Properties

Modulus 8016
Conductor 4008
Order 166
Real no
Primitive no
Minimal no
Parity even
Orbit label 8016.bf

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([83,83,83,88]))
 
pari: [g,chi] = znchar(Mod(215,8016))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Modulus = 8016
Conductor = 4008
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 166
Real = no
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1 \\ if not primitive returns [cond,factorization]
 
Primitive = no
Minimal = no
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 
Parity = even
Orbit label = 8016.bf
Orbit index = 32

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 ]
 

\(\chi_{8016}(215,\cdot)\) \(\chi_{8016}(263,\cdot)\) \(\chi_{8016}(311,\cdot)\) \(\chi_{8016}(359,\cdot)\) \(\chi_{8016}(455,\cdot)\) \(\chi_{8016}(503,\cdot)\) \(\chi_{8016}(551,\cdot)\) \(\chi_{8016}(599,\cdot)\) \(\chi_{8016}(695,\cdot)\) \(\chi_{8016}(743,\cdot)\) \(\chi_{8016}(839,\cdot)\) \(\chi_{8016}(935,\cdot)\) \(\chi_{8016}(1031,\cdot)\) \(\chi_{8016}(1079,\cdot)\) \(\chi_{8016}(1175,\cdot)\) \(\chi_{8016}(1223,\cdot)\) \(\chi_{8016}(1319,\cdot)\) \(\chi_{8016}(1367,\cdot)\) \(\chi_{8016}(1463,\cdot)\) \(\chi_{8016}(1511,\cdot)\) \(\chi_{8016}(1559,\cdot)\) \(\chi_{8016}(1655,\cdot)\) \(\chi_{8016}(1703,\cdot)\) \(\chi_{8016}(1751,\cdot)\) \(\chi_{8016}(1895,\cdot)\) \(\chi_{8016}(1991,\cdot)\) \(\chi_{8016}(2183,\cdot)\) \(\chi_{8016}(2279,\cdot)\) \(\chi_{8016}(2423,\cdot)\) \(\chi_{8016}(2471,\cdot)\) ...

Values on generators

\((3007,2005,5345,673)\) → \((-1,-1,-1,e\left(\frac{44}{83}\right))\)

Values

-11571113171923252931
\(1\)\(1\)\(e\left(\frac{44}{83}\right)\)\(e\left(\frac{9}{166}\right)\)\(e\left(\frac{57}{166}\right)\)\(e\left(\frac{17}{166}\right)\)\(e\left(\frac{99}{166}\right)\)\(e\left(\frac{62}{83}\right)\)\(e\left(\frac{40}{83}\right)\)\(e\left(\frac{5}{83}\right)\)\(e\left(\frac{43}{83}\right)\)\(e\left(\frac{35}{166}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{83})\)