LMFDB - Group of Dirichlet characters of modulus 3233

Show commands: PariGP / SageMath

sage: H = DirichletGroup(3233)

pari: g = idealstar(,3233,2)

Character group

sage: G.order() pari: g.no
Order	=	3120
sage: H.invariants() pari: g.cyc
Structure	=	$C_{4}\times C_{780}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{3233}(1221,\cdot)$, $\chi_{3233}(2015,\cdot)$

First 32 of 3120 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	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$11$
$\chi_{3233}(1,\cdot)$	3233.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{3233}(2,\cdot)$	3233.cw	780	yes	$1$	$1$	$e\left(\frac{7}{195}\right)$	$e\left(\frac{111}{260}\right)$	$e\left(\frac{14}{195}\right)$	$e\left(\frac{211}{780}\right)$	$e\left(\frac{361}{780}\right)$	$e\left(\frac{67}{780}\right)$	$e\left(\frac{7}{65}\right)$	$e\left(\frac{111}{130}\right)$	$e\left(\frac{239}{780}\right)$	$e\left(\frac{19}{52}\right)$
$\chi_{3233}(3,\cdot)$	3233.cq	260	yes	$-1$	$1$	$e\left(\frac{111}{260}\right)$	$e\left(\frac{41}{260}\right)$	$e\left(\frac{111}{130}\right)$	$e\left(\frac{147}{260}\right)$	$e\left(\frac{38}{65}\right)$	$e\left(\frac{31}{65}\right)$	$e\left(\frac{73}{260}\right)$	$e\left(\frac{41}{130}\right)$	$e\left(\frac{129}{130}\right)$	$e\left(\frac{6}{13}\right)$
$\chi_{3233}(4,\cdot)$	3233.ct	390	yes	$1$	$1$	$e\left(\frac{14}{195}\right)$	$e\left(\frac{111}{130}\right)$	$e\left(\frac{28}{195}\right)$	$e\left(\frac{211}{390}\right)$	$e\left(\frac{361}{390}\right)$	$e\left(\frac{67}{390}\right)$	$e\left(\frac{14}{65}\right)$	$e\left(\frac{46}{65}\right)$	$e\left(\frac{239}{390}\right)$	$e\left(\frac{19}{26}\right)$
$\chi_{3233}(5,\cdot)$	3233.cy	780	yes	$-1$	$1$	$e\left(\frac{211}{780}\right)$	$e\left(\frac{147}{260}\right)$	$e\left(\frac{211}{390}\right)$	$e\left(\frac{427}{780}\right)$	$e\left(\frac{163}{195}\right)$	$e\left(\frac{121}{195}\right)$	$e\left(\frac{211}{260}\right)$	$e\left(\frac{17}{130}\right)$	$e\left(\frac{319}{390}\right)$	$e\left(\frac{12}{13}\right)$
$\chi_{3233}(6,\cdot)$	3233.da	780	yes	$-1$	$1$	$e\left(\frac{361}{780}\right)$	$e\left(\frac{38}{65}\right)$	$e\left(\frac{361}{390}\right)$	$e\left(\frac{163}{195}\right)$	$e\left(\frac{37}{780}\right)$	$e\left(\frac{439}{780}\right)$	$e\left(\frac{101}{260}\right)$	$e\left(\frac{11}{65}\right)$	$e\left(\frac{233}{780}\right)$	$e\left(\frac{43}{52}\right)$
$\chi_{3233}(7,\cdot)$	3233.da	780	yes	$-1$	$1$	$e\left(\frac{67}{780}\right)$	$e\left(\frac{31}{65}\right)$	$e\left(\frac{67}{390}\right)$	$e\left(\frac{121}{195}\right)$	$e\left(\frac{439}{780}\right)$	$e\left(\frac{613}{780}\right)$	$e\left(\frac{67}{260}\right)$	$e\left(\frac{62}{65}\right)$	$e\left(\frac{551}{780}\right)$	$e\left(\frac{45}{52}\right)$
