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Properties

Label 3360.841
Modulus $3360$
Conductor $16$
Order $4$
Real no
Primitive no
Minimal no
Parity even

Related objects

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Show commands: Pari/GP / SageMath
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(3360, base_ring=CyclotomicField(4)) M = H._module chi = DirichletCharacter(H, M([0,3,0,0,0]))
 
Copy content pari:[g,chi] = znchar(Mod(841,3360))
 

Basic properties

Modulus: \(3360\)
Conductor: \(16\)
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 \(\chi_{16}(13,\cdot)\)
Copy content sage:chi.is_primitive()
 
Copy content pari:#znconreyconductor(g,chi)==1
 
Minimal: no
Parity: even
Copy content sage:chi.is_odd()
 
Copy content pari:zncharisodd(g,chi)
 

Galois orbit 3360.cg

\(\chi_{3360}(841,\cdot)\) \(\chi_{3360}(2521,\cdot)\)

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: \(\Q(\zeta_{16})^+\)

Values on generators

\((1471,421,1121,2017,1921)\) → \((1,-i,1,1,1)\)

First values

\(a\) \(-1\)\(1\)\(11\)\(13\)\(17\)\(19\)\(23\)\(29\)\(31\)\(37\)\(41\)\(43\)
\( \chi_{ 3360 }(841, a) \) \(1\)\(1\)\(-i\)\(i\)\(1\)\(i\)\(-1\)\(i\)\(1\)\(-i\)\(-1\)\(-i\)
Copy content sage:chi.jacobi_sum(n)
 
\( \chi_{ 3360 }(841,a) \;\) at \(\;a = \) e.g. 2