LMFDB - Group of Dirichlet characters of modulus 3933

Show commands: Magma / Pari/GP / SageMath

comment:Define the Dirichlet group

sage:G = DirichletGroup(3933)

gp:g = idealstar(,3933,2)

magma:G = FullDirichletGroup(3933);

Character group

Order	=	2376	comment:Order sage:G.order() gp:g.no magma:Order(G);
Structure	=	$C_{2}\times C_{6}\times C_{198}$	comment:Group structure sage:sorted(g.order() for g in G.gens()) gp:g.cyc magma:PrimaryInvariants(G);
Generators	=	$\chi_{3933}(875,\cdot)$, $\chi_{3933}(1864,\cdot)$, $\chi_{3933}(856,\cdot)$	comment:Generators sage:G.gens() gp:g.gen magma:Generators(G);

First 32 of 2376 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	$-1$	$1$	$2$	$4$	$5$	$7$	$8$	$10$	$11$	$13$	$14$	$16$
$\chi_{3933}(1,\cdot)$	3933.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{3933}(2,\cdot)$	3933.ef	198	yes	$1$	$1$	$e\left(\frac{40}{99}\right)$	$e\left(\frac{80}{99}\right)$	$e\left(\frac{161}{198}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{7}{33}\right)$	$e\left(\frac{43}{198}\right)$	$e\left(\frac{43}{66}\right)$	$e\left(\frac{175}{198}\right)$	$e\left(\frac{13}{99}\right)$	$e\left(\frac{61}{99}\right)$
$\chi_{3933}(4,\cdot)$	3933.ea	99	yes	$1$	$1$	$e\left(\frac{80}{99}\right)$	$e\left(\frac{61}{99}\right)$	$e\left(\frac{62}{99}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{14}{33}\right)$	$e\left(\frac{43}{99}\right)$	$e\left(\frac{10}{33}\right)$	$e\left(\frac{76}{99}\right)$	$e\left(\frac{26}{99}\right)$	$e\left(\frac{23}{99}\right)$
$\chi_{3933}(5,\cdot)$	3933.eg	198	yes	$1$	$1$	$e\left(\frac{161}{198}\right)$	$e\left(\frac{62}{99}\right)$	$e\left(\frac{43}{99}\right)$	$e\left(\frac{35}{66}\right)$	$e\left(\frac{29}{66}\right)$	$e\left(\frac{49}{198}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{74}{99}\right)$	$e\left(\frac{34}{99}\right)$	$e\left(\frac{25}{99}\right)$
$\chi_{3933}(7,\cdot)$	3933.cy	66	yes	$-1$	$1$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{35}{66}\right)$	$e\left(\frac{5}{66}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{17}{66}\right)$	$e\left(\frac{29}{66}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{53}{66}\right)$	$e\left(\frac{10}{11}\right)$
$\chi_{3933}(8,\cdot)$	3933.do	66	no	$1$	$1$	$e\left(\frac{7}{33}\right)$	$e\left(\frac{14}{33}\right)$	$e\left(\frac{29}{66}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{43}{66}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{43}{66}\right)$	$e\left(\frac{13}{33}\right)$	$e\left(\frac{28}{33}\right)$
$\chi_{3933}(10,\cdot)$	3933.eh	198	no	$1$	$1$	$e\left(\frac{43}{198}\right)$	$e\left(\frac{43}{99}\right)$	$e\left(\frac{49}{198}\right)$	$e\left(\frac{17}{66}\right)$	$e\left(\frac{43}{66}\right)$	$e\left(\frac{46}{99}\right)$	$e\left(\frac{37}{66}\right)$	$e\left(\frac{125}{198}\right)$	$e\left(\frac{47}{99}\right)$	$e\left(\frac{86}{99}\right)$
$\chi_{3933}(11,\cdot)$	3933.db	66	yes	$1$	$1$	$e\left(\frac{43}{66}\right)$	$e\left(\frac{10}{33}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{29}{66}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{37}{66}\right)$	$e\left(\frac{28}{33}\right)$	$e\left(\frac{13}{33}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{20}{33}\right)$
