LMFDB - Group of Dirichlet characters of modulus 4740

Show commands: Magma / Pari/GP / SageMath

comment:Define the Dirichlet group

sage:G = DirichletGroup(4740)

gp:g = idealstar(,4740,2)

magma:G := FullDirichletGroup(4740);

Character group

Order	=	1248	comment:Order sage:G.order() gp:g.no magma:Order(G);
Structure	=	$C_{2}\times C_{2}\times C_{2}\times C_{156}$	comment:Group structure sage:sorted(g.order() for g in G.gens()) gp:g.cyc magma:PrimaryInvariants(AbelianGroup(G));
Generators	=	$\chi_{4740}(2371,\cdot)$, $\chi_{4740}(3161,\cdot)$, $\chi_{4740}(1897,\cdot)$, $\chi_{4740}(1741,\cdot)$	comment:Generators sage:G.gens() gp:g.gen magma:Generators(G);

First 32 of 1248 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	$-1$	$1$	$7$	$11$	$13$	$17$	$19$	$23$	$29$	$31$	$37$	$41$
$\chi_{4740}(1,\cdot)$	4740.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{4740}(7,\cdot)$	4740.dn	156	no	$-1$	$1$	$e\left(\frac{119}{156}\right)$	$e\left(\frac{55}{78}\right)$	$e\left(\frac{133}{156}\right)$	$e\left(\frac{27}{52}\right)$	$e\left(\frac{29}{39}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{38}{39}\right)$	$e\left(\frac{43}{78}\right)$	$e\left(\frac{25}{156}\right)$	$e\left(\frac{25}{26}\right)$
$\chi_{4740}(11,\cdot)$	4740.db	78	no	$1$	$1$	$e\left(\frac{55}{78}\right)$	$e\left(\frac{11}{39}\right)$	$e\left(\frac{25}{39}\right)$	$e\left(\frac{21}{26}\right)$	$e\left(\frac{31}{78}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{7}{78}\right)$	$e\left(\frac{25}{78}\right)$	$e\left(\frac{22}{39}\right)$	$e\left(\frac{23}{26}\right)$
$\chi_{4740}(13,\cdot)$	4740.do	156	no	$-1$	$1$	$e\left(\frac{133}{156}\right)$	$e\left(\frac{25}{39}\right)$	$e\left(\frac{11}{156}\right)$	$e\left(\frac{47}{52}\right)$	$e\left(\frac{35}{78}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{23}{78}\right)$	$e\left(\frac{16}{39}\right)$	$e\left(\frac{5}{156}\right)$	$e\left(\frac{9}{13}\right)$
$\chi_{4740}(17,\cdot)$	4740.cu	52	no	$-1$	$1$	$e\left(\frac{27}{52}\right)$	$e\left(\frac{21}{26}\right)$	$e\left(\frac{47}{52}\right)$	$e\left(\frac{21}{52}\right)$	$e\left(\frac{3}{26}\right)$	$i$	$e\left(\frac{25}{26}\right)$	$e\left(\frac{1}{13}\right)$	$e\left(\frac{19}{52}\right)$	$e\left(\frac{9}{13}\right)$
$\chi_{4740}(19,\cdot)$	4740.dd	78	no	$-1$	$1$	$e\left(\frac{29}{39}\right)$	$e\left(\frac{31}{78}\right)$	$e\left(\frac{35}{78}\right)$	$e\left(\frac{3}{26}\right)$	$e\left(\frac{49}{78}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{20}{39}\right)$	$e\left(\frac{37}{78}\right)$	$e\left(\frac{23}{78}\right)$	$e\left(\frac{10}{13}\right)$
$\chi_{4740}(23,\cdot)$	4740.bo	12	yes	$-1$	$1$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{7}{12}\right)$	$i$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{12}\right)$	$-1$
