LMFDB - Group of Dirichlet characters of modulus 2093

Show commands: PariGP / SageMath

sage: H = DirichletGroup(2093)

pari: g = idealstar(,2093,2)

Character group

sage: G.order() pari: g.no
Order	=	1584
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{6}\times C_{132}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{2093}(1795,\cdot)$, $\chi_{2093}(1289,\cdot)$, $\chi_{2093}(1730,\cdot)$

First 32 of 1584 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	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$8$	$9$	$10$	$11$	$12$
$\chi_{2093}(1,\cdot)$	2093.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{2093}(2,\cdot)$	2093.em	132	yes	$-1$	$1$	$e\left(\frac{41}{44}\right)$	$e\left(\frac{4}{33}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{67}{132}\right)$	$e\left(\frac{7}{132}\right)$	$e\left(\frac{35}{44}\right)$	$e\left(\frac{8}{33}\right)$	$e\left(\frac{29}{66}\right)$	$e\left(\frac{97}{132}\right)$	$e\left(\frac{65}{66}\right)$
$\chi_{2093}(3,\cdot)$	2093.du	66	yes	$-1$	$1$	$e\left(\frac{4}{33}\right)$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{8}{33}\right)$	$e\left(\frac{37}{66}\right)$	$e\left(\frac{17}{66}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{25}{66}\right)$
$\chi_{2093}(4,\cdot)$	2093.dy	66	yes	$1$	$1$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{8}{33}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{1}{66}\right)$	$e\left(\frac{7}{66}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{16}{33}\right)$	$e\left(\frac{29}{33}\right)$	$e\left(\frac{31}{66}\right)$	$e\left(\frac{32}{33}\right)$
$\chi_{2093}(5,\cdot)$	2093.ed	132	yes	$-1$	$1$	$e\left(\frac{67}{132}\right)$	$e\left(\frac{37}{66}\right)$	$e\left(\frac{1}{66}\right)$	$e\left(\frac{127}{132}\right)$	$e\left(\frac{3}{44}\right)$	$e\left(\frac{23}{44}\right)$	$e\left(\frac{4}{33}\right)$	$e\left(\frac{31}{66}\right)$	$e\left(\frac{131}{132}\right)$	$e\left(\frac{19}{33}\right)$
$\chi_{2093}(6,\cdot)$	2093.ee	132	yes	$1$	$1$	$e\left(\frac{7}{132}\right)$	$e\left(\frac{17}{66}\right)$	$e\left(\frac{7}{66}\right)$	$e\left(\frac{3}{44}\right)$	$e\left(\frac{41}{132}\right)$	$e\left(\frac{7}{44}\right)$	$e\left(\frac{17}{33}\right)$	$e\left(\frac{4}{33}\right)$	$e\left(\frac{37}{132}\right)$	$e\left(\frac{4}{11}\right)$
$\chi_{2093}(8,\cdot)$	2093.cv	44	no	$-1$	$1$	$e\left(\frac{35}{44}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{23}{44}\right)$	$e\left(\frac{7}{44}\right)$	$e\left(\frac{17}{44}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{9}{44}\right)$	$e\left(\frac{21}{22}\right)$
$\chi_{2093}(9,\cdot)$	2093.cr	33	yes	$1$	$1$	$e\left(\frac{8}{33}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{16}{33}\right)$	$e\left(\frac{4}{33}\right)$	$e\left(\frac{17}{33}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{25}{33}\right)$
$\chi_{2093}(10,\cdot)$	2093.dl	66	yes	$1$	$1$	$e\left(\frac{29}{66}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{29}{33}\right)$	$e\left(\frac{31}{66}\right)$	$e\left(\frac{4}{33}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{37}{66}\right)$
