LMFDB - Group of Dirichlet characters of modulus 2366

Show commands: Magma / Pari/GP / SageMath

comment:Define the Dirichlet group

sage:G = DirichletGroup(2366)

gp:g = idealstar(,2366,2)

magma:G = FullDirichletGroup(2366);

Character group

Order	=	936	comment:Order sage:G.order() gp:g.no magma:Order(G);
Structure	=	$C_{6}\times C_{156}$	comment:Group structure sage:sorted(g.order() for g in G.gens()) gp:g.cyc magma:PrimaryInvariants(G);
Generators	=	$\chi_{2366}(339,\cdot)$, $\chi_{2366}(2199,\cdot)$	comment:Generators sage:G.gens() gp:g.gen magma:Generators(G);

First 32 of 936 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	$-1$	$1$	$3$	$5$	$9$	$11$	$15$	$17$	$19$	$23$	$25$	$27$
$\chi_{2366}(1,\cdot)$	2366.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{2366}(3,\cdot)$	2366.by	78	no	$-1$	$1$	$e\left(\frac{19}{26}\right)$	$e\left(\frac{77}{78}\right)$	$e\left(\frac{6}{13}\right)$	$e\left(\frac{7}{13}\right)$	$e\left(\frac{28}{39}\right)$	$e\left(\frac{17}{78}\right)$	$-1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{38}{39}\right)$	$e\left(\frac{5}{26}\right)$
$\chi_{2366}(5,\cdot)$	2366.cc	156	no	$1$	$1$	$e\left(\frac{77}{78}\right)$	$e\left(\frac{107}{156}\right)$	$e\left(\frac{38}{39}\right)$	$e\left(\frac{43}{156}\right)$	$e\left(\frac{35}{52}\right)$	$e\left(\frac{10}{39}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{29}{78}\right)$	$e\left(\frac{25}{26}\right)$
$\chi_{2366}(9,\cdot)$	2366.bi	39	no	$1$	$1$	$e\left(\frac{6}{13}\right)$	$e\left(\frac{38}{39}\right)$	$e\left(\frac{12}{13}\right)$	$e\left(\frac{1}{13}\right)$	$e\left(\frac{17}{39}\right)$	$e\left(\frac{17}{39}\right)$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{37}{39}\right)$	$e\left(\frac{5}{13}\right)$
$\chi_{2366}(11,\cdot)$	2366.ca	156	no	$-1$	$1$	$e\left(\frac{7}{13}\right)$	$e\left(\frac{43}{156}\right)$	$e\left(\frac{1}{13}\right)$	$e\left(\frac{35}{52}\right)$	$e\left(\frac{127}{156}\right)$	$e\left(\frac{5}{78}\right)$	$i$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{43}{78}\right)$	$e\left(\frac{8}{13}\right)$
$\chi_{2366}(15,\cdot)$	2366.cf	156	no	$-1$	$1$	$e\left(\frac{28}{39}\right)$	$e\left(\frac{35}{52}\right)$	$e\left(\frac{17}{39}\right)$	$e\left(\frac{127}{156}\right)$	$e\left(\frac{61}{156}\right)$	$e\left(\frac{37}{78}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{9}{26}\right)$	$e\left(\frac{2}{13}\right)$
$\chi_{2366}(17,\cdot)$	2366.bs	78	no	$-1$	$1$	$e\left(\frac{17}{78}\right)$	$e\left(\frac{10}{39}\right)$	$e\left(\frac{17}{39}\right)$	$e\left(\frac{5}{78}\right)$	$e\left(\frac{37}{78}\right)$	$e\left(\frac{21}{26}\right)$	$e\left(\frac{2}{3}\right)$	$1$	$e\left(\frac{20}{39}\right)$	$e\left(\frac{17}{26}\right)$
$\chi_{2366}(19,\cdot)$	2366.w	12	no	$1$	$1$	$-1$	$e\left(\frac{11}{12}\right)$	$1$	$i$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{2}{3}\right)$	$i$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{6}\right)$	$-1$
