LMFDB - Dirichlet character orbit 162240.xa

Show commands: PariGP / SageMath

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(162240, base_ring=CyclotomicField(52))

M = H._module

chi = DirichletCharacter(H, M([26,39,26,13,21]))

chi.galois_orbit()

[g,chi] = znchar(Mod(47,162240))

order = charorder(g,chi)

[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$162240$
Conductor:	$40560$	sage: chi.conductor() pari: znconreyconductor(g,chi)
Order:	$52$	sage: chi.multiplicative_order() pari: charorder(g,chi)
Real:	no
Primitive:	no, induced from 40560.ne	sage: chi.is_primitive() pari: #znconreyconductor(g,chi)==1
Minimal:	no
Parity:	even	sage: chi.is_odd() pari: zncharisodd(g,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	$-1$	$1$	$7$	$11$	$17$	$19$	$23$	$29$	$31$	$37$	$41$	$43$
$\chi_{162240}(47,\cdot)$	$1$	$1$	$e\left(\frac{6}{13}\right)$	$e\left(\frac{9}{26}\right)$	$e\left(\frac{37}{52}\right)$	$-1$	$-i$	$e\left(\frac{21}{52}\right)$	$e\left(\frac{51}{52}\right)$	$e\left(\frac{51}{52}\right)$	$e\left(\frac{17}{52}\right)$	$e\left(\frac{7}{26}\right)$
$\chi_{162240}(3983,\cdot)$	$1$	$1$	$e\left(\frac{3}{13}\right)$	$e\left(\frac{11}{26}\right)$	$e\left(\frac{51}{52}\right)$	$-1$	$i$	$e\left(\frac{43}{52}\right)$	$e\left(\frac{45}{52}\right)$	$e\left(\frac{45}{52}\right)$	$e\left(\frac{15}{52}\right)$	$e\left(\frac{23}{26}\right)$
$\chi_{162240}(12527,\cdot)$	$1$	$1$	$e\left(\frac{9}{13}\right)$	$e\left(\frac{7}{26}\right)$	$e\left(\frac{49}{52}\right)$	$-1$	$-i$	$e\left(\frac{25}{52}\right)$	$e\left(\frac{31}{52}\right)$	$e\left(\frac{31}{52}\right)$	$e\left(\frac{45}{52}\right)$	$e\left(\frac{17}{26}\right)$
$\chi_{162240}(25007,\cdot)$	$1$	$1$	$e\left(\frac{12}{13}\right)$	$e\left(\frac{5}{26}\right)$	$e\left(\frac{9}{52}\right)$	$-1$	$-i$	$e\left(\frac{29}{52}\right)$	$e\left(\frac{11}{52}\right)$	$e\left(\frac{11}{52}\right)$	$e\left(\frac{21}{52}\right)$	$e\left(\frac{1}{26}\right)$
$\chi_{162240}(28943,\cdot)$	$1$	$1$	$e\left(\frac{10}{13}\right)$	$e\left(\frac{15}{26}\right)$	$e\left(\frac{27}{52}\right)$	$-1$	$i$	$e\left(\frac{35}{52}\right)$	$e\left(\frac{33}{52}\right)$	$e\left(\frac{33}{52}\right)$	$e\left(\frac{11}{52}\right)$	$e\left(\frac{3}{26}\right)$
$\chi_{162240}(37487,\cdot)$	$1$	$1$	$e\left(\frac{2}{13}\right)$	$e\left(\frac{3}{26}\right)$	$e\left(\frac{21}{52}\right)$	$-1$	$-i$	$e\left(\frac{33}{52}\right)$	$e\left(\frac{43}{52}\right)$	$e\left(\frac{43}{52}\right)$	$e\left(\frac{49}{52}\right)$	$e\left(\frac{11}{26}\right)$
