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Properties

Label 3255.92
Modulus $3255$
Conductor $465$
Order $4$
Real no
Primitive no
Minimal yes
Parity odd

Related objects

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Show commands: Pari/GP / SageMath
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(3255, base_ring=CyclotomicField(4)) M = H._module chi = DirichletCharacter(H, M([2,1,0,2]))
 
Copy content pari:[g,chi] = znchar(Mod(92,3255))
 

Basic properties

Modulus: \(3255\)
Conductor: \(465\)
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 \(\chi_{465}(92,\cdot)\)
Copy content sage:chi.is_primitive()
 
Copy content pari:#znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: odd
Copy content sage:chi.is_odd()
 
Copy content pari:zncharisodd(g,chi)
 

Galois orbit 3255.z

\(\chi_{3255}(92,\cdot)\) \(\chi_{3255}(743,\cdot)\)

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: 4.0.1081125.1

Values on generators

\((2171,652,1396,2731)\) → \((-1,i,1,-1)\)

First values

\(a\) \(-1\)\(1\)\(2\)\(4\)\(8\)\(11\)\(13\)\(16\)\(17\)\(19\)\(22\)\(23\)
\( \chi_{ 3255 }(92, a) \) \(-1\)\(1\)\(-i\)\(-1\)\(i\)\(1\)\(i\)\(1\)\(i\)\(-1\)\(-i\)\(-i\)
Copy content sage:chi.jacobi_sum(n)
 
\( \chi_{ 3255 }(92,a) \;\) at \(\;a = \) e.g. 2