$\chi_{3933}(13,\cdot)$	3933.ee	198	yes	$-1$	$1$	$e\left(\frac{175}{198}\right)$	$e\left(\frac{76}{99}\right)$	$e\left(\frac{74}{99}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{43}{66}\right)$	$e\left(\frac{125}{198}\right)$	$e\left(\frac{13}{33}\right)$	$e\left(\frac{191}{198}\right)$	$e\left(\frac{193}{198}\right)$	$e\left(\frac{53}{99}\right)$
$\chi_{3933}(14,\cdot)$	3933.ek	198	yes	$-1$	$1$	$e\left(\frac{13}{99}\right)$	$e\left(\frac{26}{99}\right)$	$e\left(\frac{34}{99}\right)$	$e\left(\frac{53}{66}\right)$	$e\left(\frac{13}{33}\right)$	$e\left(\frac{47}{99}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{193}{198}\right)$	$e\left(\frac{185}{198}\right)$	$e\left(\frac{52}{99}\right)$
$\chi_{3933}(16,\cdot)$	3933.ea	99	yes	$1$	$1$	$e\left(\frac{61}{99}\right)$	$e\left(\frac{23}{99}\right)$	$e\left(\frac{25}{99}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{28}{33}\right)$	$e\left(\frac{86}{99}\right)$	$e\left(\frac{20}{33}\right)$	$e\left(\frac{53}{99}\right)$	$e\left(\frac{52}{99}\right)$	$e\left(\frac{46}{99}\right)$
$\chi_{3933}(17,\cdot)$	3933.ei	198	no	$1$	$1$	$e\left(\frac{137}{198}\right)$	$e\left(\frac{38}{99}\right)$	$e\left(\frac{70}{99}\right)$	$e\left(\frac{25}{66}\right)$	$e\left(\frac{5}{66}\right)$	$e\left(\frac{79}{198}\right)$	$e\left(\frac{1}{33}\right)$	$e\left(\frac{23}{99}\right)$	$e\left(\frac{7}{99}\right)$	$e\left(\frac{76}{99}\right)$
$\chi_{3933}(20,\cdot)$	3933.di	66	no	$1$	$1$	$e\left(\frac{41}{66}\right)$	$e\left(\frac{8}{33}\right)$	$e\left(\frac{2}{33}\right)$	$e\left(\frac{65}{66}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{7}{33}\right)$	$e\left(\frac{17}{33}\right)$	$e\left(\frac{20}{33}\right)$	$e\left(\frac{16}{33}\right)$
$\chi_{3933}(22,\cdot)$	3933.cg	18	yes	$1$	$1$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{7}{9}\right)$	$-1$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{2}{9}\right)$
$\chi_{3933}(25,\cdot)$	3933.eb	99	yes	$1$	$1$	$e\left(\frac{62}{99}\right)$	$e\left(\frac{25}{99}\right)$	$e\left(\frac{86}{99}\right)$	$e\left(\frac{2}{33}\right)$	$e\left(\frac{29}{33}\right)$	$e\left(\frac{49}{99}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{49}{99}\right)$	$e\left(\frac{68}{99}\right)$	$e\left(\frac{50}{99}\right)$
$\chi_{3933}(26,\cdot)$	3933.dd	66	no	$-1$	$1$	$e\left(\frac{19}{66}\right)$	$e\left(\frac{19}{33}\right)$	$e\left(\frac{37}{66}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{28}{33}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{28}{33}\right)$	$e\left(\frac{7}{66}\right)$	$e\left(\frac{5}{33}\right)$
$\chi_{3933}(28,\cdot)$	3933.el	198	no	$-1$	$1$	$e\left(\frac{53}{99}\right)$	$e\left(\frac{7}{99}\right)$	$e\left(\frac{31}{198}\right)$	$e\left(\frac{35}{66}\right)$	$e\left(\frac{20}{33}\right)$	$e\left(\frac{137}{198}\right)$	$e\left(\frac{49}{66}\right)$	$e\left(\frac{85}{99}\right)$	$e\left(\frac{13}{198}\right)$	$e\left(\frac{14}{99}\right)$
$\chi_{3933}(29,\cdot)$	3933.et	198	yes	$1$	$1$	$e\left(\frac{74}{99}\right)$	$e\left(\frac{49}{99}\right)$	$e\left(\frac{151}{198}\right)$	$e\left(\frac{29}{33}\right)$	$e\left(\frac{8}{33}\right)$	$e\left(\frac{101}{198}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{101}{198}\right)$	$e\left(\frac{62}{99}\right)$	$e\left(\frac{98}{99}\right)$
