Properties

Modulus 4008
Conductor 4008
Order 166
Real no
Primitive yes
Minimal yes
Parity even
Orbit label 4008.x

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([83,83,83,28]))
 
pari: [g,chi] = znchar(Mod(11,4008))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Modulus = 4008
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 = yes
Minimal = yes
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 
Parity = even
Orbit label = 4008.x
Orbit index = 24

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 ]
 

\(\chi_{4008}(11,\cdot)\) \(\chi_{4008}(107,\cdot)\) \(\chi_{4008}(179,\cdot)\) \(\chi_{4008}(203,\cdot)\) \(\chi_{4008}(251,\cdot)\) \(\chi_{4008}(275,\cdot)\) \(\chi_{4008}(299,\cdot)\) \(\chi_{4008}(395,\cdot)\) \(\chi_{4008}(419,\cdot)\) \(\chi_{4008}(467,\cdot)\) \(\chi_{4008}(491,\cdot)\) \(\chi_{4008}(515,\cdot)\) \(\chi_{4008}(539,\cdot)\) \(\chi_{4008}(563,\cdot)\) \(\chi_{4008}(731,\cdot)\) \(\chi_{4008}(755,\cdot)\) \(\chi_{4008}(851,\cdot)\) \(\chi_{4008}(899,\cdot)\) \(\chi_{4008}(923,\cdot)\) \(\chi_{4008}(947,\cdot)\) \(\chi_{4008}(1067,\cdot)\) \(\chi_{4008}(1091,\cdot)\) \(\chi_{4008}(1139,\cdot)\) \(\chi_{4008}(1187,\cdot)\) \(\chi_{4008}(1211,\cdot)\) \(\chi_{4008}(1235,\cdot)\) \(\chi_{4008}(1283,\cdot)\) \(\chi_{4008}(1331,\cdot)\) \(\chi_{4008}(1355,\cdot)\) \(\chi_{4008}(1451,\cdot)\) ...

Values on generators

\((3007,2005,1337,673)\) → \((-1,-1,-1,e\left(\frac{14}{83}\right))\)

Values

-11571113171923252931
\(1\)\(1\)\(e\left(\frac{14}{83}\right)\)\(e\left(\frac{67}{166}\right)\)\(e\left(\frac{37}{166}\right)\)\(e\left(\frac{145}{166}\right)\)\(e\left(\frac{73}{166}\right)\)\(e\left(\frac{65}{83}\right)\)\(e\left(\frac{58}{83}\right)\)\(e\left(\frac{28}{83}\right)\)\(e\left(\frac{25}{83}\right)\)\(e\left(\frac{113}{166}\right)\)
value at  e.g. 2

Related number fields

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