LMFDB - Group of Dirichlet characters of modulus 13132

Show commands: PariGP / SageMath

sage: H = DirichletGroup(13132)

pari: g = idealstar(,13132,2)

Character group

sage: G.order() pari: g.no
Order	=	5544
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{6}\times C_{462}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{13132}(6567,\cdot)$, $\chi_{13132}(4021,\cdot)$, $\chi_{13132}(7841,\cdot)$

First 32 of 5544 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	$-1$	$1$	$3$	$5$	$9$	$11$	$13$	$15$	$17$	$19$	$23$	$25$
$\chi_{13132}(1,\cdot)$	13132.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{13132}(3,\cdot)$	13132.fr	462	yes	$-1$	$1$	$e\left(\frac{263}{462}\right)$	$e\left(\frac{128}{231}\right)$	$e\left(\frac{32}{231}\right)$	$e\left(\frac{73}{231}\right)$	$e\left(\frac{1}{77}\right)$	$e\left(\frac{19}{154}\right)$	$e\left(\frac{191}{462}\right)$	$e\left(\frac{8}{33}\right)$	$e\left(\frac{439}{462}\right)$	$e\left(\frac{25}{231}\right)$
$\chi_{13132}(5,\cdot)$	13132.fi	462	no	$1$	$1$	$e\left(\frac{128}{231}\right)$	$e\left(\frac{100}{231}\right)$	$e\left(\frac{25}{231}\right)$	$e\left(\frac{13}{462}\right)$	$e\left(\frac{8}{77}\right)$	$e\left(\frac{76}{77}\right)$	$e\left(\frac{373}{462}\right)$	$e\left(\frac{29}{66}\right)$	$e\left(\frac{139}{231}\right)$	$e\left(\frac{200}{231}\right)$
$\chi_{13132}(9,\cdot)$	13132.ez	231	no	$1$	$1$	$e\left(\frac{32}{231}\right)$	$e\left(\frac{25}{231}\right)$	$e\left(\frac{64}{231}\right)$	$e\left(\frac{146}{231}\right)$	$e\left(\frac{2}{77}\right)$	$e\left(\frac{19}{77}\right)$	$e\left(\frac{191}{231}\right)$	$e\left(\frac{16}{33}\right)$	$e\left(\frac{208}{231}\right)$	$e\left(\frac{50}{231}\right)$
$\chi_{13132}(11,\cdot)$	13132.fo	462	yes	$1$	$1$	$e\left(\frac{73}{231}\right)$	$e\left(\frac{13}{462}\right)$	$e\left(\frac{146}{231}\right)$	$e\left(\frac{26}{77}\right)$	$e\left(\frac{191}{462}\right)$	$e\left(\frac{53}{154}\right)$	$e\left(\frac{5}{231}\right)$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{111}{154}\right)$	$e\left(\frac{13}{231}\right)$
$\chi_{13132}(13,\cdot)$	13132.gd	462	no	$1$	$1$	$e\left(\frac{1}{77}\right)$	$e\left(\frac{8}{77}\right)$	$e\left(\frac{2}{77}\right)$	$e\left(\frac{191}{462}\right)$	$e\left(\frac{92}{231}\right)$	$e\left(\frac{9}{77}\right)$	$e\left(\frac{31}{462}\right)$	$e\left(\frac{25}{66}\right)$	$e\left(\frac{212}{231}\right)$	$e\left(\frac{16}{77}\right)$
$\chi_{13132}(15,\cdot)$	13132.et	154	yes	$-1$	$1$	$e\left(\frac{19}{154}\right)$	$e\left(\frac{76}{77}\right)$	$e\left(\frac{19}{77}\right)$	$e\left(\frac{53}{154}\right)$	$e\left(\frac{9}{77}\right)$	$e\left(\frac{17}{154}\right)$	$e\left(\frac{17}{77}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{85}{154}\right)$	$e\left(\frac{75}{77}\right)$