$\chi_{2093}(11,\cdot)$	2093.ea	132	yes	$1$	$1$	$e\left(\frac{97}{132}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{31}{66}\right)$	$e\left(\frac{131}{132}\right)$	$e\left(\frac{37}{132}\right)$	$e\left(\frac{9}{44}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{19}{44}\right)$	$e\left(\frac{1}{66}\right)$
$\chi_{2093}(12,\cdot)$	2093.df	66	yes	$-1$	$1$	$e\left(\frac{65}{66}\right)$	$e\left(\frac{25}{66}\right)$	$e\left(\frac{32}{33}\right)$	$e\left(\frac{19}{33}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{25}{33}\right)$	$e\left(\frac{37}{66}\right)$	$e\left(\frac{1}{66}\right)$	$e\left(\frac{23}{66}\right)$
$\chi_{2093}(15,\cdot)$	2093.el	132	no	$1$	$1$	$e\left(\frac{83}{132}\right)$	$e\left(\frac{23}{33}\right)$	$e\left(\frac{17}{66}\right)$	$e\left(\frac{23}{44}\right)$	$e\left(\frac{43}{132}\right)$	$e\left(\frac{39}{44}\right)$	$e\left(\frac{13}{33}\right)$	$e\left(\frac{5}{33}\right)$	$e\left(\frac{71}{132}\right)$	$e\left(\frac{21}{22}\right)$
$\chi_{2093}(16,\cdot)$	2093.cq	33	yes	$1$	$1$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{16}{33}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{1}{33}\right)$	$e\left(\frac{7}{33}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{32}{33}\right)$	$e\left(\frac{25}{33}\right)$	$e\left(\frac{31}{33}\right)$	$e\left(\frac{31}{33}\right)$
$\chi_{2093}(17,\cdot)$	2093.dw	66	yes	$1$	$1$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{61}{66}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{43}{66}\right)$	$e\left(\frac{2}{33}\right)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{28}{33}\right)$	$e\left(\frac{26}{33}\right)$	$e\left(\frac{23}{33}\right)$	$e\left(\frac{13}{66}\right)$
$\chi_{2093}(18,\cdot)$	2093.ei	132	yes	$-1$	$1$	$e\left(\frac{23}{132}\right)$	$e\left(\frac{13}{33}\right)$	$e\left(\frac{23}{66}\right)$	$e\left(\frac{83}{132}\right)$	$e\left(\frac{25}{44}\right)$	$e\left(\frac{23}{44}\right)$	$e\left(\frac{26}{33}\right)$	$e\left(\frac{53}{66}\right)$	$e\left(\frac{109}{132}\right)$	$e\left(\frac{49}{66}\right)$
$\chi_{2093}(19,\cdot)$	2093.ep	132	yes	$-1$	$1$	$e\left(\frac{59}{132}\right)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{59}{66}\right)$	$e\left(\frac{79}{132}\right)$	$e\left(\frac{113}{132}\right)$	$e\left(\frac{15}{44}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{17}{44}\right)$	$e\left(\frac{10}{33}\right)$
$\chi_{2093}(20,\cdot)$	2093.ec	132	yes	$-1$	$1$	$e\left(\frac{49}{132}\right)$	$e\left(\frac{53}{66}\right)$	$e\left(\frac{49}{66}\right)$	$e\left(\frac{43}{44}\right)$	$e\left(\frac{23}{132}\right)$	$e\left(\frac{5}{44}\right)$	$e\left(\frac{20}{33}\right)$	$e\left(\frac{23}{66}\right)$	$e\left(\frac{61}{132}\right)$	$e\left(\frac{6}{11}\right)$
$\chi_{2093}(22,\cdot)$	2093.w	6	no	$-1$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$-1$	$e\left(\frac{1}{3}\right)$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{6}\right)$	$1$