$\chi_{2366}(23,\cdot)$	2366.o	6	no	$1$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$	$1$	$e\left(\frac{5}{6}\right)$	$1$	$e\left(\frac{1}{3}\right)$	$1$
$\chi_{2366}(25,\cdot)$	2366.bw	78	no	$1$	$1$	$e\left(\frac{38}{39}\right)$	$e\left(\frac{29}{78}\right)$	$e\left(\frac{37}{39}\right)$	$e\left(\frac{43}{78}\right)$	$e\left(\frac{9}{26}\right)$	$e\left(\frac{20}{39}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{29}{39}\right)$	$e\left(\frac{12}{13}\right)$
$\chi_{2366}(27,\cdot)$	2366.bh	26	no	$-1$	$1$	$e\left(\frac{5}{26}\right)$	$e\left(\frac{25}{26}\right)$	$e\left(\frac{5}{13}\right)$	$e\left(\frac{8}{13}\right)$	$e\left(\frac{2}{13}\right)$	$e\left(\frac{17}{26}\right)$	$-1$	$1$	$e\left(\frac{12}{13}\right)$	$e\left(\frac{15}{26}\right)$
$\chi_{2366}(29,\cdot)$	2366.bj	39	no	$1$	$1$	$e\left(\frac{31}{39}\right)$	$e\left(\frac{4}{13}\right)$	$e\left(\frac{23}{39}\right)$	$e\left(\frac{16}{39}\right)$	$e\left(\frac{4}{39}\right)$	$e\left(\frac{17}{39}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{8}{13}\right)$	$e\left(\frac{5}{13}\right)$
$\chi_{2366}(31,\cdot)$	2366.cc	156	no	$1$	$1$	$e\left(\frac{67}{78}\right)$	$e\left(\frac{7}{156}\right)$	$e\left(\frac{28}{39}\right)$	$e\left(\frac{83}{156}\right)$	$e\left(\frac{47}{52}\right)$	$e\left(\frac{32}{39}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{7}{78}\right)$	$e\left(\frac{15}{26}\right)$
$\chi_{2366}(33,\cdot)$	2366.ch	156	no	$1$	$1$	$e\left(\frac{7}{26}\right)$	$e\left(\frac{41}{156}\right)$	$e\left(\frac{7}{13}\right)$	$e\left(\frac{11}{52}\right)$	$e\left(\frac{83}{156}\right)$	$e\left(\frac{11}{39}\right)$	$-i$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{41}{78}\right)$	$e\left(\frac{21}{26}\right)$
$\chi_{2366}(37,\cdot)$	2366.cg	156	no	$-1$	$1$	$e\left(\frac{14}{39}\right)$	$e\left(\frac{59}{156}\right)$	$e\left(\frac{28}{39}\right)$	$e\left(\frac{5}{156}\right)$	$e\left(\frac{115}{156}\right)$	$e\left(\frac{17}{26}\right)$	$e\left(\frac{7}{12}\right)$	$-1$	$e\left(\frac{59}{78}\right)$	$e\left(\frac{1}{13}\right)$
$\chi_{2366}(41,\cdot)$	2366.cd	156	no	$1$	$1$	$e\left(\frac{5}{78}\right)$	$e\left(\frac{21}{52}\right)$	$e\left(\frac{5}{39}\right)$	$e\left(\frac{19}{156}\right)$	$e\left(\frac{73}{156}\right)$	$e\left(\frac{2}{39}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{21}{26}\right)$	$e\left(\frac{5}{26}\right)$
$\chi_{2366}(43,\cdot)$	2366.bx	78	no	$1$	$1$	$e\left(\frac{38}{39}\right)$	$e\left(\frac{1}{26}\right)$	$e\left(\frac{37}{39}\right)$	$e\left(\frac{43}{78}\right)$	$e\left(\frac{1}{78}\right)$	$e\left(\frac{7}{39}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{13}\right)$	$e\left(\frac{12}{13}\right)$
$\chi_{2366}(45,\cdot)$	2366.cb	156	no	$1$	$1$	$e\left(\frac{35}{78}\right)$	$e\left(\frac{103}{156}\right)$	$e\left(\frac{35}{39}\right)$	$e\left(\frac{55}{156}\right)$	$e\left(\frac{17}{156}\right)$	$e\left(\frac{9}{13}\right)$	$e\left(\frac{11}{12}\right)$	$-1$	$e\left(\frac{25}{78}\right)$	$e\left(\frac{9}{26}\right)$
