LMFDB - Group of Dirichlet characters of modulus 6019

Show commands: PariGP / SageMath

sage: H = DirichletGroup(6019)

pari: g = idealstar(,6019,2)

Character group

sage: G.order() pari: g.no
Order	=	5544
sage: H.invariants() pari: g.cyc
Structure	=	$C_{6}\times C_{924}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{6019}(2316,\cdot)$, $\chi_{6019}(1392,\cdot)$

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	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$11$
$\chi_{6019}(1,\cdot)$	6019.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{6019}(2,\cdot)$	6019.el	924	yes	$-1$	$1$	$e\left(\frac{541}{924}\right)$	$e\left(\frac{94}{231}\right)$	$e\left(\frac{79}{462}\right)$	$e\left(\frac{877}{924}\right)$	$e\left(\frac{131}{132}\right)$	$e\left(\frac{163}{924}\right)$	$e\left(\frac{233}{308}\right)$	$e\left(\frac{188}{231}\right)$	$e\left(\frac{247}{462}\right)$	$e\left(\frac{691}{924}\right)$
$\chi_{6019}(3,\cdot)$	6019.ea	462	yes	$-1$	$1$	$e\left(\frac{94}{231}\right)$	$e\left(\frac{155}{462}\right)$	$e\left(\frac{188}{231}\right)$	$e\left(\frac{125}{462}\right)$	$e\left(\frac{49}{66}\right)$	$e\left(\frac{461}{462}\right)$	$e\left(\frac{17}{77}\right)$	$e\left(\frac{155}{231}\right)$	$e\left(\frac{313}{462}\right)$	$e\left(\frac{197}{462}\right)$
$\chi_{6019}(4,\cdot)$	6019.ed	462	yes	$1$	$1$	$e\left(\frac{79}{462}\right)$	$e\left(\frac{188}{231}\right)$	$e\left(\frac{79}{231}\right)$	$e\left(\frac{415}{462}\right)$	$e\left(\frac{65}{66}\right)$	$e\left(\frac{163}{462}\right)$	$e\left(\frac{79}{154}\right)$	$e\left(\frac{145}{231}\right)$	$e\left(\frac{16}{231}\right)$	$e\left(\frac{229}{462}\right)$
$\chi_{6019}(5,\cdot)$	6019.eo	924	yes	$1$	$1$	$e\left(\frac{877}{924}\right)$	$e\left(\frac{125}{462}\right)$	$e\left(\frac{415}{462}\right)$	$e\left(\frac{527}{924}\right)$	$e\left(\frac{29}{132}\right)$	$e\left(\frac{199}{308}\right)$	$e\left(\frac{261}{308}\right)$	$e\left(\frac{125}{231}\right)$	$e\left(\frac{40}{77}\right)$	$e\left(\frac{817}{924}\right)$
$\chi_{6019}(6,\cdot)$	6019.di	132	yes	$1$	$1$	$e\left(\frac{131}{132}\right)$	$e\left(\frac{49}{66}\right)$	$e\left(\frac{65}{66}\right)$	$e\left(\frac{29}{132}\right)$	$e\left(\frac{97}{132}\right)$	$e\left(\frac{23}{132}\right)$	$e\left(\frac{43}{44}\right)$	$e\left(\frac{16}{33}\right)$	$e\left(\frac{7}{33}\right)$	$e\left(\frac{23}{132}\right)$
$\chi_{6019}(7,\cdot)$	6019.en	924	yes	$1$	$1$	$e\left(\frac{163}{924}\right)$	$e\left(\frac{461}{462}\right)$	$e\left(\frac{163}{462}\right)$	$e\left(\frac{199}{308}\right)$	$e\left(\frac{23}{132}\right)$	$e\left(\frac{695}{924}\right)$	$e\left(\frac{163}{308}\right)$	$e\left(\frac{230}{231}\right)$	$e\left(\frac{190}{231}\right)$	$e\left(\frac{607}{924}\right)$