$\chi_{3933}(31,\cdot)$	3933.dc	66	yes	$-1$	$1$	$e\left(\frac{47}{66}\right)$	$e\left(\frac{14}{33}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{17}{33}\right)$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{65}{66}\right)$	$e\left(\frac{26}{33}\right)$	$e\left(\frac{43}{66}\right)$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{28}{33}\right)$
$\chi_{3933}(32,\cdot)$	3933.ef	198	yes	$1$	$1$	$e\left(\frac{2}{99}\right)$	$e\left(\frac{4}{99}\right)$	$e\left(\frac{13}{198}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{2}{33}\right)$	$e\left(\frac{17}{198}\right)$	$e\left(\frac{17}{66}\right)$	$e\left(\frac{83}{198}\right)$	$e\left(\frac{65}{99}\right)$	$e\left(\frac{8}{99}\right)$
$\chi_{3933}(34,\cdot)$	3933.ej	198	yes	$1$	$1$	$e\left(\frac{19}{198}\right)$	$e\left(\frac{19}{99}\right)$	$e\left(\frac{103}{198}\right)$	$e\left(\frac{7}{66}\right)$	$e\left(\frac{19}{66}\right)$	$e\left(\frac{61}{99}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{23}{198}\right)$	$e\left(\frac{20}{99}\right)$	$e\left(\frac{38}{99}\right)$
$\chi_{3933}(35,\cdot)$	3933.ep	198	no	$-1$	$1$	$e\left(\frac{107}{198}\right)$	$e\left(\frac{8}{99}\right)$	$e\left(\frac{191}{198}\right)$	$e\left(\frac{20}{33}\right)$	$e\left(\frac{41}{66}\right)$	$e\left(\frac{50}{99}\right)$	$e\left(\frac{23}{66}\right)$	$e\left(\frac{83}{99}\right)$	$e\left(\frac{29}{198}\right)$	$e\left(\frac{16}{99}\right)$
$\chi_{3933}(37,\cdot)$	3933.ct	22	no	$1$	$1$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{7}{11}\right)$
$\chi_{3933}(40,\cdot)$	3933.ej	198	yes	$1$	$1$	$e\left(\frac{5}{198}\right)$	$e\left(\frac{5}{99}\right)$	$e\left(\frac{173}{198}\right)$	$e\left(\frac{47}{66}\right)$	$e\left(\frac{5}{66}\right)$	$e\left(\frac{89}{99}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{79}{198}\right)$	$e\left(\frac{73}{99}\right)$	$e\left(\frac{10}{99}\right)$
$\chi_{3933}(41,\cdot)$	3933.et	198	yes	$1$	$1$	$e\left(\frac{64}{99}\right)$	$e\left(\frac{29}{99}\right)$	$e\left(\frac{53}{198}\right)$	$e\left(\frac{1}{33}\right)$	$e\left(\frac{31}{33}\right)$	$e\left(\frac{181}{198}\right)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{181}{198}\right)$	$e\left(\frac{67}{99}\right)$	$e\left(\frac{58}{99}\right)$
$\chi_{3933}(43,\cdot)$	3933.ew	198	yes	$-1$	$1$	$e\left(\frac{1}{99}\right)$	$e\left(\frac{2}{99}\right)$	$e\left(\frac{155}{198}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{1}{33}\right)$	$e\left(\frac{157}{198}\right)$	$e\left(\frac{25}{66}\right)$	$e\left(\frac{95}{99}\right)$	$e\left(\frac{65}{198}\right)$	$e\left(\frac{4}{99}\right)$
$\chi_{3933}(44,\cdot)$	3933.ei	198	no	$1$	$1$	$e\left(\frac{91}{198}\right)$	$e\left(\frac{91}{99}\right)$	$e\left(\frac{53}{99}\right)$	$e\left(\frac{59}{66}\right)$	$e\left(\frac{25}{66}\right)$	$e\left(\frac{197}{198}\right)$	$e\left(\frac{5}{33}\right)$	$e\left(\frac{16}{99}\right)$	$e\left(\frac{35}{99}\right)$	$e\left(\frac{83}{99}\right)$
$\chi_{3933}(47,\cdot)$	3933.by	18	no	$-1$	$1$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{9}\right)$	$-1$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{4}{9}\right)$
