LMFDB - Group of Dirichlet characters of modulus 6004

Show commands: PariGP / SageMath

sage: H = DirichletGroup(6004)

pari: g = idealstar(,6004,2)

Character group

sage: G.order() pari: g.no
Order	=	2808
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{6}\times C_{234}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{6004}(3003,\cdot)$, $\chi_{6004}(2529,\cdot)$, $\chi_{6004}(3953,\cdot)$

First 32 of 2808 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	$-1$	$1$	$3$	$5$	$7$	$9$	$11$	$13$	$15$	$17$	$21$	$23$
$\chi_{6004}(1,\cdot)$	6004.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{6004}(3,\cdot)$	6004.es	234	yes	$-1$	$1$	$e\left(\frac{211}{234}\right)$	$e\left(\frac{41}{117}\right)$	$e\left(\frac{20}{39}\right)$	$e\left(\frac{94}{117}\right)$	$e\left(\frac{1}{26}\right)$	$e\left(\frac{11}{234}\right)$	$e\left(\frac{59}{234}\right)$	$e\left(\frac{115}{234}\right)$	$e\left(\frac{97}{234}\right)$	$e\left(\frac{5}{18}\right)$
$\chi_{6004}(5,\cdot)$	6004.ea	117	no	$1$	$1$	$e\left(\frac{41}{117}\right)$	$e\left(\frac{59}{117}\right)$	$e\left(\frac{6}{13}\right)$	$e\left(\frac{82}{117}\right)$	$e\left(\frac{28}{39}\right)$	$e\left(\frac{55}{117}\right)$	$e\left(\frac{100}{117}\right)$	$e\left(\frac{68}{117}\right)$	$e\left(\frac{95}{117}\right)$	$e\left(\frac{4}{9}\right)$
$\chi_{6004}(7,\cdot)$	6004.dp	78	yes	$1$	$1$	$e\left(\frac{20}{39}\right)$	$e\left(\frac{6}{13}\right)$	$e\left(\frac{20}{39}\right)$	$e\left(\frac{1}{39}\right)$	$e\left(\frac{55}{78}\right)$	$e\left(\frac{10}{13}\right)$	$e\left(\frac{38}{39}\right)$	$e\left(\frac{47}{78}\right)$	$e\left(\frac{1}{39}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{6004}(9,\cdot)$	6004.eb	117	no	$1$	$1$	$e\left(\frac{94}{117}\right)$	$e\left(\frac{82}{117}\right)$	$e\left(\frac{1}{39}\right)$	$e\left(\frac{71}{117}\right)$	$e\left(\frac{1}{13}\right)$	$e\left(\frac{11}{117}\right)$	$e\left(\frac{59}{117}\right)$	$e\left(\frac{115}{117}\right)$	$e\left(\frac{97}{117}\right)$	$e\left(\frac{5}{9}\right)$
$\chi_{6004}(11,\cdot)$	6004.dw	78	yes	$-1$	$1$	$e\left(\frac{1}{26}\right)$	$e\left(\frac{28}{39}\right)$	$e\left(\frac{55}{78}\right)$	$e\left(\frac{1}{13}\right)$	$e\left(\frac{61}{78}\right)$	$e\left(\frac{38}{39}\right)$	$e\left(\frac{59}{78}\right)$	$e\left(\frac{38}{39}\right)$	$e\left(\frac{29}{39}\right)$	$-1$
$\chi_{6004}(13,\cdot)$	6004.ef	234	no	$-1$	$1$	$e\left(\frac{11}{234}\right)$	$e\left(\frac{55}{117}\right)$	$e\left(\frac{10}{13}\right)$	$e\left(\frac{11}{117}\right)$	$e\left(\frac{38}{39}\right)$	$e\left(\frac{49}{234}\right)$	$e\left(\frac{121}{234}\right)$	$e\left(\frac{109}{117}\right)$	$e\left(\frac{191}{234}\right)$	$e\left(\frac{8}{9}\right)$
