LMFDB - Dirichlet character orbit 4740.do

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comment:Define the Dirichlet character orbit

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(4740, base_ring=CyclotomicField(156)) M = H._module chi = DirichletCharacter(H, M([0,0,117,68])) chi.galois_orbit()

gp:[g,chi] = znchar(Mod(13, 4740)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

magma:// Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("4740.13"); order := Order(chi); { chi^k : k in [1..order-1] | GCD(k,order) eq 1 };

Basic properties

Modulus:	$4740$	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	$395$	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	$156$	comment:Order sage:chi.multiplicative_order() gp:charorder(g,chi) magma:Order(chi);
Real:	no	comment:Whether the character is real sage:chi.multiplicative_order() <= 2 gp:charorder(g,chi) <= 2 magma:Order(chi) le 2;
Primitive:	no, induced from 395.x	comment:If the character is primitive sage:chi.is_primitive() gp:#znconreyconductor(g,chi)==1 magma:IsPrimitive(chi);
Minimal:	yes
Parity:	odd	comment:Parity sage:chi.is_odd() gp:zncharisodd(g,chi) magma:IsOdd(chi);

Related number fields

Field of values:	$\Q(\zeta_{156})$	comment:Field of values of chi sage:CyclotomicField(chi.multiplicative_order()) gp:nfinit(polcyclo(charorder(g,chi))) magma:CyclotomicField(Order(chi));
Fixed field:	Number field defined by a degree 156 polynomial (not computed)	comment:Fixed field sage:chi.fixed_field()