$\chi_{4740}(29,\cdot)$	4740.de	78	no	$1$	$1$	$e\left(\frac{38}{39}\right)$	$e\left(\frac{7}{78}\right)$	$e\left(\frac{23}{78}\right)$	$e\left(\frac{25}{26}\right)$	$e\left(\frac{20}{39}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{39}\right)$	$e\left(\frac{35}{39}\right)$	$e\left(\frac{7}{39}\right)$	$e\left(\frac{1}{13}\right)$
$\chi_{4740}(31,\cdot)$	4740.cx	78	no	$-1$	$1$	$e\left(\frac{43}{78}\right)$	$e\left(\frac{25}{78}\right)$	$e\left(\frac{16}{39}\right)$	$e\left(\frac{1}{13}\right)$	$e\left(\frac{37}{78}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{35}{39}\right)$	$e\left(\frac{55}{78}\right)$	$e\left(\frac{25}{39}\right)$	$e\left(\frac{11}{13}\right)$
$\chi_{4740}(37,\cdot)$	4740.dp	156	no	$1$	$1$	$e\left(\frac{25}{156}\right)$	$e\left(\frac{22}{39}\right)$	$e\left(\frac{5}{156}\right)$	$e\left(\frac{19}{52}\right)$	$e\left(\frac{23}{78}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{7}{39}\right)$	$e\left(\frac{25}{39}\right)$	$e\left(\frac{137}{156}\right)$	$e\left(\frac{7}{26}\right)$
$\chi_{4740}(41,\cdot)$	4740.ci	26	no	$1$	$1$	$e\left(\frac{25}{26}\right)$	$e\left(\frac{23}{26}\right)$	$e\left(\frac{9}{13}\right)$	$e\left(\frac{9}{13}\right)$	$e\left(\frac{10}{13}\right)$	$-1$	$e\left(\frac{1}{13}\right)$	$e\left(\frac{11}{13}\right)$	$e\left(\frac{7}{26}\right)$	$e\left(\frac{8}{13}\right)$
$\chi_{4740}(43,\cdot)$	4740.dn	156	no	$-1$	$1$	$e\left(\frac{85}{156}\right)$	$e\left(\frac{17}{78}\right)$	$e\left(\frac{95}{156}\right)$	$e\left(\frac{49}{52}\right)$	$e\left(\frac{4}{39}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{16}{39}\right)$	$e\left(\frac{53}{78}\right)$	$e\left(\frac{107}{156}\right)$	$e\left(\frac{3}{26}\right)$
$\chi_{4740}(47,\cdot)$	4740.dq	156	yes	$1$	$1$	$e\left(\frac{131}{156}\right)$	$e\left(\frac{17}{39}\right)$	$e\left(\frac{73}{156}\right)$	$e\left(\frac{33}{52}\right)$	$e\left(\frac{8}{39}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{25}{78}\right)$	$e\left(\frac{67}{78}\right)$	$e\left(\frac{97}{156}\right)$	$e\left(\frac{3}{13}\right)$
$\chi_{4740}(49,\cdot)$	4740.da	78	no	$1$	$1$	$e\left(\frac{41}{78}\right)$	$e\left(\frac{16}{39}\right)$	$e\left(\frac{55}{78}\right)$	$e\left(\frac{1}{26}\right)$	$e\left(\frac{19}{39}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{37}{39}\right)$	$e\left(\frac{4}{39}\right)$	$e\left(\frac{25}{78}\right)$	$e\left(\frac{12}{13}\right)$
$\chi_{4740}(53,\cdot)$	4740.dk	156	no	$-1$	$1$	$e\left(\frac{11}{156}\right)$	$e\left(\frac{49}{78}\right)$	$e\left(\frac{127}{156}\right)$	$e\left(\frac{51}{52}\right)$	$e\left(\frac{7}{78}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{67}{78}\right)$	$e\left(\frac{11}{39}\right)$	$e\left(\frac{79}{156}\right)$	$e\left(\frac{7}{13}\right)$
