LMFDB - Group of Dirichlet characters of modulus 5488

Show commands: PariGP / SageMath

sage: H = DirichletGroup(5488)

pari: g = idealstar(,5488,2)

Character group

sage: G.order() pari: g.no
Order	=	2352
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{2}\times C_{588}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{5488}(687,\cdot)$, $\chi_{5488}(4117,\cdot)$, $\chi_{5488}(689,\cdot)$

First 32 of 2352 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	$-1$	$1$	$3$	$5$	$9$	$11$	$13$	$15$	$17$	$19$	$23$	$25$
$\chi_{5488}(1,\cdot)$	5488.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{5488}(3,\cdot)$	5488.cs	588	yes	$1$	$1$	$e\left(\frac{443}{588}\right)$	$e\left(\frac{499}{588}\right)$	$e\left(\frac{149}{294}\right)$	$e\left(\frac{563}{588}\right)$	$e\left(\frac{43}{196}\right)$	$e\left(\frac{59}{98}\right)$	$e\left(\frac{25}{294}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{82}{147}\right)$	$e\left(\frac{205}{294}\right)$
$\chi_{5488}(5,\cdot)$	5488.cr	588	yes	$-1$	$1$	$e\left(\frac{499}{588}\right)$	$e\left(\frac{65}{588}\right)$	$e\left(\frac{205}{294}\right)$	$e\left(\frac{451}{588}\right)$	$e\left(\frac{169}{196}\right)$	$e\left(\frac{47}{49}\right)$	$e\left(\frac{137}{294}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{199}{294}\right)$	$e\left(\frac{65}{294}\right)$
$\chi_{5488}(9,\cdot)$	5488.co	294	no	$1$	$1$	$e\left(\frac{149}{294}\right)$	$e\left(\frac{205}{294}\right)$	$e\left(\frac{2}{147}\right)$	$e\left(\frac{269}{294}\right)$	$e\left(\frac{43}{98}\right)$	$e\left(\frac{10}{49}\right)$	$e\left(\frac{25}{147}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{17}{147}\right)$	$e\left(\frac{58}{147}\right)$
$\chi_{5488}(11,\cdot)$	5488.cq	588	yes	$-1$	$1$	$e\left(\frac{563}{588}\right)$	$e\left(\frac{451}{588}\right)$	$e\left(\frac{269}{294}\right)$	$e\left(\frac{533}{588}\right)$	$e\left(\frac{75}{196}\right)$	$e\left(\frac{71}{98}\right)$	$e\left(\frac{101}{147}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{4}{147}\right)$	$e\left(\frac{157}{294}\right)$
$\chi_{5488}(13,\cdot)$	5488.ch	196	yes	$-1$	$1$	$e\left(\frac{43}{196}\right)$	$e\left(\frac{169}{196}\right)$	$e\left(\frac{43}{98}\right)$	$e\left(\frac{75}{196}\right)$	$e\left(\frac{103}{196}\right)$	$e\left(\frac{4}{49}\right)$	$e\left(\frac{23}{98}\right)$	$-i$	$e\left(\frac{47}{98}\right)$	$e\left(\frac{71}{98}\right)$
$\chi_{5488}(15,\cdot)$	5488.ca	98	no	$-1$	$1$	$e\left(\frac{59}{98}\right)$	$e\left(\frac{47}{49}\right)$	$e\left(\frac{10}{49}\right)$	$e\left(\frac{71}{98}\right)$	$e\left(\frac{4}{49}\right)$	$e\left(\frac{55}{98}\right)$	$e\left(\frac{27}{49}\right)$	$-1$	$e\left(\frac{23}{98}\right)$	$e\left(\frac{45}{49}\right)$