First 31 of 48 characters in Galois orbit

Character	$-1$	$1$	$7$	$11$	$13$	$17$	$19$	$23$	$29$	$31$	$37$	$41$
$\chi_{4740}(13,\cdot)$	$-1$	$1$	$e\left(\frac{133}{156}\right)$	$e\left(\frac{25}{39}\right)$	$e\left(\frac{11}{156}\right)$	$e\left(\frac{47}{52}\right)$	$e\left(\frac{35}{78}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{23}{78}\right)$	$e\left(\frac{16}{39}\right)$	$e\left(\frac{5}{156}\right)$	$e\left(\frac{9}{13}\right)$
$\chi_{4740}(73,\cdot)$	$-1$	$1$	$e\left(\frac{101}{156}\right)$	$e\left(\frac{14}{39}\right)$	$e\left(\frac{67}{156}\right)$	$e\left(\frac{31}{52}\right)$	$e\left(\frac{43}{78}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{55}{78}\right)$	$e\left(\frac{23}{39}\right)$	$e\left(\frac{73}{156}\right)$	$e\left(\frac{4}{13}\right)$
$\chi_{4740}(253,\cdot)$	$-1$	$1$	$e\left(\frac{97}{156}\right)$	$e\left(\frac{37}{39}\right)$	$e\left(\frac{35}{156}\right)$	$e\left(\frac{3}{52}\right)$	$e\left(\frac{5}{78}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{59}{78}\right)$	$e\left(\frac{19}{39}\right)$	$e\left(\frac{101}{156}\right)$	$e\left(\frac{5}{13}\right)$
$\chi_{4740}(277,\cdot)$	$-1$	$1$	$e\left(\frac{83}{156}\right)$	$e\left(\frac{20}{39}\right)$	$e\left(\frac{1}{156}\right)$	$e\left(\frac{9}{52}\right)$	$e\left(\frac{67}{78}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{73}{78}\right)$	$e\left(\frac{5}{39}\right)$	$e\left(\frac{43}{156}\right)$	$e\left(\frac{2}{13}\right)$
$\chi_{4740}(313,\cdot)$	$-1$	$1$	$e\left(\frac{145}{156}\right)$	$e\left(\frac{34}{39}\right)$	$e\left(\frac{107}{156}\right)$	$e\left(\frac{27}{52}\right)$	$e\left(\frac{71}{78}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{11}{78}\right)$	$e\left(\frac{28}{39}\right)$	$e\left(\frac{77}{156}\right)$	$e\left(\frac{6}{13}\right)$
$\chi_{4740}(397,\cdot)$	$-1$	$1$	$e\left(\frac{151}{156}\right)$	$e\left(\frac{19}{39}\right)$	$e\left(\frac{77}{156}\right)$	$e\left(\frac{17}{52}\right)$	$e\left(\frac{11}{78}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{5}{78}\right)$	$e\left(\frac{34}{39}\right)$	$e\left(\frac{35}{156}\right)$	$e\left(\frac{11}{13}\right)$
$\chi_{4740}(493,\cdot)$	$-1$	$1$	$e\left(\frac{77}{156}\right)$	$e\left(\frac{35}{39}\right)$	$e\left(\frac{31}{156}\right)$	$e\left(\frac{19}{52}\right)$	$e\left(\frac{49}{78}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{78}\right)$	$e\left(\frac{38}{39}\right)$	$e\left(\frac{85}{156}\right)$	$e\left(\frac{10}{13}\right)$
$\chi_{4740}(637,\cdot)$	$-1$	$1$	$e\left(\frac{59}{156}\right)$	$e\left(\frac{2}{39}\right)$	$e\left(\frac{121}{156}\right)$	$e\left(\frac{49}{52}\right)$	$e\left(\frac{73}{78}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{19}{78}\right)$	$e\left(\frac{20}{39}\right)$	$e\left(\frac{55}{156}\right)$	$e\left(\frac{8}{13}\right)$
$\chi_{4740}(913,\cdot)$	$-1$	$1$	$e\left(\frac{61}{156}\right)$	$e\left(\frac{10}{39}\right)$	$e\left(\frac{59}{156}\right)$	$e\left(\frac{11}{52}\right)$	$e\left(\frac{53}{78}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{17}{78}\right)$	$e\left(\frac{22}{39}\right)$	$e\left(\frac{41}{156}\right)$	$e\left(\frac{1}{13}\right)$
$\chi_{4740}(973,\cdot)$	$-1$	$1$	$e\left(\frac{1}{156}\right)$	$e\left(\frac{4}{39}\right)$	$e\left(\frac{47}{156}\right)$	$e\left(\frac{7}{52}\right)$	$e\left(\frac{29}{78}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{77}{78}\right)$	$e\left(\frac{1}{39}\right)$	$e\left(\frac{149}{156}\right)$	$e\left(\frac{3}{13}\right)$