$\chi_{162240}(41423,\cdot)$	$1$	$1$	$e\left(\frac{7}{13}\right)$	$e\left(\frac{17}{26}\right)$	$e\left(\frac{15}{52}\right)$	$-1$	$i$	$e\left(\frac{31}{52}\right)$	$e\left(\frac{1}{52}\right)$	$e\left(\frac{1}{52}\right)$	$e\left(\frac{35}{52}\right)$	$e\left(\frac{19}{26}\right)$
$\chi_{162240}(49967,\cdot)$	$1$	$1$	$e\left(\frac{5}{13}\right)$	$e\left(\frac{1}{26}\right)$	$e\left(\frac{33}{52}\right)$	$-1$	$-i$	$e\left(\frac{37}{52}\right)$	$e\left(\frac{23}{52}\right)$	$e\left(\frac{23}{52}\right)$	$e\left(\frac{25}{52}\right)$	$e\left(\frac{21}{26}\right)$
$\chi_{162240}(53903,\cdot)$	$1$	$1$	$e\left(\frac{4}{13}\right)$	$e\left(\frac{19}{26}\right)$	$e\left(\frac{3}{52}\right)$	$-1$	$i$	$e\left(\frac{27}{52}\right)$	$e\left(\frac{21}{52}\right)$	$e\left(\frac{21}{52}\right)$	$e\left(\frac{7}{52}\right)$	$e\left(\frac{9}{26}\right)$
$\chi_{162240}(62447,\cdot)$	$1$	$1$	$e\left(\frac{8}{13}\right)$	$e\left(\frac{25}{26}\right)$	$e\left(\frac{45}{52}\right)$	$-1$	$-i$	$e\left(\frac{41}{52}\right)$	$e\left(\frac{3}{52}\right)$	$e\left(\frac{3}{52}\right)$	$e\left(\frac{1}{52}\right)$	$e\left(\frac{5}{26}\right)$
$\chi_{162240}(66383,\cdot)$	$1$	$1$	$e\left(\frac{1}{13}\right)$	$e\left(\frac{21}{26}\right)$	$e\left(\frac{43}{52}\right)$	$-1$	$i$	$e\left(\frac{23}{52}\right)$	$e\left(\frac{41}{52}\right)$	$e\left(\frac{41}{52}\right)$	$e\left(\frac{31}{52}\right)$	$e\left(\frac{25}{26}\right)$
$\chi_{162240}(74927,\cdot)$	$1$	$1$	$e\left(\frac{11}{13}\right)$	$e\left(\frac{23}{26}\right)$	$e\left(\frac{5}{52}\right)$	$-1$	$-i$	$e\left(\frac{45}{52}\right)$	$e\left(\frac{35}{52}\right)$	$e\left(\frac{35}{52}\right)$	$e\left(\frac{29}{52}\right)$	$e\left(\frac{15}{26}\right)$
$\chi_{162240}(78863,\cdot)$	$1$	$1$	$e\left(\frac{11}{13}\right)$	$e\left(\frac{23}{26}\right)$	$e\left(\frac{31}{52}\right)$	$-1$	$i$	$e\left(\frac{19}{52}\right)$	$e\left(\frac{9}{52}\right)$	$e\left(\frac{9}{52}\right)$	$e\left(\frac{3}{52}\right)$	$e\left(\frac{15}{26}\right)$
$\chi_{162240}(87407,\cdot)$	$1$	$1$	$e\left(\frac{1}{13}\right)$	$e\left(\frac{21}{26}\right)$	$e\left(\frac{17}{52}\right)$	$-1$	$-i$	$e\left(\frac{49}{52}\right)$	$e\left(\frac{15}{52}\right)$	$e\left(\frac{15}{52}\right)$	$e\left(\frac{5}{52}\right)$	$e\left(\frac{25}{26}\right)$
$\chi_{162240}(91343,\cdot)$	$1$	$1$	$e\left(\frac{8}{13}\right)$	$e\left(\frac{25}{26}\right)$	$e\left(\frac{19}{52}\right)$	$-1$	$i$	$e\left(\frac{15}{52}\right)$	$e\left(\frac{29}{52}\right)$	$e\left(\frac{29}{52}\right)$	$e\left(\frac{27}{52}\right)$	$e\left(\frac{5}{26}\right)$
