Properties

Label 2960.1259
Modulus $2960$
Conductor $80$
Order $4$
Real no
Primitive no
Minimal yes
Parity odd

Related objects

Learn more

Show commands: Pari/GP / SageMath
sage: from sage.modular.dirichlet import DirichletCharacter
 
sage: H = DirichletGroup(2960, base_ring=CyclotomicField(4))
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([2,1,2,0]))
 
pari: [g,chi] = znchar(Mod(1259,2960))
 

Basic properties

Modulus: \(2960\)
Conductor: \(80\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(4\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from \(\chi_{80}(59,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: odd
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 2960.bf

\(\chi_{2960}(1259,\cdot)\) \(\chi_{2960}(2739,\cdot)\)

sage: chi.galois_orbit()
 
pari: order = charorder(g,chi)
 
pari: [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Related number fields

Field of values: \(\Q(\sqrt{-1}) \)
Fixed field: 4.0.51200.2

Values on generators

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

Values

\(-1\)\(1\)\(3\)\(7\)\(9\)\(11\)\(13\)\(17\)\(19\)\(21\)\(23\)\(27\)
\(-1\)\(1\)\(-i\)\(-1\)\(-1\)\(-i\)\(i\)\(-1\)\(i\)\(i\)\(-1\)\(i\)
sage: chi.jacobi_sum(n)
 
\( \chi_{ 2960 }(1259,a) \;\) at \(\;a = \) e.g. 2