$\chi_{6019}(8,\cdot)$	6019.dv	308	yes	$-1$	$1$	$e\left(\frac{233}{308}\right)$	$e\left(\frac{17}{77}\right)$	$e\left(\frac{79}{154}\right)$	$e\left(\frac{261}{308}\right)$	$e\left(\frac{43}{44}\right)$	$e\left(\frac{163}{308}\right)$	$e\left(\frac{83}{308}\right)$	$e\left(\frac{34}{77}\right)$	$e\left(\frac{93}{154}\right)$	$e\left(\frac{75}{308}\right)$
$\chi_{6019}(9,\cdot)$	6019.dq	231	yes	$1$	$1$	$e\left(\frac{188}{231}\right)$	$e\left(\frac{155}{231}\right)$	$e\left(\frac{145}{231}\right)$	$e\left(\frac{125}{231}\right)$	$e\left(\frac{16}{33}\right)$	$e\left(\frac{230}{231}\right)$	$e\left(\frac{34}{77}\right)$	$e\left(\frac{79}{231}\right)$	$e\left(\frac{82}{231}\right)$	$e\left(\frac{197}{231}\right)$
$\chi_{6019}(10,\cdot)$	6019.eg	462	yes	$-1$	$1$	$e\left(\frac{247}{462}\right)$	$e\left(\frac{313}{462}\right)$	$e\left(\frac{16}{231}\right)$	$e\left(\frac{40}{77}\right)$	$e\left(\frac{7}{33}\right)$	$e\left(\frac{190}{231}\right)$	$e\left(\frac{93}{154}\right)$	$e\left(\frac{82}{231}\right)$	$e\left(\frac{25}{462}\right)$	$e\left(\frac{146}{231}\right)$
$\chi_{6019}(11,\cdot)$	6019.em	924	yes	$1$	$1$	$e\left(\frac{691}{924}\right)$	$e\left(\frac{197}{462}\right)$	$e\left(\frac{229}{462}\right)$	$e\left(\frac{817}{924}\right)$	$e\left(\frac{23}{132}\right)$	$e\left(\frac{607}{924}\right)$	$e\left(\frac{75}{308}\right)$	$e\left(\frac{197}{231}\right)$	$e\left(\frac{146}{231}\right)$	$e\left(\frac{79}{924}\right)$
$\chi_{6019}(12,\cdot)$	6019.dn	154	yes	$-1$	$1$	$e\left(\frac{89}{154}\right)$	$e\left(\frac{23}{154}\right)$	$e\left(\frac{12}{77}\right)$	$e\left(\frac{13}{77}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{27}{77}\right)$	$e\left(\frac{113}{154}\right)$	$e\left(\frac{23}{77}\right)$	$e\left(\frac{115}{154}\right)$	$e\left(\frac{71}{77}\right)$
$\chi_{6019}(14,\cdot)$	6019.ce	42	no	$-1$	$1$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{17}{42}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{25}{42}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{17}{42}\right)$
$\chi_{6019}(15,\cdot)$	6019.dk	132	yes	$-1$	$1$	$e\left(\frac{47}{132}\right)$	$e\left(\frac{20}{33}\right)$	$e\left(\frac{47}{66}\right)$	$e\left(\frac{37}{44}\right)$	$e\left(\frac{127}{132}\right)$	$e\left(\frac{85}{132}\right)$	$e\left(\frac{3}{44}\right)$	$e\left(\frac{7}{33}\right)$	$e\left(\frac{13}{66}\right)$	$e\left(\frac{41}{132}\right)$
$\chi_{6019}(16,\cdot)$	6019.dq	231	yes	$1$	$1$	$e\left(\frac{79}{231}\right)$	$e\left(\frac{145}{231}\right)$	$e\left(\frac{158}{231}\right)$	$e\left(\frac{184}{231}\right)$	$e\left(\frac{32}{33}\right)$	$e\left(\frac{163}{231}\right)$	$e\left(\frac{2}{77}\right)$	$e\left(\frac{59}{231}\right)$	$e\left(\frac{32}{231}\right)$	$e\left(\frac{229}{231}\right)$