$\chi_{2366}(47,\cdot)$	2366.cc	156	no	$1$	$1$	$e\left(\frac{71}{78}\right)$	$e\left(\frac{125}{156}\right)$	$e\left(\frac{32}{39}\right)$	$e\left(\frac{145}{156}\right)$	$e\left(\frac{37}{52}\right)$	$e\left(\frac{31}{39}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{47}{78}\right)$	$e\left(\frac{19}{26}\right)$
$\chi_{2366}(51,\cdot)$	2366.bw	78	no	$1$	$1$	$e\left(\frac{37}{39}\right)$	$e\left(\frac{19}{78}\right)$	$e\left(\frac{35}{39}\right)$	$e\left(\frac{47}{78}\right)$	$e\left(\frac{5}{26}\right)$	$e\left(\frac{1}{39}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{19}{39}\right)$	$e\left(\frac{11}{13}\right)$
$\chi_{2366}(53,\cdot)$	2366.bk	39	no	$1$	$1$	$e\left(\frac{2}{39}\right)$	$e\left(\frac{10}{39}\right)$	$e\left(\frac{4}{39}\right)$	$e\left(\frac{35}{39}\right)$	$e\left(\frac{4}{13}\right)$	$e\left(\frac{38}{39}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{20}{39}\right)$	$e\left(\frac{2}{13}\right)$
$\chi_{2366}(55,\cdot)$	2366.bu	78	no	$-1$	$1$	$e\left(\frac{41}{78}\right)$	$e\left(\frac{25}{26}\right)$	$e\left(\frac{2}{39}\right)$	$e\left(\frac{37}{39}\right)$	$e\left(\frac{19}{39}\right)$	$e\left(\frac{25}{78}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{12}{13}\right)$	$e\left(\frac{15}{26}\right)$
$\chi_{2366}(57,\cdot)$	2366.bm	52	no	$-1$	$1$	$e\left(\frac{3}{13}\right)$	$e\left(\frac{47}{52}\right)$	$e\left(\frac{6}{13}\right)$	$e\left(\frac{41}{52}\right)$	$e\left(\frac{7}{52}\right)$	$e\left(\frac{23}{26}\right)$	$-i$	$-1$	$e\left(\frac{21}{26}\right)$	$e\left(\frac{9}{13}\right)$
$\chi_{2366}(59,\cdot)$	2366.cb	156	no	$1$	$1$	$e\left(\frac{77}{78}\right)$	$e\left(\frac{133}{156}\right)$	$e\left(\frac{38}{39}\right)$	$e\left(\frac{121}{156}\right)$	$e\left(\frac{131}{156}\right)$	$e\left(\frac{12}{13}\right)$	$e\left(\frac{5}{12}\right)$	$-1$	$e\left(\frac{55}{78}\right)$	$e\left(\frac{25}{26}\right)$
$\chi_{2366}(61,\cdot)$	2366.by	78	no	$-1$	$1$	$e\left(\frac{3}{26}\right)$	$e\left(\frac{19}{78}\right)$	$e\left(\frac{3}{13}\right)$	$e\left(\frac{10}{13}\right)$	$e\left(\frac{14}{39}\right)$	$e\left(\frac{67}{78}\right)$	$-1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{19}{39}\right)$	$e\left(\frac{9}{26}\right)$
$\chi_{2366}(67,\cdot)$	2366.ca	156	no	$-1$	$1$	$e\left(\frac{1}{13}\right)$	$e\left(\frac{73}{156}\right)$	$e\left(\frac{2}{13}\right)$	$e\left(\frac{5}{52}\right)$	$e\left(\frac{85}{156}\right)$	$e\left(\frac{23}{78}\right)$	$-i$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{73}{78}\right)$	$e\left(\frac{3}{13}\right)$
$\chi_{2366}(69,\cdot)$	2366.bp	78	no	$-1$	$1$	$e\left(\frac{31}{78}\right)$	$e\left(\frac{2}{13}\right)$	$e\left(\frac{31}{39}\right)$	$e\left(\frac{55}{78}\right)$	$e\left(\frac{43}{78}\right)$	$e\left(\frac{17}{78}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{4}{13}\right)$	$e\left(\frac{5}{26}\right)$
$\chi_{2366}(71,\cdot)$	2366.cf	156	no	$-1$	$1$	$e\left(\frac{35}{39}\right)$	$e\left(\frac{47}{52}\right)$	$e\left(\frac{31}{39}\right)$	$e\left(\frac{71}{156}\right)$	$e\left(\frac{125}{156}\right)$	$e\left(\frac{17}{78}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{21}{26}\right)$	$e\left(\frac{9}{13}\right)$