$\chi_{6004}(15,\cdot)$	6004.ep	234	yes	$-1$	$1$	$e\left(\frac{59}{234}\right)$	$e\left(\frac{100}{117}\right)$	$e\left(\frac{38}{39}\right)$	$e\left(\frac{59}{117}\right)$	$e\left(\frac{59}{78}\right)$	$e\left(\frac{121}{234}\right)$	$e\left(\frac{25}{234}\right)$	$e\left(\frac{17}{234}\right)$	$e\left(\frac{53}{234}\right)$	$e\left(\frac{13}{18}\right)$
$\chi_{6004}(17,\cdot)$	6004.ek	234	no	$-1$	$1$	$e\left(\frac{115}{234}\right)$	$e\left(\frac{68}{117}\right)$	$e\left(\frac{47}{78}\right)$	$e\left(\frac{115}{117}\right)$	$e\left(\frac{38}{39}\right)$	$e\left(\frac{109}{117}\right)$	$e\left(\frac{17}{234}\right)$	$e\left(\frac{49}{234}\right)$	$e\left(\frac{11}{117}\right)$	$e\left(\frac{1}{9}\right)$
$\chi_{6004}(21,\cdot)$	6004.er	234	no	$-1$	$1$	$e\left(\frac{97}{234}\right)$	$e\left(\frac{95}{117}\right)$	$e\left(\frac{1}{39}\right)$	$e\left(\frac{97}{117}\right)$	$e\left(\frac{29}{39}\right)$	$e\left(\frac{191}{234}\right)$	$e\left(\frac{53}{234}\right)$	$e\left(\frac{11}{117}\right)$	$e\left(\frac{103}{234}\right)$	$e\left(\frac{1}{9}\right)$
$\chi_{6004}(23,\cdot)$	6004.cd	18	yes	$-1$	$1$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{9}\right)$	$-1$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{7}{18}\right)$
$\chi_{6004}(25,\cdot)$	6004.ea	117	no	$1$	$1$	$e\left(\frac{82}{117}\right)$	$e\left(\frac{1}{117}\right)$	$e\left(\frac{12}{13}\right)$	$e\left(\frac{47}{117}\right)$	$e\left(\frac{17}{39}\right)$	$e\left(\frac{110}{117}\right)$	$e\left(\frac{83}{117}\right)$	$e\left(\frac{19}{117}\right)$	$e\left(\frac{73}{117}\right)$	$e\left(\frac{8}{9}\right)$
$\chi_{6004}(27,\cdot)$	6004.dg	78	yes	$-1$	$1$	$e\left(\frac{55}{78}\right)$	$e\left(\frac{2}{39}\right)$	$e\left(\frac{7}{13}\right)$	$e\left(\frac{16}{39}\right)$	$e\left(\frac{3}{26}\right)$	$e\left(\frac{11}{78}\right)$	$e\left(\frac{59}{78}\right)$	$e\left(\frac{37}{78}\right)$	$e\left(\frac{19}{78}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{6004}(29,\cdot)$	6004.eh	234	no	$1$	$1$	$e\left(\frac{49}{117}\right)$	$e\left(\frac{100}{117}\right)$	$e\left(\frac{11}{78}\right)$	$e\left(\frac{98}{117}\right)$	$e\left(\frac{12}{13}\right)$	$e\left(\frac{121}{234}\right)$	$e\left(\frac{32}{117}\right)$	$e\left(\frac{95}{234}\right)$	$e\left(\frac{131}{234}\right)$	$e\left(\frac{5}{9}\right)$
$\chi_{6004}(31,\cdot)$	6004.dn	78	yes	$1$	$1$	$e\left(\frac{2}{39}\right)$	$e\left(\frac{11}{13}\right)$	$e\left(\frac{43}{78}\right)$	$e\left(\frac{4}{39}\right)$	$e\left(\frac{25}{78}\right)$	$e\left(\frac{15}{26}\right)$	$e\left(\frac{35}{39}\right)$	$e\left(\frac{16}{39}\right)$	$e\left(\frac{47}{78}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{6004}(33,\cdot)$	6004.el	234	no	$1$	$1$	$e\left(\frac{110}{117}\right)$	$e\left(\frac{8}{117}\right)$	$e\left(\frac{17}{78}\right)$	$e\left(\frac{103}{117}\right)$	$e\left(\frac{32}{39}\right)$	$e\left(\frac{5}{234}\right)$	$e\left(\frac{1}{117}\right)$	$e\left(\frac{109}{234}\right)$	$e\left(\frac{37}{234}\right)$	$e\left(\frac{7}{9}\right)$