$\chi_{4740}(997,\cdot)$	$-1$	$1$	$e\left(\frac{43}{156}\right)$	$e\left(\frac{16}{39}\right)$	$e\left(\frac{149}{156}\right)$	$e\left(\frac{41}{52}\right)$	$e\left(\frac{77}{78}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{35}{78}\right)$	$e\left(\frac{4}{39}\right)$	$e\left(\frac{11}{156}\right)$	$e\left(\frac{12}{13}\right)$
$\chi_{4740}(1117,\cdot)$	$-1$	$1$	$e\left(\frac{71}{156}\right)$	$e\left(\frac{11}{39}\right)$	$e\left(\frac{61}{156}\right)$	$e\left(\frac{29}{52}\right)$	$e\left(\frac{31}{78}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{7}{78}\right)$	$e\left(\frac{32}{39}\right)$	$e\left(\frac{127}{156}\right)$	$e\left(\frac{5}{13}\right)$
$\chi_{4740}(1273,\cdot)$	$-1$	$1$	$e\left(\frac{17}{156}\right)$	$e\left(\frac{29}{39}\right)$	$e\left(\frac{19}{156}\right)$	$e\left(\frac{15}{52}\right)$	$e\left(\frac{25}{78}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{61}{78}\right)$	$e\left(\frac{17}{39}\right)$	$e\left(\frac{37}{156}\right)$	$e\left(\frac{12}{13}\right)$
$\chi_{4740}(1393,\cdot)$	$-1$	$1$	$e\left(\frac{113}{156}\right)$	$e\left(\frac{23}{39}\right)$	$e\left(\frac{7}{156}\right)$	$e\left(\frac{11}{52}\right)$	$e\left(\frac{1}{78}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{43}{78}\right)$	$e\left(\frac{35}{39}\right)$	$e\left(\frac{145}{156}\right)$	$e\left(\frac{1}{13}\right)$
$\chi_{4740}(1453,\cdot)$	$-1$	$1$	$e\left(\frac{125}{156}\right)$	$e\left(\frac{32}{39}\right)$	$e\left(\frac{103}{156}\right)$	$e\left(\frac{43}{52}\right)$	$e\left(\frac{37}{78}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{31}{78}\right)$	$e\left(\frac{8}{39}\right)$	$e\left(\frac{61}{156}\right)$	$e\left(\frac{11}{13}\right)$
$\chi_{4740}(1537,\cdot)$	$-1$	$1$	$e\left(\frac{7}{156}\right)$	$e\left(\frac{28}{39}\right)$	$e\left(\frac{17}{156}\right)$	$e\left(\frac{49}{52}\right)$	$e\left(\frac{47}{78}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{71}{78}\right)$	$e\left(\frac{7}{39}\right)$	$e\left(\frac{107}{156}\right)$	$e\left(\frac{8}{13}\right)$
$\chi_{4740}(1573,\cdot)$	$-1$	$1$	$e\left(\frac{41}{156}\right)$	$e\left(\frac{8}{39}\right)$	$e\left(\frac{55}{156}\right)$	$e\left(\frac{27}{52}\right)$	$e\left(\frac{19}{78}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{37}{78}\right)$	$e\left(\frac{2}{39}\right)$	$e\left(\frac{25}{156}\right)$	$e\left(\frac{6}{13}\right)$
$\chi_{4740}(1837,\cdot)$	$-1$	$1$	$e\left(\frac{127}{156}\right)$	$e\left(\frac{1}{39}\right)$	$e\left(\frac{41}{156}\right)$	$e\left(\frac{5}{52}\right)$	$e\left(\frac{17}{78}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{29}{78}\right)$	$e\left(\frac{10}{39}\right)$	$e\left(\frac{47}{156}\right)$	$e\left(\frac{4}{13}\right)$
$\chi_{4740}(2017,\cdot)$	$-1$	$1$	$e\left(\frac{103}{156}\right)$	$e\left(\frac{22}{39}\right)$	$e\left(\frac{5}{156}\right)$	$e\left(\frac{45}{52}\right)$	$e\left(\frac{23}{78}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{53}{78}\right)$	$e\left(\frac{25}{39}\right)$	$e\left(\frac{59}{156}\right)$	$e\left(\frac{10}{13}\right)$
$\chi_{4740}(2137,\cdot)$	$-1$	$1$	$e\left(\frac{107}{156}\right)$	$e\left(\frac{38}{39}\right)$	$e\left(\frac{37}{156}\right)$	$e\left(\frac{21}{52}\right)$	$e\left(\frac{61}{78}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{49}{78}\right)$	$e\left(\frac{29}{39}\right)$	$e\left(\frac{31}{156}\right)$	$e\left(\frac{9}{13}\right)$
$\chi_{4740}(2173,\cdot)$	$-1$	$1$	$e\left(\frac{5}{156}\right)$	$e\left(\frac{20}{39}\right)$	$e\left(\frac{79}{156}\right)$	$e\left(\frac{35}{52}\right)$	$e\left(\frac{67}{78}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{73}{78}\right)$	$e\left(\frac{5}{39}\right)$	$e\left(\frac{121}{156}\right)$	$e\left(\frac{2}{13}\right)$
