Properties

Modulus 8016
Conductor 1336
Order 166
Real no
Primitive no
Minimal no
Parity even
Orbit label 8016.bc

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([83,83,0,29]))
 
pari: [g,chi] = znchar(Mod(55,8016))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Modulus = 8016
Conductor = 1336
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.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 ]
 

\(\chi_{8016}(55,\cdot)\) \(\chi_{8016}(103,\cdot)\) \(\chi_{8016}(151,\cdot)\) \(\chi_{8016}(247,\cdot)\) \(\chi_{8016}(439,\cdot)\) \(\chi_{8016}(487,\cdot)\) \(\chi_{8016}(535,\cdot)\) \(\chi_{8016}(583,\cdot)\) \(\chi_{8016}(727,\cdot)\) \(\chi_{8016}(823,\cdot)\) \(\chi_{8016}(1015,\cdot)\) \(\chi_{8016}(1111,\cdot)\) \(\chi_{8016}(1255,\cdot)\) \(\chi_{8016}(1303,\cdot)\) \(\chi_{8016}(1351,\cdot)\) \(\chi_{8016}(1447,\cdot)\) \(\chi_{8016}(1495,\cdot)\) \(\chi_{8016}(1543,\cdot)\) \(\chi_{8016}(1639,\cdot)\) \(\chi_{8016}(1687,\cdot)\) \(\chi_{8016}(1783,\cdot)\) \(\chi_{8016}(1831,\cdot)\) \(\chi_{8016}(1927,\cdot)\) \(\chi_{8016}(1975,\cdot)\) \(\chi_{8016}(2071,\cdot)\) \(\chi_{8016}(2167,\cdot)\) \(\chi_{8016}(2263,\cdot)\) \(\chi_{8016}(2311,\cdot)\) \(\chi_{8016}(2407,\cdot)\) \(\chi_{8016}(2455,\cdot)\) ...

Values on generators

\((3007,2005,5345,673)\) → \((-1,-1,1,e\left(\frac{29}{166}\right))\)

Values

-11571113171923252931
\(1\)\(1\)\(e\left(\frac{56}{83}\right)\)\(e\left(\frac{19}{166}\right)\)\(e\left(\frac{74}{83}\right)\)\(e\left(\frac{41}{83}\right)\)\(e\left(\frac{43}{166}\right)\)\(e\left(\frac{11}{83}\right)\)\(e\left(\frac{66}{83}\right)\)\(e\left(\frac{29}{83}\right)\)\(e\left(\frac{117}{166}\right)\)\(e\left(\frac{37}{166}\right)\)
value at  e.g. 2

Related number fields

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