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Properties

Label 1368.eb
Modulus 13681368
Conductor 13681368
Order 1818
Real no
Primitive yes
Minimal yes
Parity even

Related objects

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Show commands: PariGP / SageMath
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1368, base_ring=CyclotomicField(18))
 
M = H._module
 
chi = DirichletCharacter(H, M([9,9,15,10]))
 
chi.galois_orbit()
 
[g,chi] = znchar(Mod(131,1368))
 
order = charorder(g,chi)
 
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: 13681368
Conductor: 13681368
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: 1818
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: yes
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Related number fields

Field of values: Q(ζ9)\Q(\zeta_{9})
Fixed field: Number field defined by a degree 18 polynomial

Characters in Galois orbit

Character −1-1 11 55 77 1111 1313 1717 2323 2525 2929 3131 3535
χ1368(131,⋅)\chi_{1368}(131,\cdot) 11 11 e(59)e\left(\frac{5}{9}\right) e(16)e\left(\frac{1}{6}\right) −1-1 e(1718)e\left(\frac{17}{18}\right) e(118)e\left(\frac{1}{18}\right) e(79)e\left(\frac{7}{9}\right) e(19)e\left(\frac{1}{9}\right) e(79)e\left(\frac{7}{9}\right) −1-1 e(1318)e\left(\frac{13}{18}\right)
χ1368(347,⋅)\chi_{1368}(347,\cdot) 11 11 e(89)e\left(\frac{8}{9}\right) e(16)e\left(\frac{1}{6}\right) −1-1 e(1118)e\left(\frac{11}{18}\right) e(718)e\left(\frac{7}{18}\right) e(49)e\left(\frac{4}{9}\right) e(79)e\left(\frac{7}{9}\right) e(49)e\left(\frac{4}{9}\right) −1-1 e(118)e\left(\frac{1}{18}\right)
χ1368(443,⋅)\chi_{1368}(443,\cdot) 11 11 e(79)e\left(\frac{7}{9}\right) e(56)e\left(\frac{5}{6}\right) −1-1 e(1318)e\left(\frac{13}{18}\right) e(518)e\left(\frac{5}{18}\right) e(89)e\left(\frac{8}{9}\right) e(59)e\left(\frac{5}{9}\right) e(89)e\left(\frac{8}{9}\right) −1-1 e(1118)e\left(\frac{11}{18}\right)
χ1368(491,⋅)\chi_{1368}(491,\cdot) 11 11 e(29)e\left(\frac{2}{9}\right) e(16)e\left(\frac{1}{6}\right) −1-1 e(518)e\left(\frac{5}{18}\right) e(1318)e\left(\frac{13}{18}\right) e(19)e\left(\frac{1}{9}\right) e(49)e\left(\frac{4}{9}\right) e(19)e\left(\frac{1}{9}\right) −1-1 e(718)e\left(\frac{7}{18}\right)
χ1368(731,⋅)\chi_{1368}(731,\cdot) 11 11 e(49)e\left(\frac{4}{9}\right) e(56)e\left(\frac{5}{6}\right) −1-1 e(118)e\left(\frac{1}{18}\right) e(1718)e\left(\frac{17}{18}\right) e(29)e\left(\frac{2}{9}\right) e(89)e\left(\frac{8}{9}\right) e(29)e\left(\frac{2}{9}\right) −1-1 e(518)e\left(\frac{5}{18}\right)
χ1368(1163,⋅)\chi_{1368}(1163,\cdot) 11 11 e(19)e\left(\frac{1}{9}\right) e(56)e\left(\frac{5}{6}\right) −1-1 e(718)e\left(\frac{7}{18}\right) e(1118)e\left(\frac{11}{18}\right) e(59)e\left(\frac{5}{9}\right) e(29)e\left(\frac{2}{9}\right) e(59)e\left(\frac{5}{9}\right) −1-1 e(1718)e\left(\frac{17}{18}\right)