Properties

Conductor 87
Order 28
Real No
Primitive No
Parity Even
Orbit Label 6003.bp

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(6003)
 
sage: chi = H[530]
 
pari: [g,chi] = znchar(Mod(530,6003))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 87
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 28
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 = Even
Orbit label = 6003.bp
Orbit index = 42

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 ]
 

\(\chi_{6003}(530,\cdot)\) \(\chi_{6003}(1772,\cdot)\) \(\chi_{6003}(2186,\cdot)\) \(\chi_{6003}(2393,\cdot)\) \(\chi_{6003}(2600,\cdot)\) \(\chi_{6003}(3014,\cdot)\) \(\chi_{6003}(3221,\cdot)\) \(\chi_{6003}(3635,\cdot)\) \(\chi_{6003}(3842,\cdot)\) \(\chi_{6003}(4049,\cdot)\) \(\chi_{6003}(4463,\cdot)\) \(\chi_{6003}(5705,\cdot)\)

Inducing primitive character

\(\chi_{87}(8,\cdot)\)

Values on generators

\((668,3133,4555)\) → \((-1,1,e\left(\frac{3}{28}\right))\)

Values

-11245781011131416
\(1\)\(1\)\(e\left(\frac{17}{28}\right)\)\(e\left(\frac{3}{14}\right)\)\(e\left(\frac{6}{7}\right)\)\(e\left(\frac{2}{7}\right)\)\(e\left(\frac{23}{28}\right)\)\(e\left(\frac{13}{28}\right)\)\(e\left(\frac{5}{28}\right)\)\(e\left(\frac{13}{14}\right)\)\(e\left(\frac{25}{28}\right)\)\(e\left(\frac{3}{7}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{28})\)