LMFDB - Dirichlet character orbit 4640.gx

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comment:Define the Dirichlet character orbit

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(4640, base_ring=CyclotomicField(56)) M = H._module chi = DirichletCharacter(H, M([0,35,42,16])) chi.galois_orbit()

gp:[g,chi] = znchar(Mod(53, 4640)) 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("4640.53"); order := Order(chi); { chi^k : k in [1..order-1] | GCD(k,order) eq 1 };

Basic properties

Modulus:	$4640$	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	$4640$	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	$56$	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:	yes	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:	$\Q(\zeta_{56})$	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 56 polynomial	comment:Fixed field sage:chi.fixed_field()

Characters in Galois orbit

Character	$-1$	$1$	$3$	$7$	$9$	$11$	$13$	$17$	$19$	$21$	$23$	$27$
$\chi_{4640}(53,\cdot)$	$-1$	$1$	$e\left(\frac{31}{56}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{3}{28}\right)$	$e\left(\frac{15}{56}\right)$	$e\left(\frac{43}{56}\right)$	$i$	$e\left(\frac{25}{56}\right)$	$e\left(\frac{55}{56}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{37}{56}\right)$
$\chi_{4640}(373,\cdot)$	$-1$	$1$	$e\left(\frac{55}{56}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{27}{28}\right)$	$e\left(\frac{23}{56}\right)$	$e\left(\frac{51}{56}\right)$	$i$	$e\left(\frac{1}{56}\right)$	$e\left(\frac{47}{56}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{53}{56}\right)$
$\chi_{4640}(397,\cdot)$	$-1$	$1$	$e\left(\frac{37}{56}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{9}{28}\right)$	$e\left(\frac{45}{56}\right)$	$e\left(\frac{17}{56}\right)$	$-i$	$e\left(\frac{19}{56}\right)$	$e\left(\frac{53}{56}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{55}{56}\right)$
$\chi_{4640}(877,\cdot)$	$-1$	$1$	$e\left(\frac{29}{56}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{1}{28}\right)$	$e\left(\frac{5}{56}\right)$	$e\left(\frac{33}{56}\right)$	$-i$	$e\left(\frac{27}{56}\right)$	$e\left(\frac{37}{56}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{31}{56}\right)$
$\chi_{4640}(1093,\cdot)$	$-1$	$1$	$e\left(\frac{51}{56}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{23}{28}\right)$	$e\left(\frac{3}{56}\right)$	$e\left(\frac{31}{56}\right)$	$i$	$e\left(\frac{5}{56}\right)$	$e\left(\frac{11}{56}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{41}{56}\right)$
$\chi_{4640}(1357,\cdot)$	$-1$	$1$	$e\left(\frac{53}{56}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{25}{28}\right)$	$e\left(\frac{13}{56}\right)$	$e\left(\frac{41}{56}\right)$	$-i$	$e\left(\frac{3}{56}\right)$	$e\left(\frac{29}{56}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{47}{56}\right)$
$\chi_{4640}(1437,\cdot)$	$-1$	$1$	$e\left(\frac{33}{56}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{5}{28}\right)$	$e\left(\frac{25}{56}\right)$	$e\left(\frac{53}{56}\right)$	$-i$	$e\left(\frac{23}{56}\right)$	$e\left(\frac{17}{56}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{43}{56}\right)$
$\chi_{4640}(1573,\cdot)$	$-1$	$1$	$e\left(\frac{43}{56}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{19}{56}\right)$	$e\left(\frac{47}{56}\right)$	$i$	$e\left(\frac{13}{56}\right)$	$e\left(\frac{51}{56}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{17}{56}\right)$
$\chi_{4640}(1677,\cdot)$	$-1$	$1$	$e\left(\frac{45}{56}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{17}{28}\right)$	$e\left(\frac{29}{56}\right)$	$e\left(\frac{1}{56}\right)$	$-i$	$e\left(\frac{11}{56}\right)$	$e\left(\frac{13}{56}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{23}{56}\right)$
$\chi_{4640}(1997,\cdot)$	$-1$	$1$	$e\left(\frac{13}{56}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{37}{56}\right)$	$e\left(\frac{9}{56}\right)$	$-i$	$e\left(\frac{43}{56}\right)$	$e\left(\frac{5}{56}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{39}{56}\right)$