$\chi_{3933}(49,\cdot)$	3933.cu	33	yes	$1$	$1$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{2}{33}\right)$	$e\left(\frac{5}{33}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{17}{33}\right)$	$e\left(\frac{29}{33}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{20}{33}\right)$	$e\left(\frac{9}{11}\right)$
$\chi_{3933}(50,\cdot)$	3933.dv	66	yes	$1$	$1$	$e\left(\frac{1}{33}\right)$	$e\left(\frac{2}{33}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{26}{33}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{47}{66}\right)$	$e\left(\frac{31}{66}\right)$	$e\left(\frac{25}{66}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{4}{33}\right)$
$\chi_{3933}(52,\cdot)$	3933.ee	198	yes	$-1$	$1$	$e\left(\frac{137}{198}\right)$	$e\left(\frac{38}{99}\right)$	$e\left(\frac{37}{99}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{5}{66}\right)$	$e\left(\frac{13}{198}\right)$	$e\left(\frac{23}{33}\right)$	$e\left(\frac{145}{198}\right)$	$e\left(\frac{47}{198}\right)$	$e\left(\frac{76}{99}\right)$
$\chi_{3933}(53,\cdot)$	3933.em	198	no	$-1$	$1$	$e\left(\frac{83}{99}\right)$	$e\left(\frac{67}{99}\right)$	$e\left(\frac{14}{99}\right)$	$e\left(\frac{5}{66}\right)$	$e\left(\frac{17}{33}\right)$	$e\left(\frac{97}{99}\right)$	$e\left(\frac{20}{33}\right)$	$e\left(\frac{29}{198}\right)$	$e\left(\frac{181}{198}\right)$	$e\left(\frac{35}{99}\right)$

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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 $\F_{q}$
Belyi maps

Modulus	$3933$
Structure	\(C_{2}\times C_{6}\times C_{198}\)
Order	$2376$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(4\)	\(5\)	\(7\)	\(8\)	\(10\)	\(11\)	\(13\)	\(14\)	\(16\)
\(\chi_{3933}(1,\cdot)\)	3933.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{3933}(2,\cdot)\)	3933.ef	198	yes	\(1\)	\(1\)	\(e\left(\frac{40}{99}\right)\)	\(e\left(\frac{80}{99}\right)\)	\(e\left(\frac{161}{198}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{7}{33}\right)\)	\(e\left(\frac{43}{198}\right)\)	\(e\left(\frac{43}{66}\right)\)	\(e\left(\frac{175}{198}\right)\)	\(e\left(\frac{13}{99}\right)\)	\(e\left(\frac{61}{99}\right)\)
\(\chi_{3933}(4,\cdot)\)	3933.ea	99	yes	\(1\)	\(1\)	\(e\left(\frac{80}{99}\right)\)	\(e\left(\frac{61}{99}\right)\)	\(e\left(\frac{62}{99}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{14}{33}\right)\)	\(e\left(\frac{43}{99}\right)\)	\(e\left(\frac{10}{33}\right)\)	\(e\left(\frac{76}{99}\right)\)	\(e\left(\frac{26}{99}\right)\)	\(e\left(\frac{23}{99}\right)\)
\(\chi_{3933}(5,\cdot)\)	3933.eg	198	yes	\(1\)	\(1\)	\(e\left(\frac{161}{198}\right)\)	\(e\left(\frac{62}{99}\right)\)	\(e\left(\frac{43}{99}\right)\)	\(e\left(\frac{35}{66}\right)\)	\(e\left(\frac{29}{66}\right)\)	\(e\left(\frac{49}{198}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{74}{99}\right)\)	\(e\left(\frac{34}{99}\right)\)	\(e\left(\frac{25}{99}\right)\)
\(\chi_{3933}(7,\cdot)\)	3933.cy	66	yes	\(-1\)	\(1\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{35}{66}\right)\)	\(e\left(\frac{5}{66}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{17}{66}\right)\)	\(e\left(\frac{29}{66}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{53}{66}\right)\)	\(e\left(\frac{10}{11}\right)\)