$\chi_{5488}(17,\cdot)$	5488.cn	294	no	$-1$	$1$	$e\left(\frac{25}{294}\right)$	$e\left(\frac{137}{294}\right)$	$e\left(\frac{25}{147}\right)$	$e\left(\frac{101}{147}\right)$	$e\left(\frac{23}{98}\right)$	$e\left(\frac{27}{49}\right)$	$e\left(\frac{37}{294}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{139}{147}\right)$	$e\left(\frac{137}{147}\right)$
$\chi_{5488}(19,\cdot)$	5488.w	12	no	$1$	$1$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{7}{12}\right)$	$-i$	$-1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{5488}(23,\cdot)$	5488.ck	294	no	$-1$	$1$	$e\left(\frac{82}{147}\right)$	$e\left(\frac{199}{294}\right)$	$e\left(\frac{17}{147}\right)$	$e\left(\frac{4}{147}\right)$	$e\left(\frac{47}{98}\right)$	$e\left(\frac{23}{98}\right)$	$e\left(\frac{139}{147}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{289}{294}\right)$	$e\left(\frac{52}{147}\right)$
$\chi_{5488}(25,\cdot)$	5488.co	294	no	$1$	$1$	$e\left(\frac{205}{294}\right)$	$e\left(\frac{65}{294}\right)$	$e\left(\frac{58}{147}\right)$	$e\left(\frac{157}{294}\right)$	$e\left(\frac{71}{98}\right)$	$e\left(\frac{45}{49}\right)$	$e\left(\frac{137}{147}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{52}{147}\right)$	$e\left(\frac{65}{147}\right)$
$\chi_{5488}(27,\cdot)$	5488.cg	196	yes	$1$	$1$	$e\left(\frac{51}{196}\right)$	$e\left(\frac{107}{196}\right)$	$e\left(\frac{51}{98}\right)$	$e\left(\frac{171}{196}\right)$	$e\left(\frac{129}{196}\right)$	$e\left(\frac{79}{98}\right)$	$e\left(\frac{25}{98}\right)$	$-i$	$e\left(\frac{33}{49}\right)$	$e\left(\frac{9}{98}\right)$
$\chi_{5488}(29,\cdot)$	5488.cf	196	yes	$1$	$1$	$e\left(\frac{5}{196}\right)$	$e\left(\frac{47}{196}\right)$	$e\left(\frac{5}{98}\right)$	$e\left(\frac{11}{196}\right)$	$e\left(\frac{53}{196}\right)$	$e\left(\frac{13}{49}\right)$	$e\left(\frac{19}{49}\right)$	$i$	$e\left(\frac{67}{98}\right)$	$e\left(\frac{47}{98}\right)$
$\chi_{5488}(31,\cdot)$	5488.bp	42	no	$1$	$1$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{5}{42}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{25}{42}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{29}{42}\right)$	$e\left(\frac{5}{21}\right)$
$\chi_{5488}(33,\cdot)$	5488.cn	294	no	$-1$	$1$	$e\left(\frac{209}{294}\right)$	$e\left(\frac{181}{294}\right)$	$e\left(\frac{62}{147}\right)$	$e\left(\frac{127}{147}\right)$	$e\left(\frac{59}{98}\right)$	$e\left(\frac{16}{49}\right)$	$e\left(\frac{227}{294}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{86}{147}\right)$	$e\left(\frac{34}{147}\right)$
$\chi_{5488}(37,\cdot)$	5488.ct	588	yes	$1$	$1$	$e\left(\frac{1}{588}\right)$	$e\left(\frac{323}{588}\right)$	$e\left(\frac{1}{294}\right)$	$e\left(\frac{355}{588}\right)$	$e\left(\frac{95}{196}\right)$	$e\left(\frac{27}{49}\right)$	$e\left(\frac{43}{147}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{229}{294}\right)$	$e\left(\frac{29}{294}\right)$
