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Properties

Label 2394.1627
Modulus $2394$
Conductor $1197$
Order $6$
Real no
Primitive no
Minimal yes
Parity even

Related objects

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Show commands: Pari/GP / SageMath
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(2394, base_ring=CyclotomicField(6)) M = H._module chi = DirichletCharacter(H, M([4,1,5]))
 
Copy content pari:[g,chi] = znchar(Mod(1627,2394))
 

Basic properties

Modulus: \(2394\)
Conductor: \(1197\)
Copy content sage:chi.conductor()
 
Copy content pari:znconreyconductor(g,chi)
 
Order: \(6\)
Copy content sage:chi.multiplicative_order()
 
Copy content pari:charorder(g,chi)
 
Real: no
Primitive: no, induced from \(\chi_{1197}(430,\cdot)\)
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 2394.bc

\(\chi_{2394}(103,\cdot)\) \(\chi_{2394}(1627,\cdot)\)

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: \(\mathbb{Q}(\zeta_3)\)
Fixed field: 6.6.273041236853973.2

Values on generators

\((533,1711,1009)\) → \((e\left(\frac{2}{3}\right),e\left(\frac{1}{6}\right),e\left(\frac{5}{6}\right))\)

First values

\(a\) \(-1\)\(1\)\(5\)\(11\)\(13\)\(17\)\(23\)\(25\)\(29\)\(31\)\(37\)\(41\)
\( \chi_{ 2394 }(1627, a) \) \(1\)\(1\)\(-1\)\(e\left(\frac{1}{3}\right)\)\(1\)\(-1\)\(e\left(\frac{1}{3}\right)\)\(1\)\(e\left(\frac{5}{6}\right)\)\(1\)\(e\left(\frac{5}{6}\right)\)\(e\left(\frac{2}{3}\right)\)
Copy content sage:chi.jacobi_sum(n)
 
\( \chi_{ 2394 }(1627,a) \;\) at \(\;a = \) e.g. 2