$\chi_{4740}(2257,\cdot)$	$-1$	$1$	$e\left(\frac{115}{156}\right)$	$e\left(\frac{31}{39}\right)$	$e\left(\frac{101}{156}\right)$	$e\left(\frac{25}{52}\right)$	$e\left(\frac{59}{78}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{41}{78}\right)$	$e\left(\frac{37}{39}\right)$	$e\left(\frac{131}{156}\right)$	$e\left(\frac{7}{13}\right)$
$\chi_{4740}(2293,\cdot)$	$-1$	$1$	$e\left(\frac{73}{156}\right)$	$e\left(\frac{19}{39}\right)$	$e\left(\frac{155}{156}\right)$	$e\left(\frac{43}{52}\right)$	$e\left(\frac{11}{78}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{5}{78}\right)$	$e\left(\frac{34}{39}\right)$	$e\left(\frac{113}{156}\right)$	$e\left(\frac{11}{13}\right)$
$\chi_{4740}(2317,\cdot)$	$-1$	$1$	$e\left(\frac{11}{156}\right)$	$e\left(\frac{5}{39}\right)$	$e\left(\frac{49}{156}\right)$	$e\left(\frac{25}{52}\right)$	$e\left(\frac{7}{78}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{67}{78}\right)$	$e\left(\frac{11}{39}\right)$	$e\left(\frac{79}{156}\right)$	$e\left(\frac{7}{13}\right)$
$\chi_{4740}(2533,\cdot)$	$-1$	$1$	$e\left(\frac{137}{156}\right)$	$e\left(\frac{2}{39}\right)$	$e\left(\frac{43}{156}\right)$	$e\left(\frac{23}{52}\right)$	$e\left(\frac{73}{78}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{19}{78}\right)$	$e\left(\frac{20}{39}\right)$	$e\left(\frac{133}{156}\right)$	$e\left(\frac{8}{13}\right)$
$\chi_{4740}(2737,\cdot)$	$-1$	$1$	$e\left(\frac{31}{156}\right)$	$e\left(\frac{7}{39}\right)$	$e\left(\frac{53}{156}\right)$	$e\left(\frac{9}{52}\right)$	$e\left(\frac{41}{78}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{47}{78}\right)$	$e\left(\frac{31}{39}\right)$	$e\left(\frac{95}{156}\right)$	$e\left(\frac{2}{13}\right)$
$\chi_{4740}(2797,\cdot)$	$-1$	$1$	$e\left(\frac{131}{156}\right)$	$e\left(\frac{17}{39}\right)$	$e\left(\frac{73}{156}\right)$	$e\left(\frac{33}{52}\right)$	$e\left(\frac{55}{78}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{25}{78}\right)$	$e\left(\frac{14}{39}\right)$	$e\left(\frac{19}{156}\right)$	$e\left(\frac{3}{13}\right)$
$\chi_{4740}(2857,\cdot)$	$-1$	$1$	$e\left(\frac{55}{156}\right)$	$e\left(\frac{25}{39}\right)$	$e\left(\frac{89}{156}\right)$	$e\left(\frac{21}{52}\right)$	$e\left(\frac{35}{78}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{23}{78}\right)$	$e\left(\frac{16}{39}\right)$	$e\left(\frac{83}{156}\right)$	$e\left(\frac{9}{13}\right)$
$\chi_{4740}(2893,\cdot)$	$-1$	$1$	$e\left(\frac{121}{156}\right)$	$e\left(\frac{16}{39}\right)$	$e\left(\frac{71}{156}\right)$	$e\left(\frac{15}{52}\right)$	$e\left(\frac{77}{78}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{35}{78}\right)$	$e\left(\frac{4}{39}\right)$	$e\left(\frac{89}{156}\right)$	$e\left(\frac{12}{13}\right)$
$\chi_{4740}(2917,\cdot)$	$-1$	$1$	$e\left(\frac{23}{156}\right)$	$e\left(\frac{14}{39}\right)$	$e\left(\frac{145}{156}\right)$	$e\left(\frac{5}{52}\right)$	$e\left(\frac{43}{78}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{55}{78}\right)$	$e\left(\frac{23}{39}\right)$	$e\left(\frac{151}{156}\right)$	$e\left(\frac{4}{13}\right)$
$\chi_{4740}(3013,\cdot)$	$-1$	$1$	$e\left(\frac{149}{156}\right)$	$e\left(\frac{11}{39}\right)$	$e\left(\frac{139}{156}\right)$	$e\left(\frac{3}{52}\right)$	$e\left(\frac{31}{78}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{7}{78}\right)$	$e\left(\frac{32}{39}\right)$	$e\left(\frac{49}{156}\right)$	$e\left(\frac{5}{13}\right)$