$\chi_{4640}(2053,\cdot)$	$-1$	$1$	$e\left(\frac{11}{56}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{11}{28}\right)$	$e\left(\frac{27}{56}\right)$	$e\left(\frac{55}{56}\right)$	$i$	$e\left(\frac{45}{56}\right)$	$e\left(\frac{43}{56}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{33}{56}\right)$
$\chi_{4640}(2133,\cdot)$	$-1$	$1$	$e\left(\frac{47}{56}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{19}{28}\right)$	$e\left(\frac{39}{56}\right)$	$e\left(\frac{11}{56}\right)$	$i$	$e\left(\frac{9}{56}\right)$	$e\left(\frac{31}{56}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{29}{56}\right)$
$\chi_{4640}(2373,\cdot)$	$-1$	$1$	$e\left(\frac{3}{56}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{3}{28}\right)$	$e\left(\frac{43}{56}\right)$	$e\left(\frac{15}{56}\right)$	$i$	$e\left(\frac{53}{56}\right)$	$e\left(\frac{27}{56}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{9}{56}\right)$
$\chi_{4640}(2693,\cdot)$	$-1$	$1$	$e\left(\frac{27}{56}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{27}{28}\right)$	$e\left(\frac{51}{56}\right)$	$e\left(\frac{23}{56}\right)$	$i$	$e\left(\frac{29}{56}\right)$	$e\left(\frac{19}{56}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{25}{56}\right)$
$\chi_{4640}(2717,\cdot)$	$-1$	$1$	$e\left(\frac{9}{56}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{9}{28}\right)$	$e\left(\frac{17}{56}\right)$	$e\left(\frac{45}{56}\right)$	$-i$	$e\left(\frac{47}{56}\right)$	$e\left(\frac{25}{56}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{27}{56}\right)$
$\chi_{4640}(3197,\cdot)$	$-1$	$1$	$e\left(\frac{1}{56}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{1}{28}\right)$	$e\left(\frac{33}{56}\right)$	$e\left(\frac{5}{56}\right)$	$-i$	$e\left(\frac{55}{56}\right)$	$e\left(\frac{9}{56}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{3}{56}\right)$
$\chi_{4640}(3413,\cdot)$	$-1$	$1$	$e\left(\frac{23}{56}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{23}{28}\right)$	$e\left(\frac{31}{56}\right)$	$e\left(\frac{3}{56}\right)$	$i$	$e\left(\frac{33}{56}\right)$	$e\left(\frac{39}{56}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{13}{56}\right)$
$\chi_{4640}(3677,\cdot)$	$-1$	$1$	$e\left(\frac{25}{56}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{25}{28}\right)$	$e\left(\frac{41}{56}\right)$	$e\left(\frac{13}{56}\right)$	$-i$	$e\left(\frac{31}{56}\right)$	$e\left(\frac{1}{56}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{19}{56}\right)$
$\chi_{4640}(3757,\cdot)$	$-1$	$1$	$e\left(\frac{5}{56}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{5}{28}\right)$	$e\left(\frac{53}{56}\right)$	$e\left(\frac{25}{56}\right)$	$-i$	$e\left(\frac{51}{56}\right)$	$e\left(\frac{45}{56}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{15}{56}\right)$
$\chi_{4640}(3893,\cdot)$	$-1$	$1$	$e\left(\frac{15}{56}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{47}{56}\right)$	$e\left(\frac{19}{56}\right)$	$i$	$e\left(\frac{41}{56}\right)$	$e\left(\frac{23}{56}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{45}{56}\right)$
$\chi_{4640}(3997,\cdot)$	$-1$	$1$	$e\left(\frac{17}{56}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{17}{28}\right)$	$e\left(\frac{1}{56}\right)$	$e\left(\frac{29}{56}\right)$	$-i$	$e\left(\frac{39}{56}\right)$	$e\left(\frac{41}{56}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{51}{56}\right)$
$\chi_{4640}(4317,\cdot)$	$-1$	$1$	$e\left(\frac{41}{56}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{9}{56}\right)$	$e\left(\frac{37}{56}\right)$	$-i$	$e\left(\frac{15}{56}\right)$	$e\left(\frac{33}{56}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{11}{56}\right)$
$\chi_{4640}(4373,\cdot)$	$-1$	$1$	$e\left(\frac{39}{56}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{11}{28}\right)$	$e\left(\frac{55}{56}\right)$	$e\left(\frac{27}{56}\right)$	$i$	$e\left(\frac{17}{56}\right)$	$e\left(\frac{15}{56}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{5}{56}\right)$
$\chi_{4640}(4453,\cdot)$	$-1$	$1$	$e\left(\frac{19}{56}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{19}{28}\right)$	$e\left(\frac{11}{56}\right)$	$e\left(\frac{39}{56}\right)$	$i$	$e\left(\frac{37}{56}\right)$	$e\left(\frac{3}{56}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{1}{56}\right)$

