Properties

Conductor 5
Order 4
Real No
Primitive No
Parity Odd
Orbit Label 1225.g

Related objects

Learn more about

Show commands for: SageMath / Pari/GP
sage: from dirichlet_conrey import DirichletGroup_conrey # requires nonstandard Sage package to be installed
sage: H = DirichletGroup_conrey(1225)
sage: chi = H[932]
pari: [g,chi] = znchar(Mod(932,1225))

Basic properties

sage: chi.conductor()
pari: znconreyconductor(g,chi)
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
sage: chi.is_odd()
pari: zncharisodd(g,chi)
Parity = Odd
Orbit label = 1225.g
Orbit index = 7

Galois orbit

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

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

Inducing primitive character

\(\chi_{5}(2,\cdot)\)

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 \(\Q(i)\)