$\chi_{6004}(35,\cdot)$	6004.et	234	yes	$1$	$1$	$e\left(\frac{101}{117}\right)$	$e\left(\frac{113}{117}\right)$	$e\left(\frac{38}{39}\right)$	$e\left(\frac{85}{117}\right)$	$e\left(\frac{11}{26}\right)$	$e\left(\frac{28}{117}\right)$	$e\left(\frac{97}{117}\right)$	$e\left(\frac{43}{234}\right)$	$e\left(\frac{98}{117}\right)$	$e\left(\frac{5}{18}\right)$
$\chi_{6004}(37,\cdot)$	6004.ds	78	no	$1$	$1$	$e\left(\frac{29}{39}\right)$	$e\left(\frac{4}{39}\right)$	$e\left(\frac{71}{78}\right)$	$e\left(\frac{19}{39}\right)$	$e\left(\frac{22}{39}\right)$	$e\left(\frac{61}{78}\right)$	$e\left(\frac{11}{13}\right)$	$e\left(\frac{3}{26}\right)$	$e\left(\frac{17}{26}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{6004}(39,\cdot)$	6004.dt	78	no	$1$	$1$	$e\left(\frac{37}{39}\right)$	$e\left(\frac{32}{39}\right)$	$e\left(\frac{11}{39}\right)$	$e\left(\frac{35}{39}\right)$	$e\left(\frac{1}{78}\right)$	$e\left(\frac{10}{39}\right)$	$e\left(\frac{10}{13}\right)$	$e\left(\frac{11}{26}\right)$	$e\left(\frac{3}{13}\right)$	$e\left(\frac{1}{6}\right)$
$\chi_{6004}(41,\cdot)$	6004.el	234	no	$1$	$1$	$e\left(\frac{41}{117}\right)$	$e\left(\frac{20}{117}\right)$	$e\left(\frac{23}{78}\right)$	$e\left(\frac{82}{117}\right)$	$e\left(\frac{2}{39}\right)$	$e\left(\frac{71}{234}\right)$	$e\left(\frac{61}{117}\right)$	$e\left(\frac{97}{234}\right)$	$e\left(\frac{151}{234}\right)$	$e\left(\frac{4}{9}\right)$
$\chi_{6004}(43,\cdot)$	6004.et	234	yes	$1$	$1$	$e\left(\frac{80}{117}\right)$	$e\left(\frac{20}{117}\right)$	$e\left(\frac{5}{39}\right)$	$e\left(\frac{43}{117}\right)$	$e\left(\frac{23}{26}\right)$	$e\left(\frac{94}{117}\right)$	$e\left(\frac{100}{117}\right)$	$e\left(\frac{19}{234}\right)$	$e\left(\frac{95}{117}\right)$	$e\left(\frac{11}{18}\right)$
$\chi_{6004}(45,\cdot)$	6004.cu	39	no	$1$	$1$	$e\left(\frac{2}{13}\right)$	$e\left(\frac{8}{39}\right)$	$e\left(\frac{19}{39}\right)$	$e\left(\frac{4}{13}\right)$	$e\left(\frac{31}{39}\right)$	$e\left(\frac{22}{39}\right)$	$e\left(\frac{14}{39}\right)$	$e\left(\frac{22}{39}\right)$	$e\left(\frac{25}{39}\right)$	$1$
$\chi_{6004}(47,\cdot)$	6004.et	234	yes	$1$	$1$	$e\left(\frac{4}{117}\right)$	$e\left(\frac{1}{117}\right)$	$e\left(\frac{10}{39}\right)$	$e\left(\frac{8}{117}\right)$	$e\left(\frac{7}{26}\right)$	$e\left(\frac{110}{117}\right)$	$e\left(\frac{5}{117}\right)$	$e\left(\frac{77}{234}\right)$	$e\left(\frac{34}{117}\right)$	$e\left(\frac{1}{18}\right)$
$\chi_{6004}(49,\cdot)$	6004.cv	39	no	$1$	$1$	$e\left(\frac{1}{39}\right)$	$e\left(\frac{12}{13}\right)$	$e\left(\frac{1}{39}\right)$	$e\left(\frac{2}{39}\right)$	$e\left(\frac{16}{39}\right)$	$e\left(\frac{7}{13}\right)$	$e\left(\frac{37}{39}\right)$	$e\left(\frac{8}{39}\right)$	$e\left(\frac{2}{39}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{6004}(51,\cdot)$	6004.ev	234	yes	$1$	$1$	$e\left(\frac{46}{117}\right)$	$e\left(\frac{109}{117}\right)$	$e\left(\frac{3}{26}\right)$	$e\left(\frac{92}{117}\right)$	$e\left(\frac{1}{78}\right)$	$e\left(\frac{229}{234}\right)$	$e\left(\frac{38}{117}\right)$	$e\left(\frac{82}{117}\right)$	$e\left(\frac{119}{234}\right)$	$e\left(\frac{7}{18}\right)$
