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Properties

Label 2340.523
Modulus $2340$
Conductor $260$
Order $12$
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(12)) M = H._module chi = DirichletCharacter(H, M([6,0,9,4]))
 
Copy content pari:[g,chi] = znchar(Mod(523,2340))
 

Basic properties

Modulus: \(2340\)
Conductor: \(260\)
Copy content sage:chi.conductor()
 
Copy content pari:znconreyconductor(g,chi)
 
Order: \(12\)
Copy content sage:chi.multiplicative_order()
 
Copy content pari:charorder(g,chi)
 
Real: no
Primitive: no, induced from \(\chi_{260}(3,\cdot)\)
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.go

\(\chi_{2340}(523,\cdot)\) \(\chi_{2340}(1387,\cdot)\) \(\chi_{2340}(1927,\cdot)\) \(\chi_{2340}(2323,\cdot)\)

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: \(\Q(\zeta_{12})\)
Fixed field: 12.12.6525845768000000000.1

Values on generators

\((1171,2081,937,1081)\) → \((-1,1,-i,e\left(\frac{1}{3}\right))\)

First values

\(a\) \(-1\)\(1\)\(7\)\(11\)\(17\)\(19\)\(23\)\(29\)\(31\)\(37\)\(41\)\(43\)
\( \chi_{ 2340 }(523, a) \) \(1\)\(1\)\(e\left(\frac{11}{12}\right)\)\(e\left(\frac{5}{6}\right)\)\(e\left(\frac{5}{12}\right)\)\(e\left(\frac{2}{3}\right)\)\(e\left(\frac{1}{12}\right)\)\(e\left(\frac{5}{6}\right)\)\(-1\)\(e\left(\frac{1}{12}\right)\)\(e\left(\frac{1}{3}\right)\)\(e\left(\frac{5}{12}\right)\)
Copy content sage:chi.jacobi_sum(n)
 
\( \chi_{ 2340 }(523,a) \;\) at \(\;a = \) e.g. 2