LMFDB - Group of Dirichlet characters of modulus 4014

Show commands: PariGP / SageMath

sage: H = DirichletGroup(4014)

pari: g = idealstar(,4014,2)

Character group

sage: G.order() pari: g.no
Order	=	1332
sage: H.invariants() pari: g.cyc
Structure	=	$C_{6}\times C_{222}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{4014}(893,\cdot)$, $\chi_{4014}(2233,\cdot)$

First 32 of 1332 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	$-1$	$1$	$5$	$7$	$11$	$13$	$17$	$19$	$23$	$25$	$29$	$31$
$\chi_{4014}(1,\cdot)$	4014.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{4014}(5,\cdot)$	4014.bk	222	no	$1$	$1$	$e\left(\frac{94}{111}\right)$	$e\left(\frac{58}{111}\right)$	$e\left(\frac{27}{37}\right)$	$e\left(\frac{133}{222}\right)$	$e\left(\frac{17}{74}\right)$	$e\left(\frac{106}{111}\right)$	$e\left(\frac{19}{37}\right)$	$e\left(\frac{77}{111}\right)$	$e\left(\frac{11}{74}\right)$	$e\left(\frac{20}{37}\right)$
$\chi_{4014}(7,\cdot)$	4014.bb	111	no	$1$	$1$	$e\left(\frac{58}{111}\right)$	$e\left(\frac{35}{111}\right)$	$e\left(\frac{98}{111}\right)$	$e\left(\frac{43}{111}\right)$	$e\left(\frac{8}{37}\right)$	$e\left(\frac{26}{37}\right)$	$e\left(\frac{58}{111}\right)$	$e\left(\frac{5}{111}\right)$	$e\left(\frac{83}{111}\right)$	$e\left(\frac{100}{111}\right)$
$\chi_{4014}(11,\cdot)$	4014.bc	222	no	$1$	$1$	$e\left(\frac{27}{37}\right)$	$e\left(\frac{98}{111}\right)$	$e\left(\frac{82}{111}\right)$	$e\left(\frac{41}{222}\right)$	$e\left(\frac{67}{74}\right)$	$e\left(\frac{100}{111}\right)$	$e\left(\frac{44}{111}\right)$	$e\left(\frac{17}{37}\right)$	$e\left(\frac{191}{222}\right)$	$e\left(\frac{95}{111}\right)$
$\chi_{4014}(13,\cdot)$	4014.bf	222	no	$-1$	$1$	$e\left(\frac{133}{222}\right)$	$e\left(\frac{43}{111}\right)$	$e\left(\frac{41}{222}\right)$	$e\left(\frac{1}{222}\right)$	$e\left(\frac{13}{37}\right)$	$e\left(\frac{33}{37}\right)$	$e\left(\frac{133}{222}\right)$	$e\left(\frac{22}{111}\right)$	$e\left(\frac{10}{111}\right)$	$e\left(\frac{107}{111}\right)$
$\chi_{4014}(17,\cdot)$	4014.w	74	no	$-1$	$1$	$e\left(\frac{17}{74}\right)$	$e\left(\frac{8}{37}\right)$	$e\left(\frac{67}{74}\right)$	$e\left(\frac{13}{37}\right)$	$e\left(\frac{67}{74}\right)$	$e\left(\frac{21}{37}\right)$	$e\left(\frac{17}{74}\right)$	$e\left(\frac{17}{37}\right)$	$e\left(\frac{39}{74}\right)$	$e\left(\frac{7}{37}\right)$
$\chi_{4014}(19,\cdot)$	4014.z	111	no	$1$	$1$	$e\left(\frac{106}{111}\right)$	$e\left(\frac{26}{37}\right)$	$e\left(\frac{100}{111}\right)$	$e\left(\frac{33}{37}\right)$	$e\left(\frac{21}{37}\right)$	$e\left(\frac{29}{111}\right)$	$e\left(\frac{32}{111}\right)$	$e\left(\frac{101}{111}\right)$	$e\left(\frac{19}{111}\right)$	$e\left(\frac{59}{111}\right)$
$\chi_{4014}(23,\cdot)$	4014.bc	222	no	$1$	$1$	$e\left(\frac{19}{37}\right)$	$e\left(\frac{58}{111}\right)$	$e\left(\frac{44}{111}\right)$	$e\left(\frac{133}{222}\right)$	$e\left(\frac{17}{74}\right)$	$e\left(\frac{32}{111}\right)$	$e\left(\frac{94}{111}\right)$	$e\left(\frac{1}{37}\right)$	$e\left(\frac{181}{222}\right)$	$e\left(\frac{97}{111}\right)$