$\chi_{3233}(8,\cdot)$	3233.cs	260	yes	$1$	$1$	$e\left(\frac{7}{65}\right)$	$e\left(\frac{73}{260}\right)$	$e\left(\frac{14}{65}\right)$	$e\left(\frac{211}{260}\right)$	$e\left(\frac{101}{260}\right)$	$e\left(\frac{67}{260}\right)$	$e\left(\frac{21}{65}\right)$	$e\left(\frac{73}{130}\right)$	$e\left(\frac{239}{260}\right)$	$e\left(\frac{5}{52}\right)$
$\chi_{3233}(9,\cdot)$	3233.cd	130	yes	$1$	$1$	$e\left(\frac{111}{130}\right)$	$e\left(\frac{41}{130}\right)$	$e\left(\frac{46}{65}\right)$	$e\left(\frac{17}{130}\right)$	$e\left(\frac{11}{65}\right)$	$e\left(\frac{62}{65}\right)$	$e\left(\frac{73}{130}\right)$	$e\left(\frac{41}{65}\right)$	$e\left(\frac{64}{65}\right)$	$e\left(\frac{12}{13}\right)$
$\chi_{3233}(10,\cdot)$	3233.cx	780	yes	$-1$	$1$	$e\left(\frac{239}{780}\right)$	$e\left(\frac{129}{130}\right)$	$e\left(\frac{239}{390}\right)$	$e\left(\frac{319}{390}\right)$	$e\left(\frac{233}{780}\right)$	$e\left(\frac{551}{780}\right)$	$e\left(\frac{239}{260}\right)$	$e\left(\frac{64}{65}\right)$	$e\left(\frac{97}{780}\right)$	$e\left(\frac{15}{52}\right)$
$\chi_{3233}(11,\cdot)$	3233.bo	52	yes	$-1$	$1$	$e\left(\frac{19}{52}\right)$	$e\left(\frac{6}{13}\right)$	$e\left(\frac{19}{26}\right)$	$e\left(\frac{12}{13}\right)$	$e\left(\frac{43}{52}\right)$	$e\left(\frac{45}{52}\right)$	$e\left(\frac{5}{52}\right)$	$e\left(\frac{12}{13}\right)$	$e\left(\frac{15}{52}\right)$	$e\left(\frac{23}{52}\right)$
$\chi_{3233}(12,\cdot)$	3233.cz	780	yes	$-1$	$1$	$e\left(\frac{389}{780}\right)$	$e\left(\frac{3}{260}\right)$	$e\left(\frac{389}{390}\right)$	$e\left(\frac{83}{780}\right)$	$e\left(\frac{199}{390}\right)$	$e\left(\frac{253}{390}\right)$	$e\left(\frac{129}{260}\right)$	$e\left(\frac{3}{130}\right)$	$e\left(\frac{118}{195}\right)$	$e\left(\frac{5}{26}\right)$
$\chi_{3233}(13,\cdot)$	3233.bm	39	yes	$1$	$1$	$e\left(\frac{5}{39}\right)$	$e\left(\frac{11}{13}\right)$	$e\left(\frac{10}{39}\right)$	$e\left(\frac{14}{39}\right)$	$e\left(\frac{38}{39}\right)$	$e\left(\frac{5}{39}\right)$	$e\left(\frac{5}{13}\right)$	$e\left(\frac{9}{13}\right)$	$e\left(\frac{19}{39}\right)$	$e\left(\frac{10}{13}\right)$
$\chi_{3233}(14,\cdot)$	3233.cj	156	yes	$-1$	$1$	$e\left(\frac{19}{156}\right)$	$e\left(\frac{47}{52}\right)$	$e\left(\frac{19}{78}\right)$	$e\left(\frac{139}{156}\right)$	$e\left(\frac{1}{39}\right)$	$e\left(\frac{34}{39}\right)$	$e\left(\frac{19}{52}\right)$	$e\left(\frac{21}{26}\right)$	$e\left(\frac{1}{78}\right)$	$e\left(\frac{3}{13}\right)$
$\chi_{3233}(15,\cdot)$	3233.cm	195	yes	$1$	$1$	$e\left(\frac{136}{195}\right)$	$e\left(\frac{47}{65}\right)$	$e\left(\frac{77}{195}\right)$	$e\left(\frac{22}{195}\right)$	$e\left(\frac{82}{195}\right)$	$e\left(\frac{19}{195}\right)$	$e\left(\frac{6}{65}\right)$	$e\left(\frac{29}{65}\right)$	$e\left(\frac{158}{195}\right)$	$e\left(\frac{5}{13}\right)$
$\chi_{3233}(16,\cdot)$	3233.cm	195	yes	$1$	$1$	$e\left(\frac{28}{195}\right)$	$e\left(\frac{46}{65}\right)$	$e\left(\frac{56}{195}\right)$	$e\left(\frac{16}{195}\right)$	$e\left(\frac{166}{195}\right)$	$e\left(\frac{67}{195}\right)$	$e\left(\frac{28}{65}\right)$	$e\left(\frac{27}{65}\right)$	$e\left(\frac{44}{195}\right)$	$e\left(\frac{6}{13}\right)$
