Properties

Modulus 4008
Conductor 2004
Order 166
Real no
Primitive no
Minimal no
Parity even
Orbit label 4008.bc

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([83,0,83,116]))
 
pari: [g,chi] = znchar(Mod(695,4008))
 

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 = even
Orbit label = 4008.bc
Orbit index = 29

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 ]
 

\(\chi_{4008}(47,\cdot)\) \(\chi_{4008}(191,\cdot)\) \(\chi_{4008}(215,\cdot)\) \(\chi_{4008}(239,\cdot)\) \(\chi_{4008}(263,\cdot)\) \(\chi_{4008}(311,\cdot)\) \(\chi_{4008}(359,\cdot)\) \(\chi_{4008}(383,\cdot)\) \(\chi_{4008}(431,\cdot)\) \(\chi_{4008}(455,\cdot)\) \(\chi_{4008}(503,\cdot)\) \(\chi_{4008}(551,\cdot)\) \(\chi_{4008}(599,\cdot)\) \(\chi_{4008}(623,\cdot)\) \(\chi_{4008}(671,\cdot)\) \(\chi_{4008}(695,\cdot)\) \(\chi_{4008}(743,\cdot)\) \(\chi_{4008}(767,\cdot)\) \(\chi_{4008}(815,\cdot)\) \(\chi_{4008}(839,\cdot)\) \(\chi_{4008}(863,\cdot)\) \(\chi_{4008}(911,\cdot)\) \(\chi_{4008}(935,\cdot)\) \(\chi_{4008}(959,\cdot)\) \(\chi_{4008}(1031,\cdot)\) \(\chi_{4008}(1079,\cdot)\) \(\chi_{4008}(1175,\cdot)\) \(\chi_{4008}(1223,\cdot)\) \(\chi_{4008}(1295,\cdot)\) \(\chi_{4008}(1319,\cdot)\) ...

Values on generators

\((3007,2005,1337,673)\) → \((-1,1,-1,e\left(\frac{58}{83}\right))\)

Values

-11571113171923252931
\(1\)\(1\)\(e\left(\frac{33}{166}\right)\)\(e\left(\frac{159}{166}\right)\)\(e\left(\frac{47}{83}\right)\)\(e\left(\frac{81}{83}\right)\)\(e\left(\frac{89}{166}\right)\)\(e\left(\frac{5}{166}\right)\)\(e\left(\frac{15}{83}\right)\)\(e\left(\frac{33}{83}\right)\)\(e\left(\frac{53}{166}\right)\)\(e\left(\frac{65}{166}\right)\)
value at  e.g. 2

Related number fields

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