↑

Properties

Label 1344.769
Modulus $1344$
Conductor $7$
Order $2$
Real yes
Primitive no
Minimal no
Parity odd

Related objects

Downloads

Learn more

Show commands: Pari/GP / SageMath
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1344, base_ring=CyclotomicField(2)) M = H._module chi = DirichletCharacter(H, M([0,0,0,1]))
 
Copy content pari:[g,chi] = znchar(Mod(769,1344))
 

Basic properties

Modulus: \(1344\)
Conductor: \(7\)
Copy content sage:chi.conductor()
 
Copy content pari:znconreyconductor(g,chi)
 
Order: \(2\)
Copy content sage:chi.multiplicative_order()
 
Copy content pari:charorder(g,chi)
 
Real: yes
Primitive: no, induced from \(\chi_{7}(6,\cdot)\)
Copy content sage:chi.is_primitive()
 
Copy content pari:#znconreyconductor(g,chi)==1
 
Minimal: no
Parity: odd
Copy content sage:chi.is_odd()
 
Copy content pari:zncharisodd(g,chi)
 

Galois orbit 1344.f

\(\chi_{1344}(769,\cdot)\)

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: \(\Q\)
Fixed field: \(\Q(\sqrt{-7}) \)

Values on generators

\((127,1093,449,577)\) → \((1,1,1,-1)\)

First values

\(a\) \(-1\)\(1\)\(5\)\(11\)\(13\)\(17\)\(19\)\(23\)\(25\)\(29\)\(31\)\(37\)
\( \chi_{ 1344 }(769, a) \) \(-1\)\(1\)\(-1\)\(1\)\(-1\)\(-1\)\(-1\)\(1\)\(1\)\(1\)\(-1\)\(1\)
Copy content sage:chi.jacobi_sum(n)
 
\( \chi_{ 1344 }(769,a) \;\) at \(\;a = \) e.g. 2