LMFDB - Dirichlet character orbit 7632.ei

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comment:Define the Dirichlet character orbit

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(7632, base_ring=CyclotomicField(52)) M = H._module chi = DirichletCharacter(H, M([0,13,0,30])) chi.galois_orbit()

gp:[g,chi] = znchar(Mod(37, 7632)) 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("7632.37"); order := Order(chi); { chi^k : k in [1..order-1] | GCD(k,order) eq 1 };

Basic properties

Modulus:	$7632$	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	$848$	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	$52$	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 848.bk	comment:If the character is primitive sage:chi.is_primitive() gp:#znconreyconductor(g,chi)==1 magma:IsPrimitive(chi);
Minimal:	yes
Parity:	even	comment:Parity sage:chi.is_odd() gp:zncharisodd(g,chi) magma:IsOdd(chi);

Related number fields

Field of values:	$\Q(\zeta_{52})$
Fixed field:	Number field defined by a degree 52 polynomial

Characters in Galois orbit

Character	$-1$	$1$	$5$	$7$	$11$	$13$	$17$	$19$	$23$	$25$	$29$	$31$
$\chi_{7632}(37,\cdot)$	$1$	$1$	$e\left(\frac{19}{52}\right)$	$e\left(\frac{15}{26}\right)$	$e\left(\frac{37}{52}\right)$	$e\left(\frac{31}{52}\right)$	$e\left(\frac{10}{13}\right)$	$e\left(\frac{5}{52}\right)$	$1$	$e\left(\frac{19}{26}\right)$	$e\left(\frac{15}{52}\right)$	$e\left(\frac{1}{26}\right)$
$\chi_{7632}(325,\cdot)$	$1$	$1$	$e\left(\frac{47}{52}\right)$	$e\left(\frac{7}{26}\right)$	$e\left(\frac{45}{52}\right)$	$e\left(\frac{11}{52}\right)$	$e\left(\frac{9}{13}\right)$	$e\left(\frac{37}{52}\right)$	$1$	$e\left(\frac{21}{26}\right)$	$e\left(\frac{7}{52}\right)$	$e\left(\frac{23}{26}\right)$
$\chi_{7632}(541,\cdot)$	$1$	$1$	$e\left(\frac{9}{52}\right)$	$e\left(\frac{3}{26}\right)$	$e\left(\frac{23}{52}\right)$	$e\left(\frac{1}{52}\right)$	$e\left(\frac{2}{13}\right)$	$e\left(\frac{27}{52}\right)$	$1$	$e\left(\frac{9}{26}\right)$	$e\left(\frac{29}{52}\right)$	$e\left(\frac{21}{26}\right)$
$\chi_{7632}(1045,\cdot)$	$1$	$1$	$e\left(\frac{31}{52}\right)$	$e\left(\frac{19}{26}\right)$	$e\left(\frac{33}{52}\right)$	$e\left(\frac{15}{52}\right)$	$e\left(\frac{4}{13}\right)$	$e\left(\frac{41}{52}\right)$	$1$	$e\left(\frac{5}{26}\right)$	$e\left(\frac{19}{52}\right)$	$e\left(\frac{3}{26}\right)$
$\chi_{7632}(1117,\cdot)$	$1$	$1$	$e\left(\frac{29}{52}\right)$	$e\left(\frac{1}{26}\right)$	$e\left(\frac{51}{52}\right)$	$e\left(\frac{9}{52}\right)$	$e\left(\frac{5}{13}\right)$	$e\left(\frac{35}{52}\right)$	$1$	$e\left(\frac{3}{26}\right)$	$e\left(\frac{1}{52}\right)$	$e\left(\frac{7}{26}\right)$
$\chi_{7632}(2269,\cdot)$	$1$	$1$	$e\left(\frac{33}{52}\right)$	$e\left(\frac{11}{26}\right)$	$e\left(\frac{15}{52}\right)$	$e\left(\frac{21}{52}\right)$	$e\left(\frac{3}{13}\right)$	$e\left(\frac{47}{52}\right)$	$1$	$e\left(\frac{7}{26}\right)$	$e\left(\frac{37}{52}\right)$	$e\left(\frac{25}{26}\right)$