$\chi_{162240}(99887,\cdot)$	$1$	$1$	$e\left(\frac{4}{13}\right)$	$e\left(\frac{19}{26}\right)$	$e\left(\frac{29}{52}\right)$	$-1$	$-i$	$e\left(\frac{1}{52}\right)$	$e\left(\frac{47}{52}\right)$	$e\left(\frac{47}{52}\right)$	$e\left(\frac{33}{52}\right)$	$e\left(\frac{9}{26}\right)$
$\chi_{162240}(103823,\cdot)$	$1$	$1$	$e\left(\frac{5}{13}\right)$	$e\left(\frac{1}{26}\right)$	$e\left(\frac{7}{52}\right)$	$-1$	$i$	$e\left(\frac{11}{52}\right)$	$e\left(\frac{49}{52}\right)$	$e\left(\frac{49}{52}\right)$	$e\left(\frac{51}{52}\right)$	$e\left(\frac{21}{26}\right)$
$\chi_{162240}(112367,\cdot)$	$1$	$1$	$e\left(\frac{7}{13}\right)$	$e\left(\frac{17}{26}\right)$	$e\left(\frac{41}{52}\right)$	$-1$	$-i$	$e\left(\frac{5}{52}\right)$	$e\left(\frac{27}{52}\right)$	$e\left(\frac{27}{52}\right)$	$e\left(\frac{9}{52}\right)$	$e\left(\frac{19}{26}\right)$
$\chi_{162240}(116303,\cdot)$	$1$	$1$	$e\left(\frac{2}{13}\right)$	$e\left(\frac{3}{26}\right)$	$e\left(\frac{47}{52}\right)$	$-1$	$i$	$e\left(\frac{7}{52}\right)$	$e\left(\frac{17}{52}\right)$	$e\left(\frac{17}{52}\right)$	$e\left(\frac{23}{52}\right)$	$e\left(\frac{11}{26}\right)$
$\chi_{162240}(124847,\cdot)$	$1$	$1$	$e\left(\frac{10}{13}\right)$	$e\left(\frac{15}{26}\right)$	$e\left(\frac{1}{52}\right)$	$-1$	$-i$	$e\left(\frac{9}{52}\right)$	$e\left(\frac{7}{52}\right)$	$e\left(\frac{7}{52}\right)$	$e\left(\frac{37}{52}\right)$	$e\left(\frac{3}{26}\right)$
$\chi_{162240}(128783,\cdot)$	$1$	$1$	$e\left(\frac{12}{13}\right)$	$e\left(\frac{5}{26}\right)$	$e\left(\frac{35}{52}\right)$	$-1$	$i$	$e\left(\frac{3}{52}\right)$	$e\left(\frac{37}{52}\right)$	$e\left(\frac{37}{52}\right)$	$e\left(\frac{47}{52}\right)$	$e\left(\frac{1}{26}\right)$
$\chi_{162240}(141263,\cdot)$	$1$	$1$	$e\left(\frac{9}{13}\right)$	$e\left(\frac{7}{26}\right)$	$e\left(\frac{23}{52}\right)$	$-1$	$i$	$e\left(\frac{51}{52}\right)$	$e\left(\frac{5}{52}\right)$	$e\left(\frac{5}{52}\right)$	$e\left(\frac{19}{52}\right)$	$e\left(\frac{17}{26}\right)$
$\chi_{162240}(149807,\cdot)$	$1$	$1$	$e\left(\frac{3}{13}\right)$	$e\left(\frac{11}{26}\right)$	$e\left(\frac{25}{52}\right)$	$-1$	$-i$	$e\left(\frac{17}{52}\right)$	$e\left(\frac{19}{52}\right)$	$e\left(\frac{19}{52}\right)$	$e\left(\frac{41}{52}\right)$	$e\left(\frac{23}{26}\right)$
$\chi_{162240}(153743,\cdot)$	$1$	$1$	$e\left(\frac{6}{13}\right)$	$e\left(\frac{9}{26}\right)$	$e\left(\frac{11}{52}\right)$	$-1$	$i$	$e\left(\frac{47}{52}\right)$	$e\left(\frac{25}{52}\right)$	$e\left(\frac{25}{52}\right)$	$e\left(\frac{43}{52}\right)$	$e\left(\frac{7}{26}\right)$