$\chi_{2366}(73,\cdot)$	2366.cc	156	no	$1$	$1$	$e\left(\frac{55}{78}\right)$	$e\left(\frac{121}{156}\right)$	$e\left(\frac{16}{39}\right)$	$e\left(\frac{53}{156}\right)$	$e\left(\frac{25}{52}\right)$	$e\left(\frac{35}{39}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{43}{78}\right)$	$e\left(\frac{3}{26}\right)$
$\chi_{2366}(75,\cdot)$	2366.bs	78	no	$-1$	$1$	$e\left(\frac{55}{78}\right)$	$e\left(\frac{14}{39}\right)$	$e\left(\frac{16}{39}\right)$	$e\left(\frac{7}{78}\right)$	$e\left(\frac{5}{78}\right)$	$e\left(\frac{19}{26}\right)$	$e\left(\frac{1}{3}\right)$	$1$	$e\left(\frac{28}{39}\right)$	$e\left(\frac{3}{26}\right)$
$\chi_{2366}(79,\cdot)$	2366.bk	39	no	$1$	$1$	$e\left(\frac{16}{39}\right)$	$e\left(\frac{2}{39}\right)$	$e\left(\frac{32}{39}\right)$	$e\left(\frac{7}{39}\right)$	$e\left(\frac{6}{13}\right)$	$e\left(\frac{31}{39}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{4}{39}\right)$	$e\left(\frac{3}{13}\right)$
$\chi_{2366}(81,\cdot)$	2366.bi	39	no	$1$	$1$	$e\left(\frac{12}{13}\right)$	$e\left(\frac{37}{39}\right)$	$e\left(\frac{11}{13}\right)$	$e\left(\frac{2}{13}\right)$	$e\left(\frac{34}{39}\right)$	$e\left(\frac{34}{39}\right)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{35}{39}\right)$	$e\left(\frac{10}{13}\right)$

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Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Modulus	$2366$
Structure	\(C_{6}\times C_{156}\)
Order	$936$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(3\)	\(5\)	\(9\)	\(11\)	\(15\)	\(17\)	\(19\)	\(23\)	\(25\)	\(27\)
\(\chi_{2366}(1,\cdot)\)	2366.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{2366}(3,\cdot)\)	2366.by	78	no	\(-1\)	\(1\)	\(e\left(\frac{19}{26}\right)\)	\(e\left(\frac{77}{78}\right)\)	\(e\left(\frac{6}{13}\right)\)	\(e\left(\frac{7}{13}\right)\)	\(e\left(\frac{28}{39}\right)\)	\(e\left(\frac{17}{78}\right)\)	\(-1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{38}{39}\right)\)	\(e\left(\frac{5}{26}\right)\)
\(\chi_{2366}(5,\cdot)\)	2366.cc	156	no	\(1\)	\(1\)	\(e\left(\frac{77}{78}\right)\)	\(e\left(\frac{107}{156}\right)\)	\(e\left(\frac{38}{39}\right)\)	\(e\left(\frac{43}{156}\right)\)	\(e\left(\frac{35}{52}\right)\)	\(e\left(\frac{10}{39}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{29}{78}\right)\)	\(e\left(\frac{25}{26}\right)\)
\(\chi_{2366}(9,\cdot)\)	2366.bi	39	no	\(1\)	\(1\)	\(e\left(\frac{6}{13}\right)\)	\(e\left(\frac{38}{39}\right)\)	\(e\left(\frac{12}{13}\right)\)	\(e\left(\frac{1}{13}\right)\)	\(e\left(\frac{17}{39}\right)\)	\(e\left(\frac{17}{39}\right)\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{37}{39}\right)\)	\(e\left(\frac{5}{13}\right)\)
\(\chi_{2366}(11,\cdot)\)	2366.ca	156	no	\(-1\)	\(1\)	\(e\left(\frac{7}{13}\right)\)	\(e\left(\frac{43}{156}\right)\)	\(e\left(\frac{1}{13}\right)\)	\(e\left(\frac{35}{52}\right)\)	\(e\left(\frac{127}{156}\right)\)	\(e\left(\frac{5}{78}\right)\)	\(i\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{43}{78}\right)\)	\(e\left(\frac{8}{13}\right)\)
