Properties

Modulus 8016
Conductor 668
Order 166
Real no
Primitive no
Minimal yes
Parity even
Orbit label 8016.bn

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([83,0,0,65]))
 
pari: [g,chi] = znchar(Mod(79,8016))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Modulus = 8016
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 = yes
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 
Parity = even
Orbit label = 8016.bn
Orbit index = 40

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 ]
 

\(\chi_{8016}(79,\cdot)\) \(\chi_{8016}(271,\cdot)\) \(\chi_{8016}(463,\cdot)\) \(\chi_{8016}(511,\cdot)\) \(\chi_{8016}(607,\cdot)\) \(\chi_{8016}(703,\cdot)\) \(\chi_{8016}(751,\cdot)\) \(\chi_{8016}(799,\cdot)\) \(\chi_{8016}(895,\cdot)\) \(\chi_{8016}(991,\cdot)\) \(\chi_{8016}(1039,\cdot)\) \(\chi_{8016}(1279,\cdot)\) \(\chi_{8016}(1327,\cdot)\) \(\chi_{8016}(1375,\cdot)\) \(\chi_{8016}(1471,\cdot)\) \(\chi_{8016}(1663,\cdot)\) \(\chi_{8016}(1711,\cdot)\) \(\chi_{8016}(2047,\cdot)\) \(\chi_{8016}(2095,\cdot)\) \(\chi_{8016}(2143,\cdot)\) \(\chi_{8016}(2191,\cdot)\) \(\chi_{8016}(2239,\cdot)\) \(\chi_{8016}(2335,\cdot)\) \(\chi_{8016}(2383,\cdot)\) \(\chi_{8016}(2575,\cdot)\) \(\chi_{8016}(2623,\cdot)\) \(\chi_{8016}(2767,\cdot)\) \(\chi_{8016}(2815,\cdot)\) \(\chi_{8016}(2959,\cdot)\) \(\chi_{8016}(3151,\cdot)\) ...

Values on generators

\((3007,2005,5345,673)\) → \((-1,1,1,e\left(\frac{65}{166}\right))\)

Values

-11571113171923252931
\(1\)\(1\)\(e\left(\frac{65}{166}\right)\)\(e\left(\frac{117}{166}\right)\)\(e\left(\frac{77}{166}\right)\)\(e\left(\frac{55}{166}\right)\)\(e\left(\frac{125}{166}\right)\)\(e\left(\frac{35}{166}\right)\)\(e\left(\frac{22}{83}\right)\)\(e\left(\frac{65}{83}\right)\)\(e\left(\frac{61}{83}\right)\)\(e\left(\frac{123}{166}\right)\)
value at  e.g. 2

Related number fields

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