Properties

Conductor 6017
Order 78
Real no
Primitive yes
Minimal yes
Parity even
Orbit label 6017.bk

Related objects

Learn more about

Show commands for: Pari/GP / SageMath
sage: from dirichlet_conrey import DirichletGroup_conrey # requires nonstandard Sage package to be installed
 
sage: H = DirichletGroup_conrey(6017)
 
sage: chi = H[692]
 
pari: [g,chi] = znchar(Mod(692,6017))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 6017
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 78
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.bk
Orbit index = 37

Galois orbit

sage: chi.sage_character().galois_orbit()
 
pari: order = charorder(g,chi)
 
pari: [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

\(\chi_{6017}(692,\cdot)\) \(\chi_{6017}(769,\cdot)\) \(\chi_{6017}(1594,\cdot)\) \(\chi_{6017}(1957,\cdot)\) \(\chi_{6017}(2067,\cdot)\) \(\chi_{6017}(2177,\cdot)\) \(\chi_{6017}(2496,\cdot)\) \(\chi_{6017}(2518,\cdot)\) \(\chi_{6017}(2606,\cdot)\) \(\chi_{6017}(2639,\cdot)\) \(\chi_{6017}(2837,\cdot)\) \(\chi_{6017}(2980,\cdot)\) \(\chi_{6017}(3101,\cdot)\) \(\chi_{6017}(3365,\cdot)\) \(\chi_{6017}(3596,\cdot)\) \(\chi_{6017}(4080,\cdot)\) \(\chi_{6017}(4322,\cdot)\) \(\chi_{6017}(4355,\cdot)\) \(\chi_{6017}(4949,\cdot)\) \(\chi_{6017}(4982,\cdot)\) \(\chi_{6017}(5334,\cdot)\) \(\chi_{6017}(5576,\cdot)\) \(\chi_{6017}(5598,\cdot)\) \(\chi_{6017}(5818,\cdot)\)

Values on generators

\((3830,2190)\) → \((-1,e\left(\frac{71}{78}\right))\)

Values

-11234567891012
\(1\)\(1\)\(e\left(\frac{16}{39}\right)\)\(-1\)\(e\left(\frac{32}{39}\right)\)\(e\left(\frac{73}{78}\right)\)\(e\left(\frac{71}{78}\right)\)\(e\left(\frac{10}{39}\right)\)\(e\left(\frac{3}{13}\right)\)\(1\)\(e\left(\frac{9}{26}\right)\)\(e\left(\frac{25}{78}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{39})\)