\)	\(e\left(\frac{121}{171}\right)\)	\(e\left(\frac{33}{38}\right)\)	\(e\left(\frac{43}{114}\right)\)	\(e\left(\frac{211}{342}\right)\)	\(e\left(\frac{335}{342}\right)\)	\(e\left(\frac{170}{171}\right)\)	\(e\left(\frac{71}{171}\right)\)	\(e\left(\frac{101}{171}\right)\)	\(e\left(\frac{59}{114}\right)\)	\(e\left(\frac{197}{342}\right)\)
\(\chi_{51984}(25,\cdot)\)	51984.nl	342	no	\(1\)	\(1\)	\(e\left(\frac{203}{342}\right)\)	\(e\left(\frac{10}{57}\right)\)	\(e\left(\frac{21}{38}\right)\)	\(e\left(\frac{67}{342}\right)\)	\(e\left(\frac{106}{171}\right)\)	\(e\left(\frac{71}{171}\right)\)	\(e\left(\frac{32}{171}\right)\)	\(e\left(\frac{79}{342}\right)\)	\(e\left(\frac{8}{19}\right)\)	\(e\left(\frac{263}{342}\right)\)
\(\chi_{51984}(29,\cdot)\)	51984.og	684	yes	\(1\)	\(1\)	\(e\left(\frac{79}{684}\right)\)	\(e\left(\frac{71}{114}\right)\)	\(e\left(\frac{75}{76}\right)\)	\(e\left(\frac{641}{684}\right)\)	\(e\left(\frac{251}{342}\right)\)	\(e\left(\frac{101}{171}\right)\)	\(e\left(\frac{79}{342}\right)\)	\(e\left(\frac{179}{684}\right)\)	\(e\left(\frac{15}{38}\right)\)	\(e\left(\frac{505}{684}\right)\)
\(\chi_{51984}(31,\cdot)\)	51984.in	114	no	\(1\)	\(1\)	\(e\left(\frac{4}{19}\right)\)	\(e\left(\frac{83}{114}\right)\)	\(e\left(\frac{23}{114}\right)\)	\(e\left(\frac{17}{114}\right)\)	\(e\left(\frac{13}{57}\right)\)	\(e\left(\frac{59}{114}\right)\)	\(e\left(\frac{8}{19}\right)\)	\(e\left(\frac{15}{38}\right)\)	\(e\left(\frac{35}{57}\right)\)	\(e\left(\frac{107}{114}\right)\)
\(\chi_{51984}(35,\cdot)\)	51984.ok	684	no	\(1\)	\(1\)	\(e\left(\frac{263}{684}\right)\)	\(e\left(\frac{31}{57}\right)\)	\(e\left(\frac{155}{228}\right)\)	\(e\left(\frac{499}{684}\right)\)	\(e\left(\frac{319}{342}\right)\)	\(e\left(\frac{197}{342}\right)\)	\(e\left(\frac{263}{342}\right)\)	\(e\left(\frac{505}{684}\right)\)	\(e\left(\frac{107}{114}\right)\)	\(e\left(\frac{635}{684}\right)\)
\(\chi_{51984}(37,\cdot)\)	51984.ij	76	no	\(-1\)	\(1\)	\(e\left(\frac{59}{76}\right)\)	\(e\left(\frac{9}{38}\right)\)	\(e\left(\frac{51}{76}\right)\)	\(e\left(\frac{3}{76}\right)\)	\(e\left(\frac{14}{19}\right)\)	\(e\left(\frac{27}{38}\right)\)	\(e\left(\frac{21}{38}\right)\)	\(e\left(\frac{75}{76}\right)\)	\(e\left(\frac{33}{38}\right)\)	\(e\left(\frac{1}{76}\right)\)
\(\chi_{51984}(41,\cdot)\)	51984.nb	342	no	\(1\)	\(1\)	\(e\left(\frac{20}{171}\right)\)	\(e\left(\frac{41}{57}\right)\)	\(e\left(\frac{6}{19}\right)\)	\(e\left(\frac{106}{171}\right)\)	\(e\left(\frac{265}{342}\right)\)	\(e\left(\frac{263}{342}\right)\)	\(e\left(\frac{40}{171}\right)\)	\(e\left(\frac{227}{342}\right)\)	\(e\left(\frac{1}{38}\right)\)	\(e\left(\frac{143}{171}\right)\)