\(\chi_{2366}(15,\cdot)\)	2366.cf	156	no	\(-1\)	\(1\)	\(e\left(\frac{28}{39}\right)\)	\(e\left(\frac{35}{52}\right)\)	\(e\left(\frac{17}{39}\right)\)	\(e\left(\frac{127}{156}\right)\)	\(e\left(\frac{61}{156}\right)\)	\(e\left(\frac{37}{78}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{9}{26}\right)\)	\(e\left(\frac{2}{13}\right)\)
\(\chi_{2366}(17,\cdot)\)	2366.bs	78	no	\(-1\)	\(1\)	\(e\left(\frac{17}{78}\right)\)	\(e\left(\frac{10}{39}\right)\)	\(e\left(\frac{17}{39}\right)\)	\(e\left(\frac{5}{78}\right)\)	\(e\left(\frac{37}{78}\right)\)	\(e\left(\frac{21}{26}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(1\)	\(e\left(\frac{20}{39}\right)\)	\(e\left(\frac{17}{26}\right)\)
\(\chi_{2366}(19,\cdot)\)	2366.w	12	no	\(1\)	\(1\)	\(-1\)	\(e\left(\frac{11}{12}\right)\)	\(1\)	\(i\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(i\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(-1\)
\(\chi_{2366}(23,\cdot)\)	2366.o	6	no	\(1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(1\)
\(\chi_{2366}(25,\cdot)\)	2366.bw	78	no	\(1\)	\(1\)	\(e\left(\frac{38}{39}\right)\)	\(e\left(\frac{29}{78}\right)\)	\(e\left(\frac{37}{39}\right)\)	\(e\left(\frac{43}{78}\right)\)	\(e\left(\frac{9}{26}\right)\)	\(e\left(\frac{20}{39}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{29}{39}\right)\)	\(e\left(\frac{12}{13}\right)\)
\(\chi_{2366}(27,\cdot)\)	2366.bh	26	no	\(-1\)	\(1\)	\(e\left(\frac{5}{26}\right)\)	\(e\left(\frac{25}{26}\right)\)	\(e\left(\frac{5}{13}\right)\)	\(e\left(\frac{8}{13}\right)\)	\(e\left(\frac{2}{13}\right)\)	\(e\left(\frac{17}{26}\right)\)	\(-1\)	\(1\)	\(e\left(\frac{12}{13}\right)\)	\(e\left(\frac{15}{26}\right)\)
\(\chi_{2366}(29,\cdot)\)	2366.bj	39	no	\(1\)	\(1\)	\(e\left(\frac{31}{39}\right)\)	\(e\left(\frac{4}{13}\right)\)	\(e\left(\frac{23}{39}\right)\)	\(e\left(\frac{16}{39}\right)\)	\(e\left(\frac{4}{39}\right)\)	\(e\left(\frac{17}{39}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{8}{13}\right)\)	\(e\left(\frac{5}{13}\right)\)
\(\chi_{2366}(31,\cdot)\)	2366.cc	156	no	\(1\)	\(1\)	\(e\left(\frac{67}{78}\right)\)	\(e\left(\frac{7}{156}\right)\)	\(e\left(\frac{28}{39}\right)\)	\(e\left(\frac{83}{156}\right)\)	\(e\left(\frac{47}{52}\right)\)	\(e\left(\frac{32}{39}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{7}{78}\right)\)	\(e\left(\frac{15}{26}\right)\)
\(\chi_{2366}(33,\cdot)\)	2366.ch	156	no	\(1\)	\(1\)	\(e\left(\frac{7}{26}\right)\)	\(e\left(\frac{41}{156}\right)\)	\(e\left(\frac{7}{13}\right)\)	\(e\left(\frac{11}{52}\right)\)	\(e\left(\frac{83}{156}\right)\)	\(e\left(\frac{11}{39}\right)\)	\(-i\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{41}{78}\right)\)	\(e\left(\frac{21}{26}\right)\)
\(\chi_{2366}(37,\cdot)\)	2366.cg	156	no	\(-1\)	\(1\)	\(e\left(\frac{14}{39}\right)\)	\(e\left(\frac{59}{156}\right)\)	\(e\left(\frac{28}{39}\right)\)	\(e\left(\frac{5}{156}\right)\)	\(e\left(\frac{115}{156}\right)\)	\(e\left(\frac{17}{26}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(-1\)	\(e\left(\frac{59}{78}\right)\)	\(e\left(\frac{1}{13}\right)\)