$\chi_{4740}(59,\cdot)$	4740.cz	78	yes	$-1$	$1$	$e\left(\frac{5}{78}\right)$	$e\left(\frac{1}{39}\right)$	$e\left(\frac{1}{78}\right)$	$e\left(\frac{9}{26}\right)$	$e\left(\frac{17}{78}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{34}{39}\right)$	$e\left(\frac{59}{78}\right)$	$e\left(\frac{2}{39}\right)$	$e\left(\frac{4}{13}\right)$
$\chi_{4740}(61,\cdot)$	4740.ce	26	no	$-1$	$1$	$e\left(\frac{15}{26}\right)$	$e\left(\frac{3}{13}\right)$	$e\left(\frac{8}{13}\right)$	$e\left(\frac{3}{26}\right)$	$e\left(\frac{6}{13}\right)$	$1$	$e\left(\frac{9}{26}\right)$	$e\left(\frac{4}{13}\right)$	$e\left(\frac{25}{26}\right)$	$e\left(\frac{7}{26}\right)$
$\chi_{4740}(67,\cdot)$	4740.cs	52	no	$1$	$1$	$e\left(\frac{19}{52}\right)$	$e\left(\frac{9}{26}\right)$	$e\left(\frac{35}{52}\right)$	$e\left(\frac{9}{52}\right)$	$e\left(\frac{9}{13}\right)$	$i$	$e\left(\frac{7}{26}\right)$	$e\left(\frac{25}{26}\right)$	$e\left(\frac{49}{52}\right)$	$e\left(\frac{2}{13}\right)$
$\chi_{4740}(71,\cdot)$	4740.bx	26	no	$-1$	$1$	$e\left(\frac{2}{13}\right)$	$e\left(\frac{6}{13}\right)$	$e\left(\frac{3}{13}\right)$	$e\left(\frac{3}{13}\right)$	$e\left(\frac{11}{26}\right)$	$1$	$e\left(\frac{9}{13}\right)$	$e\left(\frac{3}{26}\right)$	$e\left(\frac{11}{26}\right)$	$e\left(\frac{7}{13}\right)$
$\chi_{4740}(73,\cdot)$	4740.do	156	no	$-1$	$1$	$e\left(\frac{101}{156}\right)$	$e\left(\frac{14}{39}\right)$	$e\left(\frac{67}{156}\right)$	$e\left(\frac{31}{52}\right)$	$e\left(\frac{43}{78}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{55}{78}\right)$	$e\left(\frac{23}{39}\right)$	$e\left(\frac{73}{156}\right)$	$e\left(\frac{4}{13}\right)$
$\chi_{4740}(77,\cdot)$	4740.dk	156	no	$-1$	$1$	$e\left(\frac{73}{156}\right)$	$e\left(\frac{77}{78}\right)$	$e\left(\frac{77}{156}\right)$	$e\left(\frac{17}{52}\right)$	$e\left(\frac{11}{78}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{5}{78}\right)$	$e\left(\frac{34}{39}\right)$	$e\left(\frac{113}{156}\right)$	$e\left(\frac{11}{13}\right)$
$\chi_{4740}(83,\cdot)$	4740.dr	156	yes	$-1$	$1$	$e\left(\frac{107}{156}\right)$	$e\left(\frac{38}{39}\right)$	$e\left(\frac{115}{156}\right)$	$e\left(\frac{21}{52}\right)$	$e\left(\frac{11}{39}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{5}{39}\right)$	$e\left(\frac{19}{78}\right)$	$e\left(\frac{109}{156}\right)$	$e\left(\frac{5}{26}\right)$
$\chi_{4740}(89,\cdot)$	4740.ck	26	no	$-1$	$1$	$e\left(\frac{9}{26}\right)$	$e\left(\frac{1}{26}\right)$	$e\left(\frac{7}{26}\right)$	$e\left(\frac{10}{13}\right)$	$e\left(\frac{1}{13}\right)$	$1$	$e\left(\frac{21}{26}\right)$	$e\left(\frac{5}{13}\right)$	$e\left(\frac{15}{26}\right)$	$e\left(\frac{25}{26}\right)$
$\chi_{4740}(91,\cdot)$	4740.cb	26	no	$1$	$1$	$e\left(\frac{8}{13}\right)$	$e\left(\frac{9}{26}\right)$	$e\left(\frac{12}{13}\right)$	$e\left(\frac{11}{26}\right)$	$e\left(\frac{5}{26}\right)$	$-1$	$e\left(\frac{7}{26}\right)$	$e\left(\frac{25}{26}\right)$	$e\left(\frac{5}{26}\right)$	$e\left(\frac{17}{26}\right)$