\(\chi_{51984}(43,\cdot)\)	51984.nx	684	yes	\(-1\)	\(1\)	\(e\left(\frac{587}{684}\right)\)	\(e\left(\frac{9}{19}\right)\)	\(e\left(\frac{211}{228}\right)\)	\(e\left(\frac{73}{684}\right)\)	\(e\left(\frac{62}{171}\right)\)	\(e\left(\frac{91}{171}\right)\)	\(e\left(\frac{245}{342}\right)\)	\(e\left(\frac{1}{684}\right)\)	\(e\left(\frac{103}{114}\right)\)	\(e\left(\frac{227}{684}\right)\)
\(\chi_{51984}(47,\cdot)\)	51984.mm	342	no	\(1\)	\(1\)	\(e\left(\frac{161}{342}\right)\)	\(e\left(\frac{65}{114}\right)\)	\(e\left(\frac{8}{19}\right)\)	\(e\left(\frac{59}{171}\right)\)	\(e\left(\frac{233}{342}\right)\)	\(e\left(\frac{74}{171}\right)\)	\(e\left(\frac{161}{171}\right)\)	\(e\left(\frac{157}{342}\right)\)	\(e\left(\frac{33}{38}\right)\)	\(e\left(\frac{7}{171}\right)\)
\(\chi_{51984}(49,\cdot)\)	51984.ic	57	no	\(1\)	\(1\)	\(e\left(\frac{10}{57}\right)\)	\(e\left(\frac{52}{57}\right)\)	\(e\left(\frac{46}{57}\right)\)	\(e\left(\frac{5}{19}\right)\)	\(e\left(\frac{14}{57}\right)\)	\(e\left(\frac{14}{19}\right)\)	\(e\left(\frac{20}{57}\right)\)	\(e\left(\frac{14}{57}\right)\)	\(e\left(\frac{26}{57}\right)\)	\(e\left(\frac{5}{57}\right)\)
\(\chi_{51984}(53,\cdot)\)	51984.od	684	no	\(1\)	\(1\)	\(e\left(\frac{37}{684}\right)\)	\(e\left(\frac{103}{114}\right)\)	\(e\left(\frac{115}{228}\right)\)	\(e\left(\frac{407}{684}\right)\)	\(e\left(\frac{119}{342}\right)\)	\(e\left(\frac{74}{171}\right)\)	\(e\left(\frac{37}{342}\right)\)	\(e\left(\frac{257}{684}\right)\)	\(e\left(\frac{61}{114}\right)\)	\(e\left(\frac{655}{684}\right)\)
\(\chi_{51984}(55,\cdot)\)	51984.mt	342	no	\(-1\)	\(1\)	\(e\left(\frac{25}{342}\right)\)	\(e\left(\frac{113}{114}\right)\)	\(e\left(\frac{35}{57}\right)\)	\(e\left(\frac{275}{342}\right)\)	\(e\left(\frac{122}{171}\right)\)	\(e\left(\frac{29}{342}\right)\)	\(e\left(\frac{25}{171}\right)\)	\(e\left(\frac{35}{342}\right)\)	\(e\left(\frac{47}{114}\right)\)	\(e\left(\frac{11}{171}\right)\)
\(\chi_{51984}(59,\cdot)\)	51984.oi	684	yes	\(-1\)	\(1\)	\(e\left(\frac{137}{684}\right)\)	\(e\left(\frac{41}{57}\right)\)	\(e\left(\frac{43}{76}\right)\)	\(e\left(\frac{367}{684}\right)\)	\(e\left(\frac{37}{342}\right)\)	\(e\left(\frac{149}{342}\right)\)	\(e\left(\frac{137}{342}\right)\)	\(e\left(\frac{397}{684}\right)\)	\(e\left(\frac{10}{19}\right)\)	\(e\left(\frac{629}{684}\right)\)
