Properties

Modulus 8016
Conductor 501
Order 166
Real no
Primitive no
Minimal no
Parity even
Orbit label 8016.bb

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([0,0,83,53]))
 
pari: [g,chi] = znchar(Mod(17,8016))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Modulus = 8016
Conductor = 501
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.bb
Orbit index = 28

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 ]
 

\(\chi_{8016}(17,\cdot)\) \(\chi_{8016}(113,\cdot)\) \(\chi_{8016}(161,\cdot)\) \(\chi_{8016}(257,\cdot)\) \(\chi_{8016}(305,\cdot)\) \(\chi_{8016}(401,\cdot)\) \(\chi_{8016}(497,\cdot)\) \(\chi_{8016}(593,\cdot)\) \(\chi_{8016}(641,\cdot)\) \(\chi_{8016}(737,\cdot)\) \(\chi_{8016}(785,\cdot)\) \(\chi_{8016}(833,\cdot)\) \(\chi_{8016}(881,\cdot)\) \(\chi_{8016}(977,\cdot)\) \(\chi_{8016}(1025,\cdot)\) \(\chi_{8016}(1073,\cdot)\) \(\chi_{8016}(1121,\cdot)\) \(\chi_{8016}(1409,\cdot)\) \(\chi_{8016}(1649,\cdot)\) \(\chi_{8016}(1793,\cdot)\) \(\chi_{8016}(1889,\cdot)\) \(\chi_{8016}(1985,\cdot)\) \(\chi_{8016}(2129,\cdot)\) \(\chi_{8016}(2273,\cdot)\) \(\chi_{8016}(2417,\cdot)\) \(\chi_{8016}(2609,\cdot)\) \(\chi_{8016}(2801,\cdot)\) \(\chi_{8016}(2849,\cdot)\) \(\chi_{8016}(2945,\cdot)\) \(\chi_{8016}(3041,\cdot)\) ...

Values on generators

\((3007,2005,5345,673)\) → \((1,1,-1,e\left(\frac{53}{166}\right))\)

Values

-11571113171923252931
\(1\)\(1\)\(e\left(\frac{68}{83}\right)\)\(e\left(\frac{56}{83}\right)\)\(e\left(\frac{73}{166}\right)\)\(e\left(\frac{147}{166}\right)\)\(e\left(\frac{35}{83}\right)\)\(e\left(\frac{43}{83}\right)\)\(e\left(\frac{9}{83}\right)\)\(e\left(\frac{53}{83}\right)\)\(e\left(\frac{65}{166}\right)\)\(e\left(\frac{61}{83}\right)\)
value at  e.g. 2

Related number fields

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