$\chi_{4740}(97,\cdot)$	4740.cq	52	no	$-1$	$1$	$e\left(\frac{17}{52}\right)$	$e\left(\frac{3}{13}\right)$	$e\left(\frac{19}{52}\right)$	$e\left(\frac{45}{52}\right)$	$e\left(\frac{25}{26}\right)$	$-i$	$e\left(\frac{9}{26}\right)$	$e\left(\frac{4}{13}\right)$	$e\left(\frac{37}{52}\right)$	$e\left(\frac{10}{13}\right)$
$\chi_{4740}(101,\cdot)$	4740.ca	26	no	$-1$	$1$	$e\left(\frac{12}{13}\right)$	$e\left(\frac{7}{26}\right)$	$e\left(\frac{5}{13}\right)$	$e\left(\frac{23}{26}\right)$	$e\left(\frac{7}{13}\right)$	$-1$	$e\left(\frac{17}{26}\right)$	$e\left(\frac{9}{13}\right)$	$e\left(\frac{7}{13}\right)$	$e\left(\frac{19}{26}\right)$
$\chi_{4740}(103,\cdot)$	4740.bs	12	no	$-1$	$1$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{11}{12}\right)$	$i$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{11}{12}\right)$	$-1$
$\chi_{4740}(107,\cdot)$	4740.dq	156	yes	$1$	$1$	$e\left(\frac{31}{156}\right)$	$e\left(\frac{7}{39}\right)$	$e\left(\frac{53}{156}\right)$	$e\left(\frac{9}{52}\right)$	$e\left(\frac{1}{39}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{47}{78}\right)$	$e\left(\frac{23}{78}\right)$	$e\left(\frac{17}{156}\right)$	$e\left(\frac{2}{13}\right)$
$\chi_{4740}(109,\cdot)$	4740.di	78	no	$-1$	$1$	$e\left(\frac{1}{39}\right)$	$e\left(\frac{16}{39}\right)$	$e\left(\frac{55}{78}\right)$	$e\left(\frac{7}{13}\right)$	$e\left(\frac{19}{39}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{35}{78}\right)$	$e\left(\frac{4}{39}\right)$	$e\left(\frac{32}{39}\right)$	$e\left(\frac{11}{26}\right)$
$\chi_{4740}(113,\cdot)$	4740.dk	156	no	$-1$	$1$	$e\left(\frac{115}{156}\right)$	$e\left(\frac{23}{78}\right)$	$e\left(\frac{23}{156}\right)$	$e\left(\frac{51}{52}\right)$	$e\left(\frac{59}{78}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{41}{78}\right)$	$e\left(\frac{37}{39}\right)$	$e\left(\frac{131}{156}\right)$	$e\left(\frac{7}{13}\right)$
$\chi_{4740}(119,\cdot)$	4740.dh	78	yes	$1$	$1$	$e\left(\frac{11}{39}\right)$	$e\left(\frac{20}{39}\right)$	$e\left(\frac{59}{78}\right)$	$e\left(\frac{12}{13}\right)$	$e\left(\frac{67}{78}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{73}{78}\right)$	$e\left(\frac{49}{78}\right)$	$e\left(\frac{41}{78}\right)$	$e\left(\frac{17}{26}\right)$
$\chi_{4740}(121,\cdot)$	4740.cm	39	no	$1$	$1$	$e\left(\frac{16}{39}\right)$	$e\left(\frac{22}{39}\right)$	$e\left(\frac{11}{39}\right)$	$e\left(\frac{8}{13}\right)$	$e\left(\frac{31}{39}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{7}{39}\right)$	$e\left(\frac{25}{39}\right)$	$e\left(\frac{5}{39}\right)$	$e\left(\frac{10}{13}\right)$

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Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$ over number fields
Genus 2 curves