$\chi_{6019}(17,\cdot)$	6019.ed	462	yes	$1$	$1$	$e\left(\frac{439}{462}\right)$	$e\left(\frac{71}{231}\right)$	$e\left(\frac{208}{231}\right)$	$e\left(\frac{271}{462}\right)$	$e\left(\frac{17}{66}\right)$	$e\left(\frac{397}{462}\right)$	$e\left(\frac{131}{154}\right)$	$e\left(\frac{142}{231}\right)$	$e\left(\frac{124}{231}\right)$	$e\left(\frac{331}{462}\right)$
$\chi_{6019}(18,\cdot)$	6019.dv	308	yes	$-1$	$1$	$e\left(\frac{123}{308}\right)$	$e\left(\frac{6}{77}\right)$	$e\left(\frac{123}{154}\right)$	$e\left(\frac{151}{308}\right)$	$e\left(\frac{21}{44}\right)$	$e\left(\frac{53}{308}\right)$	$e\left(\frac{61}{308}\right)$	$e\left(\frac{12}{77}\right)$	$e\left(\frac{137}{154}\right)$	$e\left(\frac{185}{308}\right)$
$\chi_{6019}(19,\cdot)$	6019.em	924	yes	$1$	$1$	$e\left(\frac{89}{924}\right)$	$e\left(\frac{127}{462}\right)$	$e\left(\frac{89}{462}\right)$	$e\left(\frac{719}{924}\right)$	$e\left(\frac{49}{132}\right)$	$e\left(\frac{593}{924}\right)$	$e\left(\frac{89}{308}\right)$	$e\left(\frac{127}{231}\right)$	$e\left(\frac{202}{231}\right)$	$e\left(\frac{65}{924}\right)$
$\chi_{6019}(20,\cdot)$	6019.ei	924	yes	$1$	$1$	$e\left(\frac{37}{308}\right)$	$e\left(\frac{13}{154}\right)$	$e\left(\frac{37}{154}\right)$	$e\left(\frac{433}{924}\right)$	$e\left(\frac{9}{44}\right)$	$e\left(\frac{923}{924}\right)$	$e\left(\frac{111}{308}\right)$	$e\left(\frac{13}{77}\right)$	$e\left(\frac{136}{231}\right)$	$e\left(\frac{117}{308}\right)$
$\chi_{6019}(21,\cdot)$	6019.z	12	yes	$-1$	$1$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{11}{12}\right)$	$-i$	$-i$	$e\left(\frac{2}{3}\right)$	$-1$	$e\left(\frac{1}{12}\right)$
$\chi_{6019}(22,\cdot)$	6019.o	6	yes	$-1$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{6019}(23,\cdot)$	6019.eg	462	yes	$-1$	$1$	$e\left(\frac{325}{462}\right)$	$e\left(\frac{193}{462}\right)$	$e\left(\frac{94}{231}\right)$	$e\left(\frac{4}{77}\right)$	$e\left(\frac{4}{33}\right)$	$e\left(\frac{19}{231}\right)$	$e\left(\frac{17}{154}\right)$	$e\left(\frac{193}{231}\right)$	$e\left(\frac{349}{462}\right)$	$e\left(\frac{107}{231}\right)$
$\chi_{6019}(24,\cdot)$	6019.em	924	yes	$1$	$1$	$e\left(\frac{151}{924}\right)$	$e\left(\frac{257}{462}\right)$	$e\left(\frac{151}{462}\right)$	$e\left(\frac{109}{924}\right)$	$e\left(\frac{95}{132}\right)$	$e\left(\frac{487}{924}\right)$	$e\left(\frac{151}{308}\right)$	$e\left(\frac{26}{231}\right)$	$e\left(\frac{65}{231}\right)$	$e\left(\frac{619}{924}\right)$
$\chi_{6019}(25,\cdot)$	6019.ec	462	yes	$1$	$1$	$e\left(\frac{415}{462}\right)$	$e\left(\frac{125}{231}\right)$	$e\left(\frac{184}{231}\right)$	$e\left(\frac{65}{462}\right)$	$e\left(\frac{29}{66}\right)$	$e\left(\frac{45}{154}\right)$	$e\left(\frac{107}{154}\right)$	$e\left(\frac{19}{231}\right)$	$e\left(\frac{3}{77}\right)$	$e\left(\frac{355}{462}\right)$
$\chi_{6019}(27,\cdot)$	6019.dp	154	no	$-1$	$1$	$e\left(\frac{17}{77}\right)$	$e\left(\frac{1}{154}\right)$	$e\left(\frac{34}{77}\right)$	$e\left(\frac{125}{154}\right)$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{153}{154}\right)$	$e\left(\frac{51}{77}\right)$	$e\left(\frac{1}{77}\right)$	$e\left(\frac{5}{154}\right)$	$e\left(\frac{43}{154}\right)$