Overview	Random
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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	\(-1\)	\(1\)	\(3\)	\(7\)	\(9\)	\(11\)	\(13\)	\(17\)	\(19\)	\(21\)	\(23\)	\(27\)
\(\chi_{4640}(53,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{31}{56}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{3}{28}\right)\)	\(e\left(\frac{15}{56}\right)\)	\(e\left(\frac{43}{56}\right)\)	\(i\)	\(e\left(\frac{25}{56}\right)\)	\(e\left(\frac{55}{56}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{37}{56}\right)\)
\(\chi_{4640}(373,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{55}{56}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{27}{28}\right)\)	\(e\left(\frac{23}{56}\right)\)	\(e\left(\frac{51}{56}\right)\)	\(i\)	\(e\left(\frac{1}{56}\right)\)	\(e\left(\frac{47}{56}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{53}{56}\right)\)
\(\chi_{4640}(397,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{37}{56}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{9}{28}\right)\)	\(e\left(\frac{45}{56}\right)\)	\(e\left(\frac{17}{56}\right)\)	\(-i\)	\(e\left(\frac{19}{56}\right)\)	\(e\left(\frac{53}{56}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{55}{56}\right)\)
\(\chi_{4640}(877,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{29}{56}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{1}{28}\right)\)	\(e\left(\frac{5}{56}\right)\)	\(e\left(\frac{33}{56}\right)\)	\(-i\)	\(e\left(\frac{27}{56}\right)\)	\(e\left(\frac{37}{56}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{31}{56}\right)\)
\(\chi_{4640}(1093,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{51}{56}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{23}{28}\right)\)	\(e\left(\frac{3}{56}\right)\)	\(e\left(\frac{31}{56}\right)\)	\(i\)	\(e\left(\frac{5}{56}\right)\)	\(e\left(\frac{11}{56}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{41}{56}\right)\)
\(\chi_{4640}(1357,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{53}{56}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{25}{28}\right)\)	\(e\left(\frac{13}{56}\right)\)	\(e\left(\frac{41}{56}\right)\)	\(-i\)	\(e\left(\frac{3}{56}\right)\)	\(e\left(\frac{29}{56}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{47}{56}\right)\)
\(\chi_{4640}(1437,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{33}{56}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{5}{28}\right)\)	\(e\left(\frac{25}{56}\right)\)	\(e\left(\frac{53}{56}\right)\)	\(-i\)	\(e\left(\frac{23}{56}\right)\)	\(e\left(\frac{17}{56}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{43}{56}\right)\)
\(\chi_{4640}(1573,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{43}{56}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{15}{28}\right)\)	\(e\left(\frac{19}{56}\right)\)	\(e\left(\frac{47}{56}\right)\)	\(i\)	\(e\left(\frac{13}{56}\right)\)	\(e\left(\frac{51}{56}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{17}{56}\right)\)
\(\chi_{4640}(1677,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{45}{56}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{17}{28}\right)\)	\(e\left(\frac{29}{56}\right)\)	\(e\left(\frac{1}{56}\right)\)	\(-i\)	\(e\left(\frac{11}{56}\right)\)	\(e\left(\frac{13}{56}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{23}{56}\right)\)
\(\chi_{4640}(1997,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{13}{56}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{13}{28}\right)\)	\(e\left(\frac{37}{56}\right)\)	\(e\left(\frac{9}{56}\right)\)	\(-i\)	\(e\left(\frac{43}{56}\right)\)	\(e\left(\frac{5}{56}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{39}{56}\right)\)
\(\chi_{4640}(2053,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{11}{56}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{11}{28}\right)\)	\(e\left(\frac{27}{56}\right)\)	\(e\left(\frac{55}{56}\right)\)	\(i\)	\(e\left(\frac{45}{56}\right)\)	\(e\left(\frac{43}{56}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{33}{56}\right)\)
\(\chi_{4640}(2133,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{47}{56}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{19}{28}\right)\)	\(e\left(\frac{39}{56}\right)\)	\(e\left(\frac{11}{56}\right)\)	\(i\)	\(e\left(\frac{9}{56}\right)\)	\(e\left(\frac{31}{56}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{29}{56}\right)\)
\(\chi_{4640}(2373,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{3}{56}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{3}{28}\right)\)	\(e\left(\frac{43}{56}\right)\)	\(e\left(\frac{15}{56}\right)\)	\(i\)	\(e\left(\frac{53}{56}\right)\)	\(e\left(\frac{27}{56}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{9}{56}\right)\)
