Properties

Modulus 8016
Conductor 4008
Order 166
Real no
Primitive no
Minimal no
Parity even
Orbit label 8016.bg

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([0,83,83,97]))
 
pari: [g,chi] = znchar(Mod(41,8016))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Modulus = 8016
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 = no
Minimal = no
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 
Parity = even
Orbit label = 8016.bg
Orbit index = 33

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 ]
 

\(\chi_{8016}(41,\cdot)\) \(\chi_{8016}(377,\cdot)\) \(\chi_{8016}(425,\cdot)\) \(\chi_{8016}(473,\cdot)\) \(\chi_{8016}(521,\cdot)\) \(\chi_{8016}(569,\cdot)\) \(\chi_{8016}(665,\cdot)\) \(\chi_{8016}(713,\cdot)\) \(\chi_{8016}(905,\cdot)\) \(\chi_{8016}(953,\cdot)\) \(\chi_{8016}(1097,\cdot)\) \(\chi_{8016}(1145,\cdot)\) \(\chi_{8016}(1289,\cdot)\) \(\chi_{8016}(1481,\cdot)\) \(\chi_{8016}(1529,\cdot)\) \(\chi_{8016}(1577,\cdot)\) \(\chi_{8016}(1721,\cdot)\) \(\chi_{8016}(2009,\cdot)\) \(\chi_{8016}(2057,\cdot)\) \(\chi_{8016}(2105,\cdot)\) \(\chi_{8016}(2153,\cdot)\) \(\chi_{8016}(2201,\cdot)\) \(\chi_{8016}(2249,\cdot)\) \(\chi_{8016}(2393,\cdot)\) \(\chi_{8016}(2441,\cdot)\) \(\chi_{8016}(2489,\cdot)\) \(\chi_{8016}(2585,\cdot)\) \(\chi_{8016}(2777,\cdot)\) \(\chi_{8016}(2825,\cdot)\) \(\chi_{8016}(2873,\cdot)\) ...

Values on generators

\((3007,2005,5345,673)\) → \((1,-1,-1,e\left(\frac{97}{166}\right))\)

Values

-11571113171923252931
\(1\)\(1\)\(e\left(\frac{97}{166}\right)\)\(e\left(\frac{79}{83}\right)\)\(e\left(\frac{30}{83}\right)\)\(e\left(\frac{57}{83}\right)\)\(e\left(\frac{39}{83}\right)\)\(e\left(\frac{65}{166}\right)\)\(e\left(\frac{29}{83}\right)\)\(e\left(\frac{14}{83}\right)\)\(e\left(\frac{54}{83}\right)\)\(e\left(\frac{49}{83}\right)\)
value at  e.g. 2

Related number fields

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