$\chi_{13132}(17,\cdot)$	13132.fx	462	no	$-1$	$1$	$e\left(\frac{191}{462}\right)$	$e\left(\frac{373}{462}\right)$	$e\left(\frac{191}{231}\right)$	$e\left(\frac{5}{231}\right)$	$e\left(\frac{31}{462}\right)$	$e\left(\frac{17}{77}\right)$	$e\left(\frac{145}{154}\right)$	$e\left(\frac{35}{66}\right)$	$e\left(\frac{178}{231}\right)$	$e\left(\frac{142}{231}\right)$
$\chi_{13132}(19,\cdot)$	13132.ei	66	no	$1$	$1$	$e\left(\frac{8}{33}\right)$	$e\left(\frac{29}{66}\right)$	$e\left(\frac{16}{33}\right)$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{25}{66}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{35}{66}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{29}{33}\right)$
$\chi_{13132}(23,\cdot)$	13132.fp	462	yes	$-1$	$1$	$e\left(\frac{439}{462}\right)$	$e\left(\frac{139}{231}\right)$	$e\left(\frac{208}{231}\right)$	$e\left(\frac{111}{154}\right)$	$e\left(\frac{212}{231}\right)$	$e\left(\frac{85}{154}\right)$	$e\left(\frac{178}{231}\right)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{117}{154}\right)$	$e\left(\frac{47}{231}\right)$
$\chi_{13132}(25,\cdot)$	13132.ez	231	no	$1$	$1$	$e\left(\frac{25}{231}\right)$	$e\left(\frac{200}{231}\right)$	$e\left(\frac{50}{231}\right)$	$e\left(\frac{13}{231}\right)$	$e\left(\frac{16}{77}\right)$	$e\left(\frac{75}{77}\right)$	$e\left(\frac{142}{231}\right)$	$e\left(\frac{29}{33}\right)$	$e\left(\frac{47}{231}\right)$	$e\left(\frac{169}{231}\right)$
$\chi_{13132}(27,\cdot)$	13132.eu	154	yes	$-1$	$1$	$e\left(\frac{109}{154}\right)$	$e\left(\frac{51}{77}\right)$	$e\left(\frac{32}{77}\right)$	$e\left(\frac{73}{77}\right)$	$e\left(\frac{3}{77}\right)$	$e\left(\frac{57}{154}\right)$	$e\left(\frac{37}{154}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{131}{154}\right)$	$e\left(\frac{25}{77}\right)$
$\chi_{13132}(29,\cdot)$	13132.bx	21	no	$1$	$1$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{6}{7}\right)$
$\chi_{13132}(31,\cdot)$	13132.dx	66	no	$-1$	$1$	$e\left(\frac{29}{66}\right)$	$e\left(\frac{17}{33}\right)$	$e\left(\frac{29}{33}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{1}{33}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{49}{66}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{1}{33}\right)$
$\chi_{13132}(33,\cdot)$	13132.fx	462	no	$-1$	$1$	$e\left(\frac{409}{462}\right)$	$e\left(\frac{269}{462}\right)$	$e\left(\frac{178}{231}\right)$	$e\left(\frac{151}{231}\right)$	$e\left(\frac{197}{462}\right)$	$e\left(\frac{36}{77}\right)$	$e\left(\frac{67}{154}\right)$	$e\left(\frac{1}{66}\right)$	$e\left(\frac{155}{231}\right)$	$e\left(\frac{38}{231}\right)$
$\chi_{13132}(37,\cdot)$	13132.by	21	no	$1$	$1$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{8}{21}\right)$	$1$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{4}{21}\right)$
$\chi_{13132}(39,\cdot)$	13132.fs	462	yes	$-1$	$1$	$e\left(\frac{269}{462}\right)$	$e\left(\frac{152}{231}\right)$	$e\left(\frac{38}{231}\right)$	$e\left(\frac{337}{462}\right)$	$e\left(\frac{95}{231}\right)$	$e\left(\frac{37}{154}\right)$	$e\left(\frac{37}{77}\right)$	$e\left(\frac{41}{66}\right)$	$e\left(\frac{401}{462}\right)$	$e\left(\frac{73}{231}\right)$