$\chi_{7632}(2341,\cdot)$	$1$	$1$	$e\left(\frac{51}{52}\right)$	$e\left(\frac{17}{26}\right)$	$e\left(\frac{9}{52}\right)$	$e\left(\frac{23}{52}\right)$	$e\left(\frac{7}{13}\right)$	$e\left(\frac{49}{52}\right)$	$1$	$e\left(\frac{25}{26}\right)$	$e\left(\frac{43}{52}\right)$	$e\left(\frac{15}{26}\right)$
$\chi_{7632}(2773,\cdot)$	$1$	$1$	$e\left(\frac{15}{52}\right)$	$e\left(\frac{5}{26}\right)$	$e\left(\frac{21}{52}\right)$	$e\left(\frac{19}{52}\right)$	$e\left(\frac{12}{13}\right)$	$e\left(\frac{45}{52}\right)$	$1$	$e\left(\frac{15}{26}\right)$	$e\left(\frac{31}{52}\right)$	$e\left(\frac{9}{26}\right)$
$\chi_{7632}(3061,\cdot)$	$1$	$1$	$e\left(\frac{23}{52}\right)$	$e\left(\frac{25}{26}\right)$	$e\left(\frac{1}{52}\right)$	$e\left(\frac{43}{52}\right)$	$e\left(\frac{8}{13}\right)$	$e\left(\frac{17}{52}\right)$	$1$	$e\left(\frac{23}{26}\right)$	$e\left(\frac{51}{52}\right)$	$e\left(\frac{19}{26}\right)$
$\chi_{7632}(3133,\cdot)$	$1$	$1$	$e\left(\frac{1}{52}\right)$	$e\left(\frac{9}{26}\right)$	$e\left(\frac{43}{52}\right)$	$e\left(\frac{29}{52}\right)$	$e\left(\frac{6}{13}\right)$	$e\left(\frac{3}{52}\right)$	$1$	$e\left(\frac{1}{26}\right)$	$e\left(\frac{9}{52}\right)$	$e\left(\frac{11}{26}\right)$
$\chi_{7632}(3205,\cdot)$	$1$	$1$	$e\left(\frac{11}{52}\right)$	$e\left(\frac{21}{26}\right)$	$e\left(\frac{5}{52}\right)$	$e\left(\frac{7}{52}\right)$	$e\left(\frac{1}{13}\right)$	$e\left(\frac{33}{52}\right)$	$1$	$e\left(\frac{11}{26}\right)$	$e\left(\frac{47}{52}\right)$	$e\left(\frac{17}{26}\right)$
$\chi_{7632}(3421,\cdot)$	$1$	$1$	$e\left(\frac{17}{52}\right)$	$e\left(\frac{23}{26}\right)$	$e\left(\frac{3}{52}\right)$	$e\left(\frac{25}{52}\right)$	$e\left(\frac{11}{13}\right)$	$e\left(\frac{51}{52}\right)$	$1$	$e\left(\frac{17}{26}\right)$	$e\left(\frac{49}{52}\right)$	$e\left(\frac{5}{26}\right)$
$\chi_{7632}(3853,\cdot)$	$1$	$1$	$e\left(\frac{45}{52}\right)$	$e\left(\frac{15}{26}\right)$	$e\left(\frac{11}{52}\right)$	$e\left(\frac{5}{52}\right)$	$e\left(\frac{10}{13}\right)$	$e\left(\frac{31}{52}\right)$	$1$	$e\left(\frac{19}{26}\right)$	$e\left(\frac{41}{52}\right)$	$e\left(\frac{1}{26}\right)$
$\chi_{7632}(4141,\cdot)$	$1$	$1$	$e\left(\frac{21}{52}\right)$	$e\left(\frac{7}{26}\right)$	$e\left(\frac{19}{52}\right)$	$e\left(\frac{37}{52}\right)$	$e\left(\frac{9}{13}\right)$	$e\left(\frac{11}{52}\right)$	$1$	$e\left(\frac{21}{26}\right)$	$e\left(\frac{33}{52}\right)$	$e\left(\frac{23}{26}\right)$
$\chi_{7632}(4357,\cdot)$	$1$	$1$	$e\left(\frac{35}{52}\right)$	$e\left(\frac{3}{26}\right)$	$e\left(\frac{49}{52}\right)$	$e\left(\frac{27}{52}\right)$	$e\left(\frac{2}{13}\right)$	$e\left(\frac{1}{52}\right)$	$1$	$e\left(\frac{9}{26}\right)$	$e\left(\frac{3}{52}\right)$	$e\left(\frac{21}{26}\right)$
