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Properties

Label 4368.ll
Modulus 43684368
Conductor 14561456
Order 1212
Real no
Primitive no
Minimal yes
Parity even

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Show commands: PariGP / SageMath
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(4368, base_ring=CyclotomicField(12))
 
M = H._module
 
chi = DirichletCharacter(H, M([0,9,0,4,2]))
 
chi.galois_orbit()
 
[g,chi] = znchar(Mod(1213,4368))
 
order = charorder(g,chi)
 
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: 43684368
Conductor: 14561456
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: 1212
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from 1456.fl
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(ζ12)\Q(\zeta_{12})
Fixed field: 12.12.6826650987153243185252139008.2

Characters in Galois orbit

Character −1-1 11 55 1111 1717 1919 2323 2525 2929 3131 3737 4141
χ4368(1213,⋅)\chi_{4368}(1213,\cdot) 11 11 e(1112)e\left(\frac{11}{12}\right) ii e(23)e\left(\frac{2}{3}\right) −i-i 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(56)e\left(\frac{5}{6}\right) e(712)e\left(\frac{7}{12}\right) e(23)e\left(\frac{2}{3}\right)
χ4368(1453,⋅)\chi_{4368}(1453,\cdot) 11 11 e(712)e\left(\frac{7}{12}\right) ii e(13)e\left(\frac{1}{3}\right) −i-i 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(16)e\left(\frac{1}{6}\right) e(1112)e\left(\frac{11}{12}\right) e(13)e\left(\frac{1}{3}\right)
χ4368(3397,⋅)\chi_{4368}(3397,\cdot) 11 11 e(512)e\left(\frac{5}{12}\right) −i-i e(23)e\left(\frac{2}{3}\right) ii 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(56)e\left(\frac{5}{6}\right) e(112)e\left(\frac{1}{12}\right) e(23)e\left(\frac{2}{3}\right)
χ4368(3637,⋅)\chi_{4368}(3637,\cdot) 11 11 e(112)e\left(\frac{1}{12}\right) −i-i e(13)e\left(\frac{1}{3}\right) ii 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(16)e\left(\frac{1}{6}\right) e(512)e\left(\frac{5}{12}\right) e(13)e\left(\frac{1}{3}\right)