$\chi_{13132}(41,\cdot)$	13132.gd	462	no	$1$	$1$	$e\left(\frac{52}{77}\right)$	$e\left(\frac{31}{77}\right)$	$e\left(\frac{27}{77}\right)$	$e\left(\frac{307}{462}\right)$	$e\left(\frac{10}{231}\right)$	$e\left(\frac{6}{77}\right)$	$e\left(\frac{149}{462}\right)$	$e\left(\frac{35}{66}\right)$	$e\left(\frac{13}{231}\right)$	$e\left(\frac{62}{77}\right)$
$\chi_{13132}(43,\cdot)$	13132.ew	154	yes	$1$	$1$	$e\left(\frac{74}{77}\right)$	$e\left(\frac{29}{154}\right)$	$e\left(\frac{71}{77}\right)$	$e\left(\frac{20}{77}\right)$	$e\left(\frac{47}{154}\right)$	$e\left(\frac{23}{154}\right)$	$e\left(\frac{23}{77}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{115}{154}\right)$	$e\left(\frac{29}{77}\right)$
$\chi_{13132}(45,\cdot)$	13132.fi	462	no	$1$	$1$	$e\left(\frac{160}{231}\right)$	$e\left(\frac{125}{231}\right)$	$e\left(\frac{89}{231}\right)$	$e\left(\frac{305}{462}\right)$	$e\left(\frac{10}{77}\right)$	$e\left(\frac{18}{77}\right)$	$e\left(\frac{293}{462}\right)$	$e\left(\frac{61}{66}\right)$	$e\left(\frac{116}{231}\right)$	$e\left(\frac{19}{231}\right)$
$\chi_{13132}(47,\cdot)$	13132.fn	462	yes	$1$	$1$	$e\left(\frac{38}{231}\right)$	$e\left(\frac{377}{462}\right)$	$e\left(\frac{76}{231}\right)$	$e\left(\frac{443}{462}\right)$	$e\left(\frac{149}{462}\right)$	$e\left(\frac{151}{154}\right)$	$e\left(\frac{71}{154}\right)$	$e\left(\frac{8}{33}\right)$	$e\left(\frac{109}{462}\right)$	$e\left(\frac{146}{231}\right)$
$\chi_{13132}(51,\cdot)$	13132.fo	462	yes	$1$	$1$	$e\left(\frac{227}{231}\right)$	$e\left(\frac{167}{462}\right)$	$e\left(\frac{223}{231}\right)$	$e\left(\frac{26}{77}\right)$	$e\left(\frac{37}{462}\right)$	$e\left(\frac{53}{154}\right)$	$e\left(\frac{82}{231}\right)$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{111}{154}\right)$	$e\left(\frac{167}{231}\right)$
$\chi_{13132}(53,\cdot)$	13132.fy	462	no	$-1$	$1$	$e\left(\frac{425}{462}\right)$	$e\left(\frac{397}{462}\right)$	$e\left(\frac{194}{231}\right)$	$e\left(\frac{221}{462}\right)$	$e\left(\frac{41}{154}\right)$	$e\left(\frac{60}{77}\right)$	$e\left(\frac{52}{231}\right)$	$e\left(\frac{32}{33}\right)$	$e\left(\frac{53}{231}\right)$	$e\left(\frac{166}{231}\right)$
$\chi_{13132}(55,\cdot)$	13132.gc	462	yes	$1$	$1$	$e\left(\frac{67}{77}\right)$	$e\left(\frac{71}{154}\right)$	$e\left(\frac{57}{77}\right)$	$e\left(\frac{169}{462}\right)$	$e\left(\frac{239}{462}\right)$	$e\left(\frac{51}{154}\right)$	$e\left(\frac{383}{462}\right)$	$e\left(\frac{7}{33}\right)$	$e\left(\frac{149}{462}\right)$	$e\left(\frac{71}{77}\right)$
$\chi_{13132}(57,\cdot)$	13132.fd	462	no	$-1$	$1$	$e\left(\frac{125}{154}\right)$	$e\left(\frac{153}{154}\right)$	$e\left(\frac{48}{77}\right)$	$e\left(\frac{41}{462}\right)$	$e\left(\frac{181}{462}\right)$	$e\left(\frac{62}{77}\right)$	$e\left(\frac{218}{231}\right)$	$e\left(\frac{14}{33}\right)$	$e\left(\frac{83}{231}\right)$	$e\left(\frac{76}{77}\right)$
