Properties

Label 2016.251
Modulus 20162016
Conductor 672672
Order 88
Real no
Primitive no
Minimal yes
Parity odd

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Show commands: PariGP / SageMath
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(2016, base_ring=CyclotomicField(8))
 
M = H._module
 
chi = DirichletCharacter(H, M([4,1,4,4]))
 
pari: [g,chi] = znchar(Mod(251,2016))
 

Basic properties

Modulus: 20162016
Conductor: 672672
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: 88
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from χ672(251,)\chi_{672}(251,\cdot)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: odd
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 2016.dn

χ2016(251,)\chi_{2016}(251,\cdot) χ2016(755,)\chi_{2016}(755,\cdot) χ2016(1259,)\chi_{2016}(1259,\cdot) χ2016(1763,)\chi_{2016}(1763,\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(ζ8)\Q(\zeta_{8})
Fixed field: 8.0.417644767346688.52

Values on generators

(127,1765,1793,577)(127,1765,1793,577)(1,e(18),1,1)(-1,e\left(\frac{1}{8}\right),-1,-1)

First values

aa 1-11155111113131717191923232525292931313737
χ2016(251,a) \chi_{ 2016 }(251, a) 1-111e(18)e\left(\frac{1}{8}\right)e(58)e\left(\frac{5}{8}\right)e(38)e\left(\frac{3}{8}\right)1-1e(78)e\left(\frac{7}{8}\right)i-iiie(78)e\left(\frac{7}{8}\right)11e(18)e\left(\frac{1}{8}\right)
sage: chi.jacobi_sum(n)
 
χ2016(251,a)   \chi_{ 2016 }(251,a) \; at   a=\;a = e.g. 2