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Properties

Label 2960.1553
Modulus $2960$
Conductor $185$
Order $4$
Real no
Primitive no
Minimal no
Parity odd

Related objects

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Show commands: Pari/GP / SageMath
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(2960, base_ring=CyclotomicField(4)) M = H._module chi = DirichletCharacter(H, M([0,0,3,2]))
 
Copy content pari:[g,chi] = znchar(Mod(1553,2960))
 

Basic properties

Modulus: \(2960\)
Conductor: \(185\)
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 \(\chi_{185}(73,\cdot)\)
Copy content sage:chi.is_primitive()
 
Copy content pari:#znconreyconductor(g,chi)==1
 
Minimal: no
Parity: odd
Copy content sage:chi.is_odd()
 
Copy content pari:zncharisodd(g,chi)
 

Galois orbit 2960.by

\(\chi_{2960}(1553,\cdot)\) \(\chi_{2960}(2737,\cdot)\)

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: 4.0.171125.1

Values on generators

\((2591,741,1777,2481)\) → \((1,1,-i,-1)\)

First values

\(a\) \(-1\)\(1\)\(3\)\(7\)\(9\)\(11\)\(13\)\(17\)\(19\)\(21\)\(23\)\(27\)
\( \chi_{ 2960 }(1553, a) \) \(-1\)\(1\)\(i\)\(-i\)\(-1\)\(1\)\(-i\)\(i\)\(1\)\(1\)\(-i\)\(-i\)
Copy content sage:chi.jacobi_sum(n)
 
\( \chi_{ 2960 }(1553,a) \;\) at \(\;a = \) e.g. 2