$\chi_{13132}(59,\cdot)$	13132.fm	462	yes	$1$	$1$	$e\left(\frac{19}{231}\right)$	$e\left(\frac{73}{462}\right)$	$e\left(\frac{38}{231}\right)$	$e\left(\frac{29}{462}\right)$	$e\left(\frac{89}{154}\right)$	$e\left(\frac{37}{154}\right)$	$e\left(\frac{299}{462}\right)$	$e\left(\frac{26}{33}\right)$	$e\left(\frac{247}{462}\right)$	$e\left(\frac{73}{231}\right)$
$\chi_{13132}(61,\cdot)$	13132.fg	462	no	$1$	$1$	$e\left(\frac{92}{231}\right)$	$e\left(\frac{43}{231}\right)$	$e\left(\frac{184}{231}\right)$	$e\left(\frac{113}{154}\right)$	$e\left(\frac{152}{231}\right)$	$e\left(\frac{45}{77}\right)$	$e\left(\frac{155}{462}\right)$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{71}{77}\right)$	$e\left(\frac{86}{231}\right)$
$\chi_{13132}(65,\cdot)$	13132.fa	231	no	$1$	$1$	$e\left(\frac{131}{231}\right)$	$e\left(\frac{124}{231}\right)$	$e\left(\frac{31}{231}\right)$	$e\left(\frac{34}{77}\right)$	$e\left(\frac{116}{231}\right)$	$e\left(\frac{8}{77}\right)$	$e\left(\frac{202}{231}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{40}{77}\right)$	$e\left(\frac{17}{231}\right)$
$\chi_{13132}(69,\cdot)$	13132.gd	462	no	$1$	$1$	$e\left(\frac{40}{77}\right)$	$e\left(\frac{12}{77}\right)$	$e\left(\frac{3}{77}\right)$	$e\left(\frac{17}{462}\right)$	$e\left(\frac{215}{231}\right)$	$e\left(\frac{52}{77}\right)$	$e\left(\frac{85}{462}\right)$	$e\left(\frac{43}{66}\right)$	$e\left(\frac{164}{231}\right)$	$e\left(\frac{24}{77}\right)$
$\chi_{13132}(71,\cdot)$	13132.ff	462	yes	$-1$	$1$	$e\left(\frac{39}{154}\right)$	$e\left(\frac{2}{77}\right)$	$e\left(\frac{39}{77}\right)$	$e\left(\frac{67}{462}\right)$	$e\left(\frac{100}{231}\right)$	$e\left(\frac{43}{154}\right)$	$e\left(\frac{52}{231}\right)$	$e\left(\frac{53}{66}\right)$	$e\left(\frac{29}{462}\right)$	$e\left(\frac{4}{77}\right)$
$\chi_{13132}(73,\cdot)$	13132.fx	462	no	$-1$	$1$	$e\left(\frac{239}{462}\right)$	$e\left(\frac{295}{462}\right)$	$e\left(\frac{8}{231}\right)$	$e\left(\frac{230}{231}\right)$	$e\left(\frac{271}{462}\right)$	$e\left(\frac{12}{77}\right)$	$e\left(\frac{125}{154}\right)$	$e\left(\frac{59}{66}\right)$	$e\left(\frac{103}{231}\right)$	$e\left(\frac{64}{231}\right)$
$\chi_{13132}(75,\cdot)$	13132.fr	462	yes	$-1$	$1$	$e\left(\frac{313}{462}\right)$	$e\left(\frac{97}{231}\right)$	$e\left(\frac{82}{231}\right)$	$e\left(\frac{86}{231}\right)$	$e\left(\frac{17}{77}\right)$	$e\left(\frac{15}{154}\right)$	$e\left(\frac{13}{462}\right)$	$e\left(\frac{4}{33}\right)$	$e\left(\frac{71}{462}\right)$	$e\left(\frac{194}{231}\right)$

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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	$13132$
Structure	\(C_{2}\times C_{6}\times C_{462}\)
Order	$5544$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(3\)	\(5\)	\(9\)	\(11\)	\(13\)	\(15\)	\(17\)	\(19\)	\(23\)	\(25\)