$\chi_{6004}(53,\cdot)$	6004.eh	234	no	$1$	$1$	$e\left(\frac{109}{117}\right)$	$e\left(\frac{115}{117}\right)$	$e\left(\frac{77}{78}\right)$	$e\left(\frac{101}{117}\right)$	$e\left(\frac{6}{13}\right)$	$e\left(\frac{145}{234}\right)$	$e\left(\frac{107}{117}\right)$	$e\left(\frac{197}{234}\right)$	$e\left(\frac{215}{234}\right)$	$e\left(\frac{8}{9}\right)$
$\chi_{6004}(55,\cdot)$	6004.cd	18	yes	$-1$	$1$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{7}{9}\right)$	$-1$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{17}{18}\right)$
$\chi_{6004}(59,\cdot)$	6004.es	234	yes	$-1$	$1$	$e\left(\frac{145}{234}\right)$	$e\left(\frac{62}{117}\right)$	$e\left(\frac{35}{39}\right)$	$e\left(\frac{28}{117}\right)$	$e\left(\frac{5}{26}\right)$	$e\left(\frac{185}{234}\right)$	$e\left(\frac{35}{234}\right)$	$e\left(\frac{211}{234}\right)$	$e\left(\frac{121}{234}\right)$	$e\left(\frac{17}{18}\right)$
$\chi_{6004}(61,\cdot)$	6004.ek	234	no	$-1$	$1$	$e\left(\frac{5}{234}\right)$	$e\left(\frac{64}{117}\right)$	$e\left(\frac{19}{78}\right)$	$e\left(\frac{5}{117}\right)$	$e\left(\frac{22}{39}\right)$	$e\left(\frac{20}{117}\right)$	$e\left(\frac{133}{234}\right)$	$e\left(\frac{53}{234}\right)$	$e\left(\frac{31}{117}\right)$	$e\left(\frac{2}{9}\right)$
$\chi_{6004}(63,\cdot)$	6004.ee	234	yes	$1$	$1$	$e\left(\frac{37}{117}\right)$	$e\left(\frac{19}{117}\right)$	$e\left(\frac{7}{13}\right)$	$e\left(\frac{74}{117}\right)$	$e\left(\frac{61}{78}\right)$	$e\left(\frac{101}{117}\right)$	$e\left(\frac{56}{117}\right)$	$e\left(\frac{137}{234}\right)$	$e\left(\frac{100}{117}\right)$	$e\left(\frac{7}{18}\right)$
$\chi_{6004}(65,\cdot)$	6004.df	78	no	$-1$	$1$	$e\left(\frac{31}{78}\right)$	$e\left(\frac{38}{39}\right)$	$e\left(\frac{3}{13}\right)$	$e\left(\frac{31}{39}\right)$	$e\left(\frac{9}{13}\right)$	$e\left(\frac{53}{78}\right)$	$e\left(\frac{29}{78}\right)$	$e\left(\frac{20}{39}\right)$	$e\left(\frac{49}{78}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{6004}(67,\cdot)$	6004.ej	234	yes	$1$	$1$	$e\left(\frac{46}{117}\right)$	$e\left(\frac{31}{117}\right)$	$e\left(\frac{61}{78}\right)$	$e\left(\frac{92}{117}\right)$	$e\left(\frac{53}{78}\right)$	$e\left(\frac{151}{234}\right)$	$e\left(\frac{77}{117}\right)$	$e\left(\frac{43}{117}\right)$	$e\left(\frac{41}{234}\right)$	$e\left(\frac{7}{18}\right)$

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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	$6004$
Structure	\(C_{2}\times C_{6}\times C_{234}\)
Order	$2808$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(3\)	\(5\)	\(7\)	\(9\)	\(11\)	\(13\)	\(15\)	\(17\)	\(21\)	\(23\)