\(\chi_{2366}(41,\cdot)\)	2366.cd	156	no	\(1\)	\(1\)	\(e\left(\frac{5}{78}\right)\)	\(e\left(\frac{21}{52}\right)\)	\(e\left(\frac{5}{39}\right)\)	\(e\left(\frac{19}{156}\right)\)	\(e\left(\frac{73}{156}\right)\)	\(e\left(\frac{2}{39}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{21}{26}\right)\)	\(e\left(\frac{5}{26}\right)\)
\(\chi_{2366}(43,\cdot)\)	2366.bx	78	no	\(1\)	\(1\)	\(e\left(\frac{38}{39}\right)\)	\(e\left(\frac{1}{26}\right)\)	\(e\left(\frac{37}{39}\right)\)	\(e\left(\frac{43}{78}\right)\)	\(e\left(\frac{1}{78}\right)\)	\(e\left(\frac{7}{39}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{13}\right)\)	\(e\left(\frac{12}{13}\right)\)
\(\chi_{2366}(45,\cdot)\)	2366.cb	156	no	\(1\)	\(1\)	\(e\left(\frac{35}{78}\right)\)	\(e\left(\frac{103}{156}\right)\)	\(e\left(\frac{35}{39}\right)\)	\(e\left(\frac{55}{156}\right)\)	\(e\left(\frac{17}{156}\right)\)	\(e\left(\frac{9}{13}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(-1\)	\(e\left(\frac{25}{78}\right)\)	\(e\left(\frac{9}{26}\right)\)
\(\chi_{2366}(47,\cdot)\)	2366.cc	156	no	\(1\)	\(1\)	\(e\left(\frac{71}{78}\right)\)	\(e\left(\frac{125}{156}\right)\)	\(e\left(\frac{32}{39}\right)\)	\(e\left(\frac{145}{156}\right)\)	\(e\left(\frac{37}{52}\right)\)	\(e\left(\frac{31}{39}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{47}{78}\right)\)	\(e\left(\frac{19}{26}\right)\)
\(\chi_{2366}(51,\cdot)\)	2366.bw	78	no	\(1\)	\(1\)	\(e\left(\frac{37}{39}\right)\)	\(e\left(\frac{19}{78}\right)\)	\(e\left(\frac{35}{39}\right)\)	\(e\left(\frac{47}{78}\right)\)	\(e\left(\frac{5}{26}\right)\)	\(e\left(\frac{1}{39}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{19}{39}\right)\)	\(e\left(\frac{11}{13}\right)\)
\(\chi_{2366}(53,\cdot)\)	2366.bk	39	no	\(1\)	\(1\)	\(e\left(\frac{2}{39}\right)\)	\(e\left(\frac{10}{39}\right)\)	\(e\left(\frac{4}{39}\right)\)	\(e\left(\frac{35}{39}\right)\)	\(e\left(\frac{4}{13}\right)\)	\(e\left(\frac{38}{39}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{20}{39}\right)\)	\(e\left(\frac{2}{13}\right)\)
\(\chi_{2366}(55,\cdot)\)	2366.bu	78	no	\(-1\)	\(1\)	\(e\left(\frac{41}{78}\right)\)	\(e\left(\frac{25}{26}\right)\)	\(e\left(\frac{2}{39}\right)\)	\(e\left(\frac{37}{39}\right)\)	\(e\left(\frac{19}{39}\right)\)	\(e\left(\frac{25}{78}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{12}{13}\right)\)	\(e\left(\frac{15}{26}\right)\)
\(\chi_{2366}(57,\cdot)\)	2366.bm	52	no	\(-1\)	\(1\)	\(e\left(\frac{3}{13}\right)\)	\(e\left(\frac{47}{52}\right)\)	\(e\left(\frac{6}{13}\right)\)	\(e\left(\frac{41}{52}\right)\)	\(e\left(\frac{7}{52}\right)\)	\(e\left(\frac{23}{26}\right)\)	\(-i\)	\(-1\)	\(e\left(\frac{21}{26}\right)\)	\(e\left(\frac{9}{13}\right)\)
\(\chi_{2366}(59,\cdot)\)	2366.cb	156	no	\(1\)	\(1\)	\(e\left(\frac{77}{78}\right)\)	\(e\left(\frac{133}{156}\right)\)	\(e\left(\frac{38}{39}\right)\)	\(e\left(\frac{121}{156}\right)\)	\(e\left(\frac{131}{156}\right)\)	\(e\left(\frac{12}{13}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(-1\)	\(e\left(\frac{55}{78}\right)\)	\(e\left(\frac{25}{26}\right)\)