$\chi_{4014}(25,\cdot)$	4014.ba	111	no	$1$	$1$	$e\left(\frac{77}{111}\right)$	$e\left(\frac{5}{111}\right)$	$e\left(\frac{17}{37}\right)$	$e\left(\frac{22}{111}\right)$	$e\left(\frac{17}{37}\right)$	$e\left(\frac{101}{111}\right)$	$e\left(\frac{1}{37}\right)$	$e\left(\frac{43}{111}\right)$	$e\left(\frac{11}{37}\right)$	$e\left(\frac{3}{37}\right)$
$\chi_{4014}(29,\cdot)$	4014.bn	222	no	$-1$	$1$	$e\left(\frac{11}{74}\right)$	$e\left(\frac{83}{111}\right)$	$e\left(\frac{191}{222}\right)$	$e\left(\frac{10}{111}\right)$	$e\left(\frac{39}{74}\right)$	$e\left(\frac{19}{111}\right)$	$e\left(\frac{181}{222}\right)$	$e\left(\frac{11}{37}\right)$	$e\left(\frac{215}{222}\right)$	$e\left(\frac{68}{111}\right)$
$\chi_{4014}(31,\cdot)$	4014.y	111	no	$1$	$1$	$e\left(\frac{20}{37}\right)$	$e\left(\frac{100}{111}\right)$	$e\left(\frac{95}{111}\right)$	$e\left(\frac{107}{111}\right)$	$e\left(\frac{7}{37}\right)$	$e\left(\frac{59}{111}\right)$	$e\left(\frac{97}{111}\right)$	$e\left(\frac{3}{37}\right)$	$e\left(\frac{68}{111}\right)$	$e\left(\frac{106}{111}\right)$
$\chi_{4014}(35,\cdot)$	4014.bj	222	no	$1$	$1$	$e\left(\frac{41}{111}\right)$	$e\left(\frac{31}{37}\right)$	$e\left(\frac{68}{111}\right)$	$e\left(\frac{73}{74}\right)$	$e\left(\frac{33}{74}\right)$	$e\left(\frac{73}{111}\right)$	$e\left(\frac{4}{111}\right)$	$e\left(\frac{82}{111}\right)$	$e\left(\frac{199}{222}\right)$	$e\left(\frac{49}{111}\right)$
$\chi_{4014}(37,\cdot)$	4014.z	111	no	$1$	$1$	$e\left(\frac{104}{111}\right)$	$e\left(\frac{29}{37}\right)$	$e\left(\frac{29}{111}\right)$	$e\left(\frac{24}{37}\right)$	$e\left(\frac{22}{37}\right)$	$e\left(\frac{85}{111}\right)$	$e\left(\frac{67}{111}\right)$	$e\left(\frac{97}{111}\right)$	$e\left(\frac{71}{111}\right)$	$e\left(\frac{16}{111}\right)$
$\chi_{4014}(41,\cdot)$	4014.bg	222	no	$-1$	$1$	$e\left(\frac{211}{222}\right)$	$e\left(\frac{34}{111}\right)$	$e\left(\frac{35}{222}\right)$	$e\left(\frac{83}{111}\right)$	$e\left(\frac{61}{74}\right)$	$e\left(\frac{2}{37}\right)$	$e\left(\frac{211}{222}\right)$	$e\left(\frac{100}{111}\right)$	$e\left(\frac{101}{222}\right)$	$e\left(\frac{2}{111}\right)$
$\chi_{4014}(43,\cdot)$	4014.ba	111	no	$1$	$1$	$e\left(\frac{71}{111}\right)$	$e\left(\frac{32}{111}\right)$	$e\left(\frac{20}{37}\right)$	$e\left(\frac{52}{111}\right)$	$e\left(\frac{20}{37}\right)$	$e\left(\frac{47}{111}\right)$	$e\left(\frac{36}{37}\right)$	$e\left(\frac{31}{111}\right)$	$e\left(\frac{26}{37}\right)$	$e\left(\frac{34}{37}\right)$
$\chi_{4014}(47,\cdot)$	4014.bn	222	no	$-1$	$1$	$e\left(\frac{65}{74}\right)$	$e\left(\frac{107}{111}\right)$	$e\left(\frac{59}{222}\right)$	$e\left(\frac{49}{111}\right)$	$e\left(\frac{69}{74}\right)$	$e\left(\frac{82}{111}\right)$	$e\left(\frac{121}{222}\right)$	$e\left(\frac{28}{37}\right)$	$e\left(\frac{221}{222}\right)$	$e\left(\frac{89}{111}\right)$