$\chi_{5488}(39,\cdot)$	5488.ck	294	no	$-1$	$1$	$e\left(\frac{143}{147}\right)$	$e\left(\frac{209}{294}\right)$	$e\left(\frac{139}{147}\right)$	$e\left(\frac{50}{147}\right)$	$e\left(\frac{73}{98}\right)$	$e\left(\frac{67}{98}\right)$	$e\left(\frac{47}{147}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{11}{294}\right)$	$e\left(\frac{62}{147}\right)$
$\chi_{5488}(41,\cdot)$	5488.cd	98	no	$-1$	$1$	$e\left(\frac{6}{49}\right)$	$e\left(\frac{27}{49}\right)$	$e\left(\frac{12}{49}\right)$	$e\left(\frac{95}{98}\right)$	$e\left(\frac{44}{49}\right)$	$e\left(\frac{33}{49}\right)$	$e\left(\frac{55}{98}\right)$	$1$	$e\left(\frac{4}{49}\right)$	$e\left(\frac{5}{49}\right)$
$\chi_{5488}(43,\cdot)$	5488.ci	196	yes	$-1$	$1$	$e\left(\frac{53}{196}\right)$	$e\left(\frac{165}{196}\right)$	$e\left(\frac{53}{98}\right)$	$e\left(\frac{195}{196}\right)$	$e\left(\frac{111}{196}\right)$	$e\left(\frac{11}{98}\right)$	$e\left(\frac{25}{49}\right)$	$i$	$e\left(\frac{17}{49}\right)$	$e\left(\frac{67}{98}\right)$
$\chi_{5488}(45,\cdot)$	5488.cr	588	yes	$-1$	$1$	$e\left(\frac{209}{588}\right)$	$e\left(\frac{475}{588}\right)$	$e\left(\frac{209}{294}\right)$	$e\left(\frac{401}{588}\right)$	$e\left(\frac{59}{196}\right)$	$e\left(\frac{8}{49}\right)$	$e\left(\frac{187}{294}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{233}{294}\right)$	$e\left(\frac{181}{294}\right)$
$\chi_{5488}(47,\cdot)$	5488.cl	294	no	$1$	$1$	$e\left(\frac{34}{147}\right)$	$e\left(\frac{61}{294}\right)$	$e\left(\frac{68}{147}\right)$	$e\left(\frac{179}{294}\right)$	$e\left(\frac{41}{98}\right)$	$e\left(\frac{43}{98}\right)$	$e\left(\frac{83}{294}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{127}{294}\right)$	$e\left(\frac{61}{147}\right)$
$\chi_{5488}(51,\cdot)$	5488.cq	588	yes	$-1$	$1$	$e\left(\frac{493}{588}\right)$	$e\left(\frac{185}{588}\right)$	$e\left(\frac{199}{294}\right)$	$e\left(\frac{379}{588}\right)$	$e\left(\frac{89}{196}\right)$	$e\left(\frac{15}{98}\right)$	$e\left(\frac{31}{147}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{74}{147}\right)$	$e\left(\frac{185}{294}\right)$
$\chi_{5488}(53,\cdot)$	5488.ct	588	yes	$1$	$1$	$e\left(\frac{461}{588}\right)$	$e\left(\frac{139}{588}\right)$	$e\left(\frac{167}{294}\right)$	$e\left(\frac{191}{588}\right)$	$e\left(\frac{87}{196}\right)$	$e\left(\frac{1}{49}\right)$	$e\left(\frac{125}{147}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{23}{294}\right)$	$e\left(\frac{139}{294}\right)$
$\chi_{5488}(55,\cdot)$	5488.bx	98	no	$1$	$1$	$e\left(\frac{79}{98}\right)$	$e\left(\frac{43}{49}\right)$	$e\left(\frac{30}{49}\right)$	$e\left(\frac{33}{49}\right)$	$e\left(\frac{12}{49}\right)$	$e\left(\frac{67}{98}\right)$	$e\left(\frac{15}{98}\right)$	$-1$	$e\left(\frac{69}{98}\right)$	$e\left(\frac{37}{49}\right)$