$\chi_{6019}(28,\cdot)$	6019.ei	924	yes	$1$	$1$	$e\left(\frac{107}{308}\right)$	$e\left(\frac{125}{154}\right)$	$e\left(\frac{107}{154}\right)$	$e\left(\frac{503}{924}\right)$	$e\left(\frac{7}{44}\right)$	$e\left(\frac{97}{924}\right)$	$e\left(\frac{13}{308}\right)$	$e\left(\frac{48}{77}\right)$	$e\left(\frac{206}{231}\right)$	$e\left(\frac{47}{308}\right)$
$\chi_{6019}(29,\cdot)$	6019.dt	231	yes	$1$	$1$	$e\left(\frac{25}{77}\right)$	$e\left(\frac{3}{77}\right)$	$e\left(\frac{50}{77}\right)$	$e\left(\frac{47}{231}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{145}{231}\right)$	$e\left(\frac{75}{77}\right)$	$e\left(\frac{6}{77}\right)$	$e\left(\frac{122}{231}\right)$	$e\left(\frac{52}{77}\right)$
$\chi_{6019}(30,\cdot)$	6019.dx	462	yes	$1$	$1$	$e\left(\frac{145}{154}\right)$	$e\left(\frac{1}{77}\right)$	$e\left(\frac{68}{77}\right)$	$e\left(\frac{365}{462}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{379}{462}\right)$	$e\left(\frac{127}{154}\right)$	$e\left(\frac{2}{77}\right)$	$e\left(\frac{169}{231}\right)$	$e\left(\frac{9}{154}\right)$
$\chi_{6019}(31,\cdot)$	6019.ej	924	yes	$-1$	$1$	$e\left(\frac{905}{924}\right)$	$e\left(\frac{185}{231}\right)$	$e\left(\frac{443}{462}\right)$	$e\left(\frac{793}{924}\right)$	$e\left(\frac{103}{132}\right)$	$e\left(\frac{241}{308}\right)$	$e\left(\frac{289}{308}\right)$	$e\left(\frac{139}{231}\right)$	$e\left(\frac{129}{154}\right)$	$e\left(\frac{635}{924}\right)$
$\chi_{6019}(32,\cdot)$	6019.el	924	yes	$-1$	$1$	$e\left(\frac{857}{924}\right)$	$e\left(\frac{8}{231}\right)$	$e\left(\frac{395}{462}\right)$	$e\left(\frac{689}{924}\right)$	$e\left(\frac{127}{132}\right)$	$e\left(\frac{815}{924}\right)$	$e\left(\frac{241}{308}\right)$	$e\left(\frac{16}{231}\right)$	$e\left(\frac{311}{462}\right)$	$e\left(\frac{683}{924}\right)$
$\chi_{6019}(33,\cdot)$	6019.dc	84	yes	$-1$	$1$	$e\left(\frac{13}{84}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{13}{84}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{55}{84}\right)$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{43}{84}\right)$
$\chi_{6019}(34,\cdot)$	6019.bq	28	yes	$-1$	$1$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{15}{28}\right)$	$i$	$e\left(\frac{1}{28}\right)$	$e\left(\frac{17}{28}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{13}{28}\right)$

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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	$6019$
Structure	\(C_{6}\times C_{924}\)
Order	$5544$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(7\)	\(8\)	\(9\)	\(10\)	\(11\)