$\chi_{4014}(49,\cdot)$	4014.bb	111	no	$1$	$1$	$e\left(\frac{5}{111}\right)$	$e\left(\frac{70}{111}\right)$	$e\left(\frac{85}{111}\right)$	$e\left(\frac{86}{111}\right)$	$e\left(\frac{16}{37}\right)$	$e\left(\frac{15}{37}\right)$	$e\left(\frac{5}{111}\right)$	$e\left(\frac{10}{111}\right)$	$e\left(\frac{55}{111}\right)$	$e\left(\frac{89}{111}\right)$
$\chi_{4014}(53,\cdot)$	4014.bd	222	no	$-1$	$1$	$e\left(\frac{127}{222}\right)$	$e\left(\frac{25}{37}\right)$	$e\left(\frac{13}{222}\right)$	$e\left(\frac{36}{37}\right)$	$e\left(\frac{29}{74}\right)$	$e\left(\frac{109}{111}\right)$	$e\left(\frac{53}{222}\right)$	$e\left(\frac{16}{111}\right)$	$e\left(\frac{139}{222}\right)$	$e\left(\frac{61}{111}\right)$
$\chi_{4014}(55,\cdot)$	4014.z	111	no	$1$	$1$	$e\left(\frac{64}{111}\right)$	$e\left(\frac{15}{37}\right)$	$e\left(\frac{52}{111}\right)$	$e\left(\frac{29}{37}\right)$	$e\left(\frac{5}{37}\right)$	$e\left(\frac{95}{111}\right)$	$e\left(\frac{101}{111}\right)$	$e\left(\frac{17}{111}\right)$	$e\left(\frac{1}{111}\right)$	$e\left(\frac{44}{111}\right)$
$\chi_{4014}(59,\cdot)$	4014.bl	222	no	$1$	$1$	$e\left(\frac{86}{111}\right)$	$e\left(\frac{94}{111}\right)$	$e\left(\frac{19}{111}\right)$	$e\left(\frac{139}{222}\right)$	$e\left(\frac{25}{74}\right)$	$e\left(\frac{36}{37}\right)$	$e\left(\frac{86}{111}\right)$	$e\left(\frac{61}{111}\right)$	$e\left(\frac{5}{222}\right)$	$e\left(\frac{110}{111}\right)$
$\chi_{4014}(61,\cdot)$	4014.bh	222	no	$-1$	$1$	$e\left(\frac{133}{222}\right)$	$e\left(\frac{80}{111}\right)$	$e\left(\frac{63}{74}\right)$	$e\left(\frac{149}{222}\right)$	$e\left(\frac{13}{37}\right)$	$e\left(\frac{62}{111}\right)$	$e\left(\frac{69}{74}\right)$	$e\left(\frac{22}{111}\right)$	$e\left(\frac{28}{37}\right)$	$e\left(\frac{11}{37}\right)$
$\chi_{4014}(65,\cdot)$	4014.bn	222	no	$-1$	$1$	$e\left(\frac{33}{74}\right)$	$e\left(\frac{101}{111}\right)$	$e\left(\frac{203}{222}\right)$	$e\left(\frac{67}{111}\right)$	$e\left(\frac{43}{74}\right)$	$e\left(\frac{94}{111}\right)$	$e\left(\frac{25}{222}\right)$	$e\left(\frac{33}{37}\right)$	$e\left(\frac{53}{222}\right)$	$e\left(\frac{56}{111}\right)$
$\chi_{4014}(67,\cdot)$	4014.bm	222	no	$-1$	$1$	$e\left(\frac{61}{74}\right)$	$e\left(\frac{97}{111}\right)$	$e\left(\frac{151}{222}\right)$	$e\left(\frac{121}{222}\right)$	$e\left(\frac{19}{37}\right)$	$e\left(\frac{65}{111}\right)$	$e\left(\frac{35}{222}\right)$	$e\left(\frac{24}{37}\right)$	$e\left(\frac{26}{111}\right)$	$e\left(\frac{34}{111}\right)$
$\chi_{4014}(71,\cdot)$	4014.bj	222	no	$1$	$1$	$e\left(\frac{49}{111}\right)$	$e\left(\frac{19}{37}\right)$	$e\left(\frac{19}{111}\right)$	$e\left(\frac{71}{74}\right)$	$e\left(\frac{25}{74}\right)$	$e\left(\frac{71}{111}\right)$	$e\left(\frac{86}{111}\right)$	$e\left(\frac{98}{111}\right)$	$e\left(\frac{5}{222}\right)$	$e\left(\frac{110}{111}\right)$
$\chi_{4014}(73,\cdot)$	4014.z	111	no	$1$	$1$	$e\left(\frac{47}{111}\right)$	$e\left(\frac{22}{37}\right)$	$e\left(\frac{59}{111}\right)$	$e\left(\frac{8}{37}\right)$	$e\left(\frac{32}{37}\right)$	$e\left(\frac{16}{111}\right)$	$e\left(\frac{10}{111}\right)$	$e\left(\frac{94}{111}\right)$	$e\left(\frac{110}{111}\right)$	$e\left(\frac{67}{111}\right)$