$\chi_{5488}(57,\cdot)$	5488.by	98	no	$1$	$1$	$e\left(\frac{33}{98}\right)$	$e\left(\frac{75}{98}\right)$	$e\left(\frac{33}{49}\right)$	$e\left(\frac{53}{98}\right)$	$e\left(\frac{95}{98}\right)$	$e\left(\frac{5}{49}\right)$	$e\left(\frac{45}{49}\right)$	$-1$	$e\left(\frac{11}{49}\right)$	$e\left(\frac{26}{49}\right)$
$\chi_{5488}(59,\cdot)$	5488.cs	588	yes	$1$	$1$	$e\left(\frac{173}{588}\right)$	$e\left(\frac{313}{588}\right)$	$e\left(\frac{173}{294}\right)$	$e\left(\frac{557}{588}\right)$	$e\left(\frac{69}{196}\right)$	$e\left(\frac{81}{98}\right)$	$e\left(\frac{31}{294}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{37}{147}\right)$	$e\left(\frac{19}{294}\right)$
$\chi_{5488}(61,\cdot)$	5488.cr	588	yes	$-1$	$1$	$e\left(\frac{85}{588}\right)$	$e\left(\frac{407}{588}\right)$	$e\left(\frac{85}{294}\right)$	$e\left(\frac{481}{588}\right)$	$e\left(\frac{39}{196}\right)$	$e\left(\frac{41}{49}\right)$	$e\left(\frac{107}{294}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{61}{294}\right)$	$e\left(\frac{113}{294}\right)$
$\chi_{5488}(65,\cdot)$	5488.ce	147	no	$1$	$1$	$e\left(\frac{10}{147}\right)$	$e\left(\frac{143}{147}\right)$	$e\left(\frac{20}{147}\right)$	$e\left(\frac{22}{147}\right)$	$e\left(\frac{19}{49}\right)$	$e\left(\frac{2}{49}\right)$	$e\left(\frac{103}{147}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{23}{147}\right)$	$e\left(\frac{139}{147}\right)$
$\chi_{5488}(67,\cdot)$	5488.bw	84	no	$-1$	$1$	$e\left(\frac{11}{84}\right)$	$e\left(\frac{67}{84}\right)$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{41}{84}\right)$	$e\left(\frac{23}{28}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{25}{42}\right)$
$\chi_{5488}(69,\cdot)$	5488.ch	196	yes	$-1$	$1$	$e\left(\frac{61}{196}\right)$	$e\left(\frac{103}{196}\right)$	$e\left(\frac{61}{98}\right)$	$e\left(\frac{193}{196}\right)$	$e\left(\frac{137}{196}\right)$	$e\left(\frac{41}{49}\right)$	$e\left(\frac{3}{98}\right)$	$i$	$e\left(\frac{53}{98}\right)$	$e\left(\frac{5}{98}\right)$
$\chi_{5488}(71,\cdot)$	5488.cc	98	no	$-1$	$1$	$e\left(\frac{11}{49}\right)$	$e\left(\frac{1}{98}\right)$	$e\left(\frac{22}{49}\right)$	$e\left(\frac{34}{49}\right)$	$e\left(\frac{47}{98}\right)$	$e\left(\frac{23}{98}\right)$	$e\left(\frac{30}{49}\right)$	$1$	$e\left(\frac{31}{98}\right)$	$e\left(\frac{1}{49}\right)$
$\chi_{5488}(73,\cdot)$	5488.cj	294	no	$-1$	$1$	$e\left(\frac{113}{147}\right)$	$e\left(\frac{43}{147}\right)$	$e\left(\frac{79}{147}\right)$	$e\left(\frac{115}{294}\right)$	$e\left(\frac{4}{49}\right)$	$e\left(\frac{3}{49}\right)$	$e\left(\frac{211}{294}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{10}{147}\right)$	$e\left(\frac{86}{147}\right)$

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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	$5488$
Structure	\(C_{2}\times C_{2}\times C_{588}\)
Order	$2352$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(3\)	\(5\)	\(9\)	\(11\)	\(13\)	\(15\)	\(17\)	\(19\)	\(23\)	\(25\)