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

Character	\(-1\)	\(1\)	\(7\)	\(11\)	\(13\)	\(17\)	\(19\)	\(23\)	\(29\)	\(31\)	\(37\)	\(41\)
\(\chi_{4740}(13,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{133}{156}\right)\)	\(e\left(\frac{25}{39}\right)\)	\(e\left(\frac{11}{156}\right)\)	\(e\left(\frac{47}{52}\right)\)	\(e\left(\frac{35}{78}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{23}{78}\right)\)	\(e\left(\frac{16}{39}\right)\)	\(e\left(\frac{5}{156}\right)\)	\(e\left(\frac{9}{13}\right)\)
\(\chi_{4740}(73,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{101}{156}\right)\)	\(e\left(\frac{14}{39}\right)\)	\(e\left(\frac{67}{156}\right)\)	\(e\left(\frac{31}{52}\right)\)	\(e\left(\frac{43}{78}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{55}{78}\right)\)	\(e\left(\frac{23}{39}\right)\)	\(e\left(\frac{73}{156}\right)\)	\(e\left(\frac{4}{13}\right)\)
\(\chi_{4740}(253,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{97}{156}\right)\)	\(e\left(\frac{37}{39}\right)\)	\(e\left(\frac{35}{156}\right)\)	\(e\left(\frac{3}{52}\right)\)	\(e\left(\frac{5}{78}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{59}{78}\right)\)	\(e\left(\frac{19}{39}\right)\)	\(e\left(\frac{101}{156}\right)\)	\(e\left(\frac{5}{13}\right)\)
\(\chi_{4740}(277,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{83}{156}\right)\)	\(e\left(\frac{20}{39}\right)\)	\(e\left(\frac{1}{156}\right)\)	\(e\left(\frac{9}{52}\right)\)	\(e\left(\frac{67}{78}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{73}{78}\right)\)	\(e\left(\frac{5}{39}\right)\)	\(e\left(\frac{43}{156}\right)\)	\(e\left(\frac{2}{13}\right)\)
\(\chi_{4740}(313,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{145}{156}\right)\)	\(e\left(\frac{34}{39}\right)\)	\(e\left(\frac{107}{156}\right)\)	\(e\left(\frac{27}{52}\right)\)	\(e\left(\frac{71}{78}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{11}{78}\right)\)	\(e\left(\frac{28}{39}\right)\)	\(e\left(\frac{77}{156}\right)\)	\(e\left(\frac{6}{13}\right)\)
\(\chi_{4740}(397,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{151}{156}\right)\)	\(e\left(\frac{19}{39}\right)\)	\(e\left(\frac{77}{156}\right)\)	\(e\left(\frac{17}{52}\right)\)	\(e\left(\frac{11}{78}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{5}{78}\right)\)	\(e\left(\frac{34}{39}\right)\)	\(e\left(\frac{35}{156}\right)\)	\(e\left(\frac{11}{13}\right)\)
\(\chi_{4740}(493,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{77}{156}\right)\)	\(e\left(\frac{35}{39}\right)\)	\(e\left(\frac{31}{156}\right)\)	\(e\left(\frac{19}{52}\right)\)	\(e\left(\frac{49}{78}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{1}{78}\right)\)	\(e\left(\frac{38}{39}\right)\)	\(e\left(\frac{85}{156}\right)\)	\(e\left(\frac{10}{13}\right)\)
\(\chi_{4740}(637,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{59}{156}\right)\)	\(e\left(\frac{2}{39}\right)\)	\(e\left(\frac{121}{156}\right)\)	\(e\left(\frac{49}{52}\right)\)	\(e\left(\frac{73}{78}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{19}{78}\right)\)	\(e\left(\frac{20}{39}\right)\)	\(e\left(\frac{55}{156}\right)\)	\(e\left(\frac{8}{13}\right)\)