\(\chi_{6004}(1,\cdot)\)	6004.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{6004}(3,\cdot)\)	6004.es	234	yes	\(-1\)	\(1\)	\(e\left(\frac{211}{234}\right)\)	\(e\left(\frac{41}{117}\right)\)	\(e\left(\frac{20}{39}\right)\)	\(e\left(\frac{94}{117}\right)\)	\(e\left(\frac{1}{26}\right)\)	\(e\left(\frac{11}{234}\right)\)	\(e\left(\frac{59}{234}\right)\)	\(e\left(\frac{115}{234}\right)\)	\(e\left(\frac{97}{234}\right)\)	\(e\left(\frac{5}{18}\right)\)
\(\chi_{6004}(5,\cdot)\)	6004.ea	117	no	\(1\)	\(1\)	\(e\left(\frac{41}{117}\right)\)	\(e\left(\frac{59}{117}\right)\)	\(e\left(\frac{6}{13}\right)\)	\(e\left(\frac{82}{117}\right)\)	\(e\left(\frac{28}{39}\right)\)	\(e\left(\frac{55}{117}\right)\)	\(e\left(\frac{100}{117}\right)\)	\(e\left(\frac{68}{117}\right)\)	\(e\left(\frac{95}{117}\right)\)	\(e\left(\frac{4}{9}\right)\)
\(\chi_{6004}(7,\cdot)\)	6004.dp	78	yes	\(1\)	\(1\)	\(e\left(\frac{20}{39}\right)\)	\(e\left(\frac{6}{13}\right)\)	\(e\left(\frac{20}{39}\right)\)	\(e\left(\frac{1}{39}\right)\)	\(e\left(\frac{55}{78}\right)\)	\(e\left(\frac{10}{13}\right)\)	\(e\left(\frac{38}{39}\right)\)	\(e\left(\frac{47}{78}\right)\)	\(e\left(\frac{1}{39}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{6004}(9,\cdot)\)	6004.eb	117	no	\(1\)	\(1\)	\(e\left(\frac{94}{117}\right)\)	\(e\left(\frac{82}{117}\right)\)	\(e\left(\frac{1}{39}\right)\)	\(e\left(\frac{71}{117}\right)\)	\(e\left(\frac{1}{13}\right)\)	\(e\left(\frac{11}{117}\right)\)	\(e\left(\frac{59}{117}\right)\)	\(e\left(\frac{115}{117}\right)\)	\(e\left(\frac{97}{117}\right)\)	\(e\left(\frac{5}{9}\right)\)
\(\chi_{6004}(11,\cdot)\)	6004.dw	78	yes	\(-1\)	\(1\)	\(e\left(\frac{1}{26}\right)\)	\(e\left(\frac{28}{39}\right)\)	\(e\left(\frac{55}{78}\right)\)	\(e\left(\frac{1}{13}\right)\)	\(e\left(\frac{61}{78}\right)\)	\(e\left(\frac{38}{39}\right)\)	\(e\left(\frac{59}{78}\right)\)	\(e\left(\frac{38}{39}\right)\)	\(e\left(\frac{29}{39}\right)\)	\(-1\)
\(\chi_{6004}(13,\cdot)\)	6004.ef	234	no	\(-1\)	\(1\)	\(e\left(\frac{11}{234}\right)\)	\(e\left(\frac{55}{117}\right)\)	\(e\left(\frac{10}{13}\right)\)	\(e\left(\frac{11}{117}\right)\)	\(e\left(\frac{38}{39}\right)\)	\(e\left(\frac{49}{234}\right)\)	\(e\left(\frac{121}{234}\right)\)	\(e\left(\frac{109}{117}\right)\)	\(e\left(\frac{191}{234}\right)\)	\(e\left(\frac{8}{9}\right)\)
\(\chi_{6004}(15,\cdot)\)	6004.ep	234	yes	\(-1\)	\(1\)	\(e\left(\frac{59}{234}\right)\)	\(e\left(\frac{100}{117}\right)\)	\(e\left(\frac{38}{39}\right)\)	\(e\left(\frac{59}{117}\right)\)	\(e\left(\frac{59}{78}\right)\)	\(e\left(\frac{121}{234}\right)\)	\(e\left(\frac{25}{234}\right)\)	\(e\left(\frac{17}{234}\right)\)	\(e\left(\frac{53}{234}\right)\)	\(e\left(\frac{13}{18}\right)\)