\(\chi_{3933}(8,\cdot)\)	3933.do	66	no	\(1\)	\(1\)	\(e\left(\frac{7}{33}\right)\)	\(e\left(\frac{14}{33}\right)\)	\(e\left(\frac{29}{66}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{43}{66}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{43}{66}\right)\)	\(e\left(\frac{13}{33}\right)\)	\(e\left(\frac{28}{33}\right)\)
\(\chi_{3933}(10,\cdot)\)	3933.eh	198	no	\(1\)	\(1\)	\(e\left(\frac{43}{198}\right)\)	\(e\left(\frac{43}{99}\right)\)	\(e\left(\frac{49}{198}\right)\)	\(e\left(\frac{17}{66}\right)\)	\(e\left(\frac{43}{66}\right)\)	\(e\left(\frac{46}{99}\right)\)	\(e\left(\frac{37}{66}\right)\)	\(e\left(\frac{125}{198}\right)\)	\(e\left(\frac{47}{99}\right)\)	\(e\left(\frac{86}{99}\right)\)
\(\chi_{3933}(11,\cdot)\)	3933.db	66	yes	\(1\)	\(1\)	\(e\left(\frac{43}{66}\right)\)	\(e\left(\frac{10}{33}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{29}{66}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{37}{66}\right)\)	\(e\left(\frac{28}{33}\right)\)	\(e\left(\frac{13}{33}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{20}{33}\right)\)
\(\chi_{3933}(13,\cdot)\)	3933.ee	198	yes	\(-1\)	\(1\)	\(e\left(\frac{175}{198}\right)\)	\(e\left(\frac{76}{99}\right)\)	\(e\left(\frac{74}{99}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{43}{66}\right)\)	\(e\left(\frac{125}{198}\right)\)	\(e\left(\frac{13}{33}\right)\)	\(e\left(\frac{191}{198}\right)\)	\(e\left(\frac{193}{198}\right)\)	\(e\left(\frac{53}{99}\right)\)
\(\chi_{3933}(14,\cdot)\)	3933.ek	198	yes	\(-1\)	\(1\)	\(e\left(\frac{13}{99}\right)\)	\(e\left(\frac{26}{99}\right)\)	\(e\left(\frac{34}{99}\right)\)	\(e\left(\frac{53}{66}\right)\)	\(e\left(\frac{13}{33}\right)\)	\(e\left(\frac{47}{99}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{193}{198}\right)\)	\(e\left(\frac{185}{198}\right)\)	\(e\left(\frac{52}{99}\right)\)
\(\chi_{3933}(16,\cdot)\)	3933.ea	99	yes	\(1\)	\(1\)	\(e\left(\frac{61}{99}\right)\)	\(e\left(\frac{23}{99}\right)\)	\(e\left(\frac{25}{99}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{28}{33}\right)\)	\(e\left(\frac{86}{99}\right)\)	\(e\left(\frac{20}{33}\right)\)	\(e\left(\frac{53}{99}\right)\)	\(e\left(\frac{52}{99}\right)\)	\(e\left(\frac{46}{99}\right)\)
\(\chi_{3933}(17,\cdot)\)	3933.ei	198	no	\(1\)	\(1\)	\(e\left(\frac{137}{198}\right)\)	\(e\left(\frac{38}{99}\right)\)	\(e\left(\frac{70}{99}\right)\)	\(e\left(\frac{25}{66}\right)\)	\(e\left(\frac{5}{66}\right)\)	\(e\left(\frac{79}{198}\right)\)	\(e\left(\frac{1}{33}\right)\)	\(e\left(\frac{23}{99}\right)\)	\(e\left(\frac{7}{99}\right)\)	\(e\left(\frac{76}{99}\right)\)
\(\chi_{3933}(20,\cdot)\)	3933.di	66	no	\(1\)	\(1\)	\(e\left(\frac{41}{66}\right)\)	\(e\left(\frac{8}{33}\right)\)	\(e\left(\frac{2}{33}\right)\)	\(e\left(\frac{65}{66}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{7}{33}\right)\)	\(e\left(\frac{17}{33}\right)\)	\(e\left(\frac{20}{33}\right)\)	\(e\left(\frac{16}{33}\right)\)
\(\chi_{3933}(22,\cdot)\)	3933.cg	18	yes	\(1\)	\(1\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(-1\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{2}{9}\right)\)