\(\chi_{13132}(1,\cdot)\)	13132.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{13132}(3,\cdot)\)	13132.fr	462	yes	\(-1\)	\(1\)	\(e\left(\frac{263}{462}\right)\)	\(e\left(\frac{128}{231}\right)\)	\(e\left(\frac{32}{231}\right)\)	\(e\left(\frac{73}{231}\right)\)	\(e\left(\frac{1}{77}\right)\)	\(e\left(\frac{19}{154}\right)\)	\(e\left(\frac{191}{462}\right)\)	\(e\left(\frac{8}{33}\right)\)	\(e\left(\frac{439}{462}\right)\)	\(e\left(\frac{25}{231}\right)\)
\(\chi_{13132}(5,\cdot)\)	13132.fi	462	no	\(1\)	\(1\)	\(e\left(\frac{128}{231}\right)\)	\(e\left(\frac{100}{231}\right)\)	\(e\left(\frac{25}{231}\right)\)	\(e\left(\frac{13}{462}\right)\)	\(e\left(\frac{8}{77}\right)\)	\(e\left(\frac{76}{77}\right)\)	\(e\left(\frac{373}{462}\right)\)	\(e\left(\frac{29}{66}\right)\)	\(e\left(\frac{139}{231}\right)\)	\(e\left(\frac{200}{231}\right)\)
\(\chi_{13132}(9,\cdot)\)	13132.ez	231	no	\(1\)	\(1\)	\(e\left(\frac{32}{231}\right)\)	\(e\left(\frac{25}{231}\right)\)	\(e\left(\frac{64}{231}\right)\)	\(e\left(\frac{146}{231}\right)\)	\(e\left(\frac{2}{77}\right)\)	\(e\left(\frac{19}{77}\right)\)	\(e\left(\frac{191}{231}\right)\)	\(e\left(\frac{16}{33}\right)\)	\(e\left(\frac{208}{231}\right)\)	\(e\left(\frac{50}{231}\right)\)
\(\chi_{13132}(11,\cdot)\)	13132.fo	462	yes	\(1\)	\(1\)	\(e\left(\frac{73}{231}\right)\)	\(e\left(\frac{13}{462}\right)\)	\(e\left(\frac{146}{231}\right)\)	\(e\left(\frac{26}{77}\right)\)	\(e\left(\frac{191}{462}\right)\)	\(e\left(\frac{53}{154}\right)\)	\(e\left(\frac{5}{231}\right)\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{111}{154}\right)\)	\(e\left(\frac{13}{231}\right)\)
\(\chi_{13132}(13,\cdot)\)	13132.gd	462	no	\(1\)	\(1\)	\(e\left(\frac{1}{77}\right)\)	\(e\left(\frac{8}{77}\right)\)	\(e\left(\frac{2}{77}\right)\)	\(e\left(\frac{191}{462}\right)\)	\(e\left(\frac{92}{231}\right)\)	\(e\left(\frac{9}{77}\right)\)	\(e\left(\frac{31}{462}\right)\)	\(e\left(\frac{25}{66}\right)\)	\(e\left(\frac{212}{231}\right)\)	\(e\left(\frac{16}{77}\right)\)
\(\chi_{13132}(15,\cdot)\)	13132.et	154	yes	\(-1\)	\(1\)	\(e\left(\frac{19}{154}\right)\)	\(e\left(\frac{76}{77}\right)\)	\(e\left(\frac{19}{77}\right)\)	\(e\left(\frac{53}{154}\right)\)	\(e\left(\frac{9}{77}\right)\)	\(e\left(\frac{17}{154}\right)\)	\(e\left(\frac{17}{77}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{85}{154}\right)\)	\(e\left(\frac{75}{77}\right)\)
\(\chi_{13132}(17,\cdot)\)	13132.fx	462	no	\(-1\)	\(1\)	\(e\left(\frac{191}{462}\right)\)	\(e\left(\frac{373}{462}\right)\)	\(e\left(\frac{191}{231}\right)\)	\(e\left(\frac{5}{231}\right)\)	\(e\left(\frac{31}{462}\right)\)	\(e\left(\frac{17}{77}\right)\)	\(e\left(\frac{145}{154}\right)\)	\(e\left(\frac{35}{66}\right)\)	\(e\left(\frac{178}{231}\right)\)	\(e\left(\frac{142}{231}\right)\)