\(\chi_{5488}(1,\cdot)\)	5488.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{5488}(3,\cdot)\)	5488.cs	588	yes	\(1\)	\(1\)	\(e\left(\frac{443}{588}\right)\)	\(e\left(\frac{499}{588}\right)\)	\(e\left(\frac{149}{294}\right)\)	\(e\left(\frac{563}{588}\right)\)	\(e\left(\frac{43}{196}\right)\)	\(e\left(\frac{59}{98}\right)\)	\(e\left(\frac{25}{294}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{82}{147}\right)\)	\(e\left(\frac{205}{294}\right)\)
\(\chi_{5488}(5,\cdot)\)	5488.cr	588	yes	\(-1\)	\(1\)	\(e\left(\frac{499}{588}\right)\)	\(e\left(\frac{65}{588}\right)\)	\(e\left(\frac{205}{294}\right)\)	\(e\left(\frac{451}{588}\right)\)	\(e\left(\frac{169}{196}\right)\)	\(e\left(\frac{47}{49}\right)\)	\(e\left(\frac{137}{294}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{199}{294}\right)\)	\(e\left(\frac{65}{294}\right)\)
\(\chi_{5488}(9,\cdot)\)	5488.co	294	no	\(1\)	\(1\)	\(e\left(\frac{149}{294}\right)\)	\(e\left(\frac{205}{294}\right)\)	\(e\left(\frac{2}{147}\right)\)	\(e\left(\frac{269}{294}\right)\)	\(e\left(\frac{43}{98}\right)\)	\(e\left(\frac{10}{49}\right)\)	\(e\left(\frac{25}{147}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{17}{147}\right)\)	\(e\left(\frac{58}{147}\right)\)
\(\chi_{5488}(11,\cdot)\)	5488.cq	588	yes	\(-1\)	\(1\)	\(e\left(\frac{563}{588}\right)\)	\(e\left(\frac{451}{588}\right)\)	\(e\left(\frac{269}{294}\right)\)	\(e\left(\frac{533}{588}\right)\)	\(e\left(\frac{75}{196}\right)\)	\(e\left(\frac{71}{98}\right)\)	\(e\left(\frac{101}{147}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{4}{147}\right)\)	\(e\left(\frac{157}{294}\right)\)
\(\chi_{5488}(13,\cdot)\)	5488.ch	196	yes	\(-1\)	\(1\)	\(e\left(\frac{43}{196}\right)\)	\(e\left(\frac{169}{196}\right)\)	\(e\left(\frac{43}{98}\right)\)	\(e\left(\frac{75}{196}\right)\)	\(e\left(\frac{103}{196}\right)\)	\(e\left(\frac{4}{49}\right)\)	\(e\left(\frac{23}{98}\right)\)	\(-i\)	\(e\left(\frac{47}{98}\right)\)	\(e\left(\frac{71}{98}\right)\)
\(\chi_{5488}(15,\cdot)\)	5488.ca	98	no	\(-1\)	\(1\)	\(e\left(\frac{59}{98}\right)\)	\(e\left(\frac{47}{49}\right)\)	\(e\left(\frac{10}{49}\right)\)	\(e\left(\frac{71}{98}\right)\)	\(e\left(\frac{4}{49}\right)\)	\(e\left(\frac{55}{98}\right)\)	\(e\left(\frac{27}{49}\right)\)	\(-1\)	\(e\left(\frac{23}{98}\right)\)	\(e\left(\frac{45}{49}\right)\)
\(\chi_{5488}(17,\cdot)\)	5488.cn	294	no	\(-1\)	\(1\)	\(e\left(\frac{25}{294}\right)\)	\(e\left(\frac{137}{294}\right)\)	\(e\left(\frac{25}{147}\right)\)	\(e\left(\frac{101}{147}\right)\)	\(e\left(\frac{23}{98}\right)\)	\(e\left(\frac{27}{49}\right)\)	\(e\left(\frac{37}{294}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{139}{147}\right)\)	\(e\left(\frac{137}{147}\right)\)