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 $\F_{q}$

Character	\(-1\)	\(1\)	\(7\)	\(11\)	\(17\)	\(19\)	\(23\)	\(29\)	\(31\)	\(37\)	\(41\)	\(43\)
\(\chi_{162240}(47,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{6}{13}\right)\)	\(e\left(\frac{9}{26}\right)\)	\(e\left(\frac{37}{52}\right)\)	\(-1\)	\(-i\)	\(e\left(\frac{21}{52}\right)\)	\(e\left(\frac{51}{52}\right)\)	\(e\left(\frac{51}{52}\right)\)	\(e\left(\frac{17}{52}\right)\)	\(e\left(\frac{7}{26}\right)\)
\(\chi_{162240}(3983,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{3}{13}\right)\)	\(e\left(\frac{11}{26}\right)\)	\(e\left(\frac{51}{52}\right)\)	\(-1\)	\(i\)	\(e\left(\frac{43}{52}\right)\)	\(e\left(\frac{45}{52}\right)\)	\(e\left(\frac{45}{52}\right)\)	\(e\left(\frac{15}{52}\right)\)	\(e\left(\frac{23}{26}\right)\)
\(\chi_{162240}(12527,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{9}{13}\right)\)	\(e\left(\frac{7}{26}\right)\)	\(e\left(\frac{49}{52}\right)\)	\(-1\)	\(-i\)	\(e\left(\frac{25}{52}\right)\)	\(e\left(\frac{31}{52}\right)\)	\(e\left(\frac{31}{52}\right)\)	\(e\left(\frac{45}{52}\right)\)	\(e\left(\frac{17}{26}\right)\)
\(\chi_{162240}(25007,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{12}{13}\right)\)	\(e\left(\frac{5}{26}\right)\)	\(e\left(\frac{9}{52}\right)\)	\(-1\)	\(-i\)	\(e\left(\frac{29}{52}\right)\)	\(e\left(\frac{11}{52}\right)\)	\(e\left(\frac{11}{52}\right)\)	\(e\left(\frac{21}{52}\right)\)	\(e\left(\frac{1}{26}\right)\)
\(\chi_{162240}(28943,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{10}{13}\right)\)	\(e\left(\frac{15}{26}\right)\)	\(e\left(\frac{27}{52}\right)\)	\(-1\)	\(i\)	\(e\left(\frac{35}{52}\right)\)	\(e\left(\frac{33}{52}\right)\)	\(e\left(\frac{33}{52}\right)\)	\(e\left(\frac{11}{52}\right)\)	\(e\left(\frac{3}{26}\right)\)
\(\chi_{162240}(37487,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{2}{13}\right)\)	\(e\left(\frac{3}{26}\right)\)	\(e\left(\frac{21}{52}\right)\)	\(-1\)	\(-i\)	\(e\left(\frac{33}{52}\right)\)	\(e\left(\frac{43}{52}\right)\)	\(e\left(\frac{43}{52}\right)\)	\(e\left(\frac{49}{52}\right)\)	\(e\left(\frac{11}{26}\right)\)
\(\chi_{162240}(41423,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{13}\right)\)	\(e\left(\frac{17}{26}\right)\)	\(e\left(\frac{15}{52}\right)\)	\(-1\)	\(i\)	\(e\left(\frac{31}{52}\right)\)	\(e\left(\frac{1}{52}\right)\)	\(e\left(\frac{1}{52}\right)\)	\(e\left(\frac{35}{52}\right)\)	\(e\left(\frac{19}{26}\right)\)
\(\chi_{162240}(49967,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{5}{13}\right)\)	\(e\left(\frac{1}{26}\right)\)	\(e\left(\frac{33}{52}\right)\)	\(-1\)	\(-i\)	\(e\left(\frac{37}{52}\right)\)	\(e\left(\frac{23}{52}\right)\)	\(e\left(\frac{23}{52}\right)\)	\(e\left(\frac{25}{52}\right)\)	\(e\left(\frac{21}{26}\right)\)