\(\chi_{6019}(1,\cdot)\)	6019.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{6019}(2,\cdot)\)	6019.el	924	yes	\(-1\)	\(1\)	\(e\left(\frac{541}{924}\right)\)	\(e\left(\frac{94}{231}\right)\)	\(e\left(\frac{79}{462}\right)\)	\(e\left(\frac{877}{924}\right)\)	\(e\left(\frac{131}{132}\right)\)	\(e\left(\frac{163}{924}\right)\)	\(e\left(\frac{233}{308}\right)\)	\(e\left(\frac{188}{231}\right)\)	\(e\left(\frac{247}{462}\right)\)	\(e\left(\frac{691}{924}\right)\)
\(\chi_{6019}(3,\cdot)\)	6019.ea	462	yes	\(-1\)	\(1\)	\(e\left(\frac{94}{231}\right)\)	\(e\left(\frac{155}{462}\right)\)	\(e\left(\frac{188}{231}\right)\)	\(e\left(\frac{125}{462}\right)\)	\(e\left(\frac{49}{66}\right)\)	\(e\left(\frac{461}{462}\right)\)	\(e\left(\frac{17}{77}\right)\)	\(e\left(\frac{155}{231}\right)\)	\(e\left(\frac{313}{462}\right)\)	\(e\left(\frac{197}{462}\right)\)
\(\chi_{6019}(4,\cdot)\)	6019.ed	462	yes	\(1\)	\(1\)	\(e\left(\frac{79}{462}\right)\)	\(e\left(\frac{188}{231}\right)\)	\(e\left(\frac{79}{231}\right)\)	\(e\left(\frac{415}{462}\right)\)	\(e\left(\frac{65}{66}\right)\)	\(e\left(\frac{163}{462}\right)\)	\(e\left(\frac{79}{154}\right)\)	\(e\left(\frac{145}{231}\right)\)	\(e\left(\frac{16}{231}\right)\)	\(e\left(\frac{229}{462}\right)\)
\(\chi_{6019}(5,\cdot)\)	6019.eo	924	yes	\(1\)	\(1\)	\(e\left(\frac{877}{924}\right)\)	\(e\left(\frac{125}{462}\right)\)	\(e\left(\frac{415}{462}\right)\)	\(e\left(\frac{527}{924}\right)\)	\(e\left(\frac{29}{132}\right)\)	\(e\left(\frac{199}{308}\right)\)	\(e\left(\frac{261}{308}\right)\)	\(e\left(\frac{125}{231}\right)\)	\(e\left(\frac{40}{77}\right)\)	\(e\left(\frac{817}{924}\right)\)
\(\chi_{6019}(6,\cdot)\)	6019.di	132	yes	\(1\)	\(1\)	\(e\left(\frac{131}{132}\right)\)	\(e\left(\frac{49}{66}\right)\)	\(e\left(\frac{65}{66}\right)\)	\(e\left(\frac{29}{132}\right)\)	\(e\left(\frac{97}{132}\right)\)	\(e\left(\frac{23}{132}\right)\)	\(e\left(\frac{43}{44}\right)\)	\(e\left(\frac{16}{33}\right)\)	\(e\left(\frac{7}{33}\right)\)	\(e\left(\frac{23}{132}\right)\)
\(\chi_{6019}(7,\cdot)\)	6019.en	924	yes	\(1\)	\(1\)	\(e\left(\frac{163}{924}\right)\)	\(e\left(\frac{461}{462}\right)\)	\(e\left(\frac{163}{462}\right)\)	\(e\left(\frac{199}{308}\right)\)	\(e\left(\frac{23}{132}\right)\)	\(e\left(\frac{695}{924}\right)\)	\(e\left(\frac{163}{308}\right)\)	\(e\left(\frac{230}{231}\right)\)	\(e\left(\frac{190}{231}\right)\)	\(e\left(\frac{607}{924}\right)\)
\(\chi_{6019}(8,\cdot)\)	6019.dv	308	yes	\(-1\)	\(1\)	\(e\left(\frac{233}{308}\right)\)	\(e\left(\frac{17}{77}\right)\)	\(e\left(\frac{79}{154}\right)\)	\(e\left(\frac{261}{308}\right)\)	\(e\left(\frac{43}{44}\right)\)	\(e\left(\frac{163}{308}\right)\)	\(e\left(\frac{83}{308}\right)\)	\(e\left(\frac{34}{77}\right)\)	\(e\left(\frac{93}{154}\right)\)	\(e\left(\frac{75}{308}\right)\)