\(\chi_{4740}(913,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{61}{156}\right)\)	\(e\left(\frac{10}{39}\right)\)	\(e\left(\frac{59}{156}\right)\)	\(e\left(\frac{11}{52}\right)\)	\(e\left(\frac{53}{78}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{17}{78}\right)\)	\(e\left(\frac{22}{39}\right)\)	\(e\left(\frac{41}{156}\right)\)	\(e\left(\frac{1}{13}\right)\)
\(\chi_{4740}(973,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1}{156}\right)\)	\(e\left(\frac{4}{39}\right)\)	\(e\left(\frac{47}{156}\right)\)	\(e\left(\frac{7}{52}\right)\)	\(e\left(\frac{29}{78}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{77}{78}\right)\)	\(e\left(\frac{1}{39}\right)\)	\(e\left(\frac{149}{156}\right)\)	\(e\left(\frac{3}{13}\right)\)
\(\chi_{4740}(997,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{43}{156}\right)\)	\(e\left(\frac{16}{39}\right)\)	\(e\left(\frac{149}{156}\right)\)	\(e\left(\frac{41}{52}\right)\)	\(e\left(\frac{77}{78}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{35}{78}\right)\)	\(e\left(\frac{4}{39}\right)\)	\(e\left(\frac{11}{156}\right)\)	\(e\left(\frac{12}{13}\right)\)
\(\chi_{4740}(1117,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{71}{156}\right)\)	\(e\left(\frac{11}{39}\right)\)	\(e\left(\frac{61}{156}\right)\)	\(e\left(\frac{29}{52}\right)\)	\(e\left(\frac{31}{78}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{7}{78}\right)\)	\(e\left(\frac{32}{39}\right)\)	\(e\left(\frac{127}{156}\right)\)	\(e\left(\frac{5}{13}\right)\)
\(\chi_{4740}(1273,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{17}{156}\right)\)	\(e\left(\frac{29}{39}\right)\)	\(e\left(\frac{19}{156}\right)\)	\(e\left(\frac{15}{52}\right)\)	\(e\left(\frac{25}{78}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{61}{78}\right)\)	\(e\left(\frac{17}{39}\right)\)	\(e\left(\frac{37}{156}\right)\)	\(e\left(\frac{12}{13}\right)\)
\(\chi_{4740}(1393,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{113}{156}\right)\)	\(e\left(\frac{23}{39}\right)\)	\(e\left(\frac{7}{156}\right)\)	\(e\left(\frac{11}{52}\right)\)	\(e\left(\frac{1}{78}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{43}{78}\right)\)	\(e\left(\frac{35}{39}\right)\)	\(e\left(\frac{145}{156}\right)\)	\(e\left(\frac{1}{13}\right)\)
\(\chi_{4740}(1453,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{125}{156}\right)\)	\(e\left(\frac{32}{39}\right)\)	\(e\left(\frac{103}{156}\right)\)	\(e\left(\frac{43}{52}\right)\)	\(e\left(\frac{37}{78}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{31}{78}\right)\)	\(e\left(\frac{8}{39}\right)\)	\(e\left(\frac{61}{156}\right)\)	\(e\left(\frac{11}{13}\right)\)
\(\chi_{4740}(1537,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{7}{156}\right)\)	\(e\left(\frac{28}{39}\right)\)	\(e\left(\frac{17}{156}\right)\)	\(e\left(\frac{49}{52}\right)\)	\(e\left(\frac{47}{78}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{71}{78}\right)\)	\(e\left(\frac{7}{39}\right)\)	\(e\left(\frac{107}{156}\right)\)	\(e\left(\frac{8}{13}\right)\)