$\chi_{3233}(17,\cdot)$	3233.da	780	yes	$-1$	$1$	$e\left(\frac{761}{780}\right)$	$e\left(\frac{63}{65}\right)$	$e\left(\frac{371}{390}\right)$	$e\left(\frac{53}{195}\right)$	$e\left(\frac{737}{780}\right)$	$e\left(\frac{59}{780}\right)$	$e\left(\frac{241}{260}\right)$	$e\left(\frac{61}{65}\right)$	$e\left(\frac{193}{780}\right)$	$e\left(\frac{47}{52}\right)$
$\chi_{3233}(18,\cdot)$	3233.db	780	yes	$1$	$1$	$e\left(\frac{347}{390}\right)$	$e\left(\frac{193}{260}\right)$	$e\left(\frac{152}{195}\right)$	$e\left(\frac{313}{780}\right)$	$e\left(\frac{493}{780}\right)$	$e\left(\frac{31}{780}\right)$	$e\left(\frac{87}{130}\right)$	$e\left(\frac{63}{130}\right)$	$e\left(\frac{227}{780}\right)$	$e\left(\frac{15}{52}\right)$
$\chi_{3233}(19,\cdot)$	3233.cy	780	yes	$-1$	$1$	$e\left(\frac{113}{780}\right)$	$e\left(\frac{181}{260}\right)$	$e\left(\frac{113}{390}\right)$	$e\left(\frac{761}{780}\right)$	$e\left(\frac{164}{195}\right)$	$e\left(\frac{38}{195}\right)$	$e\left(\frac{113}{260}\right)$	$e\left(\frac{51}{130}\right)$	$e\left(\frac{47}{390}\right)$	$e\left(\frac{10}{13}\right)$
$\chi_{3233}(20,\cdot)$	3233.cp	260	yes	$-1$	$1$	$e\left(\frac{89}{260}\right)$	$e\left(\frac{109}{260}\right)$	$e\left(\frac{89}{130}\right)$	$e\left(\frac{23}{260}\right)$	$e\left(\frac{99}{130}\right)$	$e\left(\frac{103}{130}\right)$	$e\left(\frac{7}{260}\right)$	$e\left(\frac{109}{130}\right)$	$e\left(\frac{28}{65}\right)$	$e\left(\frac{17}{26}\right)$
$\chi_{3233}(21,\cdot)$	3233.cl	156	yes	$1$	$1$	$e\left(\frac{20}{39}\right)$	$e\left(\frac{33}{52}\right)$	$e\left(\frac{1}{39}\right)$	$e\left(\frac{29}{156}\right)$	$e\left(\frac{23}{156}\right)$	$e\left(\frac{41}{156}\right)$	$e\left(\frac{7}{13}\right)$	$e\left(\frac{7}{26}\right)$	$e\left(\frac{109}{156}\right)$	$e\left(\frac{17}{52}\right)$
$\chi_{3233}(22,\cdot)$	3233.cz	780	yes	$-1$	$1$	$e\left(\frac{313}{780}\right)$	$e\left(\frac{231}{260}\right)$	$e\left(\frac{313}{390}\right)$	$e\left(\frac{151}{780}\right)$	$e\left(\frac{113}{390}\right)$	$e\left(\frac{371}{390}\right)$	$e\left(\frac{53}{260}\right)$	$e\left(\frac{101}{130}\right)$	$e\left(\frac{116}{195}\right)$	$e\left(\frac{21}{26}\right)$
$\chi_{3233}(23,\cdot)$	3233.bf	20	yes	$1$	$1$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{17}{20}\right)$	$-i$
$\chi_{3233}(24,\cdot)$	3233.co	260	yes	$-1$	$1$	$e\left(\frac{139}{260}\right)$	$e\left(\frac{57}{130}\right)$	$e\left(\frac{9}{130}\right)$	$e\left(\frac{49}{130}\right)$	$e\left(\frac{253}{260}\right)$	$e\left(\frac{191}{260}\right)$	$e\left(\frac{157}{260}\right)$	$e\left(\frac{57}{65}\right)$	$e\left(\frac{237}{260}\right)$	$e\left(\frac{29}{52}\right)$
