Properties

Modulus 8016
Conductor 2672
Order 332
Real no
Primitive no
Minimal yes
Parity even
Orbit label 8016.br

Related objects

Learn more about

Show commands for: Pari/GP / SageMath
sage: from sage.modular.dirichlet import DirichletCharacter
 
sage: H = DirichletGroup(8016)
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([166,83,0,174]))
 
pari: [g,chi] = znchar(Mod(43,8016))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Modulus = 8016
Conductor = 2672
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 332
Real = no
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 = 8016.br
Orbit index = 44

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 ]
 

\(\chi_{8016}(43,\cdot)\) \(\chi_{8016}(67,\cdot)\) \(\chi_{8016}(91,\cdot)\) \(\chi_{8016}(139,\cdot)\) \(\chi_{8016}(163,\cdot)\) \(\chi_{8016}(187,\cdot)\) \(\chi_{8016}(235,\cdot)\) \(\chi_{8016}(259,\cdot)\) \(\chi_{8016}(307,\cdot)\) \(\chi_{8016}(331,\cdot)\) \(\chi_{8016}(379,\cdot)\) \(\chi_{8016}(403,\cdot)\) \(\chi_{8016}(451,\cdot)\) \(\chi_{8016}(499,\cdot)\) \(\chi_{8016}(547,\cdot)\) \(\chi_{8016}(571,\cdot)\) \(\chi_{8016}(619,\cdot)\) \(\chi_{8016}(643,\cdot)\) \(\chi_{8016}(691,\cdot)\) \(\chi_{8016}(739,\cdot)\) \(\chi_{8016}(763,\cdot)\) \(\chi_{8016}(787,\cdot)\) \(\chi_{8016}(811,\cdot)\) \(\chi_{8016}(955,\cdot)\) \(\chi_{8016}(1075,\cdot)\) \(\chi_{8016}(1147,\cdot)\) \(\chi_{8016}(1195,\cdot)\) \(\chi_{8016}(1243,\cdot)\) \(\chi_{8016}(1315,\cdot)\) \(\chi_{8016}(1387,\cdot)\) ...

Values on generators

\((3007,2005,5345,673)\) → \((-1,i,1,e\left(\frac{87}{166}\right))\)

Values

-11571113171923252931
\(1\)\(1\)\(e\left(\frac{257}{332}\right)\)\(e\left(\frac{70}{83}\right)\)\(e\left(\frac{141}{332}\right)\)\(e\left(\frac{243}{332}\right)\)\(e\left(\frac{129}{166}\right)\)\(e\left(\frac{215}{332}\right)\)\(e\left(\frac{147}{166}\right)\)\(e\left(\frac{91}{166}\right)\)\(e\left(\frac{121}{332}\right)\)\(e\left(\frac{111}{166}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{332})\)