\(\chi_{6004}(17,\cdot)\)	6004.ek	234	no	\(-1\)	\(1\)	\(e\left(\frac{115}{234}\right)\)	\(e\left(\frac{68}{117}\right)\)	\(e\left(\frac{47}{78}\right)\)	\(e\left(\frac{115}{117}\right)\)	\(e\left(\frac{38}{39}\right)\)	\(e\left(\frac{109}{117}\right)\)	\(e\left(\frac{17}{234}\right)\)	\(e\left(\frac{49}{234}\right)\)	\(e\left(\frac{11}{117}\right)\)	\(e\left(\frac{1}{9}\right)\)
\(\chi_{6004}(21,\cdot)\)	6004.er	234	no	\(-1\)	\(1\)	\(e\left(\frac{97}{234}\right)\)	\(e\left(\frac{95}{117}\right)\)	\(e\left(\frac{1}{39}\right)\)	\(e\left(\frac{97}{117}\right)\)	\(e\left(\frac{29}{39}\right)\)	\(e\left(\frac{191}{234}\right)\)	\(e\left(\frac{53}{234}\right)\)	\(e\left(\frac{11}{117}\right)\)	\(e\left(\frac{103}{234}\right)\)	\(e\left(\frac{1}{9}\right)\)
\(\chi_{6004}(23,\cdot)\)	6004.cd	18	yes	\(-1\)	\(1\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(-1\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{7}{18}\right)\)
\(\chi_{6004}(25,\cdot)\)	6004.ea	117	no	\(1\)	\(1\)	\(e\left(\frac{82}{117}\right)\)	\(e\left(\frac{1}{117}\right)\)	\(e\left(\frac{12}{13}\right)\)	\(e\left(\frac{47}{117}\right)\)	\(e\left(\frac{17}{39}\right)\)	\(e\left(\frac{110}{117}\right)\)	\(e\left(\frac{83}{117}\right)\)	\(e\left(\frac{19}{117}\right)\)	\(e\left(\frac{73}{117}\right)\)	\(e\left(\frac{8}{9}\right)\)
\(\chi_{6004}(27,\cdot)\)	6004.dg	78	yes	\(-1\)	\(1\)	\(e\left(\frac{55}{78}\right)\)	\(e\left(\frac{2}{39}\right)\)	\(e\left(\frac{7}{13}\right)\)	\(e\left(\frac{16}{39}\right)\)	\(e\left(\frac{3}{26}\right)\)	\(e\left(\frac{11}{78}\right)\)	\(e\left(\frac{59}{78}\right)\)	\(e\left(\frac{37}{78}\right)\)	\(e\left(\frac{19}{78}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{6004}(29,\cdot)\)	6004.eh	234	no	\(1\)	\(1\)	\(e\left(\frac{49}{117}\right)\)	\(e\left(\frac{100}{117}\right)\)	\(e\left(\frac{11}{78}\right)\)	\(e\left(\frac{98}{117}\right)\)	\(e\left(\frac{12}{13}\right)\)	\(e\left(\frac{121}{234}\right)\)	\(e\left(\frac{32}{117}\right)\)	\(e\left(\frac{95}{234}\right)\)	\(e\left(\frac{131}{234}\right)\)	\(e\left(\frac{5}{9}\right)\)
\(\chi_{6004}(31,\cdot)\)	6004.dn	78	yes	\(1\)	\(1\)	\(e\left(\frac{2}{39}\right)\)	\(e\left(\frac{11}{13}\right)\)	\(e\left(\frac{43}{78}\right)\)	\(e\left(\frac{4}{39}\right)\)	\(e\left(\frac{25}{78}\right)\)	\(e\left(\frac{15}{26}\right)\)	\(e\left(\frac{35}{39}\right)\)	\(e\left(\frac{16}{39}\right)\)	\(e\left(\frac{47}{78}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{6004}(33,\cdot)\)	6004.el	234	no	\(1\)	\(1\)	\(e\left(\frac{110}{117}\right)\)	\(e\left(\frac{8}{117}\right)\)	\(e\left(\frac{17}{78}\right)\)	\(e\left(\frac{103}{117}\right)\)	\(e\left(\frac{32}{39}\right)\)	\(e\left(\frac{5}{234}\right)\)	\(e\left(\frac{1}{117}\right)\)	\(e\left(\frac{109}{234}\right)\)	\(e\left(\frac{37}{234}\right)\)	\(e\left(\frac{7}{9}\right)\)
\(\chi_{6004}(35,\cdot)\)	6004.et	234	yes	\(1\)	\(1\)	\(e\left(\frac{101}{117}\right)\)	\(e\left(\frac{113}{117}\right)\)	\(e\left(\frac{38}{39}\right)\)	\(e\left(\frac{85}{117}\right)\)	\(e\left(\frac{11}{26}\right)\)	\(e\left(\frac{28}{117}\right)\)	\(e\left(\frac{97}{117}\right)\)	\(e\left(\frac{43}{234}\right)\)	\(e\left(\frac{98}{117}\right)\)	\(e\left(\frac{5}{18}\right)\)