$\chi_{3233}(25,\cdot)$	3233.cu	390	yes	$1$	$1$	$e\left(\frac{211}{390}\right)$	$e\left(\frac{17}{130}\right)$	$e\left(\frac{16}{195}\right)$	$e\left(\frac{37}{390}\right)$	$e\left(\frac{131}{195}\right)$	$e\left(\frac{47}{195}\right)$	$e\left(\frac{81}{130}\right)$	$e\left(\frac{17}{65}\right)$	$e\left(\frac{124}{195}\right)$	$e\left(\frac{11}{13}\right)$
$\chi_{3233}(26,\cdot)$	3233.cw	780	yes	$1$	$1$	$e\left(\frac{32}{195}\right)$	$e\left(\frac{71}{260}\right)$	$e\left(\frac{64}{195}\right)$	$e\left(\frac{491}{780}\right)$	$e\left(\frac{341}{780}\right)$	$e\left(\frac{167}{780}\right)$	$e\left(\frac{32}{65}\right)$	$e\left(\frac{71}{130}\right)$	$e\left(\frac{619}{780}\right)$	$e\left(\frac{7}{52}\right)$
$\chi_{3233}(27,\cdot)$	3233.cq	260	yes	$-1$	$1$	$e\left(\frac{73}{260}\right)$	$e\left(\frac{123}{260}\right)$	$e\left(\frac{73}{130}\right)$	$e\left(\frac{181}{260}\right)$	$e\left(\frac{49}{65}\right)$	$e\left(\frac{28}{65}\right)$	$e\left(\frac{219}{260}\right)$	$e\left(\frac{123}{130}\right)$	$e\left(\frac{127}{130}\right)$	$e\left(\frac{5}{13}\right)$
$\chi_{3233}(28,\cdot)$	3233.co	260	yes	$-1$	$1$	$e\left(\frac{41}{260}\right)$	$e\left(\frac{43}{130}\right)$	$e\left(\frac{41}{130}\right)$	$e\left(\frac{21}{130}\right)$	$e\left(\frac{127}{260}\right)$	$e\left(\frac{249}{260}\right)$	$e\left(\frac{123}{260}\right)$	$e\left(\frac{43}{65}\right)$	$e\left(\frac{83}{260}\right)$	$e\left(\frac{31}{52}\right)$
$\chi_{3233}(29,\cdot)$	3233.ch	156	yes	$-1$	$1$	$e\left(\frac{73}{156}\right)$	$e\left(\frac{7}{13}\right)$	$e\left(\frac{73}{78}\right)$	$e\left(\frac{16}{39}\right)$	$e\left(\frac{1}{156}\right)$	$e\left(\frac{151}{156}\right)$	$e\left(\frac{21}{52}\right)$	$e\left(\frac{1}{13}\right)$	$e\left(\frac{137}{156}\right)$	$e\left(\frac{3}{52}\right)$
$\chi_{3233}(30,\cdot)$	3233.by	60	yes	$1$	$1$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{23}{60}\right)$	$e\left(\frac{53}{60}\right)$	$e\left(\frac{11}{60}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{7}{60}\right)$	$-i$
$\chi_{3233}(31,\cdot)$	3233.db	780	yes	$1$	$1$	$e\left(\frac{241}{390}\right)$	$e\left(\frac{179}{260}\right)$	$e\left(\frac{46}{195}\right)$	$e\left(\frac{359}{780}\right)$	$e\left(\frac{239}{780}\right)$	$e\left(\frac{53}{780}\right)$	$e\left(\frac{111}{130}\right)$	$e\left(\frac{49}{130}\right)$	$e\left(\frac{61}{780}\right)$	$e\left(\frac{29}{52}\right)$
$\chi_{3233}(32,\cdot)$	3233.cl	156	yes	$1$	$1$	$e\left(\frac{7}{39}\right)$	$e\left(\frac{7}{52}\right)$	$e\left(\frac{14}{39}\right)$	$e\left(\frac{55}{156}\right)$	$e\left(\frac{49}{156}\right)$	$e\left(\frac{67}{156}\right)$	$e\left(\frac{7}{13}\right)$	$e\left(\frac{7}{26}\right)$	$e\left(\frac{83}{156}\right)$	$e\left(\frac{43}{52}\right)$

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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	$3233$
Structure	\(C_{4}\times C_{780}\)
Order	$3120$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(7\)	\(8\)	\(9\)	\(10\)	\(11\)
