Properties

Label 4080.41
Modulus 40804080
Conductor 408408
Order 1616
Real no
Primitive no
Minimal no
Parity even

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Show commands: PariGP / SageMath
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(4080, base_ring=CyclotomicField(16))
 
M = H._module
 
chi = DirichletCharacter(H, M([0,8,8,0,11]))
 
pari: [g,chi] = znchar(Mod(41,4080))
 

Basic properties

Modulus: 40804080
Conductor: 408408
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: 1616
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from χ408(245,)\chi_{408}(245,\cdot)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: no
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 4080.ji

χ4080(41,)\chi_{4080}(41,\cdot) χ4080(521,)\chi_{4080}(521,\cdot) χ4080(1961,)\chi_{4080}(1961,\cdot) χ4080(2441,)\chi_{4080}(2441,\cdot) χ4080(2681,)\chi_{4080}(2681,\cdot) χ4080(2921,)\chi_{4080}(2921,\cdot) χ4080(3641,)\chi_{4080}(3641,\cdot) χ4080(3881,)\chi_{4080}(3881,\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(ζ16)\Q(\zeta_{16})
Fixed field: 16.16.315082116699567604562361581568.1

Values on generators

(511,3061,1361,817,241)(511,3061,1361,817,241)(1,1,1,1,e(1116))(1,-1,-1,1,e\left(\frac{11}{16}\right))

First values

aa 1-11177111113131919232329293131373741414343
χ4080(41,a) \chi_{ 4080 }(41, a) 1111e(916)e\left(\frac{9}{16}\right)e(1316)e\left(\frac{13}{16}\right)iie(18)e\left(\frac{1}{8}\right)e(1316)e\left(\frac{13}{16}\right)e(1516)e\left(\frac{15}{16}\right)e(316)e\left(\frac{3}{16}\right)e(316)e\left(\frac{3}{16}\right)e(116)e\left(\frac{1}{16}\right)e(78)e\left(\frac{7}{8}\right)
sage: chi.jacobi_sum(n)
 
χ4080(41,a)   \chi_{ 4080 }(41,a) \; at   a=\;a = e.g. 2