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Properties

Label 2340.53
Modulus $2340$
Conductor $15$
Order $4$
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(2340, base_ring=CyclotomicField(4)) M = H._module chi = DirichletCharacter(H, M([0,2,3,0]))
 
Copy content pari:[g,chi] = znchar(Mod(53,2340))
 

Basic properties

Modulus: \(2340\)
Conductor: \(15\)
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 \(\chi_{15}(8,\cdot)\)
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 2340.y

\(\chi_{2340}(53,\cdot)\) \(\chi_{2340}(1457,\cdot)\)

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: \(\Q(\zeta_{15})^+\)

Values on generators

\((1171,2081,937,1081)\) → \((1,-1,-i,1)\)

First values

\(a\) \(-1\)\(1\)\(7\)\(11\)\(17\)\(19\)\(23\)\(29\)\(31\)\(37\)\(41\)\(43\)
\( \chi_{ 2340 }(53, a) \) \(1\)\(1\)\(-i\)\(-1\)\(i\)\(-1\)\(-i\)\(1\)\(1\)\(-i\)\(-1\)\(i\)
Copy content sage:chi.jacobi_sum(n)
 
\( \chi_{ 2340 }(53,a) \;\) at \(\;a = \) e.g. 2