Properties

Modulus 4008
Conductor 2004
Order 166
Real no
Primitive no
Minimal no
Parity odd
Orbit label 4008.v

Related objects

Learn more about

Show commands for: Pari/GP / SageMath
sage: from sage.modular.dirichlet import DirichletCharacter
 
sage: H = DirichletGroup(4008)
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([83,0,83,99]))
 
pari: [g,chi] = znchar(Mod(23,4008))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Modulus = 4008
Conductor = 2004
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 = odd
Orbit label = 4008.v
Orbit index = 22

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 ]
 

\(\chi_{4008}(23,\cdot)\) \(\chi_{4008}(71,\cdot)\) \(\chi_{4008}(95,\cdot)\) \(\chi_{4008}(119,\cdot)\) \(\chi_{4008}(143,\cdot)\) \(\chi_{4008}(287,\cdot)\) \(\chi_{4008}(407,\cdot)\) \(\chi_{4008}(479,\cdot)\) \(\chi_{4008}(527,\cdot)\) \(\chi_{4008}(575,\cdot)\) \(\chi_{4008}(647,\cdot)\) \(\chi_{4008}(719,\cdot)\) \(\chi_{4008}(791,\cdot)\) \(\chi_{4008}(887,\cdot)\) \(\chi_{4008}(983,\cdot)\) \(\chi_{4008}(1007,\cdot)\) \(\chi_{4008}(1055,\cdot)\) \(\chi_{4008}(1103,\cdot)\) \(\chi_{4008}(1127,\cdot)\) \(\chi_{4008}(1151,\cdot)\) \(\chi_{4008}(1199,\cdot)\) \(\chi_{4008}(1247,\cdot)\) \(\chi_{4008}(1271,\cdot)\) \(\chi_{4008}(1391,\cdot)\) \(\chi_{4008}(1415,\cdot)\) \(\chi_{4008}(1439,\cdot)\) \(\chi_{4008}(1487,\cdot)\) \(\chi_{4008}(1583,\cdot)\) \(\chi_{4008}(1607,\cdot)\) \(\chi_{4008}(1775,\cdot)\) ...

Values on generators

\((3007,2005,1337,673)\) → \((-1,1,-1,e\left(\frac{99}{166}\right))\)

Values

-11571113171923252931
\(-1\)\(1\)\(e\left(\frac{8}{83}\right)\)\(e\left(\frac{145}{166}\right)\)\(e\left(\frac{58}{83}\right)\)\(e\left(\frac{71}{166}\right)\)\(e\left(\frac{9}{83}\right)\)\(e\left(\frac{15}{166}\right)\)\(e\left(\frac{7}{166}\right)\)\(e\left(\frac{16}{83}\right)\)\(e\left(\frac{159}{166}\right)\)\(e\left(\frac{29}{166}\right)\)
value at  e.g. 2

Related number fields

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