$\chi_{4014}(77,\cdot)$	4014.bk	222	no	$1$	$1$	$e\left(\frac{28}{111}\right)$	$e\left(\frac{22}{111}\right)$	$e\left(\frac{23}{37}\right)$	$e\left(\frac{127}{222}\right)$	$e\left(\frac{9}{74}\right)$	$e\left(\frac{67}{111}\right)$	$e\left(\frac{34}{37}\right)$	$e\left(\frac{56}{111}\right)$	$e\left(\frac{45}{74}\right)$	$e\left(\frac{28}{37}\right)$
$\chi_{4014}(79,\cdot)$	4014.bm	222	no	$-1$	$1$	$e\left(\frac{21}{74}\right)$	$e\left(\frac{71}{111}\right)$	$e\left(\frac{35}{222}\right)$	$e\left(\frac{203}{222}\right)$	$e\left(\frac{12}{37}\right)$	$e\left(\frac{43}{111}\right)$	$e\left(\frac{211}{222}\right)$	$e\left(\frac{21}{37}\right)$	$e\left(\frac{106}{111}\right)$	$e\left(\frac{2}{111}\right)$
$\chi_{4014}(83,\cdot)$	4014.bn	222	no	$-1$	$1$	$e\left(\frac{39}{74}\right)$	$e\left(\frac{5}{111}\right)$	$e\left(\frac{65}{222}\right)$	$e\left(\frac{22}{111}\right)$	$e\left(\frac{71}{74}\right)$	$e\left(\frac{64}{111}\right)$	$e\left(\frac{43}{222}\right)$	$e\left(\frac{2}{37}\right)$	$e\left(\frac{29}{222}\right)$	$e\left(\frac{83}{111}\right)$
$\chi_{4014}(85,\cdot)$	4014.bh	222	no	$-1$	$1$	$e\left(\frac{17}{222}\right)$	$e\left(\frac{82}{111}\right)$	$e\left(\frac{47}{74}\right)$	$e\left(\frac{211}{222}\right)$	$e\left(\frac{5}{37}\right)$	$e\left(\frac{58}{111}\right)$	$e\left(\frac{55}{74}\right)$	$e\left(\frac{17}{111}\right)$	$e\left(\frac{25}{37}\right)$	$e\left(\frac{27}{37}\right)$
$\chi_{4014}(89,\cdot)$	4014.bd	222	no	$-1$	$1$	$e\left(\frac{71}{222}\right)$	$e\left(\frac{30}{37}\right)$	$e\left(\frac{23}{222}\right)$	$e\left(\frac{21}{37}\right)$	$e\left(\frac{57}{74}\right)$	$e\left(\frac{5}{111}\right)$	$e\left(\frac{145}{222}\right)$	$e\left(\frac{71}{111}\right)$	$e\left(\frac{41}{222}\right)$	$e\left(\frac{14}{111}\right)$
$\chi_{4014}(91,\cdot)$	4014.x	74	no	$-1$	$1$	$e\left(\frac{9}{74}\right)$	$e\left(\frac{26}{37}\right)$	$e\left(\frac{5}{74}\right)$	$e\left(\frac{29}{74}\right)$	$e\left(\frac{21}{37}\right)$	$e\left(\frac{22}{37}\right)$	$e\left(\frac{9}{74}\right)$	$e\left(\frac{9}{37}\right)$	$e\left(\frac{31}{37}\right)$	$e\left(\frac{32}{37}\right)$
$\chi_{4014}(95,\cdot)$	4014.bl	222	no	$1$	$1$	$e\left(\frac{89}{111}\right)$	$e\left(\frac{25}{111}\right)$	$e\left(\frac{70}{111}\right)$	$e\left(\frac{109}{222}\right)$	$e\left(\frac{59}{74}\right)$	$e\left(\frac{8}{37}\right)$	$e\left(\frac{89}{111}\right)$	$e\left(\frac{67}{111}\right)$	$e\left(\frac{71}{222}\right)$	$e\left(\frac{8}{111}\right)$

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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	$4014$
Structure	\(C_{6}\times C_{222}\)
Order	$1332$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(5\)	\(7\)	\(11\)	\(13\)	\(17\)	\(19\)	\(23\)	\(25\)	\(29\)	\(31\)