\(\chi_{162240}(53903,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{4}{13}\right)\)	\(e\left(\frac{19}{26}\right)\)	\(e\left(\frac{3}{52}\right)\)	\(-1\)	\(i\)	\(e\left(\frac{27}{52}\right)\)	\(e\left(\frac{21}{52}\right)\)	\(e\left(\frac{21}{52}\right)\)	\(e\left(\frac{7}{52}\right)\)	\(e\left(\frac{9}{26}\right)\)
\(\chi_{162240}(62447,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{8}{13}\right)\)	\(e\left(\frac{25}{26}\right)\)	\(e\left(\frac{45}{52}\right)\)	\(-1\)	\(-i\)	\(e\left(\frac{41}{52}\right)\)	\(e\left(\frac{3}{52}\right)\)	\(e\left(\frac{3}{52}\right)\)	\(e\left(\frac{1}{52}\right)\)	\(e\left(\frac{5}{26}\right)\)
\(\chi_{162240}(66383,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{13}\right)\)	\(e\left(\frac{21}{26}\right)\)	\(e\left(\frac{43}{52}\right)\)	\(-1\)	\(i\)	\(e\left(\frac{23}{52}\right)\)	\(e\left(\frac{41}{52}\right)\)	\(e\left(\frac{41}{52}\right)\)	\(e\left(\frac{31}{52}\right)\)	\(e\left(\frac{25}{26}\right)\)
\(\chi_{162240}(74927,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{13}\right)\)	\(e\left(\frac{23}{26}\right)\)	\(e\left(\frac{5}{52}\right)\)	\(-1\)	\(-i\)	\(e\left(\frac{45}{52}\right)\)	\(e\left(\frac{35}{52}\right)\)	\(e\left(\frac{35}{52}\right)\)	\(e\left(\frac{29}{52}\right)\)	\(e\left(\frac{15}{26}\right)\)
\(\chi_{162240}(78863,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{13}\right)\)	\(e\left(\frac{23}{26}\right)\)	\(e\left(\frac{31}{52}\right)\)	\(-1\)	\(i\)	\(e\left(\frac{19}{52}\right)\)	\(e\left(\frac{9}{52}\right)\)	\(e\left(\frac{9}{52}\right)\)	\(e\left(\frac{3}{52}\right)\)	\(e\left(\frac{15}{26}\right)\)
\(\chi_{162240}(87407,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{13}\right)\)	\(e\left(\frac{21}{26}\right)\)	\(e\left(\frac{17}{52}\right)\)	\(-1\)	\(-i\)	\(e\left(\frac{49}{52}\right)\)	\(e\left(\frac{15}{52}\right)\)	\(e\left(\frac{15}{52}\right)\)	\(e\left(\frac{5}{52}\right)\)	\(e\left(\frac{25}{26}\right)\)
\(\chi_{162240}(91343,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{8}{13}\right)\)	\(e\left(\frac{25}{26}\right)\)	\(e\left(\frac{19}{52}\right)\)	\(-1\)	\(i\)	\(e\left(\frac{15}{52}\right)\)	\(e\left(\frac{29}{52}\right)\)	\(e\left(\frac{29}{52}\right)\)	\(e\left(\frac{27}{52}\right)\)	\(e\left(\frac{5}{26}\right)\)
\(\chi_{162240}(99887,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{4}{13}\right)\)	\(e\left(\frac{19}{26}\right)\)	\(e\left(\frac{29}{52}\right)\)	\(-1\)	\(-i\)	\(e\left(\frac{1}{52}\right)\)	\(e\left(\frac{47}{52}\right)\)	\(e\left(\frac{47}{52}\right)\)	\(e\left(\frac{33}{52}\right)\)	\(e\left(\frac{9}{26}\right)\)
\(\chi_{162240}(103823,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{5}{13}\right)\)	\(e\left(\frac{1}{26}\right)\)	\(e\left(\frac{7}{52}\right)\)	\(-1\)	\(i\)	\(e\left(\frac{11}{52}\right)\)	\(e\left(\frac{49}{52}\right)\)	\(e\left(\frac{49}{52}\right)\)	\(e\left(\frac{51}{52}\right)\)	\(e\left(\frac{21}{26}\right)\)