\(\chi_{6004}(37,\cdot)\)	6004.ds	78	no	\(1\)	\(1\)	\(e\left(\frac{29}{39}\right)\)	\(e\left(\frac{4}{39}\right)\)	\(e\left(\frac{71}{78}\right)\)	\(e\left(\frac{19}{39}\right)\)	\(e\left(\frac{22}{39}\right)\)	\(e\left(\frac{61}{78}\right)\)	\(e\left(\frac{11}{13}\right)\)	\(e\left(\frac{3}{26}\right)\)	\(e\left(\frac{17}{26}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{6004}(39,\cdot)\)	6004.dt	78	no	\(1\)	\(1\)	\(e\left(\frac{37}{39}\right)\)	\(e\left(\frac{32}{39}\right)\)	\(e\left(\frac{11}{39}\right)\)	\(e\left(\frac{35}{39}\right)\)	\(e\left(\frac{1}{78}\right)\)	\(e\left(\frac{10}{39}\right)\)	\(e\left(\frac{10}{13}\right)\)	\(e\left(\frac{11}{26}\right)\)	\(e\left(\frac{3}{13}\right)\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{6004}(41,\cdot)\)	6004.el	234	no	\(1\)	\(1\)	\(e\left(\frac{41}{117}\right)\)	\(e\left(\frac{20}{117}\right)\)	\(e\left(\frac{23}{78}\right)\)	\(e\left(\frac{82}{117}\right)\)	\(e\left(\frac{2}{39}\right)\)	\(e\left(\frac{71}{234}\right)\)	\(e\left(\frac{61}{117}\right)\)	\(e\left(\frac{97}{234}\right)\)	\(e\left(\frac{151}{234}\right)\)	\(e\left(\frac{4}{9}\right)\)
\(\chi_{6004}(43,\cdot)\)	6004.et	234	yes	\(1\)	\(1\)	\(e\left(\frac{80}{117}\right)\)	\(e\left(\frac{20}{117}\right)\)	\(e\left(\frac{5}{39}\right)\)	\(e\left(\frac{43}{117}\right)\)	\(e\left(\frac{23}{26}\right)\)	\(e\left(\frac{94}{117}\right)\)	\(e\left(\frac{100}{117}\right)\)	\(e\left(\frac{19}{234}\right)\)	\(e\left(\frac{95}{117}\right)\)	\(e\left(\frac{11}{18}\right)\)
\(\chi_{6004}(45,\cdot)\)	6004.cu	39	no	\(1\)	\(1\)	\(e\left(\frac{2}{13}\right)\)	\(e\left(\frac{8}{39}\right)\)	\(e\left(\frac{19}{39}\right)\)	\(e\left(\frac{4}{13}\right)\)	\(e\left(\frac{31}{39}\right)\)	\(e\left(\frac{22}{39}\right)\)	\(e\left(\frac{14}{39}\right)\)	\(e\left(\frac{22}{39}\right)\)	\(e\left(\frac{25}{39}\right)\)	\(1\)
\(\chi_{6004}(47,\cdot)\)	6004.et	234	yes	\(1\)	\(1\)	\(e\left(\frac{4}{117}\right)\)	\(e\left(\frac{1}{117}\right)\)	\(e\left(\frac{10}{39}\right)\)	\(e\left(\frac{8}{117}\right)\)	\(e\left(\frac{7}{26}\right)\)	\(e\left(\frac{110}{117}\right)\)	\(e\left(\frac{5}{117}\right)\)	\(e\left(\frac{77}{234}\right)\)	\(e\left(\frac{34}{117}\right)\)	\(e\left(\frac{1}{18}\right)\)
\(\chi_{6004}(49,\cdot)\)	6004.cv	39	no	\(1\)	\(1\)	\(e\left(\frac{1}{39}\right)\)	\(e\left(\frac{12}{13}\right)\)	\(e\left(\frac{1}{39}\right)\)	\(e\left(\frac{2}{39}\right)\)	\(e\left(\frac{16}{39}\right)\)	\(e\left(\frac{7}{13}\right)\)	\(e\left(\frac{37}{39}\right)\)	\(e\left(\frac{8}{39}\right)\)	\(e\left(\frac{2}{39}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{6004}(51,\cdot)\)	6004.ev	234	yes	\(1\)	\(1\)	\(e\left(\frac{46}{117}\right)\)	\(e\left(\frac{109}{117}\right)\)	\(e\left(\frac{3}{26}\right)\)	\(e\left(\frac{92}{117}\right)\)	\(e\left(\frac{1}{78}\right)\)	\(e\left(\frac{229}{234}\right)\)	\(e\left(\frac{38}{117}\right)\)	\(e\left(\frac{82}{117}\right)\)	\(e\left(\frac{119}{234}\right)\)	\(e\left(\frac{7}{18}\right)\)