\(\chi_{6019}(9,\cdot)\)	6019.dq	231	yes	\(1\)	\(1\)	\(e\left(\frac{188}{231}\right)\)	\(e\left(\frac{155}{231}\right)\)	\(e\left(\frac{145}{231}\right)\)	\(e\left(\frac{125}{231}\right)\)	\(e\left(\frac{16}{33}\right)\)	\(e\left(\frac{230}{231}\right)\)	\(e\left(\frac{34}{77}\right)\)	\(e\left(\frac{79}{231}\right)\)	\(e\left(\frac{82}{231}\right)\)	\(e\left(\frac{197}{231}\right)\)
\(\chi_{6019}(10,\cdot)\)	6019.eg	462	yes	\(-1\)	\(1\)	\(e\left(\frac{247}{462}\right)\)	\(e\left(\frac{313}{462}\right)\)	\(e\left(\frac{16}{231}\right)\)	\(e\left(\frac{40}{77}\right)\)	\(e\left(\frac{7}{33}\right)\)	\(e\left(\frac{190}{231}\right)\)	\(e\left(\frac{93}{154}\right)\)	\(e\left(\frac{82}{231}\right)\)	\(e\left(\frac{25}{462}\right)\)	\(e\left(\frac{146}{231}\right)\)
\(\chi_{6019}(11,\cdot)\)	6019.em	924	yes	\(1\)	\(1\)	\(e\left(\frac{691}{924}\right)\)	\(e\left(\frac{197}{462}\right)\)	\(e\left(\frac{229}{462}\right)\)	\(e\left(\frac{817}{924}\right)\)	\(e\left(\frac{23}{132}\right)\)	\(e\left(\frac{607}{924}\right)\)	\(e\left(\frac{75}{308}\right)\)	\(e\left(\frac{197}{231}\right)\)	\(e\left(\frac{146}{231}\right)\)	\(e\left(\frac{79}{924}\right)\)
\(\chi_{6019}(12,\cdot)\)	6019.dn	154	yes	\(-1\)	\(1\)	\(e\left(\frac{89}{154}\right)\)	\(e\left(\frac{23}{154}\right)\)	\(e\left(\frac{12}{77}\right)\)	\(e\left(\frac{13}{77}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{27}{77}\right)\)	\(e\left(\frac{113}{154}\right)\)	\(e\left(\frac{23}{77}\right)\)	\(e\left(\frac{115}{154}\right)\)	\(e\left(\frac{71}{77}\right)\)
\(\chi_{6019}(14,\cdot)\)	6019.ce	42	no	\(-1\)	\(1\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{17}{42}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{25}{42}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{17}{42}\right)\)
\(\chi_{6019}(15,\cdot)\)	6019.dk	132	yes	\(-1\)	\(1\)	\(e\left(\frac{47}{132}\right)\)	\(e\left(\frac{20}{33}\right)\)	\(e\left(\frac{47}{66}\right)\)	\(e\left(\frac{37}{44}\right)\)	\(e\left(\frac{127}{132}\right)\)	\(e\left(\frac{85}{132}\right)\)	\(e\left(\frac{3}{44}\right)\)	\(e\left(\frac{7}{33}\right)\)	\(e\left(\frac{13}{66}\right)\)	\(e\left(\frac{41}{132}\right)\)
\(\chi_{6019}(16,\cdot)\)	6019.dq	231	yes	\(1\)	\(1\)	\(e\left(\frac{79}{231}\right)\)	\(e\left(\frac{145}{231}\right)\)	\(e\left(\frac{158}{231}\right)\)	\(e\left(\frac{184}{231}\right)\)	\(e\left(\frac{32}{33}\right)\)	\(e\left(\frac{163}{231}\right)\)	\(e\left(\frac{2}{77}\right)\)	\(e\left(\frac{59}{231}\right)\)	\(e\left(\frac{32}{231}\right)\)	\(e\left(\frac{229}{231}\right)\)
\(\chi_{6019}(17,\cdot)\)	6019.ed	462	yes	\(1\)	\(1\)	\(e\left(\frac{439}{462}\right)\)	\(e\left(\frac{71}{231}\right)\)	\(e\left(\frac{208}{231}\right)\)	\(e\left(\frac{271}{462}\right)\)	\(e\left(\frac{17}{66}\right)\)	\(e\left(\frac{397}{462}\right)\)	\(e\left(\frac{131}{154}\right)\)	\(e\left(\frac{142}{231}\right)\)	\(e\left(\frac{124}{231}\right)\)	\(e\left(\frac{331}{462}\right)\)
