Properties

Label 1900.1443
Modulus $1900$
Conductor $380$
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(1900, base_ring=CyclotomicField(4))
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([2,3,2]))
 
pari: [g,chi] = znchar(Mod(1443,1900))
 

Basic properties

Modulus: \(1900\)
Conductor: \(380\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(4\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from \(\chi_{380}(303,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: odd
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 1900.j

\(\chi_{1900}(607,\cdot)\) \(\chi_{1900}(1443,\cdot)\)

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: 4.0.722000.3

Values on generators

\((951,77,401)\) → \((-1,-i,-1)\)

Values

\(-1\)\(1\)\(3\)\(7\)\(9\)\(11\)\(13\)\(17\)\(21\)\(23\)\(27\)\(29\)
\(-1\)\(1\)\(i\)\(i\)\(-1\)\(-1\)\(-i\)\(-i\)\(-1\)\(-i\)\(-i\)\(1\)
sage: chi.jacobi_sum(n)
 
\( \chi_{ 1900 }(1443,a) \;\) at \(\;a = \) e.g. 2