Properties

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

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([0,83,0,2]))
 
pari: [g,chi] = znchar(Mod(25,8016))
 

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.bj
Orbit index = 36

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 ]
 

\(\chi_{8016}(25,\cdot)\) \(\chi_{8016}(121,\cdot)\) \(\chi_{8016}(169,\cdot)\) \(\chi_{8016}(217,\cdot)\) \(\chi_{8016}(265,\cdot)\) \(\chi_{8016}(361,\cdot)\) \(\chi_{8016}(409,\cdot)\) \(\chi_{8016}(505,\cdot)\) \(\chi_{8016}(601,\cdot)\) \(\chi_{8016}(697,\cdot)\) \(\chi_{8016}(745,\cdot)\) \(\chi_{8016}(841,\cdot)\) \(\chi_{8016}(889,\cdot)\) \(\chi_{8016}(985,\cdot)\) \(\chi_{8016}(1033,\cdot)\) \(\chi_{8016}(1129,\cdot)\) \(\chi_{8016}(1177,\cdot)\) \(\chi_{8016}(1225,\cdot)\) \(\chi_{8016}(1321,\cdot)\) \(\chi_{8016}(1369,\cdot)\) \(\chi_{8016}(1417,\cdot)\) \(\chi_{8016}(1561,\cdot)\) \(\chi_{8016}(1657,\cdot)\) \(\chi_{8016}(1849,\cdot)\) \(\chi_{8016}(1945,\cdot)\) \(\chi_{8016}(2089,\cdot)\) \(\chi_{8016}(2137,\cdot)\) \(\chi_{8016}(2185,\cdot)\) \(\chi_{8016}(2233,\cdot)\) \(\chi_{8016}(2425,\cdot)\) ...

Values on generators

\((3007,2005,5345,673)\) → \((1,-1,1,e\left(\frac{1}{83}\right))\)

Values

-11571113171923252931
\(1\)\(1\)\(e\left(\frac{85}{166}\right)\)\(e\left(\frac{35}{83}\right)\)\(e\left(\frac{139}{166}\right)\)\(e\left(\frac{123}{166}\right)\)\(e\left(\frac{53}{83}\right)\)\(e\left(\frac{33}{166}\right)\)\(e\left(\frac{16}{83}\right)\)\(e\left(\frac{2}{83}\right)\)\(e\left(\frac{51}{166}\right)\)\(e\left(\frac{7}{83}\right)\)
value at  e.g. 2

Related number fields

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