\(\chi_{3233}(1,\cdot)\)	3233.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{3233}(2,\cdot)\)	3233.cw	780	yes	\(1\)	\(1\)	\(e\left(\frac{7}{195}\right)\)	\(e\left(\frac{111}{260}\right)\)	\(e\left(\frac{14}{195}\right)\)	\(e\left(\frac{211}{780}\right)\)	\(e\left(\frac{361}{780}\right)\)	\(e\left(\frac{67}{780}\right)\)	\(e\left(\frac{7}{65}\right)\)	\(e\left(\frac{111}{130}\right)\)	\(e\left(\frac{239}{780}\right)\)	\(e\left(\frac{19}{52}\right)\)
\(\chi_{3233}(3,\cdot)\)	3233.cq	260	yes	\(-1\)	\(1\)	\(e\left(\frac{111}{260}\right)\)	\(e\left(\frac{41}{260}\right)\)	\(e\left(\frac{111}{130}\right)\)	\(e\left(\frac{147}{260}\right)\)	\(e\left(\frac{38}{65}\right)\)	\(e\left(\frac{31}{65}\right)\)	\(e\left(\frac{73}{260}\right)\)	\(e\left(\frac{41}{130}\right)\)	\(e\left(\frac{129}{130}\right)\)	\(e\left(\frac{6}{13}\right)\)
\(\chi_{3233}(4,\cdot)\)	3233.ct	390	yes	\(1\)	\(1\)	\(e\left(\frac{14}{195}\right)\)	\(e\left(\frac{111}{130}\right)\)	\(e\left(\frac{28}{195}\right)\)	\(e\left(\frac{211}{390}\right)\)	\(e\left(\frac{361}{390}\right)\)	\(e\left(\frac{67}{390}\right)\)	\(e\left(\frac{14}{65}\right)\)	\(e\left(\frac{46}{65}\right)\)	\(e\left(\frac{239}{390}\right)\)	\(e\left(\frac{19}{26}\right)\)
\(\chi_{3233}(5,\cdot)\)	3233.cy	780	yes	\(-1\)	\(1\)	\(e\left(\frac{211}{780}\right)\)	\(e\left(\frac{147}{260}\right)\)	\(e\left(\frac{211}{390}\right)\)	\(e\left(\frac{427}{780}\right)\)	\(e\left(\frac{163}{195}\right)\)	\(e\left(\frac{121}{195}\right)\)	\(e\left(\frac{211}{260}\right)\)	\(e\left(\frac{17}{130}\right)\)	\(e\left(\frac{319}{390}\right)\)	\(e\left(\frac{12}{13}\right)\)
\(\chi_{3233}(6,\cdot)\)	3233.da	780	yes	\(-1\)	\(1\)	\(e\left(\frac{361}{780}\right)\)	\(e\left(\frac{38}{65}\right)\)	\(e\left(\frac{361}{390}\right)\)	\(e\left(\frac{163}{195}\right)\)	\(e\left(\frac{37}{780}\right)\)	\(e\left(\frac{439}{780}\right)\)	\(e\left(\frac{101}{260}\right)\)	\(e\left(\frac{11}{65}\right)\)	\(e\left(\frac{233}{780}\right)\)	\(e\left(\frac{43}{52}\right)\)
\(\chi_{3233}(7,\cdot)\)	3233.da	780	yes	\(-1\)	\(1\)	\(e\left(\frac{67}{780}\right)\)	\(e\left(\frac{31}{65}\right)\)	\(e\left(\frac{67}{390}\right)\)	\(e\left(\frac{121}{195}\right)\)	\(e\left(\frac{439}{780}\right)\)	\(e\left(\frac{613}{780}\right)\)	\(e\left(\frac{67}{260}\right)\)	\(e\left(\frac{62}{65}\right)\)	\(e\left(\frac{551}{780}\right)\)	\(e\left(\frac{45}{52}\right)\)
\(\chi_{3233}(8,\cdot)\)	3233.cs	260	yes	\(1\)	\(1\)	\(e\left(\frac{7}{65}\right)\)	\(e\left(\frac{73}{260}\right)\)	\(e\left(\frac{14}{65}\right)\)	\(e\left(\frac{211}{260}\right)\)	\(e\left(\frac{101}{260}\right)\)	\(e\left(\frac{67}{260}\right)\)	\(e\left(\frac{21}{65}\right)\)	\(e\left(\frac{73}{130}\right)\)	\(e\left(\frac{239}{260}\right)\)	\(e\left(\frac{5}{52}\right)\)
