Properties

Label 2664.1285
Modulus 26642664
Conductor 26642664
Order 66
Real no
Primitive yes
Minimal yes
Parity even

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Show commands: PariGP / SageMath
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(2664, base_ring=CyclotomicField(6))
 
M = H._module
 
chi = DirichletCharacter(H, M([0,3,4,1]))
 
pari: [g,chi] = znchar(Mod(1285,2664))
 

Basic properties

Modulus: 26642664
Conductor: 26642664
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: 66
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)
 

Galois orbit 2664.cd

χ2664(85,)\chi_{2664}(85,\cdot) χ2664(1285,)\chi_{2664}(1285,\cdot)

sage: chi.galois_orbit()
 
order = charorder(g,chi)
 
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Related number fields

Field of values: Q(ζ3)\mathbb{Q}(\zeta_3)
Fixed field: 6.6.232942439361024.1

Values on generators

(1999,1333,2369,1297)(1999,1333,2369,1297)(1,1,e(23),e(16))(1,-1,e\left(\frac{2}{3}\right),e\left(\frac{1}{6}\right))

First values

aa 1-111557711111313171719192323252529293131
χ2664(1285,a) \chi_{ 2664 }(1285, a) 1111e(23)e\left(\frac{2}{3}\right)11e(16)e\left(\frac{1}{6}\right)e(23)e\left(\frac{2}{3}\right)e(16)e\left(\frac{1}{6}\right)e(13)e\left(\frac{1}{3}\right)e(56)e\left(\frac{5}{6}\right)e(13)e\left(\frac{1}{3}\right)e(23)e\left(\frac{2}{3}\right)e(56)e\left(\frac{5}{6}\right)
sage: chi.jacobi_sum(n)
 
χ2664(1285,a)   \chi_{ 2664 }(1285,a) \; at   a=\;a = e.g. 2