\(\chi_{13132}(19,\cdot)\)	13132.ei	66	no	\(1\)	\(1\)	\(e\left(\frac{8}{33}\right)\)	\(e\left(\frac{29}{66}\right)\)	\(e\left(\frac{16}{33}\right)\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{25}{66}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{35}{66}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{29}{33}\right)\)
\(\chi_{13132}(23,\cdot)\)	13132.fp	462	yes	\(-1\)	\(1\)	\(e\left(\frac{439}{462}\right)\)	\(e\left(\frac{139}{231}\right)\)	\(e\left(\frac{208}{231}\right)\)	\(e\left(\frac{111}{154}\right)\)	\(e\left(\frac{212}{231}\right)\)	\(e\left(\frac{85}{154}\right)\)	\(e\left(\frac{178}{231}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{117}{154}\right)\)	\(e\left(\frac{47}{231}\right)\)
\(\chi_{13132}(25,\cdot)\)	13132.ez	231	no	\(1\)	\(1\)	\(e\left(\frac{25}{231}\right)\)	\(e\left(\frac{200}{231}\right)\)	\(e\left(\frac{50}{231}\right)\)	\(e\left(\frac{13}{231}\right)\)	\(e\left(\frac{16}{77}\right)\)	\(e\left(\frac{75}{77}\right)\)	\(e\left(\frac{142}{231}\right)\)	\(e\left(\frac{29}{33}\right)\)	\(e\left(\frac{47}{231}\right)\)	\(e\left(\frac{169}{231}\right)\)
\(\chi_{13132}(27,\cdot)\)	13132.eu	154	yes	\(-1\)	\(1\)	\(e\left(\frac{109}{154}\right)\)	\(e\left(\frac{51}{77}\right)\)	\(e\left(\frac{32}{77}\right)\)	\(e\left(\frac{73}{77}\right)\)	\(e\left(\frac{3}{77}\right)\)	\(e\left(\frac{57}{154}\right)\)	\(e\left(\frac{37}{154}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{131}{154}\right)\)	\(e\left(\frac{25}{77}\right)\)
\(\chi_{13132}(29,\cdot)\)	13132.bx	21	no	\(1\)	\(1\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{6}{7}\right)\)
\(\chi_{13132}(31,\cdot)\)	13132.dx	66	no	\(-1\)	\(1\)	\(e\left(\frac{29}{66}\right)\)	\(e\left(\frac{17}{33}\right)\)	\(e\left(\frac{29}{33}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{1}{33}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{49}{66}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{1}{33}\right)\)
\(\chi_{13132}(33,\cdot)\)	13132.fx	462	no	\(-1\)	\(1\)	\(e\left(\frac{409}{462}\right)\)	\(e\left(\frac{269}{462}\right)\)	\(e\left(\frac{178}{231}\right)\)	\(e\left(\frac{151}{231}\right)\)	\(e\left(\frac{197}{462}\right)\)	\(e\left(\frac{36}{77}\right)\)	\(e\left(\frac{67}{154}\right)\)	\(e\left(\frac{1}{66}\right)\)	\(e\left(\frac{155}{231}\right)\)	\(e\left(\frac{38}{231}\right)\)
\(\chi_{13132}(37,\cdot)\)	13132.by	21	no	\(1\)	\(1\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(1\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{4}{21}\right)\)
\(\chi_{13132}(39,\cdot)\)	13132.fs	462	yes	\(-1\)	\(1\)	\(e\left(\frac{269}{462}\right)\)	\(e\left(\frac{152}{231}\right)\)	\(e\left(\frac{38}{231}\right)\)	\(e\left(\frac{337}{462}\right)\)	\(e\left(\frac{95}{231}\right)\)	\(e\left(\frac{37}{154}\right)\)	\(e\left(\frac{37}{77}\right)\)	\(e\left(\frac{41}{66}\right)\)	\(e\left(\frac{401}{462}\right)\)	\(e\left(\frac{73}{231}\right)\)