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Modulus	$4740$
Structure	\(C_{2}\times C_{2}\times C_{2}\times C_{156}\)
Order	$1248$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(7\)	\(11\)	\(13\)	\(17\)	\(19\)	\(23\)	\(29\)	\(31\)	\(37\)	\(41\)
\(\chi_{4740}(1,\cdot)\)	4740.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{4740}(7,\cdot)\)	4740.dn	156	no	\(-1\)	\(1\)	\(e\left(\frac{119}{156}\right)\)	\(e\left(\frac{55}{78}\right)\)	\(e\left(\frac{133}{156}\right)\)	\(e\left(\frac{27}{52}\right)\)	\(e\left(\frac{29}{39}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{38}{39}\right)\)	\(e\left(\frac{43}{78}\right)\)	\(e\left(\frac{25}{156}\right)\)	\(e\left(\frac{25}{26}\right)\)
\(\chi_{4740}(11,\cdot)\)	4740.db	78	no	\(1\)	\(1\)	\(e\left(\frac{55}{78}\right)\)	\(e\left(\frac{11}{39}\right)\)	\(e\left(\frac{25}{39}\right)\)	\(e\left(\frac{21}{26}\right)\)	\(e\left(\frac{31}{78}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{7}{78}\right)\)	\(e\left(\frac{25}{78}\right)\)	\(e\left(\frac{22}{39}\right)\)	\(e\left(\frac{23}{26}\right)\)
\(\chi_{4740}(13,\cdot)\)	4740.do	156	no	\(-1\)	\(1\)	\(e\left(\frac{133}{156}\right)\)	\(e\left(\frac{25}{39}\right)\)	\(e\left(\frac{11}{156}\right)\)	\(e\left(\frac{47}{52}\right)\)	\(e\left(\frac{35}{78}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{23}{78}\right)\)	\(e\left(\frac{16}{39}\right)\)	\(e\left(\frac{5}{156}\right)\)	\(e\left(\frac{9}{13}\right)\)
\(\chi_{4740}(17,\cdot)\)	4740.cu	52	no	\(-1\)	\(1\)	\(e\left(\frac{27}{52}\right)\)	\(e\left(\frac{21}{26}\right)\)	\(e\left(\frac{47}{52}\right)\)	\(e\left(\frac{21}{52}\right)\)	\(e\left(\frac{3}{26}\right)\)	\(i\)	\(e\left(\frac{25}{26}\right)\)	\(e\left(\frac{1}{13}\right)\)	\(e\left(\frac{19}{52}\right)\)	\(e\left(\frac{9}{13}\right)\)
\(\chi_{4740}(19,\cdot)\)	4740.dd	78	no	\(-1\)	\(1\)	\(e\left(\frac{29}{39}\right)\)	\(e\left(\frac{31}{78}\right)\)	\(e\left(\frac{35}{78}\right)\)	\(e\left(\frac{3}{26}\right)\)	\(e\left(\frac{49}{78}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{20}{39}\right)\)	\(e\left(\frac{37}{78}\right)\)	\(e\left(\frac{23}{78}\right)\)	\(e\left(\frac{10}{13}\right)\)
\(\chi_{4740}(23,\cdot)\)	4740.bo	12	yes	\(-1\)	\(1\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(i\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(-1\)
\(\chi_{4740}(29,\cdot)\)	4740.de	78	no	\(1\)	\(1\)	\(e\left(\frac{38}{39}\right)\)	\(e\left(\frac{7}{78}\right)\)	\(e\left(\frac{23}{78}\right)\)	\(e\left(\frac{25}{26}\right)\)	\(e\left(\frac{20}{39}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{2}{39}\right)\)	\(e\left(\frac{35}{39}\right)\)	\(e\left(\frac{7}{39}\right)\)	\(e\left(\frac{1}{13}\right)\)
