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Properties

Label 8325.dp
Modulus 83258325
Conductor 16651665
Order 1212
Real no
Primitive no
Minimal yes
Parity even

Related objects

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Show commands: PariGP / SageMath
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(8325, base_ring=CyclotomicField(12))
 
M = H._module
 
chi = DirichletCharacter(H, M([2,3,2]))
 
chi.galois_orbit()
 
[g,chi] = znchar(Mod(2432,8325))
 
order = charorder(g,chi)
 
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: 83258325
Conductor: 16651665
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: 1212
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from 1665.dh
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: Number field defined by a degree 12 polynomial

Characters in Galois orbit

Character −1-1 11 22 44 77 88 1111 1313 1414 1616 1717 1919
χ8325(2432,⋅)\chi_{8325}(2432,\cdot) 11 11 e(712)e\left(\frac{7}{12}\right) e(16)e\left(\frac{1}{6}\right) ii −i-i e(16)e\left(\frac{1}{6}\right) e(1112)e\left(\frac{11}{12}\right) e(56)e\left(\frac{5}{6}\right) e(13)e\left(\frac{1}{3}\right) e(1112)e\left(\frac{11}{12}\right) e(13)e\left(\frac{1}{3}\right)
χ8325(4118,⋅)\chi_{8325}(4118,\cdot) 11 11 e(512)e\left(\frac{5}{12}\right) e(56)e\left(\frac{5}{6}\right) −i-i ii e(56)e\left(\frac{5}{6}\right) e(112)e\left(\frac{1}{12}\right) e(16)e\left(\frac{1}{6}\right) e(23)e\left(\frac{2}{3}\right) e(112)e\left(\frac{1}{12}\right) e(23)e\left(\frac{2}{3}\right)
χ8325(6782,⋅)\chi_{8325}(6782,\cdot) 11 11 e(1112)e\left(\frac{11}{12}\right) e(56)e\left(\frac{5}{6}\right) ii −i-i e(56)e\left(\frac{5}{6}\right) e(712)e\left(\frac{7}{12}\right) e(16)e\left(\frac{1}{6}\right) e(23)e\left(\frac{2}{3}\right) e(712)e\left(\frac{7}{12}\right) e(23)e\left(\frac{2}{3}\right)
χ8325(8093,⋅)\chi_{8325}(8093,\cdot) 11 11 e(112)e\left(\frac{1}{12}\right) e(16)e\left(\frac{1}{6}\right) −i-i ii e(16)e\left(\frac{1}{6}\right) e(512)e\left(\frac{5}{12}\right) e(56)e\left(\frac{5}{6}\right) e(13)e\left(\frac{1}{3}\right) e(512)e\left(\frac{5}{12}\right) e(13)e\left(\frac{1}{3}\right)