\(\chi_{13132}(41,\cdot)\)	13132.gd	462	no	\(1\)	\(1\)	\(e\left(\frac{52}{77}\right)\)	\(e\left(\frac{31}{77}\right)\)	\(e\left(\frac{27}{77}\right)\)	\(e\left(\frac{307}{462}\right)\)	\(e\left(\frac{10}{231}\right)\)	\(e\left(\frac{6}{77}\right)\)	\(e\left(\frac{149}{462}\right)\)	\(e\left(\frac{35}{66}\right)\)	\(e\left(\frac{13}{231}\right)\)	\(e\left(\frac{62}{77}\right)\)
\(\chi_{13132}(43,\cdot)\)	13132.ew	154	yes	\(1\)	\(1\)	\(e\left(\frac{74}{77}\right)\)	\(e\left(\frac{29}{154}\right)\)	\(e\left(\frac{71}{77}\right)\)	\(e\left(\frac{20}{77}\right)\)	\(e\left(\frac{47}{154}\right)\)	\(e\left(\frac{23}{154}\right)\)	\(e\left(\frac{23}{77}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{115}{154}\right)\)	\(e\left(\frac{29}{77}\right)\)
\(\chi_{13132}(45,\cdot)\)	13132.fi	462	no	\(1\)	\(1\)	\(e\left(\frac{160}{231}\right)\)	\(e\left(\frac{125}{231}\right)\)	\(e\left(\frac{89}{231}\right)\)	\(e\left(\frac{305}{462}\right)\)	\(e\left(\frac{10}{77}\right)\)	\(e\left(\frac{18}{77}\right)\)	\(e\left(\frac{293}{462}\right)\)	\(e\left(\frac{61}{66}\right)\)	\(e\left(\frac{116}{231}\right)\)	\(e\left(\frac{19}{231}\right)\)
\(\chi_{13132}(47,\cdot)\)	13132.fn	462	yes	\(1\)	\(1\)	\(e\left(\frac{38}{231}\right)\)	\(e\left(\frac{377}{462}\right)\)	\(e\left(\frac{76}{231}\right)\)	\(e\left(\frac{443}{462}\right)\)	\(e\left(\frac{149}{462}\right)\)	\(e\left(\frac{151}{154}\right)\)	\(e\left(\frac{71}{154}\right)\)	\(e\left(\frac{8}{33}\right)\)	\(e\left(\frac{109}{462}\right)\)	\(e\left(\frac{146}{231}\right)\)
\(\chi_{13132}(51,\cdot)\)	13132.fo	462	yes	\(1\)	\(1\)	\(e\left(\frac{227}{231}\right)\)	\(e\left(\frac{167}{462}\right)\)	\(e\left(\frac{223}{231}\right)\)	\(e\left(\frac{26}{77}\right)\)	\(e\left(\frac{37}{462}\right)\)	\(e\left(\frac{53}{154}\right)\)	\(e\left(\frac{82}{231}\right)\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{111}{154}\right)\)	\(e\left(\frac{167}{231}\right)\)
\(\chi_{13132}(53,\cdot)\)	13132.fy	462	no	\(-1\)	\(1\)	\(e\left(\frac{425}{462}\right)\)	\(e\left(\frac{397}{462}\right)\)	\(e\left(\frac{194}{231}\right)\)	\(e\left(\frac{221}{462}\right)\)	\(e\left(\frac{41}{154}\right)\)	\(e\left(\frac{60}{77}\right)\)	\(e\left(\frac{52}{231}\right)\)	\(e\left(\frac{32}{33}\right)\)	\(e\left(\frac{53}{231}\right)\)	\(e\left(\frac{166}{231}\right)\)
\(\chi_{13132}(55,\cdot)\)	13132.gc	462	yes	\(1\)	\(1\)	\(e\left(\frac{67}{77}\right)\)	\(e\left(\frac{71}{154}\right)\)	\(e\left(\frac{57}{77}\right)\)	\(e\left(\frac{169}{462}\right)\)	\(e\left(\frac{239}{462}\right)\)	\(e\left(\frac{51}{154}\right)\)	\(e\left(\frac{383}{462}\right)\)	\(e\left(\frac{7}{33}\right)\)	\(e\left(\frac{149}{462}\right)\)	\(e\left(\frac{71}{77}\right)\)
\(\chi_{13132}(57,\cdot)\)	13132.fd	462	no	\(-1\)	\(1\)	\(e\left(\frac{125}{154}\right)\)	\(e\left(\frac{153}{154}\right)\)	\(e\left(\frac{48}{77}\right)\)	\(e\left(\frac{41}{462}\right)\)	\(e\left(\frac{181}{462}\right)\)	\(e\left(\frac{62}{77}\right)\)	\(e\left(\frac{218}{231}\right)\)	\(e\left(\frac{14}{33}\right)\)	\(e\left(\frac{83}{231}\right)\)	\(e\left(\frac{76}{77}\right)\)