\(\chi_{4740}(31,\cdot)\)	4740.cx	78	no	\(-1\)	\(1\)	\(e\left(\frac{43}{78}\right)\)	\(e\left(\frac{25}{78}\right)\)	\(e\left(\frac{16}{39}\right)\)	\(e\left(\frac{1}{13}\right)\)	\(e\left(\frac{37}{78}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{35}{39}\right)\)	\(e\left(\frac{55}{78}\right)\)	\(e\left(\frac{25}{39}\right)\)	\(e\left(\frac{11}{13}\right)\)
\(\chi_{4740}(37,\cdot)\)	4740.dp	156	no	\(1\)	\(1\)	\(e\left(\frac{25}{156}\right)\)	\(e\left(\frac{22}{39}\right)\)	\(e\left(\frac{5}{156}\right)\)	\(e\left(\frac{19}{52}\right)\)	\(e\left(\frac{23}{78}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{7}{39}\right)\)	\(e\left(\frac{25}{39}\right)\)	\(e\left(\frac{137}{156}\right)\)	\(e\left(\frac{7}{26}\right)\)
\(\chi_{4740}(41,\cdot)\)	4740.ci	26	no	\(1\)	\(1\)	\(e\left(\frac{25}{26}\right)\)	\(e\left(\frac{23}{26}\right)\)	\(e\left(\frac{9}{13}\right)\)	\(e\left(\frac{9}{13}\right)\)	\(e\left(\frac{10}{13}\right)\)	\(-1\)	\(e\left(\frac{1}{13}\right)\)	\(e\left(\frac{11}{13}\right)\)	\(e\left(\frac{7}{26}\right)\)	\(e\left(\frac{8}{13}\right)\)
\(\chi_{4740}(43,\cdot)\)	4740.dn	156	no	\(-1\)	\(1\)	\(e\left(\frac{85}{156}\right)\)	\(e\left(\frac{17}{78}\right)\)	\(e\left(\frac{95}{156}\right)\)	\(e\left(\frac{49}{52}\right)\)	\(e\left(\frac{4}{39}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{16}{39}\right)\)	\(e\left(\frac{53}{78}\right)\)	\(e\left(\frac{107}{156}\right)\)	\(e\left(\frac{3}{26}\right)\)
\(\chi_{4740}(47,\cdot)\)	4740.dq	156	yes	\(1\)	\(1\)	\(e\left(\frac{131}{156}\right)\)	\(e\left(\frac{17}{39}\right)\)	\(e\left(\frac{73}{156}\right)\)	\(e\left(\frac{33}{52}\right)\)	\(e\left(\frac{8}{39}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{25}{78}\right)\)	\(e\left(\frac{67}{78}\right)\)	\(e\left(\frac{97}{156}\right)\)	\(e\left(\frac{3}{13}\right)\)
\(\chi_{4740}(49,\cdot)\)	4740.da	78	no	\(1\)	\(1\)	\(e\left(\frac{41}{78}\right)\)	\(e\left(\frac{16}{39}\right)\)	\(e\left(\frac{55}{78}\right)\)	\(e\left(\frac{1}{26}\right)\)	\(e\left(\frac{19}{39}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{37}{39}\right)\)	\(e\left(\frac{4}{39}\right)\)	\(e\left(\frac{25}{78}\right)\)	\(e\left(\frac{12}{13}\right)\)
\(\chi_{4740}(53,\cdot)\)	4740.dk	156	no	\(-1\)	\(1\)	\(e\left(\frac{11}{156}\right)\)	\(e\left(\frac{49}{78}\right)\)	\(e\left(\frac{127}{156}\right)\)	\(e\left(\frac{51}{52}\right)\)	\(e\left(\frac{7}{78}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{67}{78}\right)\)	\(e\left(\frac{11}{39}\right)\)	\(e\left(\frac{79}{156}\right)\)	\(e\left(\frac{7}{13}\right)\)
\(\chi_{4740}(59,\cdot)\)	4740.cz	78	yes	\(-1\)	\(1\)	\(e\left(\frac{5}{78}\right)\)	\(e\left(\frac{1}{39}\right)\)	\(e\left(\frac{1}{78}\right)\)	\(e\left(\frac{9}{26}\right)\)	\(e\left(\frac{17}{78}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{34}{39}\right)\)	\(e\left(\frac{59}{78}\right)\)	\(e\left(\frac{2}{39}\right)\)	\(e\left(\frac{4}{13}\right)\)