\(\chi_{3233}(9,\cdot)\)	3233.cd	130	yes	\(1\)	\(1\)	\(e\left(\frac{111}{130}\right)\)	\(e\left(\frac{41}{130}\right)\)	\(e\left(\frac{46}{65}\right)\)	\(e\left(\frac{17}{130}\right)\)	\(e\left(\frac{11}{65}\right)\)	\(e\left(\frac{62}{65}\right)\)	\(e\left(\frac{73}{130}\right)\)	\(e\left(\frac{41}{65}\right)\)	\(e\left(\frac{64}{65}\right)\)	\(e\left(\frac{12}{13}\right)\)
\(\chi_{3233}(10,\cdot)\)	3233.cx	780	yes	\(-1\)	\(1\)	\(e\left(\frac{239}{780}\right)\)	\(e\left(\frac{129}{130}\right)\)	\(e\left(\frac{239}{390}\right)\)	\(e\left(\frac{319}{390}\right)\)	\(e\left(\frac{233}{780}\right)\)	\(e\left(\frac{551}{780}\right)\)	\(e\left(\frac{239}{260}\right)\)	\(e\left(\frac{64}{65}\right)\)	\(e\left(\frac{97}{780}\right)\)	\(e\left(\frac{15}{52}\right)\)
\(\chi_{3233}(11,\cdot)\)	3233.bo	52	yes	\(-1\)	\(1\)	\(e\left(\frac{19}{52}\right)\)	\(e\left(\frac{6}{13}\right)\)	\(e\left(\frac{19}{26}\right)\)	\(e\left(\frac{12}{13}\right)\)	\(e\left(\frac{43}{52}\right)\)	\(e\left(\frac{45}{52}\right)\)	\(e\left(\frac{5}{52}\right)\)	\(e\left(\frac{12}{13}\right)\)	\(e\left(\frac{15}{52}\right)\)	\(e\left(\frac{23}{52}\right)\)
\(\chi_{3233}(12,\cdot)\)	3233.cz	780	yes	\(-1\)	\(1\)	\(e\left(\frac{389}{780}\right)\)	\(e\left(\frac{3}{260}\right)\)	\(e\left(\frac{389}{390}\right)\)	\(e\left(\frac{83}{780}\right)\)	\(e\left(\frac{199}{390}\right)\)	\(e\left(\frac{253}{390}\right)\)	\(e\left(\frac{129}{260}\right)\)	\(e\left(\frac{3}{130}\right)\)	\(e\left(\frac{118}{195}\right)\)	\(e\left(\frac{5}{26}\right)\)
\(\chi_{3233}(13,\cdot)\)	3233.bm	39	yes	\(1\)	\(1\)	\(e\left(\frac{5}{39}\right)\)	\(e\left(\frac{11}{13}\right)\)	\(e\left(\frac{10}{39}\right)\)	\(e\left(\frac{14}{39}\right)\)	\(e\left(\frac{38}{39}\right)\)	\(e\left(\frac{5}{39}\right)\)	\(e\left(\frac{5}{13}\right)\)	\(e\left(\frac{9}{13}\right)\)	\(e\left(\frac{19}{39}\right)\)	\(e\left(\frac{10}{13}\right)\)
\(\chi_{3233}(14,\cdot)\)	3233.cj	156	yes	\(-1\)	\(1\)	\(e\left(\frac{19}{156}\right)\)	\(e\left(\frac{47}{52}\right)\)	\(e\left(\frac{19}{78}\right)\)	\(e\left(\frac{139}{156}\right)\)	\(e\left(\frac{1}{39}\right)\)	\(e\left(\frac{34}{39}\right)\)	\(e\left(\frac{19}{52}\right)\)	\(e\left(\frac{21}{26}\right)\)	\(e\left(\frac{1}{78}\right)\)	\(e\left(\frac{3}{13}\right)\)
\(\chi_{3233}(15,\cdot)\)	3233.cm	195	yes	\(1\)	\(1\)	\(e\left(\frac{136}{195}\right)\)	\(e\left(\frac{47}{65}\right)\)	\(e\left(\frac{77}{195}\right)\)	\(e\left(\frac{22}{195}\right)\)	\(e\left(\frac{82}{195}\right)\)	\(e\left(\frac{19}{195}\right)\)	\(e\left(\frac{6}{65}\right)\)	\(e\left(\frac{29}{65}\right)\)	\(e\left(\frac{158}{195}\right)\)	\(e\left(\frac{5}{13}\right)\)
\(\chi_{3233}(16,\cdot)\)	3233.cm	195	yes	\(1\)	\(1\)	\(e\left(\frac{28}{195}\right)\)	\(e\left(\frac{46}{65}\right)\)	\(e\left(\frac{56}{195}\right)\)	\(e\left(\frac{16}{195}\right)\)	\(e\left(\frac{166}{195}\right)\)	\(e\left(\frac{67}{195}\right)\)	\(e\left(\frac{28}{65}\right)\)	\(e\left(\frac{27}{65}\right)\)	\(e\left(\frac{44}{195}\right)\)	\(e\left(\frac{6}{13}\right)\)