\(\chi_{4640}(2693,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{27}{56}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{27}{28}\right)\)	\(e\left(\frac{51}{56}\right)\)	\(e\left(\frac{23}{56}\right)\)	\(i\)	\(e\left(\frac{29}{56}\right)\)	\(e\left(\frac{19}{56}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{25}{56}\right)\)
\(\chi_{4640}(2717,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{9}{56}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{9}{28}\right)\)	\(e\left(\frac{17}{56}\right)\)	\(e\left(\frac{45}{56}\right)\)	\(-i\)	\(e\left(\frac{47}{56}\right)\)	\(e\left(\frac{25}{56}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{27}{56}\right)\)
\(\chi_{4640}(3197,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1}{56}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{1}{28}\right)\)	\(e\left(\frac{33}{56}\right)\)	\(e\left(\frac{5}{56}\right)\)	\(-i\)	\(e\left(\frac{55}{56}\right)\)	\(e\left(\frac{9}{56}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{3}{56}\right)\)
\(\chi_{4640}(3413,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{23}{56}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{23}{28}\right)\)	\(e\left(\frac{31}{56}\right)\)	\(e\left(\frac{3}{56}\right)\)	\(i\)	\(e\left(\frac{33}{56}\right)\)	\(e\left(\frac{39}{56}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{13}{56}\right)\)
\(\chi_{4640}(3677,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{25}{56}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{25}{28}\right)\)	\(e\left(\frac{41}{56}\right)\)	\(e\left(\frac{13}{56}\right)\)	\(-i\)	\(e\left(\frac{31}{56}\right)\)	\(e\left(\frac{1}{56}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{19}{56}\right)\)
\(\chi_{4640}(3757,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{5}{56}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{5}{28}\right)\)	\(e\left(\frac{53}{56}\right)\)	\(e\left(\frac{25}{56}\right)\)	\(-i\)	\(e\left(\frac{51}{56}\right)\)	\(e\left(\frac{45}{56}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{15}{56}\right)\)
\(\chi_{4640}(3893,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{15}{56}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{15}{28}\right)\)	\(e\left(\frac{47}{56}\right)\)	\(e\left(\frac{19}{56}\right)\)	\(i\)	\(e\left(\frac{41}{56}\right)\)	\(e\left(\frac{23}{56}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{45}{56}\right)\)
\(\chi_{4640}(3997,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{17}{56}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{17}{28}\right)\)	\(e\left(\frac{1}{56}\right)\)	\(e\left(\frac{29}{56}\right)\)	\(-i\)	\(e\left(\frac{39}{56}\right)\)	\(e\left(\frac{41}{56}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{51}{56}\right)\)
\(\chi_{4640}(4317,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{41}{56}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{13}{28}\right)\)	\(e\left(\frac{9}{56}\right)\)	\(e\left(\frac{37}{56}\right)\)	\(-i\)	\(e\left(\frac{15}{56}\right)\)	\(e\left(\frac{33}{56}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{11}{56}\right)\)
\(\chi_{4640}(4373,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{39}{56}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{11}{28}\right)\)	\(e\left(\frac{55}{56}\right)\)	\(e\left(\frac{27}{56}\right)\)	\(i\)	\(e\left(\frac{17}{56}\right)\)	\(e\left(\frac{15}{56}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{5}{56}\right)\)
\(\chi_{4640}(4453,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{19}{56}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{19}{28}\right)\)	\(e\left(\frac{11}{56}\right)\)	\(e\left(\frac{39}{56}\right)\)	\(i\)	\(e\left(\frac{37}{56}\right)\)	\(e\left(\frac{3}{56}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{1}{56}\right)\)

Introduction

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Varieties

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Groups

Database

Properties

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Basic properties

Related number fields

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	4640.gx
Modulus	$4640$
Conductor	$4640$
Order	$56$
Real	no
Primitive	yes
Minimal	yes
Parity	odd

Modulus:	\(4640\)	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	\(4640\)	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	\(56\)	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:	yes	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);