\(\chi_{2366}(61,\cdot)\)	2366.by	78	no	\(-1\)	\(1\)	\(e\left(\frac{3}{26}\right)\)	\(e\left(\frac{19}{78}\right)\)	\(e\left(\frac{3}{13}\right)\)	\(e\left(\frac{10}{13}\right)\)	\(e\left(\frac{14}{39}\right)\)	\(e\left(\frac{67}{78}\right)\)	\(-1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{19}{39}\right)\)	\(e\left(\frac{9}{26}\right)\)
\(\chi_{2366}(67,\cdot)\)	2366.ca	156	no	\(-1\)	\(1\)	\(e\left(\frac{1}{13}\right)\)	\(e\left(\frac{73}{156}\right)\)	\(e\left(\frac{2}{13}\right)\)	\(e\left(\frac{5}{52}\right)\)	\(e\left(\frac{85}{156}\right)\)	\(e\left(\frac{23}{78}\right)\)	\(-i\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{73}{78}\right)\)	\(e\left(\frac{3}{13}\right)\)
\(\chi_{2366}(69,\cdot)\)	2366.bp	78	no	\(-1\)	\(1\)	\(e\left(\frac{31}{78}\right)\)	\(e\left(\frac{2}{13}\right)\)	\(e\left(\frac{31}{39}\right)\)	\(e\left(\frac{55}{78}\right)\)	\(e\left(\frac{43}{78}\right)\)	\(e\left(\frac{17}{78}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{4}{13}\right)\)	\(e\left(\frac{5}{26}\right)\)
\(\chi_{2366}(71,\cdot)\)	2366.cf	156	no	\(-1\)	\(1\)	\(e\left(\frac{35}{39}\right)\)	\(e\left(\frac{47}{52}\right)\)	\(e\left(\frac{31}{39}\right)\)	\(e\left(\frac{71}{156}\right)\)	\(e\left(\frac{125}{156}\right)\)	\(e\left(\frac{17}{78}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{21}{26}\right)\)	\(e\left(\frac{9}{13}\right)\)
\(\chi_{2366}(73,\cdot)\)	2366.cc	156	no	\(1\)	\(1\)	\(e\left(\frac{55}{78}\right)\)	\(e\left(\frac{121}{156}\right)\)	\(e\left(\frac{16}{39}\right)\)	\(e\left(\frac{53}{156}\right)\)	\(e\left(\frac{25}{52}\right)\)	\(e\left(\frac{35}{39}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{43}{78}\right)\)	\(e\left(\frac{3}{26}\right)\)
\(\chi_{2366}(75,\cdot)\)	2366.bs	78	no	\(-1\)	\(1\)	\(e\left(\frac{55}{78}\right)\)	\(e\left(\frac{14}{39}\right)\)	\(e\left(\frac{16}{39}\right)\)	\(e\left(\frac{7}{78}\right)\)	\(e\left(\frac{5}{78}\right)\)	\(e\left(\frac{19}{26}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(1\)	\(e\left(\frac{28}{39}\right)\)	\(e\left(\frac{3}{26}\right)\)
\(\chi_{2366}(79,\cdot)\)	2366.bk	39	no	\(1\)	\(1\)	\(e\left(\frac{16}{39}\right)\)	\(e\left(\frac{2}{39}\right)\)	\(e\left(\frac{32}{39}\right)\)	\(e\left(\frac{7}{39}\right)\)	\(e\left(\frac{6}{13}\right)\)	\(e\left(\frac{31}{39}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{4}{39}\right)\)	\(e\left(\frac{3}{13}\right)\)
\(\chi_{2366}(81,\cdot)\)	2366.bi	39	no	\(1\)	\(1\)	\(e\left(\frac{12}{13}\right)\)	\(e\left(\frac{37}{39}\right)\)	\(e\left(\frac{11}{13}\right)\)	\(e\left(\frac{2}{13}\right)\)	\(e\left(\frac{34}{39}\right)\)	\(e\left(\frac{34}{39}\right)\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{35}{39}\right)\)	\(e\left(\frac{10}{13}\right)\)

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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.