\(\chi_{4014}(1,\cdot)\)	4014.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{4014}(5,\cdot)\)	4014.bk	222	no	\(1\)	\(1\)	\(e\left(\frac{94}{111}\right)\)	\(e\left(\frac{58}{111}\right)\)	\(e\left(\frac{27}{37}\right)\)	\(e\left(\frac{133}{222}\right)\)	\(e\left(\frac{17}{74}\right)\)	\(e\left(\frac{106}{111}\right)\)	\(e\left(\frac{19}{37}\right)\)	\(e\left(\frac{77}{111}\right)\)	\(e\left(\frac{11}{74}\right)\)	\(e\left(\frac{20}{37}\right)\)
\(\chi_{4014}(7,\cdot)\)	4014.bb	111	no	\(1\)	\(1\)	\(e\left(\frac{58}{111}\right)\)	\(e\left(\frac{35}{111}\right)\)	\(e\left(\frac{98}{111}\right)\)	\(e\left(\frac{43}{111}\right)\)	\(e\left(\frac{8}{37}\right)\)	\(e\left(\frac{26}{37}\right)\)	\(e\left(\frac{58}{111}\right)\)	\(e\left(\frac{5}{111}\right)\)	\(e\left(\frac{83}{111}\right)\)	\(e\left(\frac{100}{111}\right)\)
\(\chi_{4014}(11,\cdot)\)	4014.bc	222	no	\(1\)	\(1\)	\(e\left(\frac{27}{37}\right)\)	\(e\left(\frac{98}{111}\right)\)	\(e\left(\frac{82}{111}\right)\)	\(e\left(\frac{41}{222}\right)\)	\(e\left(\frac{67}{74}\right)\)	\(e\left(\frac{100}{111}\right)\)	\(e\left(\frac{44}{111}\right)\)	\(e\left(\frac{17}{37}\right)\)	\(e\left(\frac{191}{222}\right)\)	\(e\left(\frac{95}{111}\right)\)
\(\chi_{4014}(13,\cdot)\)	4014.bf	222	no	\(-1\)	\(1\)	\(e\left(\frac{133}{222}\right)\)	\(e\left(\frac{43}{111}\right)\)	\(e\left(\frac{41}{222}\right)\)	\(e\left(\frac{1}{222}\right)\)	\(e\left(\frac{13}{37}\right)\)	\(e\left(\frac{33}{37}\right)\)	\(e\left(\frac{133}{222}\right)\)	\(e\left(\frac{22}{111}\right)\)	\(e\left(\frac{10}{111}\right)\)	\(e\left(\frac{107}{111}\right)\)
\(\chi_{4014}(17,\cdot)\)	4014.w	74	no	\(-1\)	\(1\)	\(e\left(\frac{17}{74}\right)\)	\(e\left(\frac{8}{37}\right)\)	\(e\left(\frac{67}{74}\right)\)	\(e\left(\frac{13}{37}\right)\)	\(e\left(\frac{67}{74}\right)\)	\(e\left(\frac{21}{37}\right)\)	\(e\left(\frac{17}{74}\right)\)	\(e\left(\frac{17}{37}\right)\)	\(e\left(\frac{39}{74}\right)\)	\(e\left(\frac{7}{37}\right)\)
\(\chi_{4014}(19,\cdot)\)	4014.z	111	no	\(1\)	\(1\)	\(e\left(\frac{106}{111}\right)\)	\(e\left(\frac{26}{37}\right)\)	\(e\left(\frac{100}{111}\right)\)	\(e\left(\frac{33}{37}\right)\)	\(e\left(\frac{21}{37}\right)\)	\(e\left(\frac{29}{111}\right)\)	\(e\left(\frac{32}{111}\right)\)	\(e\left(\frac{101}{111}\right)\)	\(e\left(\frac{19}{111}\right)\)	\(e\left(\frac{59}{111}\right)\)
\(\chi_{4014}(23,\cdot)\)	4014.bc	222	no	\(1\)	\(1\)	\(e\left(\frac{19}{37}\right)\)	\(e\left(\frac{58}{111}\right)\)	\(e\left(\frac{44}{111}\right)\)	\(e\left(\frac{133}{222}\right)\)	\(e\left(\frac{17}{74}\right)\)	\(e\left(\frac{32}{111}\right)\)	\(e\left(\frac{94}{111}\right)\)	\(e\left(\frac{1}{37}\right)\)	\(e\left(\frac{181}{222}\right)\)	\(e\left(\frac{97}{111}\right)\)
\(\chi_{4014}(25,\cdot)\)	4014.ba	111	no	\(1\)	\(1\)	\(e\left(\frac{77}{111}\right)\)	\(e\left(\frac{5}{111}\right)\)	\(e\left(\frac{17}{37}\right)\)	\(e\left(\frac{22}{111}\right)\)	\(e\left(\frac{17}{37}\right)\)	\(e\left(\frac{101}{111}\right)\)	\(e\left(\frac{1}{37}\right)\)	\(e\left(\frac{43}{111}\right)\)	\(e\left(\frac{11}{37}\right)\)	\(e\left(\frac{3}{37}\right)\)