$\chi_{2093}(24,\cdot)$	2093.bu	12	no	$1$	$1$	$e\left(\frac{11}{12}\right)$	$-1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{5}{12}\right)$	$-i$	$1$	$1$	$-i$	$e\left(\frac{1}{3}\right)$
$\chi_{2093}(25,\cdot)$	2093.di	66	yes	$1$	$1$	$e\left(\frac{1}{66}\right)$	$e\left(\frac{4}{33}\right)$	$e\left(\frac{1}{33}\right)$	$e\left(\frac{61}{66}\right)$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{8}{33}\right)$	$e\left(\frac{31}{33}\right)$	$e\left(\frac{65}{66}\right)$	$e\left(\frac{5}{33}\right)$
$\chi_{2093}(27,\cdot)$	2093.cl	22	no	$-1$	$1$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{3}{22}\right)$
$\chi_{2093}(29,\cdot)$	2093.cs	33	no	$1$	$1$	$e\left(\frac{32}{33}\right)$	$e\left(\frac{14}{33}\right)$	$e\left(\frac{31}{33}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{13}{33}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{28}{33}\right)$	$e\left(\frac{26}{33}\right)$	$e\left(\frac{23}{33}\right)$	$e\left(\frac{4}{11}\right)$
$\chi_{2093}(30,\cdot)$	2093.dc	66	yes	$-1$	$1$	$e\left(\frac{37}{66}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{4}{33}\right)$	$e\left(\frac{1}{33}\right)$	$e\left(\frac{25}{66}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{31}{33}\right)$
$\chi_{2093}(31,\cdot)$	2093.ef	132	yes	$1$	$1$	$e\left(\frac{83}{132}\right)$	$e\left(\frac{35}{66}\right)$	$e\left(\frac{17}{66}\right)$	$e\left(\frac{113}{132}\right)$	$e\left(\frac{7}{44}\right)$	$e\left(\frac{39}{44}\right)$	$e\left(\frac{2}{33}\right)$	$e\left(\frac{16}{33}\right)$	$e\left(\frac{49}{132}\right)$	$e\left(\frac{26}{33}\right)$
$\chi_{2093}(32,\cdot)$	2093.em	132	yes	$-1$	$1$	$e\left(\frac{29}{44}\right)$	$e\left(\frac{20}{33}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{71}{132}\right)$	$e\left(\frac{35}{132}\right)$	$e\left(\frac{43}{44}\right)$	$e\left(\frac{7}{33}\right)$	$e\left(\frac{13}{66}\right)$	$e\left(\frac{89}{132}\right)$	$e\left(\frac{61}{66}\right)$
$\chi_{2093}(33,\cdot)$	2093.ep	132	yes	$-1$	$1$	$e\left(\frac{113}{132}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{47}{66}\right)$	$e\left(\frac{73}{132}\right)$	$e\left(\frac{71}{132}\right)$	$e\left(\frac{25}{44}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{43}{44}\right)$	$e\left(\frac{13}{33}\right)$
$\chi_{2093}(34,\cdot)$	2093.cx	44	yes	$-1$	$1$	$e\left(\frac{3}{44}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{7}{44}\right)$	$e\left(\frac{5}{44}\right)$	$e\left(\frac{9}{44}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{19}{44}\right)$	$e\left(\frac{2}{11}\right)$
$\chi_{2093}(36,\cdot)$	2093.dk	66	no	$1$	$1$	$e\left(\frac{7}{66}\right)$	$e\left(\frac{17}{33}\right)$	$e\left(\frac{7}{33}\right)$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{41}{66}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{1}{33}\right)$	$e\left(\frac{8}{33}\right)$	$e\left(\frac{37}{66}\right)$	$e\left(\frac{8}{11}\right)$
