Properties

Modulus 1225
Conductor 5
Order 4
Real no
Primitive no
Minimal yes
Parity odd
Orbit label 1225.g

Related objects

Learn more about

Show commands for: Pari/GP / SageMath
sage: from sage.modular.dirichlet import DirichletCharacter
 
sage: H = DirichletGroup(1225)
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([1,0]))
 
pari: [g,chi] = znchar(Mod(932,1225))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Modulus = 1225
Conductor = 5
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 4
Real = no
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1 \\ if not primitive returns [cond,factorization]
 
Primitive = no
Minimal = yes
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 
Parity = odd
Orbit label = 1225.g
Orbit index = 7

Galois orbit

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

\(\chi_{1225}(393,\cdot)\) \(\chi_{1225}(932,\cdot)\)

Values on generators

\((1177,101)\) → \((i,1)\)

Values

-1123468911121316
\(-1\)\(1\)\(i\)\(-i\)\(-1\)\(1\)\(-i\)\(-1\)\(1\)\(i\)\(-i\)\(1\)
value at  e.g. 2

Related number fields

Field of values \(\Q(i)\)