\(\chi_{4014}(29,\cdot)\)	4014.bn	222	no	\(-1\)	\(1\)	\(e\left(\frac{11}{74}\right)\)	\(e\left(\frac{83}{111}\right)\)	\(e\left(\frac{191}{222}\right)\)	\(e\left(\frac{10}{111}\right)\)	\(e\left(\frac{39}{74}\right)\)	\(e\left(\frac{19}{111}\right)\)	\(e\left(\frac{181}{222}\right)\)	\(e\left(\frac{11}{37}\right)\)	\(e\left(\frac{215}{222}\right)\)	\(e\left(\frac{68}{111}\right)\)
\(\chi_{4014}(31,\cdot)\)	4014.y	111	no	\(1\)	\(1\)	\(e\left(\frac{20}{37}\right)\)	\(e\left(\frac{100}{111}\right)\)	\(e\left(\frac{95}{111}\right)\)	\(e\left(\frac{107}{111}\right)\)	\(e\left(\frac{7}{37}\right)\)	\(e\left(\frac{59}{111}\right)\)	\(e\left(\frac{97}{111}\right)\)	\(e\left(\frac{3}{37}\right)\)	\(e\left(\frac{68}{111}\right)\)	\(e\left(\frac{106}{111}\right)\)
\(\chi_{4014}(35,\cdot)\)	4014.bj	222	no	\(1\)	\(1\)	\(e\left(\frac{41}{111}\right)\)	\(e\left(\frac{31}{37}\right)\)	\(e\left(\frac{68}{111}\right)\)	\(e\left(\frac{73}{74}\right)\)	\(e\left(\frac{33}{74}\right)\)	\(e\left(\frac{73}{111}\right)\)	\(e\left(\frac{4}{111}\right)\)	\(e\left(\frac{82}{111}\right)\)	\(e\left(\frac{199}{222}\right)\)	\(e\left(\frac{49}{111}\right)\)
\(\chi_{4014}(37,\cdot)\)	4014.z	111	no	\(1\)	\(1\)	\(e\left(\frac{104}{111}\right)\)	\(e\left(\frac{29}{37}\right)\)	\(e\left(\frac{29}{111}\right)\)	\(e\left(\frac{24}{37}\right)\)	\(e\left(\frac{22}{37}\right)\)	\(e\left(\frac{85}{111}\right)\)	\(e\left(\frac{67}{111}\right)\)	\(e\left(\frac{97}{111}\right)\)	\(e\left(\frac{71}{111}\right)\)	\(e\left(\frac{16}{111}\right)\)
\(\chi_{4014}(41,\cdot)\)	4014.bg	222	no	\(-1\)	\(1\)	\(e\left(\frac{211}{222}\right)\)	\(e\left(\frac{34}{111}\right)\)	\(e\left(\frac{35}{222}\right)\)	\(e\left(\frac{83}{111}\right)\)	\(e\left(\frac{61}{74}\right)\)	\(e\left(\frac{2}{37}\right)\)	\(e\left(\frac{211}{222}\right)\)	\(e\left(\frac{100}{111}\right)\)	\(e\left(\frac{101}{222}\right)\)	\(e\left(\frac{2}{111}\right)\)
\(\chi_{4014}(43,\cdot)\)	4014.ba	111	no	\(1\)	\(1\)	\(e\left(\frac{71}{111}\right)\)	\(e\left(\frac{32}{111}\right)\)	\(e\left(\frac{20}{37}\right)\)	\(e\left(\frac{52}{111}\right)\)	\(e\left(\frac{20}{37}\right)\)	\(e\left(\frac{47}{111}\right)\)	\(e\left(\frac{36}{37}\right)\)	\(e\left(\frac{31}{111}\right)\)	\(e\left(\frac{26}{37}\right)\)	\(e\left(\frac{34}{37}\right)\)
\(\chi_{4014}(47,\cdot)\)	4014.bn	222	no	\(-1\)	\(1\)	\(e\left(\frac{65}{74}\right)\)	\(e\left(\frac{107}{111}\right)\)	\(e\left(\frac{59}{222}\right)\)	\(e\left(\frac{49}{111}\right)\)	\(e\left(\frac{69}{74}\right)\)	\(e\left(\frac{82}{111}\right)\)	\(e\left(\frac{121}{222}\right)\)	\(e\left(\frac{28}{37}\right)\)	\(e\left(\frac{221}{222}\right)\)	\(e\left(\frac{89}{111}\right)\)
\(\chi_{4014}(49,\cdot)\)	4014.bb	111	no	\(1\)	\(1\)	\(e\left(\frac{5}{111}\right)\)	\(e\left(\frac{70}{111}\right)\)	\(e\left(\frac{85}{111}\right)\)	\(e\left(\frac{86}{111}\right)\)	\(e\left(\frac{16}{37}\right)\)	\(e\left(\frac{15}{37}\right)\)	\(e\left(\frac{5}{111}\right)\)	\(e\left(\frac{10}{111}\right)\)	\(e\left(\frac{55}{111}\right)\)	\(e\left(\frac{89}{111}\right)\)