\(\chi_{6019}(18,\cdot)\)	6019.dv	308	yes	\(-1\)	\(1\)	\(e\left(\frac{123}{308}\right)\)	\(e\left(\frac{6}{77}\right)\)	\(e\left(\frac{123}{154}\right)\)	\(e\left(\frac{151}{308}\right)\)	\(e\left(\frac{21}{44}\right)\)	\(e\left(\frac{53}{308}\right)\)	\(e\left(\frac{61}{308}\right)\)	\(e\left(\frac{12}{77}\right)\)	\(e\left(\frac{137}{154}\right)\)	\(e\left(\frac{185}{308}\right)\)
\(\chi_{6019}(19,\cdot)\)	6019.em	924	yes	\(1\)	\(1\)	\(e\left(\frac{89}{924}\right)\)	\(e\left(\frac{127}{462}\right)\)	\(e\left(\frac{89}{462}\right)\)	\(e\left(\frac{719}{924}\right)\)	\(e\left(\frac{49}{132}\right)\)	\(e\left(\frac{593}{924}\right)\)	\(e\left(\frac{89}{308}\right)\)	\(e\left(\frac{127}{231}\right)\)	\(e\left(\frac{202}{231}\right)\)	\(e\left(\frac{65}{924}\right)\)
\(\chi_{6019}(20,\cdot)\)	6019.ei	924	yes	\(1\)	\(1\)	\(e\left(\frac{37}{308}\right)\)	\(e\left(\frac{13}{154}\right)\)	\(e\left(\frac{37}{154}\right)\)	\(e\left(\frac{433}{924}\right)\)	\(e\left(\frac{9}{44}\right)\)	\(e\left(\frac{923}{924}\right)\)	\(e\left(\frac{111}{308}\right)\)	\(e\left(\frac{13}{77}\right)\)	\(e\left(\frac{136}{231}\right)\)	\(e\left(\frac{117}{308}\right)\)
\(\chi_{6019}(21,\cdot)\)	6019.z	12	yes	\(-1\)	\(1\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(-i\)	\(-i\)	\(e\left(\frac{2}{3}\right)\)	\(-1\)	\(e\left(\frac{1}{12}\right)\)
\(\chi_{6019}(22,\cdot)\)	6019.o	6	yes	\(-1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{6019}(23,\cdot)\)	6019.eg	462	yes	\(-1\)	\(1\)	\(e\left(\frac{325}{462}\right)\)	\(e\left(\frac{193}{462}\right)\)	\(e\left(\frac{94}{231}\right)\)	\(e\left(\frac{4}{77}\right)\)	\(e\left(\frac{4}{33}\right)\)	\(e\left(\frac{19}{231}\right)\)	\(e\left(\frac{17}{154}\right)\)	\(e\left(\frac{193}{231}\right)\)	\(e\left(\frac{349}{462}\right)\)	\(e\left(\frac{107}{231}\right)\)
\(\chi_{6019}(24,\cdot)\)	6019.em	924	yes	\(1\)	\(1\)	\(e\left(\frac{151}{924}\right)\)	\(e\left(\frac{257}{462}\right)\)	\(e\left(\frac{151}{462}\right)\)	\(e\left(\frac{109}{924}\right)\)	\(e\left(\frac{95}{132}\right)\)	\(e\left(\frac{487}{924}\right)\)	\(e\left(\frac{151}{308}\right)\)	\(e\left(\frac{26}{231}\right)\)	\(e\left(\frac{65}{231}\right)\)	\(e\left(\frac{619}{924}\right)\)
\(\chi_{6019}(25,\cdot)\)	6019.ec	462	yes	\(1\)	\(1\)	\(e\left(\frac{415}{462}\right)\)	\(e\left(\frac{125}{231}\right)\)	\(e\left(\frac{184}{231}\right)\)	\(e\left(\frac{65}{462}\right)\)	\(e\left(\frac{29}{66}\right)\)	\(e\left(\frac{45}{154}\right)\)	\(e\left(\frac{107}{154}\right)\)	\(e\left(\frac{19}{231}\right)\)	\(e\left(\frac{3}{77}\right)\)	\(e\left(\frac{355}{462}\right)\)
\(\chi_{6019}(27,\cdot)\)	6019.dp	154	no	\(-1\)	\(1\)	\(e\left(\frac{17}{77}\right)\)	\(e\left(\frac{1}{154}\right)\)	\(e\left(\frac{34}{77}\right)\)	\(e\left(\frac{125}{154}\right)\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{153}{154}\right)\)	\(e\left(\frac{51}{77}\right)\)	\(e\left(\frac{1}{77}\right)\)	\(e\left(\frac{5}{154}\right)\)	\(e\left(\frac{43}{154}\right)\)
