Properties

Label 2015.1117
Modulus $2015$
Conductor $65$
Order $4$
Real no
Primitive no
Minimal yes
Parity odd

Related objects

Learn more about

Show commands for: Pari/GP / SageMath
sage: from sage.modular.dirichlet import DirichletCharacter
 
sage: H = DirichletGroup(2015)
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([1,2,0]))
 
pari: [g,chi] = znchar(Mod(1117,2015))
 

Basic properties

Modulus: \(2015\)
Conductor: \(65\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(4\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from \(\chi_{65}(12,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: odd
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 2015.r

\(\chi_{2015}(1117,\cdot)\) \(\chi_{2015}(1923,\cdot)\)

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

Values on generators

\((807,1861,716)\) → \((i,-1,1)\)

Values

\(-1\)\(1\)\(2\)\(3\)\(4\)\(6\)\(7\)\(8\)\(9\)\(11\)\(12\)\(14\)
\(-1\)\(1\)\(-i\)\(-i\)\(-1\)\(-1\)\(-i\)\(i\)\(-1\)\(-1\)\(i\)\(-1\)
value at e.g. 2

Related number fields

Field of values: \(\Q(\sqrt{-1}) \)
Fixed field: 4.0.21125.1