\(\chi_{4014}(53,\cdot)\)	4014.bd	222	no	\(-1\)	\(1\)	\(e\left(\frac{127}{222}\right)\)	\(e\left(\frac{25}{37}\right)\)	\(e\left(\frac{13}{222}\right)\)	\(e\left(\frac{36}{37}\right)\)	\(e\left(\frac{29}{74}\right)\)	\(e\left(\frac{109}{111}\right)\)	\(e\left(\frac{53}{222}\right)\)	\(e\left(\frac{16}{111}\right)\)	\(e\left(\frac{139}{222}\right)\)	\(e\left(\frac{61}{111}\right)\)
\(\chi_{4014}(55,\cdot)\)	4014.z	111	no	\(1\)	\(1\)	\(e\left(\frac{64}{111}\right)\)	\(e\left(\frac{15}{37}\right)\)	\(e\left(\frac{52}{111}\right)\)	\(e\left(\frac{29}{37}\right)\)	\(e\left(\frac{5}{37}\right)\)	\(e\left(\frac{95}{111}\right)\)	\(e\left(\frac{101}{111}\right)\)	\(e\left(\frac{17}{111}\right)\)	\(e\left(\frac{1}{111}\right)\)	\(e\left(\frac{44}{111}\right)\)
\(\chi_{4014}(59,\cdot)\)	4014.bl	222	no	\(1\)	\(1\)	\(e\left(\frac{86}{111}\right)\)	\(e\left(\frac{94}{111}\right)\)	\(e\left(\frac{19}{111}\right)\)	\(e\left(\frac{139}{222}\right)\)	\(e\left(\frac{25}{74}\right)\)	\(e\left(\frac{36}{37}\right)\)	\(e\left(\frac{86}{111}\right)\)	\(e\left(\frac{61}{111}\right)\)	\(e\left(\frac{5}{222}\right)\)	\(e\left(\frac{110}{111}\right)\)
\(\chi_{4014}(61,\cdot)\)	4014.bh	222	no	\(-1\)	\(1\)	\(e\left(\frac{133}{222}\right)\)	\(e\left(\frac{80}{111}\right)\)	\(e\left(\frac{63}{74}\right)\)	\(e\left(\frac{149}{222}\right)\)	\(e\left(\frac{13}{37}\right)\)	\(e\left(\frac{62}{111}\right)\)	\(e\left(\frac{69}{74}\right)\)	\(e\left(\frac{22}{111}\right)\)	\(e\left(\frac{28}{37}\right)\)	\(e\left(\frac{11}{37}\right)\)
\(\chi_{4014}(65,\cdot)\)	4014.bn	222	no	\(-1\)	\(1\)	\(e\left(\frac{33}{74}\right)\)	\(e\left(\frac{101}{111}\right)\)	\(e\left(\frac{203}{222}\right)\)	\(e\left(\frac{67}{111}\right)\)	\(e\left(\frac{43}{74}\right)\)	\(e\left(\frac{94}{111}\right)\)	\(e\left(\frac{25}{222}\right)\)	\(e\left(\frac{33}{37}\right)\)	\(e\left(\frac{53}{222}\right)\)	\(e\left(\frac{56}{111}\right)\)
\(\chi_{4014}(67,\cdot)\)	4014.bm	222	no	\(-1\)	\(1\)	\(e\left(\frac{61}{74}\right)\)	\(e\left(\frac{97}{111}\right)\)	\(e\left(\frac{151}{222}\right)\)	\(e\left(\frac{121}{222}\right)\)	\(e\left(\frac{19}{37}\right)\)	\(e\left(\frac{65}{111}\right)\)	\(e\left(\frac{35}{222}\right)\)	\(e\left(\frac{24}{37}\right)\)	\(e\left(\frac{26}{111}\right)\)	\(e\left(\frac{34}{111}\right)\)
\(\chi_{4014}(71,\cdot)\)	4014.bj	222	no	\(1\)	\(1\)	\(e\left(\frac{49}{111}\right)\)	\(e\left(\frac{19}{37}\right)\)	\(e\left(\frac{19}{111}\right)\)	\(e\left(\frac{71}{74}\right)\)	\(e\left(\frac{25}{74}\right)\)	\(e\left(\frac{71}{111}\right)\)	\(e\left(\frac{86}{111}\right)\)	\(e\left(\frac{98}{111}\right)\)	\(e\left(\frac{5}{222}\right)\)	\(e\left(\frac{110}{111}\right)\)
\(\chi_{4014}(73,\cdot)\)	4014.z	111	no	\(1\)	\(1\)	\(e\left(\frac{47}{111}\right)\)	\(e\left(\frac{22}{37}\right)\)	\(e\left(\frac{59}{111}\right)\)	\(e\left(\frac{8}{37}\right)\)	\(e\left(\frac{32}{37}\right)\)	\(e\left(\frac{16}{111}\right)\)	\(e\left(\frac{10}{111}\right)\)	\(e\left(\frac{94}{111}\right)\)	\(e\left(\frac{110}{111}\right)\)	\(e\left(\frac{67}{111}\right)\)
