↑

Properties

Label 4080.1141
Modulus $4080$
Conductor $272$
Order $8$
Real no
Primitive no
Minimal yes
Parity even

Related objects

Downloads

Learn more

Show commands: Pari/GP / SageMath
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(4080, base_ring=CyclotomicField(8)) M = H._module chi = DirichletCharacter(H, M([0,2,0,0,7]))
 
Copy content pari:[g,chi] = znchar(Mod(1141,4080))
 

Basic properties

Modulus: \(4080\)
Conductor: \(272\)
Copy content sage:chi.conductor()
 
Copy content pari:znconreyconductor(g,chi)
 
Order: \(8\)
Copy content sage:chi.multiplicative_order()
 
Copy content pari:charorder(g,chi)
 
Real: no
Primitive: no, induced from \(\chi_{272}(53,\cdot)\)
Copy content sage:chi.is_primitive()
 
Copy content pari:#znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
Copy content sage:chi.is_odd()
 
Copy content pari:zncharisodd(g,chi)
 

Galois orbit 4080.hh

\(\chi_{4080}(661,\cdot)\) \(\chi_{4080}(1141,\cdot)\) \(\chi_{4080}(1981,\cdot)\) \(\chi_{4080}(3901,\cdot)\)

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

Related number fields

Field of values: \(\Q(\zeta_{8})\)
Fixed field: 8.8.1721085137518592.1

Values on generators

\((511,3061,1361,817,241)\) → \((1,i,1,1,e\left(\frac{7}{8}\right))\)

First values

\(a\) \(-1\)\(1\)\(7\)\(11\)\(13\)\(19\)\(23\)\(29\)\(31\)\(37\)\(41\)\(43\)
\( \chi_{ 4080 }(1141, a) \) \(1\)\(1\)\(e\left(\frac{1}{8}\right)\)\(e\left(\frac{3}{8}\right)\)\(i\)\(1\)\(e\left(\frac{5}{8}\right)\)\(e\left(\frac{1}{8}\right)\)\(e\left(\frac{7}{8}\right)\)\(e\left(\frac{1}{8}\right)\)\(e\left(\frac{1}{8}\right)\)\(1\)
Copy content sage:chi.jacobi_sum(n)
 
\( \chi_{ 4080 }(1141,a) \;\) at \(\;a = \) e.g. 2