\(\chi_{4740}(1573,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{41}{156}\right)\)	\(e\left(\frac{8}{39}\right)\)	\(e\left(\frac{55}{156}\right)\)	\(e\left(\frac{27}{52}\right)\)	\(e\left(\frac{19}{78}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{37}{78}\right)\)	\(e\left(\frac{2}{39}\right)\)	\(e\left(\frac{25}{156}\right)\)	\(e\left(\frac{6}{13}\right)\)
\(\chi_{4740}(1837,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{127}{156}\right)\)	\(e\left(\frac{1}{39}\right)\)	\(e\left(\frac{41}{156}\right)\)	\(e\left(\frac{5}{52}\right)\)	\(e\left(\frac{17}{78}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{29}{78}\right)\)	\(e\left(\frac{10}{39}\right)\)	\(e\left(\frac{47}{156}\right)\)	\(e\left(\frac{4}{13}\right)\)
\(\chi_{4740}(2017,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{103}{156}\right)\)	\(e\left(\frac{22}{39}\right)\)	\(e\left(\frac{5}{156}\right)\)	\(e\left(\frac{45}{52}\right)\)	\(e\left(\frac{23}{78}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{53}{78}\right)\)	\(e\left(\frac{25}{39}\right)\)	\(e\left(\frac{59}{156}\right)\)	\(e\left(\frac{10}{13}\right)\)
\(\chi_{4740}(2137,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{107}{156}\right)\)	\(e\left(\frac{38}{39}\right)\)	\(e\left(\frac{37}{156}\right)\)	\(e\left(\frac{21}{52}\right)\)	\(e\left(\frac{61}{78}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{49}{78}\right)\)	\(e\left(\frac{29}{39}\right)\)	\(e\left(\frac{31}{156}\right)\)	\(e\left(\frac{9}{13}\right)\)
\(\chi_{4740}(2173,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{5}{156}\right)\)	\(e\left(\frac{20}{39}\right)\)	\(e\left(\frac{79}{156}\right)\)	\(e\left(\frac{35}{52}\right)\)	\(e\left(\frac{67}{78}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{73}{78}\right)\)	\(e\left(\frac{5}{39}\right)\)	\(e\left(\frac{121}{156}\right)\)	\(e\left(\frac{2}{13}\right)\)
\(\chi_{4740}(2257,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{115}{156}\right)\)	\(e\left(\frac{31}{39}\right)\)	\(e\left(\frac{101}{156}\right)\)	\(e\left(\frac{25}{52}\right)\)	\(e\left(\frac{59}{78}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{41}{78}\right)\)	\(e\left(\frac{37}{39}\right)\)	\(e\left(\frac{131}{156}\right)\)	\(e\left(\frac{7}{13}\right)\)
\(\chi_{4740}(2293,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{73}{156}\right)\)	\(e\left(\frac{19}{39}\right)\)	\(e\left(\frac{155}{156}\right)\)	\(e\left(\frac{43}{52}\right)\)	\(e\left(\frac{11}{78}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{5}{78}\right)\)	\(e\left(\frac{34}{39}\right)\)	\(e\left(\frac{113}{156}\right)\)	\(e\left(\frac{11}{13}\right)\)
\(\chi_{4740}(2317,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{11}{156}\right)\)	\(e\left(\frac{5}{39}\right)\)	\(e\left(\frac{49}{156}\right)\)	\(e\left(\frac{25}{52}\right)\)	\(e\left(\frac{7}{78}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{67}{78}\right)\)	\(e\left(\frac{11}{39}\right)\)	\(e\left(\frac{79}{156}\right)\)	\(e\left(\frac{7}{13}\right)\)
\(\chi_{4740}(2533,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{137}{156}\right)\)	\(e\left(\frac{2}{39}\right)\)	\(e\left(\frac{43}{156}\right)\)	\(e\left(\frac{23}{52}\right)\)	\(e\left(\frac{73}{78}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{19}{78}\right)\)	\(e\left(\frac{20}{39}\right)\)	\(e\left(\frac{133}{156}\right)\)	\(e\left(\frac{8}{13}\right)\)