\(\chi_{5488}(19,\cdot)\)	5488.w	12	no	\(1\)	\(1\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(-i\)	\(-1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{5488}(23,\cdot)\)	5488.ck	294	no	\(-1\)	\(1\)	\(e\left(\frac{82}{147}\right)\)	\(e\left(\frac{199}{294}\right)\)	\(e\left(\frac{17}{147}\right)\)	\(e\left(\frac{4}{147}\right)\)	\(e\left(\frac{47}{98}\right)\)	\(e\left(\frac{23}{98}\right)\)	\(e\left(\frac{139}{147}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{289}{294}\right)\)	\(e\left(\frac{52}{147}\right)\)
\(\chi_{5488}(25,\cdot)\)	5488.co	294	no	\(1\)	\(1\)	\(e\left(\frac{205}{294}\right)\)	\(e\left(\frac{65}{294}\right)\)	\(e\left(\frac{58}{147}\right)\)	\(e\left(\frac{157}{294}\right)\)	\(e\left(\frac{71}{98}\right)\)	\(e\left(\frac{45}{49}\right)\)	\(e\left(\frac{137}{147}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{52}{147}\right)\)	\(e\left(\frac{65}{147}\right)\)
\(\chi_{5488}(27,\cdot)\)	5488.cg	196	yes	\(1\)	\(1\)	\(e\left(\frac{51}{196}\right)\)	\(e\left(\frac{107}{196}\right)\)	\(e\left(\frac{51}{98}\right)\)	\(e\left(\frac{171}{196}\right)\)	\(e\left(\frac{129}{196}\right)\)	\(e\left(\frac{79}{98}\right)\)	\(e\left(\frac{25}{98}\right)\)	\(-i\)	\(e\left(\frac{33}{49}\right)\)	\(e\left(\frac{9}{98}\right)\)
\(\chi_{5488}(29,\cdot)\)	5488.cf	196	yes	\(1\)	\(1\)	\(e\left(\frac{5}{196}\right)\)	\(e\left(\frac{47}{196}\right)\)	\(e\left(\frac{5}{98}\right)\)	\(e\left(\frac{11}{196}\right)\)	\(e\left(\frac{53}{196}\right)\)	\(e\left(\frac{13}{49}\right)\)	\(e\left(\frac{19}{49}\right)\)	\(i\)	\(e\left(\frac{67}{98}\right)\)	\(e\left(\frac{47}{98}\right)\)
\(\chi_{5488}(31,\cdot)\)	5488.bp	42	no	\(1\)	\(1\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{5}{42}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{25}{42}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{13}{42}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{29}{42}\right)\)	\(e\left(\frac{5}{21}\right)\)
\(\chi_{5488}(33,\cdot)\)	5488.cn	294	no	\(-1\)	\(1\)	\(e\left(\frac{209}{294}\right)\)	\(e\left(\frac{181}{294}\right)\)	\(e\left(\frac{62}{147}\right)\)	\(e\left(\frac{127}{147}\right)\)	\(e\left(\frac{59}{98}\right)\)	\(e\left(\frac{16}{49}\right)\)	\(e\left(\frac{227}{294}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{86}{147}\right)\)	\(e\left(\frac{34}{147}\right)\)
\(\chi_{5488}(37,\cdot)\)	5488.ct	588	yes	\(1\)	\(1\)	\(e\left(\frac{1}{588}\right)\)	\(e\left(\frac{323}{588}\right)\)	\(e\left(\frac{1}{294}\right)\)	\(e\left(\frac{355}{588}\right)\)	\(e\left(\frac{95}{196}\right)\)	\(e\left(\frac{27}{49}\right)\)	\(e\left(\frac{43}{147}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{229}{294}\right)\)	\(e\left(\frac{29}{294}\right)\)
\(\chi_{5488}(39,\cdot)\)	5488.ck	294	no	\(-1\)	\(1\)	\(e\left(\frac{143}{147}\right)\)	\(e\left(\frac{209}{294}\right)\)	\(e\left(\frac{139}{147}\right)\)	\(e\left(\frac{50}{147}\right)\)	\(e\left(\frac{73}{98}\right)\)	\(e\left(\frac{67}{98}\right)\)	\(e\left(\frac{47}{147}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{11}{294}\right)\)	\(e\left(\frac{62}{147}\right)\)