\(\chi_{6004}(53,\cdot)\)	6004.eh	234	no	\(1\)	\(1\)	\(e\left(\frac{109}{117}\right)\)	\(e\left(\frac{115}{117}\right)\)	\(e\left(\frac{77}{78}\right)\)	\(e\left(\frac{101}{117}\right)\)	\(e\left(\frac{6}{13}\right)\)	\(e\left(\frac{145}{234}\right)\)	\(e\left(\frac{107}{117}\right)\)	\(e\left(\frac{197}{234}\right)\)	\(e\left(\frac{215}{234}\right)\)	\(e\left(\frac{8}{9}\right)\)
\(\chi_{6004}(55,\cdot)\)	6004.cd	18	yes	\(-1\)	\(1\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(-1\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{17}{18}\right)\)
\(\chi_{6004}(59,\cdot)\)	6004.es	234	yes	\(-1\)	\(1\)	\(e\left(\frac{145}{234}\right)\)	\(e\left(\frac{62}{117}\right)\)	\(e\left(\frac{35}{39}\right)\)	\(e\left(\frac{28}{117}\right)\)	\(e\left(\frac{5}{26}\right)\)	\(e\left(\frac{185}{234}\right)\)	\(e\left(\frac{35}{234}\right)\)	\(e\left(\frac{211}{234}\right)\)	\(e\left(\frac{121}{234}\right)\)	\(e\left(\frac{17}{18}\right)\)
\(\chi_{6004}(61,\cdot)\)	6004.ek	234	no	\(-1\)	\(1\)	\(e\left(\frac{5}{234}\right)\)	\(e\left(\frac{64}{117}\right)\)	\(e\left(\frac{19}{78}\right)\)	\(e\left(\frac{5}{117}\right)\)	\(e\left(\frac{22}{39}\right)\)	\(e\left(\frac{20}{117}\right)\)	\(e\left(\frac{133}{234}\right)\)	\(e\left(\frac{53}{234}\right)\)	\(e\left(\frac{31}{117}\right)\)	\(e\left(\frac{2}{9}\right)\)
\(\chi_{6004}(63,\cdot)\)	6004.ee	234	yes	\(1\)	\(1\)	\(e\left(\frac{37}{117}\right)\)	\(e\left(\frac{19}{117}\right)\)	\(e\left(\frac{7}{13}\right)\)	\(e\left(\frac{74}{117}\right)\)	\(e\left(\frac{61}{78}\right)\)	\(e\left(\frac{101}{117}\right)\)	\(e\left(\frac{56}{117}\right)\)	\(e\left(\frac{137}{234}\right)\)	\(e\left(\frac{100}{117}\right)\)	\(e\left(\frac{7}{18}\right)\)
\(\chi_{6004}(65,\cdot)\)	6004.df	78	no	\(-1\)	\(1\)	\(e\left(\frac{31}{78}\right)\)	\(e\left(\frac{38}{39}\right)\)	\(e\left(\frac{3}{13}\right)\)	\(e\left(\frac{31}{39}\right)\)	\(e\left(\frac{9}{13}\right)\)	\(e\left(\frac{53}{78}\right)\)	\(e\left(\frac{29}{78}\right)\)	\(e\left(\frac{20}{39}\right)\)	\(e\left(\frac{49}{78}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{6004}(67,\cdot)\)	6004.ej	234	yes	\(1\)	\(1\)	\(e\left(\frac{46}{117}\right)\)	\(e\left(\frac{31}{117}\right)\)	\(e\left(\frac{61}{78}\right)\)	\(e\left(\frac{92}{117}\right)\)	\(e\left(\frac{53}{78}\right)\)	\(e\left(\frac{151}{234}\right)\)	\(e\left(\frac{77}{117}\right)\)	\(e\left(\frac{43}{117}\right)\)	\(e\left(\frac{41}{234}\right)\)	\(e\left(\frac{7}{18}\right)\)

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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.