Properties

Conductor 21
Order 2
Real yes
Primitive no
Minimal yes
Parity even
Orbit label 7623.e

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(7623)
 
sage: chi = H[1574]
 
pari: [g,chi] = znchar(Mod(1574,7623))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 21
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
Minimal = yes
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 
Parity = even
Orbit label = 7623.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 ]
 

\(\chi_{7623}(1574,\cdot)\)

Values on generators

\((848,4357,4600)\) → \((-1,-1,1)\)

Values

-112458101316171920
\(1\)\(1\)\(-1\)\(1\)\(1\)\(-1\)\(-1\)\(-1\)\(1\)\(1\)\(-1\)\(1\)
value at  e.g. 2

Related number fields

Field of values \(\Q\)