$\chi_{7632}(4861,\cdot)$	$1$	$1$	$e\left(\frac{5}{52}\right)$	$e\left(\frac{19}{26}\right)$	$e\left(\frac{7}{52}\right)$	$e\left(\frac{41}{52}\right)$	$e\left(\frac{4}{13}\right)$	$e\left(\frac{15}{52}\right)$	$1$	$e\left(\frac{5}{26}\right)$	$e\left(\frac{45}{52}\right)$	$e\left(\frac{3}{26}\right)$
$\chi_{7632}(4933,\cdot)$	$1$	$1$	$e\left(\frac{3}{52}\right)$	$e\left(\frac{1}{26}\right)$	$e\left(\frac{25}{52}\right)$	$e\left(\frac{35}{52}\right)$	$e\left(\frac{5}{13}\right)$	$e\left(\frac{9}{52}\right)$	$1$	$e\left(\frac{3}{26}\right)$	$e\left(\frac{27}{52}\right)$	$e\left(\frac{7}{26}\right)$
$\chi_{7632}(6085,\cdot)$	$1$	$1$	$e\left(\frac{7}{52}\right)$	$e\left(\frac{11}{26}\right)$	$e\left(\frac{41}{52}\right)$	$e\left(\frac{47}{52}\right)$	$e\left(\frac{3}{13}\right)$	$e\left(\frac{21}{52}\right)$	$1$	$e\left(\frac{7}{26}\right)$	$e\left(\frac{11}{52}\right)$	$e\left(\frac{25}{26}\right)$
$\chi_{7632}(6157,\cdot)$	$1$	$1$	$e\left(\frac{25}{52}\right)$	$e\left(\frac{17}{26}\right)$	$e\left(\frac{35}{52}\right)$	$e\left(\frac{49}{52}\right)$	$e\left(\frac{7}{13}\right)$	$e\left(\frac{23}{52}\right)$	$1$	$e\left(\frac{25}{26}\right)$	$e\left(\frac{17}{52}\right)$	$e\left(\frac{15}{26}\right)$
$\chi_{7632}(6589,\cdot)$	$1$	$1$	$e\left(\frac{41}{52}\right)$	$e\left(\frac{5}{26}\right)$	$e\left(\frac{47}{52}\right)$	$e\left(\frac{45}{52}\right)$	$e\left(\frac{12}{13}\right)$	$e\left(\frac{19}{52}\right)$	$1$	$e\left(\frac{15}{26}\right)$	$e\left(\frac{5}{52}\right)$	$e\left(\frac{9}{26}\right)$
$\chi_{7632}(6877,\cdot)$	$1$	$1$	$e\left(\frac{49}{52}\right)$	$e\left(\frac{25}{26}\right)$	$e\left(\frac{27}{52}\right)$	$e\left(\frac{17}{52}\right)$	$e\left(\frac{8}{13}\right)$	$e\left(\frac{43}{52}\right)$	$1$	$e\left(\frac{23}{26}\right)$	$e\left(\frac{25}{52}\right)$	$e\left(\frac{19}{26}\right)$
$\chi_{7632}(6949,\cdot)$	$1$	$1$	$e\left(\frac{27}{52}\right)$	$e\left(\frac{9}{26}\right)$	$e\left(\frac{17}{52}\right)$	$e\left(\frac{3}{52}\right)$	$e\left(\frac{6}{13}\right)$	$e\left(\frac{29}{52}\right)$	$1$	$e\left(\frac{1}{26}\right)$	$e\left(\frac{35}{52}\right)$	$e\left(\frac{11}{26}\right)$
$\chi_{7632}(7021,\cdot)$	$1$	$1$	$e\left(\frac{37}{52}\right)$	$e\left(\frac{21}{26}\right)$	$e\left(\frac{31}{52}\right)$	$e\left(\frac{33}{52}\right)$	$e\left(\frac{1}{13}\right)$	$e\left(\frac{7}{52}\right)$	$1$	$e\left(\frac{11}{26}\right)$	$e\left(\frac{21}{52}\right)$	$e\left(\frac{17}{26}\right)$
$\chi_{7632}(7237,\cdot)$	$1$	$1$	$e\left(\frac{43}{52}\right)$	$e\left(\frac{23}{26}\right)$	$e\left(\frac{29}{52}\right)$	$e\left(\frac{51}{52}\right)$	$e\left(\frac{11}{13}\right)$	$e\left(\frac{25}{52}\right)$	$1$	$e\left(\frac{17}{26}\right)$	$e\left(\frac{23}{52}\right)$	$e\left(\frac{5}{26}\right)$