\(\chi_{5488}(41,\cdot)\)	5488.cd	98	no	\(-1\)	\(1\)	\(e\left(\frac{6}{49}\right)\)	\(e\left(\frac{27}{49}\right)\)	\(e\left(\frac{12}{49}\right)\)	\(e\left(\frac{95}{98}\right)\)	\(e\left(\frac{44}{49}\right)\)	\(e\left(\frac{33}{49}\right)\)	\(e\left(\frac{55}{98}\right)\)	\(1\)	\(e\left(\frac{4}{49}\right)\)	\(e\left(\frac{5}{49}\right)\)
\(\chi_{5488}(43,\cdot)\)	5488.ci	196	yes	\(-1\)	\(1\)	\(e\left(\frac{53}{196}\right)\)	\(e\left(\frac{165}{196}\right)\)	\(e\left(\frac{53}{98}\right)\)	\(e\left(\frac{195}{196}\right)\)	\(e\left(\frac{111}{196}\right)\)	\(e\left(\frac{11}{98}\right)\)	\(e\left(\frac{25}{49}\right)\)	\(i\)	\(e\left(\frac{17}{49}\right)\)	\(e\left(\frac{67}{98}\right)\)
\(\chi_{5488}(45,\cdot)\)	5488.cr	588	yes	\(-1\)	\(1\)	\(e\left(\frac{209}{588}\right)\)	\(e\left(\frac{475}{588}\right)\)	\(e\left(\frac{209}{294}\right)\)	\(e\left(\frac{401}{588}\right)\)	\(e\left(\frac{59}{196}\right)\)	\(e\left(\frac{8}{49}\right)\)	\(e\left(\frac{187}{294}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{233}{294}\right)\)	\(e\left(\frac{181}{294}\right)\)
\(\chi_{5488}(47,\cdot)\)	5488.cl	294	no	\(1\)	\(1\)	\(e\left(\frac{34}{147}\right)\)	\(e\left(\frac{61}{294}\right)\)	\(e\left(\frac{68}{147}\right)\)	\(e\left(\frac{179}{294}\right)\)	\(e\left(\frac{41}{98}\right)\)	\(e\left(\frac{43}{98}\right)\)	\(e\left(\frac{83}{294}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{127}{294}\right)\)	\(e\left(\frac{61}{147}\right)\)
\(\chi_{5488}(51,\cdot)\)	5488.cq	588	yes	\(-1\)	\(1\)	\(e\left(\frac{493}{588}\right)\)	\(e\left(\frac{185}{588}\right)\)	\(e\left(\frac{199}{294}\right)\)	\(e\left(\frac{379}{588}\right)\)	\(e\left(\frac{89}{196}\right)\)	\(e\left(\frac{15}{98}\right)\)	\(e\left(\frac{31}{147}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{74}{147}\right)\)	\(e\left(\frac{185}{294}\right)\)
\(\chi_{5488}(53,\cdot)\)	5488.ct	588	yes	\(1\)	\(1\)	\(e\left(\frac{461}{588}\right)\)	\(e\left(\frac{139}{588}\right)\)	\(e\left(\frac{167}{294}\right)\)	\(e\left(\frac{191}{588}\right)\)	\(e\left(\frac{87}{196}\right)\)	\(e\left(\frac{1}{49}\right)\)	\(e\left(\frac{125}{147}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{23}{294}\right)\)	\(e\left(\frac{139}{294}\right)\)
\(\chi_{5488}(55,\cdot)\)	5488.bx	98	no	\(1\)	\(1\)	\(e\left(\frac{79}{98}\right)\)	\(e\left(\frac{43}{49}\right)\)	\(e\left(\frac{30}{49}\right)\)	\(e\left(\frac{33}{49}\right)\)	\(e\left(\frac{12}{49}\right)\)	\(e\left(\frac{67}{98}\right)\)	\(e\left(\frac{15}{98}\right)\)	\(-1\)	\(e\left(\frac{69}{98}\right)\)	\(e\left(\frac{37}{49}\right)\)