\(\chi_{3933}(25,\cdot)\)	3933.eb	99	yes	\(1\)	\(1\)	\(e\left(\frac{62}{99}\right)\)	\(e\left(\frac{25}{99}\right)\)	\(e\left(\frac{86}{99}\right)\)	\(e\left(\frac{2}{33}\right)\)	\(e\left(\frac{29}{33}\right)\)	\(e\left(\frac{49}{99}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{49}{99}\right)\)	\(e\left(\frac{68}{99}\right)\)	\(e\left(\frac{50}{99}\right)\)
\(\chi_{3933}(26,\cdot)\)	3933.dd	66	no	\(-1\)	\(1\)	\(e\left(\frac{19}{66}\right)\)	\(e\left(\frac{19}{33}\right)\)	\(e\left(\frac{37}{66}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{28}{33}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{28}{33}\right)\)	\(e\left(\frac{7}{66}\right)\)	\(e\left(\frac{5}{33}\right)\)
\(\chi_{3933}(28,\cdot)\)	3933.el	198	no	\(-1\)	\(1\)	\(e\left(\frac{53}{99}\right)\)	\(e\left(\frac{7}{99}\right)\)	\(e\left(\frac{31}{198}\right)\)	\(e\left(\frac{35}{66}\right)\)	\(e\left(\frac{20}{33}\right)\)	\(e\left(\frac{137}{198}\right)\)	\(e\left(\frac{49}{66}\right)\)	\(e\left(\frac{85}{99}\right)\)	\(e\left(\frac{13}{198}\right)\)	\(e\left(\frac{14}{99}\right)\)
\(\chi_{3933}(29,\cdot)\)	3933.et	198	yes	\(1\)	\(1\)	\(e\left(\frac{74}{99}\right)\)	\(e\left(\frac{49}{99}\right)\)	\(e\left(\frac{151}{198}\right)\)	\(e\left(\frac{29}{33}\right)\)	\(e\left(\frac{8}{33}\right)\)	\(e\left(\frac{101}{198}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{101}{198}\right)\)	\(e\left(\frac{62}{99}\right)\)	\(e\left(\frac{98}{99}\right)\)
\(\chi_{3933}(31,\cdot)\)	3933.dc	66	yes	\(-1\)	\(1\)	\(e\left(\frac{47}{66}\right)\)	\(e\left(\frac{14}{33}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{17}{33}\right)\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{65}{66}\right)\)	\(e\left(\frac{26}{33}\right)\)	\(e\left(\frac{43}{66}\right)\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{28}{33}\right)\)
\(\chi_{3933}(32,\cdot)\)	3933.ef	198	yes	\(1\)	\(1\)	\(e\left(\frac{2}{99}\right)\)	\(e\left(\frac{4}{99}\right)\)	\(e\left(\frac{13}{198}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{2}{33}\right)\)	\(e\left(\frac{17}{198}\right)\)	\(e\left(\frac{17}{66}\right)\)	\(e\left(\frac{83}{198}\right)\)	\(e\left(\frac{65}{99}\right)\)	\(e\left(\frac{8}{99}\right)\)
\(\chi_{3933}(34,\cdot)\)	3933.ej	198	yes	\(1\)	\(1\)	\(e\left(\frac{19}{198}\right)\)	\(e\left(\frac{19}{99}\right)\)	\(e\left(\frac{103}{198}\right)\)	\(e\left(\frac{7}{66}\right)\)	\(e\left(\frac{19}{66}\right)\)	\(e\left(\frac{61}{99}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{23}{198}\right)\)	\(e\left(\frac{20}{99}\right)\)	\(e\left(\frac{38}{99}\right)\)
\(\chi_{3933}(35,\cdot)\)	3933.ep	198	no	\(-1\)	\(1\)	\(e\left(\frac{107}{198}\right)\)	\(e\left(\frac{8}{99}\right)\)	\(e\left(\frac{191}{198}\right)\)	\(e\left(\frac{20}{33}\right)\)	\(e\left(\frac{41}{66}\right)\)	\(e\left(\frac{50}{99}\right)\)	\(e\left(\frac{23}{66}\right)\)	\(e\left(\frac{83}{99}\right)\)	\(e\left(\frac{29}{198}\right)\)	\(e\left(\frac{16}{99}\right)\)
\(\chi_{3933}(37,\cdot)\)	3933.ct	22	no	\(1\)	\(1\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{7}{11}\right)\)