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

Character	\(-1\)	\(1\)	\(5\)	\(7\)	\(11\)	\(13\)	\(17\)	\(19\)	\(23\)	\(25\)	\(29\)	\(31\)
\(\chi_{7632}(37,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{19}{52}\right)\)	\(e\left(\frac{15}{26}\right)\)	\(e\left(\frac{37}{52}\right)\)	\(e\left(\frac{31}{52}\right)\)	\(e\left(\frac{10}{13}\right)\)	\(e\left(\frac{5}{52}\right)\)	\(1\)	\(e\left(\frac{19}{26}\right)\)	\(e\left(\frac{15}{52}\right)\)	\(e\left(\frac{1}{26}\right)\)
\(\chi_{7632}(325,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{47}{52}\right)\)	\(e\left(\frac{7}{26}\right)\)	\(e\left(\frac{45}{52}\right)\)	\(e\left(\frac{11}{52}\right)\)	\(e\left(\frac{9}{13}\right)\)	\(e\left(\frac{37}{52}\right)\)	\(1\)	\(e\left(\frac{21}{26}\right)\)	\(e\left(\frac{7}{52}\right)\)	\(e\left(\frac{23}{26}\right)\)
\(\chi_{7632}(541,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{9}{52}\right)\)	\(e\left(\frac{3}{26}\right)\)	\(e\left(\frac{23}{52}\right)\)	\(e\left(\frac{1}{52}\right)\)	\(e\left(\frac{2}{13}\right)\)	\(e\left(\frac{27}{52}\right)\)	\(1\)	\(e\left(\frac{9}{26}\right)\)	\(e\left(\frac{29}{52}\right)\)	\(e\left(\frac{21}{26}\right)\)
\(\chi_{7632}(1045,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{31}{52}\right)\)	\(e\left(\frac{19}{26}\right)\)	\(e\left(\frac{33}{52}\right)\)	\(e\left(\frac{15}{52}\right)\)	\(e\left(\frac{4}{13}\right)\)	\(e\left(\frac{41}{52}\right)\)	\(1\)	\(e\left(\frac{5}{26}\right)\)	\(e\left(\frac{19}{52}\right)\)	\(e\left(\frac{3}{26}\right)\)
\(\chi_{7632}(1117,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{29}{52}\right)\)	\(e\left(\frac{1}{26}\right)\)	\(e\left(\frac{51}{52}\right)\)	\(e\left(\frac{9}{52}\right)\)	\(e\left(\frac{5}{13}\right)\)	\(e\left(\frac{35}{52}\right)\)	\(1\)	\(e\left(\frac{3}{26}\right)\)	\(e\left(\frac{1}{52}\right)\)	\(e\left(\frac{7}{26}\right)\)
\(\chi_{7632}(2269,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{33}{52}\right)\)	\(e\left(\frac{11}{26}\right)\)	\(e\left(\frac{15}{52}\right)\)	\(e\left(\frac{21}{52}\right)\)	\(e\left(\frac{3}{13}\right)\)	\(e\left(\frac{47}{52}\right)\)	\(1\)	\(e\left(\frac{7}{26}\right)\)	\(e\left(\frac{37}{52}\right)\)	\(e\left(\frac{25}{26}\right)\)
\(\chi_{7632}(2341,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{51}{52}\right)\)	\(e\left(\frac{17}{26}\right)\)	\(e\left(\frac{9}{52}\right)\)	\(e\left(\frac{23}{52}\right)\)	\(e\left(\frac{7}{13}\right)\)	\(e\left(\frac{49}{52}\right)\)	\(1\)	\(e\left(\frac{25}{26}\right)\)	\(e\left(\frac{43}{52}\right)\)	\(e\left(\frac{15}{26}\right)\)
\(\chi_{7632}(2773,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{15}{52}\right)\)	\(e\left(\frac{5}{26}\right)\)	\(e\left(\frac{21}{52}\right)\)	\(e\left(\frac{19}{52}\right)\)	\(e\left(\frac{12}{13}\right)\)	\(e\left(\frac{45}{52}\right)\)	\(1\)	\(e\left(\frac{15}{26}\right)\)	\(e\left(\frac{31}{52}\right)\)	\(e\left(\frac{9}{26}\right)\)