$\chi_{2093}(37,\cdot)$	2093.en	132	yes	$1$	$1$	$e\left(\frac{7}{44}\right)$	$e\left(\frac{31}{33}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{115}{132}\right)$	$e\left(\frac{13}{132}\right)$	$e\left(\frac{21}{44}\right)$	$e\left(\frac{29}{33}\right)$	$e\left(\frac{1}{33}\right)$	$e\left(\frac{1}{132}\right)$	$e\left(\frac{17}{66}\right)$
$\chi_{2093}(38,\cdot)$	2093.de	66	yes	$1$	$1$	$e\left(\frac{25}{66}\right)$	$e\left(\frac{35}{66}\right)$	$e\left(\frac{25}{33}\right)$	$e\left(\frac{7}{66}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{2}{33}\right)$	$e\left(\frac{16}{33}\right)$	$e\left(\frac{4}{33}\right)$	$e\left(\frac{19}{66}\right)$
$\chi_{2093}(40,\cdot)$	2093.dq	66	no	$1$	$1$	$e\left(\frac{10}{33}\right)$	$e\left(\frac{61}{66}\right)$	$e\left(\frac{20}{33}\right)$	$e\left(\frac{16}{33}\right)$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{28}{33}\right)$	$e\left(\frac{26}{33}\right)$	$e\left(\frac{13}{66}\right)$	$e\left(\frac{35}{66}\right)$
$\chi_{2093}(41,\cdot)$	2093.ee	132	yes	$1$	$1$	$e\left(\frac{23}{132}\right)$	$e\left(\frac{37}{66}\right)$	$e\left(\frac{23}{66}\right)$	$e\left(\frac{35}{44}\right)$	$e\left(\frac{97}{132}\right)$	$e\left(\frac{23}{44}\right)$	$e\left(\frac{4}{33}\right)$	$e\left(\frac{32}{33}\right)$	$e\left(\frac{65}{132}\right)$	$e\left(\frac{10}{11}\right)$

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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	$2093$
Structure	\(C_{2}\times C_{6}\times C_{132}\)
Order	$1584$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(8\)	\(9\)	\(10\)	\(11\)	\(12\)
\(\chi_{2093}(1,\cdot)\)	2093.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{2093}(2,\cdot)\)	2093.em	132	yes	\(-1\)	\(1\)	\(e\left(\frac{41}{44}\right)\)	\(e\left(\frac{4}{33}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{67}{132}\right)\)	\(e\left(\frac{7}{132}\right)\)	\(e\left(\frac{35}{44}\right)\)	\(e\left(\frac{8}{33}\right)\)	\(e\left(\frac{29}{66}\right)\)	\(e\left(\frac{97}{132}\right)\)	\(e\left(\frac{65}{66}\right)\)
\(\chi_{2093}(3,\cdot)\)	2093.du	66	yes	\(-1\)	\(1\)	\(e\left(\frac{4}{33}\right)\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{8}{33}\right)\)	\(e\left(\frac{37}{66}\right)\)	\(e\left(\frac{17}{66}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{25}{66}\right)\)
\(\chi_{2093}(4,\cdot)\)	2093.dy	66	yes	\(1\)	\(1\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{8}{33}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{1}{66}\right)\)	\(e\left(\frac{7}{66}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{16}{33}\right)\)	\(e\left(\frac{29}{33}\right)\)	\(e\left(\frac{31}{66}\right)\)	\(e\left(\frac{32}{33}\right)\)
\(\chi_{2093}(5,\cdot)\)	2093.ed	132	yes	\(-1\)	\(1\)	\(e\left(\frac{67}{132}\right)\)	\(e\left(\frac{37}{66}\right)\)	\(e\left(\frac{1}{66}\right)\)	\(e\left(\frac{127}{132}\right)\)	\(e\left(\frac{3}{44}\right)\)	\(e\left(\frac{23}{44}\right)\)	\(e\left(\frac{4}{33}\right)\)	\(e\left(\frac{31}{66}\right)\)	\(e\left(\frac{131}{132}\right)\)	\(e\left(\frac{19}{33}\right)\)
