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Properties

Label 4160.gb
Modulus 41604160
Conductor 208208
Order 1212
Real no
Primitive no
Minimal no
Parity even

Related objects

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Show commands: PariGP / SageMath
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(4160, base_ring=CyclotomicField(12))
 
M = H._module
 
chi = DirichletCharacter(H, M([0,9,0,4]))
 
chi.galois_orbit()
 
[g,chi] = znchar(Mod(81,4160))
 
order = charorder(g,chi)
 
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: 41604160
Conductor: 208208
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: 1212
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from 208.bj
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(ζ12)\Q(\zeta_{12})
Fixed field: 12.12.7007073538075000832.1

Characters in Galois orbit

Character −1-1 11 33 77 99 1111 1717 1919 2121 2323 2727 2929
χ4160(81,⋅)\chi_{4160}(81,\cdot) 11 11 e(712)e\left(\frac{7}{12}\right) e(16)e\left(\frac{1}{6}\right) e(16)e\left(\frac{1}{6}\right) e(112)e\left(\frac{1}{12}\right) e(23)e\left(\frac{2}{3}\right) e(1112)e\left(\frac{11}{12}\right) −i-i e(56)e\left(\frac{5}{6}\right) −i-i e(712)e\left(\frac{7}{12}\right)
χ4160(1361,⋅)\chi_{4160}(1361,\cdot) 11 11 e(1112)e\left(\frac{11}{12}\right) e(56)e\left(\frac{5}{6}\right) e(56)e\left(\frac{5}{6}\right) e(512)e\left(\frac{5}{12}\right) e(13)e\left(\frac{1}{3}\right) e(712)e\left(\frac{7}{12}\right) −i-i e(16)e\left(\frac{1}{6}\right) −i-i e(1112)e\left(\frac{11}{12}\right)
χ4160(2161,⋅)\chi_{4160}(2161,\cdot) 11 11 e(112)e\left(\frac{1}{12}\right) e(16)e\left(\frac{1}{6}\right) e(16)e\left(\frac{1}{6}\right) e(712)e\left(\frac{7}{12}\right) e(23)e\left(\frac{2}{3}\right) e(512)e\left(\frac{5}{12}\right) ii e(56)e\left(\frac{5}{6}\right) ii e(112)e\left(\frac{1}{12}\right)
χ4160(3441,⋅)\chi_{4160}(3441,\cdot) 11 11 e(512)e\left(\frac{5}{12}\right) e(56)e\left(\frac{5}{6}\right) e(56)e\left(\frac{5}{6}\right) e(1112)e\left(\frac{11}{12}\right) e(13)e\left(\frac{1}{3}\right) e(112)e\left(\frac{1}{12}\right) ii e(16)e\left(\frac{1}{6}\right) ii e(512)e\left(\frac{5}{12}\right)