Properties

Conductor 287
Order 8
Real No
Primitive No
Parity Even
Orbit Label 6027.w

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(6027)
 
sage: chi = H[3037]
 
pari: [g,chi] = znchar(Mod(3037,6027))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 287
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 8
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 = 6027.w
Orbit index = 23

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 ]
 

\(\chi_{6027}(3037,\cdot)\) \(\chi_{6027}(3184,\cdot)\) \(\chi_{6027}(4360,\cdot)\) \(\chi_{6027}(4507,\cdot)\)

Inducing primitive character

\(\chi_{287}(167,\cdot)\)

Values on generators

\((4019,493,2794)\) → \((1,-1,e\left(\frac{3}{8}\right))\)

Values

-112458101113161719
\(1\)\(1\)\(-i\)\(-1\)\(-i\)\(i\)\(-1\)\(e\left(\frac{1}{8}\right)\)\(e\left(\frac{1}{8}\right)\)\(1\)\(e\left(\frac{7}{8}\right)\)\(e\left(\frac{7}{8}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{8})\)