\(\chi_{6019}(28,\cdot)\)	6019.ei	924	yes	\(1\)	\(1\)	\(e\left(\frac{107}{308}\right)\)	\(e\left(\frac{125}{154}\right)\)	\(e\left(\frac{107}{154}\right)\)	\(e\left(\frac{503}{924}\right)\)	\(e\left(\frac{7}{44}\right)\)	\(e\left(\frac{97}{924}\right)\)	\(e\left(\frac{13}{308}\right)\)	\(e\left(\frac{48}{77}\right)\)	\(e\left(\frac{206}{231}\right)\)	\(e\left(\frac{47}{308}\right)\)
\(\chi_{6019}(29,\cdot)\)	6019.dt	231	yes	\(1\)	\(1\)	\(e\left(\frac{25}{77}\right)\)	\(e\left(\frac{3}{77}\right)\)	\(e\left(\frac{50}{77}\right)\)	\(e\left(\frac{47}{231}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{145}{231}\right)\)	\(e\left(\frac{75}{77}\right)\)	\(e\left(\frac{6}{77}\right)\)	\(e\left(\frac{122}{231}\right)\)	\(e\left(\frac{52}{77}\right)\)
\(\chi_{6019}(30,\cdot)\)	6019.dx	462	yes	\(1\)	\(1\)	\(e\left(\frac{145}{154}\right)\)	\(e\left(\frac{1}{77}\right)\)	\(e\left(\frac{68}{77}\right)\)	\(e\left(\frac{365}{462}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{379}{462}\right)\)	\(e\left(\frac{127}{154}\right)\)	\(e\left(\frac{2}{77}\right)\)	\(e\left(\frac{169}{231}\right)\)	\(e\left(\frac{9}{154}\right)\)
\(\chi_{6019}(31,\cdot)\)	6019.ej	924	yes	\(-1\)	\(1\)	\(e\left(\frac{905}{924}\right)\)	\(e\left(\frac{185}{231}\right)\)	\(e\left(\frac{443}{462}\right)\)	\(e\left(\frac{793}{924}\right)\)	\(e\left(\frac{103}{132}\right)\)	\(e\left(\frac{241}{308}\right)\)	\(e\left(\frac{289}{308}\right)\)	\(e\left(\frac{139}{231}\right)\)	\(e\left(\frac{129}{154}\right)\)	\(e\left(\frac{635}{924}\right)\)
\(\chi_{6019}(32,\cdot)\)	6019.el	924	yes	\(-1\)	\(1\)	\(e\left(\frac{857}{924}\right)\)	\(e\left(\frac{8}{231}\right)\)	\(e\left(\frac{395}{462}\right)\)	\(e\left(\frac{689}{924}\right)\)	\(e\left(\frac{127}{132}\right)\)	\(e\left(\frac{815}{924}\right)\)	\(e\left(\frac{241}{308}\right)\)	\(e\left(\frac{16}{231}\right)\)	\(e\left(\frac{311}{462}\right)\)	\(e\left(\frac{683}{924}\right)\)
\(\chi_{6019}(33,\cdot)\)	6019.dc	84	yes	\(-1\)	\(1\)	\(e\left(\frac{13}{84}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{13}{42}\right)\)	\(e\left(\frac{13}{84}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{55}{84}\right)\)	\(e\left(\frac{13}{28}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{13}{42}\right)\)	\(e\left(\frac{43}{84}\right)\)
\(\chi_{6019}(34,\cdot)\)	6019.bq	28	yes	\(-1\)	\(1\)	\(e\left(\frac{15}{28}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{15}{28}\right)\)	\(i\)	\(e\left(\frac{1}{28}\right)\)	\(e\left(\frac{17}{28}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{13}{28}\right)\)

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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.