\(\chi_{3233}(17,\cdot)\)	3233.da	780	yes	\(-1\)	\(1\)	\(e\left(\frac{761}{780}\right)\)	\(e\left(\frac{63}{65}\right)\)	\(e\left(\frac{371}{390}\right)\)	\(e\left(\frac{53}{195}\right)\)	\(e\left(\frac{737}{780}\right)\)	\(e\left(\frac{59}{780}\right)\)	\(e\left(\frac{241}{260}\right)\)	\(e\left(\frac{61}{65}\right)\)	\(e\left(\frac{193}{780}\right)\)	\(e\left(\frac{47}{52}\right)\)
\(\chi_{3233}(18,\cdot)\)	3233.db	780	yes	\(1\)	\(1\)	\(e\left(\frac{347}{390}\right)\)	\(e\left(\frac{193}{260}\right)\)	\(e\left(\frac{152}{195}\right)\)	\(e\left(\frac{313}{780}\right)\)	\(e\left(\frac{493}{780}\right)\)	\(e\left(\frac{31}{780}\right)\)	\(e\left(\frac{87}{130}\right)\)	\(e\left(\frac{63}{130}\right)\)	\(e\left(\frac{227}{780}\right)\)	\(e\left(\frac{15}{52}\right)\)
\(\chi_{3233}(19,\cdot)\)	3233.cy	780	yes	\(-1\)	\(1\)	\(e\left(\frac{113}{780}\right)\)	\(e\left(\frac{181}{260}\right)\)	\(e\left(\frac{113}{390}\right)\)	\(e\left(\frac{761}{780}\right)\)	\(e\left(\frac{164}{195}\right)\)	\(e\left(\frac{38}{195}\right)\)	\(e\left(\frac{113}{260}\right)\)	\(e\left(\frac{51}{130}\right)\)	\(e\left(\frac{47}{390}\right)\)	\(e\left(\frac{10}{13}\right)\)
\(\chi_{3233}(20,\cdot)\)	3233.cp	260	yes	\(-1\)	\(1\)	\(e\left(\frac{89}{260}\right)\)	\(e\left(\frac{109}{260}\right)\)	\(e\left(\frac{89}{130}\right)\)	\(e\left(\frac{23}{260}\right)\)	\(e\left(\frac{99}{130}\right)\)	\(e\left(\frac{103}{130}\right)\)	\(e\left(\frac{7}{260}\right)\)	\(e\left(\frac{109}{130}\right)\)	\(e\left(\frac{28}{65}\right)\)	\(e\left(\frac{17}{26}\right)\)
\(\chi_{3233}(21,\cdot)\)	3233.cl	156	yes	\(1\)	\(1\)	\(e\left(\frac{20}{39}\right)\)	\(e\left(\frac{33}{52}\right)\)	\(e\left(\frac{1}{39}\right)\)	\(e\left(\frac{29}{156}\right)\)	\(e\left(\frac{23}{156}\right)\)	\(e\left(\frac{41}{156}\right)\)	\(e\left(\frac{7}{13}\right)\)	\(e\left(\frac{7}{26}\right)\)	\(e\left(\frac{109}{156}\right)\)	\(e\left(\frac{17}{52}\right)\)
\(\chi_{3233}(22,\cdot)\)	3233.cz	780	yes	\(-1\)	\(1\)	\(e\left(\frac{313}{780}\right)\)	\(e\left(\frac{231}{260}\right)\)	\(e\left(\frac{313}{390}\right)\)	\(e\left(\frac{151}{780}\right)\)	\(e\left(\frac{113}{390}\right)\)	\(e\left(\frac{371}{390}\right)\)	\(e\left(\frac{53}{260}\right)\)	\(e\left(\frac{101}{130}\right)\)	\(e\left(\frac{116}{195}\right)\)	\(e\left(\frac{21}{26}\right)\)
\(\chi_{3233}(23,\cdot)\)	3233.bf	20	yes	\(1\)	\(1\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(-i\)
\(\chi_{3233}(24,\cdot)\)	3233.co	260	yes	\(-1\)	\(1\)	\(e\left(\frac{139}{260}\right)\)	\(e\left(\frac{57}{130}\right)\)	\(e\left(\frac{9}{130}\right)\)	\(e\left(\frac{49}{130}\right)\)	\(e\left(\frac{253}{260}\right)\)	\(e\left(\frac{191}{260}\right)\)	\(e\left(\frac{157}{260}\right)\)	\(e\left(\frac{57}{65}\right)\)	\(e\left(\frac{237}{260}\right)\)	\(e\left(\frac{29}{52}\right)\)