\(\chi_{2093}(6,\cdot)\)	2093.ee	132	yes	\(1\)	\(1\)	\(e\left(\frac{7}{132}\right)\)	\(e\left(\frac{17}{66}\right)\)	\(e\left(\frac{7}{66}\right)\)	\(e\left(\frac{3}{44}\right)\)	\(e\left(\frac{41}{132}\right)\)	\(e\left(\frac{7}{44}\right)\)	\(e\left(\frac{17}{33}\right)\)	\(e\left(\frac{4}{33}\right)\)	\(e\left(\frac{37}{132}\right)\)	\(e\left(\frac{4}{11}\right)\)
\(\chi_{2093}(8,\cdot)\)	2093.cv	44	no	\(-1\)	\(1\)	\(e\left(\frac{35}{44}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{23}{44}\right)\)	\(e\left(\frac{7}{44}\right)\)	\(e\left(\frac{17}{44}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{9}{44}\right)\)	\(e\left(\frac{21}{22}\right)\)
\(\chi_{2093}(9,\cdot)\)	2093.cr	33	yes	\(1\)	\(1\)	\(e\left(\frac{8}{33}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{16}{33}\right)\)	\(e\left(\frac{4}{33}\right)\)	\(e\left(\frac{17}{33}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{25}{33}\right)\)
\(\chi_{2093}(10,\cdot)\)	2093.dl	66	yes	\(1\)	\(1\)	\(e\left(\frac{29}{66}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{29}{33}\right)\)	\(e\left(\frac{31}{66}\right)\)	\(e\left(\frac{4}{33}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{37}{66}\right)\)
\(\chi_{2093}(11,\cdot)\)	2093.ea	132	yes	\(1\)	\(1\)	\(e\left(\frac{97}{132}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{31}{66}\right)\)	\(e\left(\frac{131}{132}\right)\)	\(e\left(\frac{37}{132}\right)\)	\(e\left(\frac{9}{44}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{19}{44}\right)\)	\(e\left(\frac{1}{66}\right)\)
\(\chi_{2093}(12,\cdot)\)	2093.df	66	yes	\(-1\)	\(1\)	\(e\left(\frac{65}{66}\right)\)	\(e\left(\frac{25}{66}\right)\)	\(e\left(\frac{32}{33}\right)\)	\(e\left(\frac{19}{33}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{25}{33}\right)\)	\(e\left(\frac{37}{66}\right)\)	\(e\left(\frac{1}{66}\right)\)	\(e\left(\frac{23}{66}\right)\)
\(\chi_{2093}(15,\cdot)\)	2093.el	132	no	\(1\)	\(1\)	\(e\left(\frac{83}{132}\right)\)	\(e\left(\frac{23}{33}\right)\)	\(e\left(\frac{17}{66}\right)\)	\(e\left(\frac{23}{44}\right)\)	\(e\left(\frac{43}{132}\right)\)	\(e\left(\frac{39}{44}\right)\)	\(e\left(\frac{13}{33}\right)\)	\(e\left(\frac{5}{33}\right)\)	\(e\left(\frac{71}{132}\right)\)	\(e\left(\frac{21}{22}\right)\)
\(\chi_{2093}(16,\cdot)\)	2093.cq	33	yes	\(1\)	\(1\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{16}{33}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{1}{33}\right)\)	\(e\left(\frac{7}{33}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{32}{33}\right)\)	\(e\left(\frac{25}{33}\right)\)	\(e\left(\frac{31}{33}\right)\)	\(e\left(\frac{31}{33}\right)\)
\(\chi_{2093}(17,\cdot)\)	2093.dw	66	yes	\(1\)	\(1\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{61}{66}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{43}{66}\right)\)	\(e\left(\frac{2}{33}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{28}{33}\right)\)	\(e\left(\frac{26}{33}\right)\)	\(e\left(\frac{23}{33}\right)\)	\(e\left(\frac{13}{66}\right)\)