\(\chi_{162240}(112367,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{13}\right)\)	\(e\left(\frac{17}{26}\right)\)	\(e\left(\frac{41}{52}\right)\)	\(-1\)	\(-i\)	\(e\left(\frac{5}{52}\right)\)	\(e\left(\frac{27}{52}\right)\)	\(e\left(\frac{27}{52}\right)\)	\(e\left(\frac{9}{52}\right)\)	\(e\left(\frac{19}{26}\right)\)
\(\chi_{162240}(116303,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{2}{13}\right)\)	\(e\left(\frac{3}{26}\right)\)	\(e\left(\frac{47}{52}\right)\)	\(-1\)	\(i\)	\(e\left(\frac{7}{52}\right)\)	\(e\left(\frac{17}{52}\right)\)	\(e\left(\frac{17}{52}\right)\)	\(e\left(\frac{23}{52}\right)\)	\(e\left(\frac{11}{26}\right)\)
\(\chi_{162240}(124847,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{10}{13}\right)\)	\(e\left(\frac{15}{26}\right)\)	\(e\left(\frac{1}{52}\right)\)	\(-1\)	\(-i\)	\(e\left(\frac{9}{52}\right)\)	\(e\left(\frac{7}{52}\right)\)	\(e\left(\frac{7}{52}\right)\)	\(e\left(\frac{37}{52}\right)\)	\(e\left(\frac{3}{26}\right)\)
\(\chi_{162240}(128783,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{12}{13}\right)\)	\(e\left(\frac{5}{26}\right)\)	\(e\left(\frac{35}{52}\right)\)	\(-1\)	\(i\)	\(e\left(\frac{3}{52}\right)\)	\(e\left(\frac{37}{52}\right)\)	\(e\left(\frac{37}{52}\right)\)	\(e\left(\frac{47}{52}\right)\)	\(e\left(\frac{1}{26}\right)\)
\(\chi_{162240}(141263,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{9}{13}\right)\)	\(e\left(\frac{7}{26}\right)\)	\(e\left(\frac{23}{52}\right)\)	\(-1\)	\(i\)	\(e\left(\frac{51}{52}\right)\)	\(e\left(\frac{5}{52}\right)\)	\(e\left(\frac{5}{52}\right)\)	\(e\left(\frac{19}{52}\right)\)	\(e\left(\frac{17}{26}\right)\)
\(\chi_{162240}(149807,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{3}{13}\right)\)	\(e\left(\frac{11}{26}\right)\)	\(e\left(\frac{25}{52}\right)\)	\(-1\)	\(-i\)	\(e\left(\frac{17}{52}\right)\)	\(e\left(\frac{19}{52}\right)\)	\(e\left(\frac{19}{52}\right)\)	\(e\left(\frac{41}{52}\right)\)	\(e\left(\frac{23}{26}\right)\)
\(\chi_{162240}(153743,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{6}{13}\right)\)	\(e\left(\frac{9}{26}\right)\)	\(e\left(\frac{11}{52}\right)\)	\(-1\)	\(i\)	\(e\left(\frac{47}{52}\right)\)	\(e\left(\frac{25}{52}\right)\)	\(e\left(\frac{25}{52}\right)\)	\(e\left(\frac{43}{52}\right)\)	\(e\left(\frac{7}{26}\right)\)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more

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	162240.xa
Modulus	$162240$
Conductor	$40560$
Order	$52$
Real	no
Primitive	no
Minimal	no
Parity	even

Modulus:	\(162240\)
Conductor:	\(40560\)	sage: chi.conductor() pari: znconreyconductor(g,chi)
Order:	\(52\)	sage: chi.multiplicative_order() pari: charorder(g,chi)
Real:	no
Primitive:	no, induced from 40560.ne	sage: chi.is_primitive() pari: #znconreyconductor(g,chi)==1
Minimal:	no
Parity:	even	sage: chi.is_odd() pari: zncharisodd(g,chi)