\(\chi_{4740}(61,\cdot)\)	4740.ce	26	no	\(-1\)	\(1\)	\(e\left(\frac{15}{26}\right)\)	\(e\left(\frac{3}{13}\right)\)	\(e\left(\frac{8}{13}\right)\)	\(e\left(\frac{3}{26}\right)\)	\(e\left(\frac{6}{13}\right)\)	\(1\)	\(e\left(\frac{9}{26}\right)\)	\(e\left(\frac{4}{13}\right)\)	\(e\left(\frac{25}{26}\right)\)	\(e\left(\frac{7}{26}\right)\)
\(\chi_{4740}(67,\cdot)\)	4740.cs	52	no	\(1\)	\(1\)	\(e\left(\frac{19}{52}\right)\)	\(e\left(\frac{9}{26}\right)\)	\(e\left(\frac{35}{52}\right)\)	\(e\left(\frac{9}{52}\right)\)	\(e\left(\frac{9}{13}\right)\)	\(i\)	\(e\left(\frac{7}{26}\right)\)	\(e\left(\frac{25}{26}\right)\)	\(e\left(\frac{49}{52}\right)\)	\(e\left(\frac{2}{13}\right)\)
\(\chi_{4740}(71,\cdot)\)	4740.bx	26	no	\(-1\)	\(1\)	\(e\left(\frac{2}{13}\right)\)	\(e\left(\frac{6}{13}\right)\)	\(e\left(\frac{3}{13}\right)\)	\(e\left(\frac{3}{13}\right)\)	\(e\left(\frac{11}{26}\right)\)	\(1\)	\(e\left(\frac{9}{13}\right)\)	\(e\left(\frac{3}{26}\right)\)	\(e\left(\frac{11}{26}\right)\)	\(e\left(\frac{7}{13}\right)\)
\(\chi_{4740}(73,\cdot)\)	4740.do	156	no	\(-1\)	\(1\)	\(e\left(\frac{101}{156}\right)\)	\(e\left(\frac{14}{39}\right)\)	\(e\left(\frac{67}{156}\right)\)	\(e\left(\frac{31}{52}\right)\)	\(e\left(\frac{43}{78}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{55}{78}\right)\)	\(e\left(\frac{23}{39}\right)\)	\(e\left(\frac{73}{156}\right)\)	\(e\left(\frac{4}{13}\right)\)
\(\chi_{4740}(77,\cdot)\)	4740.dk	156	no	\(-1\)	\(1\)	\(e\left(\frac{73}{156}\right)\)	\(e\left(\frac{77}{78}\right)\)	\(e\left(\frac{77}{156}\right)\)	\(e\left(\frac{17}{52}\right)\)	\(e\left(\frac{11}{78}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{5}{78}\right)\)	\(e\left(\frac{34}{39}\right)\)	\(e\left(\frac{113}{156}\right)\)	\(e\left(\frac{11}{13}\right)\)
\(\chi_{4740}(83,\cdot)\)	4740.dr	156	yes	\(-1\)	\(1\)	\(e\left(\frac{107}{156}\right)\)	\(e\left(\frac{38}{39}\right)\)	\(e\left(\frac{115}{156}\right)\)	\(e\left(\frac{21}{52}\right)\)	\(e\left(\frac{11}{39}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{5}{39}\right)\)	\(e\left(\frac{19}{78}\right)\)	\(e\left(\frac{109}{156}\right)\)	\(e\left(\frac{5}{26}\right)\)
\(\chi_{4740}(89,\cdot)\)	4740.ck	26	no	\(-1\)	\(1\)	\(e\left(\frac{9}{26}\right)\)	\(e\left(\frac{1}{26}\right)\)	\(e\left(\frac{7}{26}\right)\)	\(e\left(\frac{10}{13}\right)\)	\(e\left(\frac{1}{13}\right)\)	\(1\)	\(e\left(\frac{21}{26}\right)\)	\(e\left(\frac{5}{13}\right)\)	\(e\left(\frac{15}{26}\right)\)	\(e\left(\frac{25}{26}\right)\)
\(\chi_{4740}(91,\cdot)\)	4740.cb	26	no	\(1\)	\(1\)	\(e\left(\frac{8}{13}\right)\)	\(e\left(\frac{9}{26}\right)\)	\(e\left(\frac{12}{13}\right)\)	\(e\left(\frac{11}{26}\right)\)	\(e\left(\frac{5}{26}\right)\)	\(-1\)	\(e\left(\frac{7}{26}\right)\)	\(e\left(\frac{25}{26}\right)\)	\(e\left(\frac{5}{26}\right)\)	\(e\left(\frac{17}{26}\right)\)