\(\chi_{2093}(18,\cdot)\)	2093.ei	132	yes	\(-1\)	\(1\)	\(e\left(\frac{23}{132}\right)\)	\(e\left(\frac{13}{33}\right)\)	\(e\left(\frac{23}{66}\right)\)	\(e\left(\frac{83}{132}\right)\)	\(e\left(\frac{25}{44}\right)\)	\(e\left(\frac{23}{44}\right)\)	\(e\left(\frac{26}{33}\right)\)	\(e\left(\frac{53}{66}\right)\)	\(e\left(\frac{109}{132}\right)\)	\(e\left(\frac{49}{66}\right)\)
\(\chi_{2093}(19,\cdot)\)	2093.ep	132	yes	\(-1\)	\(1\)	\(e\left(\frac{59}{132}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{59}{66}\right)\)	\(e\left(\frac{79}{132}\right)\)	\(e\left(\frac{113}{132}\right)\)	\(e\left(\frac{15}{44}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{17}{44}\right)\)	\(e\left(\frac{10}{33}\right)\)
\(\chi_{2093}(20,\cdot)\)	2093.ec	132	yes	\(-1\)	\(1\)	\(e\left(\frac{49}{132}\right)\)	\(e\left(\frac{53}{66}\right)\)	\(e\left(\frac{49}{66}\right)\)	\(e\left(\frac{43}{44}\right)\)	\(e\left(\frac{23}{132}\right)\)	\(e\left(\frac{5}{44}\right)\)	\(e\left(\frac{20}{33}\right)\)	\(e\left(\frac{23}{66}\right)\)	\(e\left(\frac{61}{132}\right)\)	\(e\left(\frac{6}{11}\right)\)
\(\chi_{2093}(22,\cdot)\)	2093.w	6	no	\(-1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(-1\)	\(e\left(\frac{1}{3}\right)\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(1\)
\(\chi_{2093}(24,\cdot)\)	2093.bu	12	no	\(1\)	\(1\)	\(e\left(\frac{11}{12}\right)\)	\(-1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(-i\)	\(1\)	\(1\)	\(-i\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{2093}(25,\cdot)\)	2093.di	66	yes	\(1\)	\(1\)	\(e\left(\frac{1}{66}\right)\)	\(e\left(\frac{4}{33}\right)\)	\(e\left(\frac{1}{33}\right)\)	\(e\left(\frac{61}{66}\right)\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{8}{33}\right)\)	\(e\left(\frac{31}{33}\right)\)	\(e\left(\frac{65}{66}\right)\)	\(e\left(\frac{5}{33}\right)\)
\(\chi_{2093}(27,\cdot)\)	2093.cl	22	no	\(-1\)	\(1\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{3}{22}\right)\)
\(\chi_{2093}(29,\cdot)\)	2093.cs	33	no	\(1\)	\(1\)	\(e\left(\frac{32}{33}\right)\)	\(e\left(\frac{14}{33}\right)\)	\(e\left(\frac{31}{33}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{13}{33}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{28}{33}\right)\)	\(e\left(\frac{26}{33}\right)\)	\(e\left(\frac{23}{33}\right)\)	\(e\left(\frac{4}{11}\right)\)
\(\chi_{2093}(30,\cdot)\)	2093.dc	66	yes	\(-1\)	\(1\)	\(e\left(\frac{37}{66}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{4}{33}\right)\)	\(e\left(\frac{1}{33}\right)\)	\(e\left(\frac{25}{66}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{31}{33}\right)\)
\(\chi_{2093}(31,\cdot)\)	2093.ef	132	yes	\(1\)	\(1\)	\(e\left(\frac{83}{132}\right)\)	\(e\left(\frac{35}{66}\right)\)	\(e\left(\frac{17}{66}\right)\)	\(e\left(\frac{113}{132}\right)\)	\(e\left(\frac{7}{44}\right)\)	\(e\left(\frac{39}{44}\right)\)	\(e\left(\frac{2}{33}\right)\)	\(e\left(\frac{16}{33}\right)\)	\(e\left(\frac{49}{132}\right)\)	\(e\left(\frac{26}{33}\right)\)