\(\chi_{51984}(61,\cdot)\)	51984.oa	684	yes	\(1\)	\(1\)	\(e\left(\frac{337}{684}\right)\)	\(e\left(\frac{59}{114}\right)\)	\(e\left(\frac{65}{76}\right)\)	\(e\left(\frac{59}{684}\right)\)	\(e\left(\frac{136}{171}\right)\)	\(e\left(\frac{37}{342}\right)\)	\(e\left(\frac{337}{342}\right)\)	\(e\left(\frac{335}{684}\right)\)	\(e\left(\frac{16}{19}\right)\)	\(e\left(\frac{7}{684}\right)\)
\(\chi_{51984}(65,\cdot)\)	51984.kq	114	no	\(1\)	\(1\)	\(e\left(\frac{15}{38}\right)\)	\(e\left(\frac{41}{57}\right)\)	\(e\left(\frac{55}{114}\right)\)	\(e\left(\frac{1}{114}\right)\)	\(e\left(\frac{25}{114}\right)\)	\(e\left(\frac{37}{114}\right)\)	\(e\left(\frac{15}{19}\right)\)	\(e\left(\frac{1}{19}\right)\)	\(e\left(\frac{41}{114}\right)\)	\(e\left(\frac{13}{114}\right)\)
\(\chi_{51984}(67,\cdot)\)	51984.ny	684	yes	\(1\)	\(1\)	\(e\left(\frac{613}{684}\right)\)	\(e\left(\frac{6}{19}\right)\)	\(e\left(\frac{185}{228}\right)\)	\(e\left(\frac{473}{684}\right)\)	\(e\left(\frac{130}{171}\right)\)	\(e\left(\frac{86}{171}\right)\)	\(e\left(\frac{271}{342}\right)\)	\(e\left(\frac{653}{684}\right)\)	\(e\left(\frac{28}{57}\right)\)	\(e\left(\frac{145}{684}\right)\)
\(\chi_{51984}(71,\cdot)\)	51984.mq	342	no	\(-1\)	\(1\)	\(e\left(\frac{101}{171}\right)\)	\(e\left(\frac{17}{114}\right)\)	\(e\left(\frac{7}{114}\right)\)	\(e\left(\frac{85}{171}\right)\)	\(e\left(\frac{241}{342}\right)\)	\(e\left(\frac{124}{171}\right)\)	\(e\left(\frac{31}{171}\right)\)	\(e\left(\frac{317}{342}\right)\)	\(e\left(\frac{28}{57}\right)\)	\(e\left(\frac{253}{342}\right)\)
\(\chi_{51984}(73,\cdot)\)	51984.ng	342	no	\(1\)	\(1\)	\(e\left(\frac{163}{342}\right)\)	\(e\left(\frac{7}{57}\right)\)	\(e\left(\frac{103}{114}\right)\)	\(e\left(\frac{83}{342}\right)\)	\(e\left(\frac{2}{171}\right)\)	\(e\left(\frac{139}{171}\right)\)	\(e\left(\frac{163}{171}\right)\)	\(e\left(\frac{23}{342}\right)\)	\(e\left(\frac{13}{57}\right)\)	\(e\left(\frac{205}{342}\right)\)
\(\chi_{51984}(77,\cdot)\)	51984.lm	228	yes	\(-1\)	\(1\)	\(e\left(\frac{197}{228}\right)\)	\(e\left(\frac{41}{114}\right)\)	\(e\left(\frac{169}{228}\right)\)	\(e\left(\frac{77}{228}\right)\)	\(e\left(\frac{1}{38}\right)\)	\(e\left(\frac{14}{57}\right)\)	\(e\left(\frac{83}{114}\right)\)	\(e\left(\frac{139}{228}\right)\)	\(e\left(\frac{53}{57}\right)\)	\(e\left(\frac{17}{76}\right)\)
\(\chi_{51984}(79,\cdot)\)	51984.nr	342	no	\(1\)	\(1\)	\(e\left(\frac{161}{171}\right)\)	\(e\left(\frac{37}{38}\right)\)	\(e\left(\frac{77}{114}\right)\)	\(e\left(\frac{179}{342}\right)\)	\(e\left(\frac{119}{171}\right)\)	\(e\left(\frac{239}{342}\right)\)	\(e\left(\frac{151}{171}\right)\)	\(e\left(\frac{143}{342}\right)\)	\(e\left(\frac{23}{57}\right)\)	\(e\left(\frac{313}{342}\right)\)