\(\chi_{7632}(3061,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{23}{52}\right)\)	\(e\left(\frac{25}{26}\right)\)	\(e\left(\frac{1}{52}\right)\)	\(e\left(\frac{43}{52}\right)\)	\(e\left(\frac{8}{13}\right)\)	\(e\left(\frac{17}{52}\right)\)	\(1\)	\(e\left(\frac{23}{26}\right)\)	\(e\left(\frac{51}{52}\right)\)	\(e\left(\frac{19}{26}\right)\)
\(\chi_{7632}(3133,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{52}\right)\)	\(e\left(\frac{9}{26}\right)\)	\(e\left(\frac{43}{52}\right)\)	\(e\left(\frac{29}{52}\right)\)	\(e\left(\frac{6}{13}\right)\)	\(e\left(\frac{3}{52}\right)\)	\(1\)	\(e\left(\frac{1}{26}\right)\)	\(e\left(\frac{9}{52}\right)\)	\(e\left(\frac{11}{26}\right)\)
\(\chi_{7632}(3205,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{52}\right)\)	\(e\left(\frac{21}{26}\right)\)	\(e\left(\frac{5}{52}\right)\)	\(e\left(\frac{7}{52}\right)\)	\(e\left(\frac{1}{13}\right)\)	\(e\left(\frac{33}{52}\right)\)	\(1\)	\(e\left(\frac{11}{26}\right)\)	\(e\left(\frac{47}{52}\right)\)	\(e\left(\frac{17}{26}\right)\)
\(\chi_{7632}(3421,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17}{52}\right)\)	\(e\left(\frac{23}{26}\right)\)	\(e\left(\frac{3}{52}\right)\)	\(e\left(\frac{25}{52}\right)\)	\(e\left(\frac{11}{13}\right)\)	\(e\left(\frac{51}{52}\right)\)	\(1\)	\(e\left(\frac{17}{26}\right)\)	\(e\left(\frac{49}{52}\right)\)	\(e\left(\frac{5}{26}\right)\)
\(\chi_{7632}(3853,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{45}{52}\right)\)	\(e\left(\frac{15}{26}\right)\)	\(e\left(\frac{11}{52}\right)\)	\(e\left(\frac{5}{52}\right)\)	\(e\left(\frac{10}{13}\right)\)	\(e\left(\frac{31}{52}\right)\)	\(1\)	\(e\left(\frac{19}{26}\right)\)	\(e\left(\frac{41}{52}\right)\)	\(e\left(\frac{1}{26}\right)\)
\(\chi_{7632}(4141,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{21}{52}\right)\)	\(e\left(\frac{7}{26}\right)\)	\(e\left(\frac{19}{52}\right)\)	\(e\left(\frac{37}{52}\right)\)	\(e\left(\frac{9}{13}\right)\)	\(e\left(\frac{11}{52}\right)\)	\(1\)	\(e\left(\frac{21}{26}\right)\)	\(e\left(\frac{33}{52}\right)\)	\(e\left(\frac{23}{26}\right)\)
\(\chi_{7632}(4357,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{35}{52}\right)\)	\(e\left(\frac{3}{26}\right)\)	\(e\left(\frac{49}{52}\right)\)	\(e\left(\frac{27}{52}\right)\)	\(e\left(\frac{2}{13}\right)\)	\(e\left(\frac{1}{52}\right)\)	\(1\)	\(e\left(\frac{9}{26}\right)\)	\(e\left(\frac{3}{52}\right)\)	\(e\left(\frac{21}{26}\right)\)
\(\chi_{7632}(4861,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{5}{52}\right)\)	\(e\left(\frac{19}{26}\right)\)	\(e\left(\frac{7}{52}\right)\)	\(e\left(\frac{41}{52}\right)\)	\(e\left(\frac{4}{13}\right)\)	\(e\left(\frac{15}{52}\right)\)	\(1\)	\(e\left(\frac{5}{26}\right)\)	\(e\left(\frac{45}{52}\right)\)	\(e\left(\frac{3}{26}\right)\)
\(\chi_{7632}(4933,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{3}{52}\right)\)	\(e\left(\frac{1}{26}\right)\)	\(e\left(\frac{25}{52}\right)\)	\(e\left(\frac{35}{52}\right)\)	\(e\left(\frac{5}{13}\right)\)	\(e\left(\frac{9}{52}\right)\)	\(1\)	\(e\left(\frac{3}{26}\right)\)	\(e\left(\frac{27}{52}\right)\)	\(e\left(\frac{7}{26}\right)\)