\(\chi_{2093}(32,\cdot)\)	2093.em	132	yes	\(-1\)	\(1\)	\(e\left(\frac{29}{44}\right)\)	\(e\left(\frac{20}{33}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{71}{132}\right)\)	\(e\left(\frac{35}{132}\right)\)	\(e\left(\frac{43}{44}\right)\)	\(e\left(\frac{7}{33}\right)\)	\(e\left(\frac{13}{66}\right)\)	\(e\left(\frac{89}{132}\right)\)	\(e\left(\frac{61}{66}\right)\)
\(\chi_{2093}(33,\cdot)\)	2093.ep	132	yes	\(-1\)	\(1\)	\(e\left(\frac{113}{132}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{47}{66}\right)\)	\(e\left(\frac{73}{132}\right)\)	\(e\left(\frac{71}{132}\right)\)	\(e\left(\frac{25}{44}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{43}{44}\right)\)	\(e\left(\frac{13}{33}\right)\)
\(\chi_{2093}(34,\cdot)\)	2093.cx	44	yes	\(-1\)	\(1\)	\(e\left(\frac{3}{44}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{7}{44}\right)\)	\(e\left(\frac{5}{44}\right)\)	\(e\left(\frac{9}{44}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{19}{44}\right)\)	\(e\left(\frac{2}{11}\right)\)
\(\chi_{2093}(36,\cdot)\)	2093.dk	66	no	\(1\)	\(1\)	\(e\left(\frac{7}{66}\right)\)	\(e\left(\frac{17}{33}\right)\)	\(e\left(\frac{7}{33}\right)\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{41}{66}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{1}{33}\right)\)	\(e\left(\frac{8}{33}\right)\)	\(e\left(\frac{37}{66}\right)\)	\(e\left(\frac{8}{11}\right)\)
\(\chi_{2093}(37,\cdot)\)	2093.en	132	yes	\(1\)	\(1\)	\(e\left(\frac{7}{44}\right)\)	\(e\left(\frac{31}{33}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{115}{132}\right)\)	\(e\left(\frac{13}{132}\right)\)	\(e\left(\frac{21}{44}\right)\)	\(e\left(\frac{29}{33}\right)\)	\(e\left(\frac{1}{33}\right)\)	\(e\left(\frac{1}{132}\right)\)	\(e\left(\frac{17}{66}\right)\)
\(\chi_{2093}(38,\cdot)\)	2093.de	66	yes	\(1\)	\(1\)	\(e\left(\frac{25}{66}\right)\)	\(e\left(\frac{35}{66}\right)\)	\(e\left(\frac{25}{33}\right)\)	\(e\left(\frac{7}{66}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{2}{33}\right)\)	\(e\left(\frac{16}{33}\right)\)	\(e\left(\frac{4}{33}\right)\)	\(e\left(\frac{19}{66}\right)\)
\(\chi_{2093}(40,\cdot)\)	2093.dq	66	no	\(1\)	\(1\)	\(e\left(\frac{10}{33}\right)\)	\(e\left(\frac{61}{66}\right)\)	\(e\left(\frac{20}{33}\right)\)	\(e\left(\frac{16}{33}\right)\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{28}{33}\right)\)	\(e\left(\frac{26}{33}\right)\)	\(e\left(\frac{13}{66}\right)\)	\(e\left(\frac{35}{66}\right)\)
\(\chi_{2093}(41,\cdot)\)	2093.ee	132	yes	\(1\)	\(1\)	\(e\left(\frac{23}{132}\right)\)	\(e\left(\frac{37}{66}\right)\)	\(e\left(\frac{23}{66}\right)\)	\(e\left(\frac{35}{44}\right)\)	\(e\left(\frac{97}{132}\right)\)	\(e\left(\frac{23}{44}\right)\)	\(e\left(\frac{4}{33}\right)\)	\(e\left(\frac{32}{33}\right)\)	\(e\left(\frac{65}{132}\right)\)	\(e\left(\frac{10}{11}\right)\)

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L-functions

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First 32 of 1584 characters

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.