\(\chi_{51984}(83,\cdot)\)	51984.lr	228	yes	\(1\)	\(1\)	\(e\left(\frac{173}{228}\right)\)	\(e\left(\frac{14}{57}\right)\)	\(e\left(\frac{203}{228}\right)\)	\(e\left(\frac{39}{76}\right)\)	\(e\left(\frac{47}{114}\right)\)	\(e\left(\frac{9}{38}\right)\)	\(e\left(\frac{59}{114}\right)\)	\(e\left(\frac{151}{228}\right)\)	\(e\left(\frac{71}{114}\right)\)	\(e\left(\frac{1}{228}\right)\)
\(\chi_{51984}(85,\cdot)\)	51984.ot	684	yes	\(1\)	\(1\)	\(e\left(\frac{415}{684}\right)\)	\(e\left(\frac{27}{38}\right)\)	\(e\left(\frac{41}{228}\right)\)	\(e\left(\frac{5}{684}\right)\)	\(e\left(\frac{112}{171}\right)\)	\(e\left(\frac{235}{342}\right)\)	\(e\left(\frac{73}{342}\right)\)	\(e\left(\frac{581}{684}\right)\)	\(e\left(\frac{25}{57}\right)\)	\(e\left(\frac{217}{684}\right)\)
\(\chi_{51984}(89,\cdot)\)	51984.nh	342	no	\(1\)	\(1\)	\(e\left(\frac{4}{171}\right)\)	\(e\left(\frac{50}{57}\right)\)	\(e\left(\frac{34}{57}\right)\)	\(e\left(\frac{44}{171}\right)\)	\(e\left(\frac{167}{342}\right)\)	\(e\left(\frac{235}{342}\right)\)	\(e\left(\frac{8}{171}\right)\)	\(e\left(\frac{319}{342}\right)\)	\(e\left(\frac{31}{114}\right)\)	\(e\left(\frac{154}{171}\right)\)
\(\chi_{51984}(91,\cdot)\)	51984.om	684	no	\(1\)	\(1\)	\(e\left(\frac{127}{684}\right)\)	\(e\left(\frac{5}{57}\right)\)	\(e\left(\frac{139}{228}\right)\)	\(e\left(\frac{371}{684}\right)\)	\(e\left(\frac{91}{171}\right)\)	\(e\left(\frac{83}{171}\right)\)	\(e\left(\frac{127}{342}\right)\)	\(e\left(\frac{383}{684}\right)\)	\(e\left(\frac{50}{57}\right)\)	\(e\left(\frac{187}{684}\right)\)
\(\chi_{51984}(97,\cdot)\)	51984.mi	342	no	\(-1\)	\(1\)	\(e\left(\frac{146}{171}\right)\)	\(e\left(\frac{13}{19}\right)\)	\(e\left(\frac{25}{57}\right)\)	\(e\left(\frac{191}{342}\right)\)	\(e\left(\frac{41}{171}\right)\)	\(e\left(\frac{85}{171}\right)\)	\(e\left(\frac{121}{171}\right)\)	\(e\left(\frac{101}{342}\right)\)	\(e\left(\frac{1}{114}\right)\)	\(e\left(\frac{92}{171}\right)\)
\(\chi_{51984}(101,\cdot)\)	51984.ob	684	yes	\(-1\)	\(1\)	\(e\left(\frac{1}{684}\right)\)	\(e\left(\frac{11}{114}\right)\)	\(e\left(\frac{25}{76}\right)\)	\(e\left(\frac{125}{684}\right)\)	\(e\left(\frac{185}{342}\right)\)	\(e\left(\frac{116}{171}\right)\)	\(e\left(\frac{1}{342}\right)\)	\(e\left(\frac{275}{684}\right)\)	\(e\left(\frac{12}{19}\right)\)	\(e\left(\frac{67}{684}\right)\)

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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.