\(\chi_{7632}(6085,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{52}\right)\)	\(e\left(\frac{11}{26}\right)\)	\(e\left(\frac{41}{52}\right)\)	\(e\left(\frac{47}{52}\right)\)	\(e\left(\frac{3}{13}\right)\)	\(e\left(\frac{21}{52}\right)\)	\(1\)	\(e\left(\frac{7}{26}\right)\)	\(e\left(\frac{11}{52}\right)\)	\(e\left(\frac{25}{26}\right)\)
\(\chi_{7632}(6157,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{25}{52}\right)\)	\(e\left(\frac{17}{26}\right)\)	\(e\left(\frac{35}{52}\right)\)	\(e\left(\frac{49}{52}\right)\)	\(e\left(\frac{7}{13}\right)\)	\(e\left(\frac{23}{52}\right)\)	\(1\)	\(e\left(\frac{25}{26}\right)\)	\(e\left(\frac{17}{52}\right)\)	\(e\left(\frac{15}{26}\right)\)
\(\chi_{7632}(6589,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{41}{52}\right)\)	\(e\left(\frac{5}{26}\right)\)	\(e\left(\frac{47}{52}\right)\)	\(e\left(\frac{45}{52}\right)\)	\(e\left(\frac{12}{13}\right)\)	\(e\left(\frac{19}{52}\right)\)	\(1\)	\(e\left(\frac{15}{26}\right)\)	\(e\left(\frac{5}{52}\right)\)	\(e\left(\frac{9}{26}\right)\)
\(\chi_{7632}(6877,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{49}{52}\right)\)	\(e\left(\frac{25}{26}\right)\)	\(e\left(\frac{27}{52}\right)\)	\(e\left(\frac{17}{52}\right)\)	\(e\left(\frac{8}{13}\right)\)	\(e\left(\frac{43}{52}\right)\)	\(1\)	\(e\left(\frac{23}{26}\right)\)	\(e\left(\frac{25}{52}\right)\)	\(e\left(\frac{19}{26}\right)\)
\(\chi_{7632}(6949,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{27}{52}\right)\)	\(e\left(\frac{9}{26}\right)\)	\(e\left(\frac{17}{52}\right)\)	\(e\left(\frac{3}{52}\right)\)	\(e\left(\frac{6}{13}\right)\)	\(e\left(\frac{29}{52}\right)\)	\(1\)	\(e\left(\frac{1}{26}\right)\)	\(e\left(\frac{35}{52}\right)\)	\(e\left(\frac{11}{26}\right)\)
\(\chi_{7632}(7021,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{37}{52}\right)\)	\(e\left(\frac{21}{26}\right)\)	\(e\left(\frac{31}{52}\right)\)	\(e\left(\frac{33}{52}\right)\)	\(e\left(\frac{1}{13}\right)\)	\(e\left(\frac{7}{52}\right)\)	\(1\)	\(e\left(\frac{11}{26}\right)\)	\(e\left(\frac{21}{52}\right)\)	\(e\left(\frac{17}{26}\right)\)
\(\chi_{7632}(7237,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{43}{52}\right)\)	\(e\left(\frac{23}{26}\right)\)	\(e\left(\frac{29}{52}\right)\)	\(e\left(\frac{51}{52}\right)\)	\(e\left(\frac{11}{13}\right)\)	\(e\left(\frac{25}{52}\right)\)	\(1\)	\(e\left(\frac{17}{26}\right)\)	\(e\left(\frac{23}{52}\right)\)	\(e\left(\frac{5}{26}\right)\)

Introduction

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Varieties

Fields

Representations

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	7632.ei
Modulus	$7632$
Conductor	$848$
Order	$52$
Real	no
Primitive	no
Minimal	yes
Parity	even

Modulus:	\(7632\)	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	\(848\)	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	\(52\)	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 848.bk	comment:If the character is primitive sage:chi.is_primitive() gp:#znconreyconductor(g,chi)==1 magma:IsPrimitive(chi);
Minimal:	yes
Parity:	even	comment:Parity sage:chi.is_odd() gp:zncharisodd(g,chi) magma:IsOdd(chi);