\(\chi_{3233}(25,\cdot)\)	3233.cu	390	yes	\(1\)	\(1\)	\(e\left(\frac{211}{390}\right)\)	\(e\left(\frac{17}{130}\right)\)	\(e\left(\frac{16}{195}\right)\)	\(e\left(\frac{37}{390}\right)\)	\(e\left(\frac{131}{195}\right)\)	\(e\left(\frac{47}{195}\right)\)	\(e\left(\frac{81}{130}\right)\)	\(e\left(\frac{17}{65}\right)\)	\(e\left(\frac{124}{195}\right)\)	\(e\left(\frac{11}{13}\right)\)
\(\chi_{3233}(26,\cdot)\)	3233.cw	780	yes	\(1\)	\(1\)	\(e\left(\frac{32}{195}\right)\)	\(e\left(\frac{71}{260}\right)\)	\(e\left(\frac{64}{195}\right)\)	\(e\left(\frac{491}{780}\right)\)	\(e\left(\frac{341}{780}\right)\)	\(e\left(\frac{167}{780}\right)\)	\(e\left(\frac{32}{65}\right)\)	\(e\left(\frac{71}{130}\right)\)	\(e\left(\frac{619}{780}\right)\)	\(e\left(\frac{7}{52}\right)\)
\(\chi_{3233}(27,\cdot)\)	3233.cq	260	yes	\(-1\)	\(1\)	\(e\left(\frac{73}{260}\right)\)	\(e\left(\frac{123}{260}\right)\)	\(e\left(\frac{73}{130}\right)\)	\(e\left(\frac{181}{260}\right)\)	\(e\left(\frac{49}{65}\right)\)	\(e\left(\frac{28}{65}\right)\)	\(e\left(\frac{219}{260}\right)\)	\(e\left(\frac{123}{130}\right)\)	\(e\left(\frac{127}{130}\right)\)	\(e\left(\frac{5}{13}\right)\)
\(\chi_{3233}(28,\cdot)\)	3233.co	260	yes	\(-1\)	\(1\)	\(e\left(\frac{41}{260}\right)\)	\(e\left(\frac{43}{130}\right)\)	\(e\left(\frac{41}{130}\right)\)	\(e\left(\frac{21}{130}\right)\)	\(e\left(\frac{127}{260}\right)\)	\(e\left(\frac{249}{260}\right)\)	\(e\left(\frac{123}{260}\right)\)	\(e\left(\frac{43}{65}\right)\)	\(e\left(\frac{83}{260}\right)\)	\(e\left(\frac{31}{52}\right)\)
\(\chi_{3233}(29,\cdot)\)	3233.ch	156	yes	\(-1\)	\(1\)	\(e\left(\frac{73}{156}\right)\)	\(e\left(\frac{7}{13}\right)\)	\(e\left(\frac{73}{78}\right)\)	\(e\left(\frac{16}{39}\right)\)	\(e\left(\frac{1}{156}\right)\)	\(e\left(\frac{151}{156}\right)\)	\(e\left(\frac{21}{52}\right)\)	\(e\left(\frac{1}{13}\right)\)	\(e\left(\frac{137}{156}\right)\)	\(e\left(\frac{3}{52}\right)\)
\(\chi_{3233}(30,\cdot)\)	3233.by	60	yes	\(1\)	\(1\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{23}{60}\right)\)	\(e\left(\frac{53}{60}\right)\)	\(e\left(\frac{11}{60}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{7}{60}\right)\)	\(-i\)
\(\chi_{3233}(31,\cdot)\)	3233.db	780	yes	\(1\)	\(1\)	\(e\left(\frac{241}{390}\right)\)	\(e\left(\frac{179}{260}\right)\)	\(e\left(\frac{46}{195}\right)\)	\(e\left(\frac{359}{780}\right)\)	\(e\left(\frac{239}{780}\right)\)	\(e\left(\frac{53}{780}\right)\)	\(e\left(\frac{111}{130}\right)\)	\(e\left(\frac{49}{130}\right)\)	\(e\left(\frac{61}{780}\right)\)	\(e\left(\frac{29}{52}\right)\)
\(\chi_{3233}(32,\cdot)\)	3233.cl	156	yes	\(1\)	\(1\)	\(e\left(\frac{7}{39}\right)\)	\(e\left(\frac{7}{52}\right)\)	\(e\left(\frac{14}{39}\right)\)	\(e\left(\frac{55}{156}\right)\)	\(e\left(\frac{49}{156}\right)\)	\(e\left(\frac{67}{156}\right)\)	\(e\left(\frac{7}{13}\right)\)	\(e\left(\frac{7}{26}\right)\)	\(e\left(\frac{83}{156}\right)\)	\(e\left(\frac{43}{52}\right)\)

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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.