Properties

Modulus 6017
Conductor 6017
Order 65
Real no
Primitive yes
Minimal yes
Parity even
Orbit label 6017.be

Related objects

Learn more about

Show commands for: Pari/GP / SageMath
sage: from sage.modular.dirichlet import DirichletCharacter
 
sage: H = DirichletGroup(6017)
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([39,10]))
 
pari: [g,chi] = znchar(Mod(4090,6017))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Modulus = 6017
Conductor = 6017
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 65
Real = no
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1 \\ if not primitive returns [cond,factorization]
 
Primitive = yes
Minimal = yes
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 
Parity = even
Orbit label = 6017.be
Orbit index = 31

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 ]
 

\(\chi_{6017}(350,\cdot)\) \(\chi_{6017}(509,\cdot)\) \(\chi_{6017}(784,\cdot)\) \(\chi_{6017}(808,\cdot)\) \(\chi_{6017}(840,\cdot)\) \(\chi_{6017}(900,\cdot)\) \(\chi_{6017}(922,\cdot)\) \(\chi_{6017}(1444,\cdot)\) \(\chi_{6017}(1534,\cdot)\) \(\chi_{6017}(1611,\cdot)\) \(\chi_{6017}(1687,\cdot)\) \(\chi_{6017}(1934,\cdot)\) \(\chi_{6017}(1994,\cdot)\) \(\chi_{6017}(2016,\cdot)\) \(\chi_{6017}(2116,\cdot)\) \(\chi_{6017}(2150,\cdot)\) \(\chi_{6017}(2160,\cdot)\) \(\chi_{6017}(2425,\cdot)\) \(\chi_{6017}(2781,\cdot)\) \(\chi_{6017}(2996,\cdot)\) \(\chi_{6017}(3028,\cdot)\) \(\chi_{6017}(3085,\cdot)\) \(\chi_{6017}(3210,\cdot)\) \(\chi_{6017}(3254,\cdot)\) \(\chi_{6017}(3635,\cdot)\) \(\chi_{6017}(3657,\cdot)\) \(\chi_{6017}(3722,\cdot)\) \(\chi_{6017}(3799,\cdot)\) \(\chi_{6017}(3875,\cdot)\) \(\chi_{6017}(4090,\cdot)\) ...

Values on generators

\((3830,2190)\) → \((e\left(\frac{3}{5}\right),e\left(\frac{2}{13}\right))\)

Values

-11234567891012
\(1\)\(1\)\(e\left(\frac{49}{65}\right)\)\(e\left(\frac{4}{5}\right)\)\(e\left(\frac{33}{65}\right)\)\(e\left(\frac{61}{65}\right)\)\(e\left(\frac{36}{65}\right)\)\(e\left(\frac{3}{65}\right)\)\(e\left(\frac{17}{65}\right)\)\(e\left(\frac{3}{5}\right)\)\(e\left(\frac{9}{13}\right)\)\(e\left(\frac{4}{13}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{65})\)