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Properties

Label 4160.fz
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([6,3,0,7]))
 
chi.galois_orbit()
 
[g,chi] = znchar(Mod(271,4160))
 
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.bf
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: 12.12.15394540563150776827904.2

Characters in Galois orbit

Character −1-1 11 33 77 99 1111 1717 1919 2121 2323 2727 2929
χ4160(271,⋅)\chi_{4160}(271,\cdot) 11 11 e(712)e\left(\frac{7}{12}\right) e(512)e\left(\frac{5}{12}\right) e(16)e\left(\frac{1}{6}\right) e(56)e\left(\frac{5}{6}\right) e(16)e\left(\frac{1}{6}\right) e(16)e\left(\frac{1}{6}\right) 11 e(56)e\left(\frac{5}{6}\right) −i-i e(112)e\left(\frac{1}{12}\right)
χ4160(431,⋅)\chi_{4160}(431,\cdot) 11 11 e(112)e\left(\frac{1}{12}\right) e(1112)e\left(\frac{11}{12}\right) e(16)e\left(\frac{1}{6}\right) e(56)e\left(\frac{5}{6}\right) e(16)e\left(\frac{1}{6}\right) e(16)e\left(\frac{1}{6}\right) 11 e(56)e\left(\frac{5}{6}\right) ii e(712)e\left(\frac{7}{12}\right)
χ4160(2191,⋅)\chi_{4160}(2191,\cdot) 11 11 e(1112)e\left(\frac{11}{12}\right) e(112)e\left(\frac{1}{12}\right) e(56)e\left(\frac{5}{6}\right) e(16)e\left(\frac{1}{6}\right) e(56)e\left(\frac{5}{6}\right) e(56)e\left(\frac{5}{6}\right) 11 e(16)e\left(\frac{1}{6}\right) −i-i e(512)e\left(\frac{5}{12}\right)
χ4160(2671,⋅)\chi_{4160}(2671,\cdot) 11 11 e(512)e\left(\frac{5}{12}\right) e(712)e\left(\frac{7}{12}\right) e(56)e\left(\frac{5}{6}\right) e(16)e\left(\frac{1}{6}\right) e(56)e\left(\frac{5}{6}\right) e(56)e\left(\frac{5}{6}\right) 11 e(16)e\left(\frac{1}{6}\right) ii e(1112)e\left(\frac{11}{12}\right)