Properties

Modulus 9128
Conductor 9128
Order 54
Real no
Primitive yes
Minimal yes
Parity odd
Orbit label 9128.fg

Related objects

Learn more about

Show commands for: Pari/GP / SageMath
sage: from sage.modular.dirichlet import DirichletCharacter
 
sage: H = DirichletGroup(9128)
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([27,27,18,38]))
 
pari: [g,chi] = znchar(Mod(2571,9128))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Modulus = 9128
Conductor = 9128
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 54
Real = no
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1 \\ if not primitive returns [cond,factorization]
 
Primitive = yes
Minimal = yes
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 
Parity = odd
Orbit label = 9128.fg
Orbit index = 137

Galois orbit

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

\(\chi_{9128}(347,\cdot)\) \(\chi_{9128}(387,\cdot)\) \(\chi_{9128}(403,\cdot)\) \(\chi_{9128}(947,\cdot)\) \(\chi_{9128}(2307,\cdot)\) \(\chi_{9128}(2571,\cdot)\) \(\chi_{9128}(2907,\cdot)\) \(\chi_{9128}(3651,\cdot)\) \(\chi_{9128}(4027,\cdot)\) \(\chi_{9128}(4139,\cdot)\) \(\chi_{9128}(4547,\cdot)\) \(\chi_{9128}(5203,\cdot)\) \(\chi_{9128}(6003,\cdot)\) \(\chi_{9128}(6675,\cdot)\) \(\chi_{9128}(7683,\cdot)\) \(\chi_{9128}(8675,\cdot)\) \(\chi_{9128}(8971,\cdot)\) \(\chi_{9128}(9123,\cdot)\)

Values on generators

\((6847,4565,1305,7337)\) → \((-1,-1,e\left(\frac{1}{3}\right),e\left(\frac{19}{27}\right))\)

Values

-1135911131517192325
\(-1\)\(1\)\(e\left(\frac{11}{27}\right)\)\(e\left(\frac{13}{18}\right)\)\(e\left(\frac{22}{27}\right)\)\(e\left(\frac{11}{27}\right)\)\(e\left(\frac{7}{18}\right)\)\(e\left(\frac{7}{54}\right)\)\(e\left(\frac{4}{9}\right)\)\(e\left(\frac{17}{27}\right)\)\(-1\)\(e\left(\frac{4}{9}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{27})\)