\(\chi_{4740}(2737,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{31}{156}\right)\)	\(e\left(\frac{7}{39}\right)\)	\(e\left(\frac{53}{156}\right)\)	\(e\left(\frac{9}{52}\right)\)	\(e\left(\frac{41}{78}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{47}{78}\right)\)	\(e\left(\frac{31}{39}\right)\)	\(e\left(\frac{95}{156}\right)\)	\(e\left(\frac{2}{13}\right)\)
\(\chi_{4740}(2797,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{131}{156}\right)\)	\(e\left(\frac{17}{39}\right)\)	\(e\left(\frac{73}{156}\right)\)	\(e\left(\frac{33}{52}\right)\)	\(e\left(\frac{55}{78}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{25}{78}\right)\)	\(e\left(\frac{14}{39}\right)\)	\(e\left(\frac{19}{156}\right)\)	\(e\left(\frac{3}{13}\right)\)
\(\chi_{4740}(2857,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{55}{156}\right)\)	\(e\left(\frac{25}{39}\right)\)	\(e\left(\frac{89}{156}\right)\)	\(e\left(\frac{21}{52}\right)\)	\(e\left(\frac{35}{78}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{23}{78}\right)\)	\(e\left(\frac{16}{39}\right)\)	\(e\left(\frac{83}{156}\right)\)	\(e\left(\frac{9}{13}\right)\)
\(\chi_{4740}(2893,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{121}{156}\right)\)	\(e\left(\frac{16}{39}\right)\)	\(e\left(\frac{71}{156}\right)\)	\(e\left(\frac{15}{52}\right)\)	\(e\left(\frac{77}{78}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{35}{78}\right)\)	\(e\left(\frac{4}{39}\right)\)	\(e\left(\frac{89}{156}\right)\)	\(e\left(\frac{12}{13}\right)\)
\(\chi_{4740}(2917,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{23}{156}\right)\)	\(e\left(\frac{14}{39}\right)\)	\(e\left(\frac{145}{156}\right)\)	\(e\left(\frac{5}{52}\right)\)	\(e\left(\frac{43}{78}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{55}{78}\right)\)	\(e\left(\frac{23}{39}\right)\)	\(e\left(\frac{151}{156}\right)\)	\(e\left(\frac{4}{13}\right)\)
\(\chi_{4740}(3013,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{149}{156}\right)\)	\(e\left(\frac{11}{39}\right)\)	\(e\left(\frac{139}{156}\right)\)	\(e\left(\frac{3}{52}\right)\)	\(e\left(\frac{31}{78}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{7}{78}\right)\)	\(e\left(\frac{32}{39}\right)\)	\(e\left(\frac{49}{156}\right)\)	\(e\left(\frac{5}{13}\right)\)

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First 31 of 48 characters in Galois orbit

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

Label	4740.do
Modulus	$4740$
Conductor	$395$
Order	$156$
Real	no
Primitive	no
Minimal	yes
Parity	odd

Modulus:	\(4740\)	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	\(395\)	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	\(156\)	comment:Order sage:chi.multiplicative_order() gp:charorder(g,chi) magma:Order(chi);
Real:	no	comment:Whether the character is real sage:chi.multiplicative_order() <= 2 gp:charorder(g,chi) <= 2 magma:Order(chi) le 2;
Primitive:	no, induced from 395.x	comment:If the character is primitive sage:chi.is_primitive() gp:#znconreyconductor(g,chi)==1 magma:IsPrimitive(chi);
Minimal:	yes
Parity:	odd	comment:Parity sage:chi.is_odd() gp:zncharisodd(g,chi) magma:IsOdd(chi);