\(\chi_{5488}(57,\cdot)\)	5488.by	98	no	\(1\)	\(1\)	\(e\left(\frac{33}{98}\right)\)	\(e\left(\frac{75}{98}\right)\)	\(e\left(\frac{33}{49}\right)\)	\(e\left(\frac{53}{98}\right)\)	\(e\left(\frac{95}{98}\right)\)	\(e\left(\frac{5}{49}\right)\)	\(e\left(\frac{45}{49}\right)\)	\(-1\)	\(e\left(\frac{11}{49}\right)\)	\(e\left(\frac{26}{49}\right)\)
\(\chi_{5488}(59,\cdot)\)	5488.cs	588	yes	\(1\)	\(1\)	\(e\left(\frac{173}{588}\right)\)	\(e\left(\frac{313}{588}\right)\)	\(e\left(\frac{173}{294}\right)\)	\(e\left(\frac{557}{588}\right)\)	\(e\left(\frac{69}{196}\right)\)	\(e\left(\frac{81}{98}\right)\)	\(e\left(\frac{31}{294}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{37}{147}\right)\)	\(e\left(\frac{19}{294}\right)\)
\(\chi_{5488}(61,\cdot)\)	5488.cr	588	yes	\(-1\)	\(1\)	\(e\left(\frac{85}{588}\right)\)	\(e\left(\frac{407}{588}\right)\)	\(e\left(\frac{85}{294}\right)\)	\(e\left(\frac{481}{588}\right)\)	\(e\left(\frac{39}{196}\right)\)	\(e\left(\frac{41}{49}\right)\)	\(e\left(\frac{107}{294}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{61}{294}\right)\)	\(e\left(\frac{113}{294}\right)\)
\(\chi_{5488}(65,\cdot)\)	5488.ce	147	no	\(1\)	\(1\)	\(e\left(\frac{10}{147}\right)\)	\(e\left(\frac{143}{147}\right)\)	\(e\left(\frac{20}{147}\right)\)	\(e\left(\frac{22}{147}\right)\)	\(e\left(\frac{19}{49}\right)\)	\(e\left(\frac{2}{49}\right)\)	\(e\left(\frac{103}{147}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{23}{147}\right)\)	\(e\left(\frac{139}{147}\right)\)
\(\chi_{5488}(67,\cdot)\)	5488.bw	84	no	\(-1\)	\(1\)	\(e\left(\frac{11}{84}\right)\)	\(e\left(\frac{67}{84}\right)\)	\(e\left(\frac{11}{42}\right)\)	\(e\left(\frac{41}{84}\right)\)	\(e\left(\frac{23}{28}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{25}{42}\right)\)
\(\chi_{5488}(69,\cdot)\)	5488.ch	196	yes	\(-1\)	\(1\)	\(e\left(\frac{61}{196}\right)\)	\(e\left(\frac{103}{196}\right)\)	\(e\left(\frac{61}{98}\right)\)	\(e\left(\frac{193}{196}\right)\)	\(e\left(\frac{137}{196}\right)\)	\(e\left(\frac{41}{49}\right)\)	\(e\left(\frac{3}{98}\right)\)	\(i\)	\(e\left(\frac{53}{98}\right)\)	\(e\left(\frac{5}{98}\right)\)
\(\chi_{5488}(71,\cdot)\)	5488.cc	98	no	\(-1\)	\(1\)	\(e\left(\frac{11}{49}\right)\)	\(e\left(\frac{1}{98}\right)\)	\(e\left(\frac{22}{49}\right)\)	\(e\left(\frac{34}{49}\right)\)	\(e\left(\frac{47}{98}\right)\)	\(e\left(\frac{23}{98}\right)\)	\(e\left(\frac{30}{49}\right)\)	\(1\)	\(e\left(\frac{31}{98}\right)\)	\(e\left(\frac{1}{49}\right)\)
\(\chi_{5488}(73,\cdot)\)	5488.cj	294	no	\(-1\)	\(1\)	\(e\left(\frac{113}{147}\right)\)	\(e\left(\frac{43}{147}\right)\)	\(e\left(\frac{79}{147}\right)\)	\(e\left(\frac{115}{294}\right)\)	\(e\left(\frac{4}{49}\right)\)	\(e\left(\frac{3}{49}\right)\)	\(e\left(\frac{211}{294}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{10}{147}\right)\)	\(e\left(\frac{86}{147}\right)\)

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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.