Properties

Label 1470.197
Modulus $1470$
Conductor $15$
Order $4$
Real no
Primitive no
Minimal yes
Parity even

Related objects

Learn more about

Show commands for: Pari/GP / SageMath
sage: from sage.modular.dirichlet import DirichletCharacter
 
sage: H = DirichletGroup(1470)
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([2,1,0]))
 
pari: [g,chi] = znchar(Mod(197,1470))
 

Basic properties

Modulus: \(1470\)
Conductor: \(15\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(4\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from \(\chi_{15}(2,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 1470.j

\(\chi_{1470}(197,\cdot)\) \(\chi_{1470}(1373,\cdot)\)

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

\((491,1177,1081)\) → \((-1,i,1)\)

Values

\(-1\)\(1\)\(11\)\(13\)\(17\)\(19\)\(23\)\(29\)\(31\)\(37\)\(41\)\(43\)
\(1\)\(1\)\(-1\)\(-i\)\(-i\)\(-1\)\(i\)\(1\)\(1\)\(i\)\(-1\)\(-i\)
value at e.g. 2

Related number fields

Field of values: \(\Q(\sqrt{-1}) \)
Fixed field: \(\Q(\zeta_{15})^+\)