Properties

Modulus 4008
Conductor 668
Order 166
Real no
Primitive no
Minimal no
Parity even
Orbit label 4008.bf

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([83,0,0,29]))
 
pari: [g,chi] = znchar(Mod(55,4008))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Modulus = 4008
Conductor = 668
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.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 ]
 

\(\chi_{4008}(55,\cdot)\) \(\chi_{4008}(79,\cdot)\) \(\chi_{4008}(103,\cdot)\) \(\chi_{4008}(151,\cdot)\) \(\chi_{4008}(247,\cdot)\) \(\chi_{4008}(271,\cdot)\) \(\chi_{4008}(439,\cdot)\) \(\chi_{4008}(463,\cdot)\) \(\chi_{4008}(487,\cdot)\) \(\chi_{4008}(511,\cdot)\) \(\chi_{4008}(535,\cdot)\) \(\chi_{4008}(583,\cdot)\) \(\chi_{4008}(607,\cdot)\) \(\chi_{4008}(703,\cdot)\) \(\chi_{4008}(727,\cdot)\) \(\chi_{4008}(751,\cdot)\) \(\chi_{4008}(799,\cdot)\) \(\chi_{4008}(823,\cdot)\) \(\chi_{4008}(895,\cdot)\) \(\chi_{4008}(991,\cdot)\) \(\chi_{4008}(1015,\cdot)\) \(\chi_{4008}(1039,\cdot)\) \(\chi_{4008}(1111,\cdot)\) \(\chi_{4008}(1255,\cdot)\) \(\chi_{4008}(1279,\cdot)\) \(\chi_{4008}(1303,\cdot)\) \(\chi_{4008}(1327,\cdot)\) \(\chi_{4008}(1351,\cdot)\) \(\chi_{4008}(1375,\cdot)\) \(\chi_{4008}(1447,\cdot)\) ...

Values on generators

\((3007,2005,1337,673)\) → \((-1,1,1,e\left(\frac{29}{166}\right))\)

Values

-11571113171923252931
\(1\)\(1\)\(e\left(\frac{29}{166}\right)\)\(e\left(\frac{19}{166}\right)\)\(e\left(\frac{65}{166}\right)\)\(e\left(\frac{165}{166}\right)\)\(e\left(\frac{43}{166}\right)\)\(e\left(\frac{105}{166}\right)\)\(e\left(\frac{66}{83}\right)\)\(e\left(\frac{29}{83}\right)\)\(e\left(\frac{17}{83}\right)\)\(e\left(\frac{37}{166}\right)\)
value at  e.g. 2

Related number fields

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