\(\chi_{3933}(40,\cdot)\)	3933.ej	198	yes	\(1\)	\(1\)	\(e\left(\frac{5}{198}\right)\)	\(e\left(\frac{5}{99}\right)\)	\(e\left(\frac{173}{198}\right)\)	\(e\left(\frac{47}{66}\right)\)	\(e\left(\frac{5}{66}\right)\)	\(e\left(\frac{89}{99}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{79}{198}\right)\)	\(e\left(\frac{73}{99}\right)\)	\(e\left(\frac{10}{99}\right)\)
\(\chi_{3933}(41,\cdot)\)	3933.et	198	yes	\(1\)	\(1\)	\(e\left(\frac{64}{99}\right)\)	\(e\left(\frac{29}{99}\right)\)	\(e\left(\frac{53}{198}\right)\)	\(e\left(\frac{1}{33}\right)\)	\(e\left(\frac{31}{33}\right)\)	\(e\left(\frac{181}{198}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{181}{198}\right)\)	\(e\left(\frac{67}{99}\right)\)	\(e\left(\frac{58}{99}\right)\)
\(\chi_{3933}(43,\cdot)\)	3933.ew	198	yes	\(-1\)	\(1\)	\(e\left(\frac{1}{99}\right)\)	\(e\left(\frac{2}{99}\right)\)	\(e\left(\frac{155}{198}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{1}{33}\right)\)	\(e\left(\frac{157}{198}\right)\)	\(e\left(\frac{25}{66}\right)\)	\(e\left(\frac{95}{99}\right)\)	\(e\left(\frac{65}{198}\right)\)	\(e\left(\frac{4}{99}\right)\)
\(\chi_{3933}(44,\cdot)\)	3933.ei	198	no	\(1\)	\(1\)	\(e\left(\frac{91}{198}\right)\)	\(e\left(\frac{91}{99}\right)\)	\(e\left(\frac{53}{99}\right)\)	\(e\left(\frac{59}{66}\right)\)	\(e\left(\frac{25}{66}\right)\)	\(e\left(\frac{197}{198}\right)\)	\(e\left(\frac{5}{33}\right)\)	\(e\left(\frac{16}{99}\right)\)	\(e\left(\frac{35}{99}\right)\)	\(e\left(\frac{83}{99}\right)\)
\(\chi_{3933}(47,\cdot)\)	3933.by	18	no	\(-1\)	\(1\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(-1\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{4}{9}\right)\)
\(\chi_{3933}(49,\cdot)\)	3933.cu	33	yes	\(1\)	\(1\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{2}{33}\right)\)	\(e\left(\frac{5}{33}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{17}{33}\right)\)	\(e\left(\frac{29}{33}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{20}{33}\right)\)	\(e\left(\frac{9}{11}\right)\)
\(\chi_{3933}(50,\cdot)\)	3933.dv	66	yes	\(1\)	\(1\)	\(e\left(\frac{1}{33}\right)\)	\(e\left(\frac{2}{33}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{26}{33}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{47}{66}\right)\)	\(e\left(\frac{31}{66}\right)\)	\(e\left(\frac{25}{66}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{4}{33}\right)\)
\(\chi_{3933}(52,\cdot)\)	3933.ee	198	yes	\(-1\)	\(1\)	\(e\left(\frac{137}{198}\right)\)	\(e\left(\frac{38}{99}\right)\)	\(e\left(\frac{37}{99}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{5}{66}\right)\)	\(e\left(\frac{13}{198}\right)\)	\(e\left(\frac{23}{33}\right)\)	\(e\left(\frac{145}{198}\right)\)	\(e\left(\frac{47}{198}\right)\)	\(e\left(\frac{76}{99}\right)\)
\(\chi_{3933}(53,\cdot)\)	3933.em	198	no	\(-1\)	\(1\)	\(e\left(\frac{83}{99}\right)\)	\(e\left(\frac{67}{99}\right)\)	\(e\left(\frac{14}{99}\right)\)	\(e\left(\frac{5}{66}\right)\)	\(e\left(\frac{17}{33}\right)\)	\(e\left(\frac{97}{99}\right)\)	\(e\left(\frac{20}{33}\right)\)	\(e\left(\frac{29}{198}\right)\)	\(e\left(\frac{181}{198}\right)\)	\(e\left(\frac{35}{99}\right)\)

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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.