\(\chi_{13132}(59,\cdot)\)	13132.fm	462	yes	\(1\)	\(1\)	\(e\left(\frac{19}{231}\right)\)	\(e\left(\frac{73}{462}\right)\)	\(e\left(\frac{38}{231}\right)\)	\(e\left(\frac{29}{462}\right)\)	\(e\left(\frac{89}{154}\right)\)	\(e\left(\frac{37}{154}\right)\)	\(e\left(\frac{299}{462}\right)\)	\(e\left(\frac{26}{33}\right)\)	\(e\left(\frac{247}{462}\right)\)	\(e\left(\frac{73}{231}\right)\)
\(\chi_{13132}(61,\cdot)\)	13132.fg	462	no	\(1\)	\(1\)	\(e\left(\frac{92}{231}\right)\)	\(e\left(\frac{43}{231}\right)\)	\(e\left(\frac{184}{231}\right)\)	\(e\left(\frac{113}{154}\right)\)	\(e\left(\frac{152}{231}\right)\)	\(e\left(\frac{45}{77}\right)\)	\(e\left(\frac{155}{462}\right)\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{71}{77}\right)\)	\(e\left(\frac{86}{231}\right)\)
\(\chi_{13132}(65,\cdot)\)	13132.fa	231	no	\(1\)	\(1\)	\(e\left(\frac{131}{231}\right)\)	\(e\left(\frac{124}{231}\right)\)	\(e\left(\frac{31}{231}\right)\)	\(e\left(\frac{34}{77}\right)\)	\(e\left(\frac{116}{231}\right)\)	\(e\left(\frac{8}{77}\right)\)	\(e\left(\frac{202}{231}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{40}{77}\right)\)	\(e\left(\frac{17}{231}\right)\)
\(\chi_{13132}(69,\cdot)\)	13132.gd	462	no	\(1\)	\(1\)	\(e\left(\frac{40}{77}\right)\)	\(e\left(\frac{12}{77}\right)\)	\(e\left(\frac{3}{77}\right)\)	\(e\left(\frac{17}{462}\right)\)	\(e\left(\frac{215}{231}\right)\)	\(e\left(\frac{52}{77}\right)\)	\(e\left(\frac{85}{462}\right)\)	\(e\left(\frac{43}{66}\right)\)	\(e\left(\frac{164}{231}\right)\)	\(e\left(\frac{24}{77}\right)\)
\(\chi_{13132}(71,\cdot)\)	13132.ff	462	yes	\(-1\)	\(1\)	\(e\left(\frac{39}{154}\right)\)	\(e\left(\frac{2}{77}\right)\)	\(e\left(\frac{39}{77}\right)\)	\(e\left(\frac{67}{462}\right)\)	\(e\left(\frac{100}{231}\right)\)	\(e\left(\frac{43}{154}\right)\)	\(e\left(\frac{52}{231}\right)\)	\(e\left(\frac{53}{66}\right)\)	\(e\left(\frac{29}{462}\right)\)	\(e\left(\frac{4}{77}\right)\)
\(\chi_{13132}(73,\cdot)\)	13132.fx	462	no	\(-1\)	\(1\)	\(e\left(\frac{239}{462}\right)\)	\(e\left(\frac{295}{462}\right)\)	\(e\left(\frac{8}{231}\right)\)	\(e\left(\frac{230}{231}\right)\)	\(e\left(\frac{271}{462}\right)\)	\(e\left(\frac{12}{77}\right)\)	\(e\left(\frac{125}{154}\right)\)	\(e\left(\frac{59}{66}\right)\)	\(e\left(\frac{103}{231}\right)\)	\(e\left(\frac{64}{231}\right)\)
\(\chi_{13132}(75,\cdot)\)	13132.fr	462	yes	\(-1\)	\(1\)	\(e\left(\frac{313}{462}\right)\)	\(e\left(\frac{97}{231}\right)\)	\(e\left(\frac{82}{231}\right)\)	\(e\left(\frac{86}{231}\right)\)	\(e\left(\frac{17}{77}\right)\)	\(e\left(\frac{15}{154}\right)\)	\(e\left(\frac{13}{462}\right)\)	\(e\left(\frac{4}{33}\right)\)	\(e\left(\frac{71}{462}\right)\)	\(e\left(\frac{194}{231}\right)\)

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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.