↑

Properties

Label 15800.6793
Modulus $15800$
Conductor $395$
Order $4$
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(15800, base_ring=CyclotomicField(4)) M = H._module chi = DirichletCharacter(H, M([0,0,3,2]))
 
Copy content pari:[g,chi] = znchar(Mod(6793,15800))
 

Basic properties

Modulus: \(15800\)
Conductor: \(395\)
Copy content sage:chi.conductor()
 
Copy content pari:znconreyconductor(g,chi)
 
Order: \(4\)
Copy content sage:chi.multiplicative_order()
 
Copy content pari:charorder(g,chi)
 
Real: no
Primitive: no, induced from \(\chi_{395}(78,\cdot)\)
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 15800.y

\(\chi_{15800}(6793,\cdot)\) \(\chi_{15800}(8057,\cdot)\)

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: \(\mathbb{Q}(i)\)
Fixed field: 4.4.780125.1

Values on generators

\((3951,7901,11377,12801)\) → \((1,1,-i,-1)\)

First values

\(a\) \(-1\)\(1\)\(3\)\(7\)\(9\)\(11\)\(13\)\(17\)\(19\)\(21\)\(23\)\(27\)
\( \chi_{ 15800 }(6793, a) \) \(1\)\(1\)\(-i\)\(i\)\(-1\)\(1\)\(i\)\(i\)\(-1\)\(1\)\(i\)\(i\)
Copy content sage:chi.jacobi_sum(n)
 
\( \chi_{ 15800 }(6793,a) \;\) at \(\;a = \) e.g. 2