Properties

Conductor 40
Order 2
Real Yes
Primitive No
Parity Odd
Orbit Label 4000.e

Related objects

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Show commands for: SageMath / Pari/GP
sage: from dirichlet_conrey import DirichletGroup_conrey # requires nonstandard Sage package to be installed
sage: H = DirichletGroup_conrey(4000)
sage: chi = H[1999]
pari: [g,chi] = znchar(Mod(1999,4000))

Basic properties

sage: chi.conductor()
pari: znconreyconductor(g,chi)
Conductor = 40
sage: chi.multiplicative_order()
pari: charorder(g,chi)
Order = 2
Real = Yes
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 = 4000.e
Orbit index = 5

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 ]

\(\chi_{4000}(1999,\cdot)\)

Inducing primitive character

\(\chi_{40}(19,\cdot)\) = \(\displaystyle\left(\frac{-40}{\bullet}\right)\)

Values on generators

\((2751,2501,1377)\) → \((-1,-1,-1)\)

Values

-1137911131719212327
\(-1\)\(1\)\(-1\)\(1\)\(1\)\(1\)\(1\)\(-1\)\(1\)\(-1\)\(1\)\(-1\)
value at  e.g. 2

Related number fields

Field of values \(\Q\)