Properties

Conductor 547
Order 39
Real no
Primitive no
Minimal yes
Parity even
Orbit label 6017.ba

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[199]
 
pari: [g,chi] = znchar(Mod(199,6017))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 547
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 39
Real = no
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1 \\ if not primitive returns [cond,factorization]
 
Primitive = no
Minimal = yes
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 
Parity = even
Orbit label = 6017.ba
Orbit index = 27

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 ]
 

\(\chi_{6017}(199,\cdot)\) \(\chi_{6017}(419,\cdot)\) \(\chi_{6017}(441,\cdot)\) \(\chi_{6017}(683,\cdot)\) \(\chi_{6017}(1035,\cdot)\) \(\chi_{6017}(1068,\cdot)\) \(\chi_{6017}(1662,\cdot)\) \(\chi_{6017}(1695,\cdot)\) \(\chi_{6017}(1937,\cdot)\) \(\chi_{6017}(2421,\cdot)\) \(\chi_{6017}(2652,\cdot)\) \(\chi_{6017}(2916,\cdot)\) \(\chi_{6017}(3037,\cdot)\) \(\chi_{6017}(3180,\cdot)\) \(\chi_{6017}(3378,\cdot)\) \(\chi_{6017}(3411,\cdot)\) \(\chi_{6017}(3499,\cdot)\) \(\chi_{6017}(3521,\cdot)\) \(\chi_{6017}(3840,\cdot)\) \(\chi_{6017}(3950,\cdot)\) \(\chi_{6017}(4060,\cdot)\) \(\chi_{6017}(4423,\cdot)\) \(\chi_{6017}(5248,\cdot)\) \(\chi_{6017}(5325,\cdot)\)

Values on generators

\((3830,2190)\) → \((1,e\left(\frac{34}{39}\right))\)

Values

-11234567891012
\(1\)\(1\)\(e\left(\frac{34}{39}\right)\)\(1\)\(e\left(\frac{29}{39}\right)\)\(e\left(\frac{2}{39}\right)\)\(e\left(\frac{34}{39}\right)\)\(e\left(\frac{31}{39}\right)\)\(e\left(\frac{8}{13}\right)\)\(1\)\(e\left(\frac{12}{13}\right)\)\(e\left(\frac{29}{39}\right)\)
value at  e.g. 2

Related number fields

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