\(\chi_{4740}(97,\cdot)\)	4740.cq	52	no	\(-1\)	\(1\)	\(e\left(\frac{17}{52}\right)\)	\(e\left(\frac{3}{13}\right)\)	\(e\left(\frac{19}{52}\right)\)	\(e\left(\frac{45}{52}\right)\)	\(e\left(\frac{25}{26}\right)\)	\(-i\)	\(e\left(\frac{9}{26}\right)\)	\(e\left(\frac{4}{13}\right)\)	\(e\left(\frac{37}{52}\right)\)	\(e\left(\frac{10}{13}\right)\)
\(\chi_{4740}(101,\cdot)\)	4740.ca	26	no	\(-1\)	\(1\)	\(e\left(\frac{12}{13}\right)\)	\(e\left(\frac{7}{26}\right)\)	\(e\left(\frac{5}{13}\right)\)	\(e\left(\frac{23}{26}\right)\)	\(e\left(\frac{7}{13}\right)\)	\(-1\)	\(e\left(\frac{17}{26}\right)\)	\(e\left(\frac{9}{13}\right)\)	\(e\left(\frac{7}{13}\right)\)	\(e\left(\frac{19}{26}\right)\)
\(\chi_{4740}(103,\cdot)\)	4740.bs	12	no	\(-1\)	\(1\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(i\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(-1\)
\(\chi_{4740}(107,\cdot)\)	4740.dq	156	yes	\(1\)	\(1\)	\(e\left(\frac{31}{156}\right)\)	\(e\left(\frac{7}{39}\right)\)	\(e\left(\frac{53}{156}\right)\)	\(e\left(\frac{9}{52}\right)\)	\(e\left(\frac{1}{39}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{47}{78}\right)\)	\(e\left(\frac{23}{78}\right)\)	\(e\left(\frac{17}{156}\right)\)	\(e\left(\frac{2}{13}\right)\)
\(\chi_{4740}(109,\cdot)\)	4740.di	78	no	\(-1\)	\(1\)	\(e\left(\frac{1}{39}\right)\)	\(e\left(\frac{16}{39}\right)\)	\(e\left(\frac{55}{78}\right)\)	\(e\left(\frac{7}{13}\right)\)	\(e\left(\frac{19}{39}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{35}{78}\right)\)	\(e\left(\frac{4}{39}\right)\)	\(e\left(\frac{32}{39}\right)\)	\(e\left(\frac{11}{26}\right)\)
\(\chi_{4740}(113,\cdot)\)	4740.dk	156	no	\(-1\)	\(1\)	\(e\left(\frac{115}{156}\right)\)	\(e\left(\frac{23}{78}\right)\)	\(e\left(\frac{23}{156}\right)\)	\(e\left(\frac{51}{52}\right)\)	\(e\left(\frac{59}{78}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{41}{78}\right)\)	\(e\left(\frac{37}{39}\right)\)	\(e\left(\frac{131}{156}\right)\)	\(e\left(\frac{7}{13}\right)\)
\(\chi_{4740}(119,\cdot)\)	4740.dh	78	yes	\(1\)	\(1\)	\(e\left(\frac{11}{39}\right)\)	\(e\left(\frac{20}{39}\right)\)	\(e\left(\frac{59}{78}\right)\)	\(e\left(\frac{12}{13}\right)\)	\(e\left(\frac{67}{78}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{73}{78}\right)\)	\(e\left(\frac{49}{78}\right)\)	\(e\left(\frac{41}{78}\right)\)	\(e\left(\frac{17}{26}\right)\)
\(\chi_{4740}(121,\cdot)\)	4740.cm	39	no	\(1\)	\(1\)	\(e\left(\frac{16}{39}\right)\)	\(e\left(\frac{22}{39}\right)\)	\(e\left(\frac{11}{39}\right)\)	\(e\left(\frac{8}{13}\right)\)	\(e\left(\frac{31}{39}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{7}{39}\right)\)	\(e\left(\frac{25}{39}\right)\)	\(e\left(\frac{5}{39}\right)\)	\(e\left(\frac{10}{13}\right)\)

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