\(\chi_{4014}(77,\cdot)\)	4014.bk	222	no	\(1\)	\(1\)	\(e\left(\frac{28}{111}\right)\)	\(e\left(\frac{22}{111}\right)\)	\(e\left(\frac{23}{37}\right)\)	\(e\left(\frac{127}{222}\right)\)	\(e\left(\frac{9}{74}\right)\)	\(e\left(\frac{67}{111}\right)\)	\(e\left(\frac{34}{37}\right)\)	\(e\left(\frac{56}{111}\right)\)	\(e\left(\frac{45}{74}\right)\)	\(e\left(\frac{28}{37}\right)\)
\(\chi_{4014}(79,\cdot)\)	4014.bm	222	no	\(-1\)	\(1\)	\(e\left(\frac{21}{74}\right)\)	\(e\left(\frac{71}{111}\right)\)	\(e\left(\frac{35}{222}\right)\)	\(e\left(\frac{203}{222}\right)\)	\(e\left(\frac{12}{37}\right)\)	\(e\left(\frac{43}{111}\right)\)	\(e\left(\frac{211}{222}\right)\)	\(e\left(\frac{21}{37}\right)\)	\(e\left(\frac{106}{111}\right)\)	\(e\left(\frac{2}{111}\right)\)
\(\chi_{4014}(83,\cdot)\)	4014.bn	222	no	\(-1\)	\(1\)	\(e\left(\frac{39}{74}\right)\)	\(e\left(\frac{5}{111}\right)\)	\(e\left(\frac{65}{222}\right)\)	\(e\left(\frac{22}{111}\right)\)	\(e\left(\frac{71}{74}\right)\)	\(e\left(\frac{64}{111}\right)\)	\(e\left(\frac{43}{222}\right)\)	\(e\left(\frac{2}{37}\right)\)	\(e\left(\frac{29}{222}\right)\)	\(e\left(\frac{83}{111}\right)\)
\(\chi_{4014}(85,\cdot)\)	4014.bh	222	no	\(-1\)	\(1\)	\(e\left(\frac{17}{222}\right)\)	\(e\left(\frac{82}{111}\right)\)	\(e\left(\frac{47}{74}\right)\)	\(e\left(\frac{211}{222}\right)\)	\(e\left(\frac{5}{37}\right)\)	\(e\left(\frac{58}{111}\right)\)	\(e\left(\frac{55}{74}\right)\)	\(e\left(\frac{17}{111}\right)\)	\(e\left(\frac{25}{37}\right)\)	\(e\left(\frac{27}{37}\right)\)
\(\chi_{4014}(89,\cdot)\)	4014.bd	222	no	\(-1\)	\(1\)	\(e\left(\frac{71}{222}\right)\)	\(e\left(\frac{30}{37}\right)\)	\(e\left(\frac{23}{222}\right)\)	\(e\left(\frac{21}{37}\right)\)	\(e\left(\frac{57}{74}\right)\)	\(e\left(\frac{5}{111}\right)\)	\(e\left(\frac{145}{222}\right)\)	\(e\left(\frac{71}{111}\right)\)	\(e\left(\frac{41}{222}\right)\)	\(e\left(\frac{14}{111}\right)\)
\(\chi_{4014}(91,\cdot)\)	4014.x	74	no	\(-1\)	\(1\)	\(e\left(\frac{9}{74}\right)\)	\(e\left(\frac{26}{37}\right)\)	\(e\left(\frac{5}{74}\right)\)	\(e\left(\frac{29}{74}\right)\)	\(e\left(\frac{21}{37}\right)\)	\(e\left(\frac{22}{37}\right)\)	\(e\left(\frac{9}{74}\right)\)	\(e\left(\frac{9}{37}\right)\)	\(e\left(\frac{31}{37}\right)\)	\(e\left(\frac{32}{37}\right)\)
\(\chi_{4014}(95,\cdot)\)	4014.bl	222	no	\(1\)	\(1\)	\(e\left(\frac{89}{111}\right)\)	\(e\left(\frac{25}{111}\right)\)	\(e\left(\frac{70}{111}\right)\)	\(e\left(\frac{109}{222}\right)\)	\(e\left(\frac{59}{74}\right)\)	\(e\left(\frac{8}{37}\right)\)	\(e\left(\frac{89}{111}\right)\)	\(e\left(\frac{67}{111}\right)\)	\(e\left(\frac{71}{222}\right)\)	\(e\left(\frac{8}{111}\right)\)

Introduction

L-functions

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Character group

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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.