Properties

Conductor 6017
Order 14
Real no
Primitive yes
Minimal yes
Parity even
Orbit label 6017.o

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[538]
 
pari: [g,chi] = znchar(Mod(538,6017))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 6017
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 14
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.o
Orbit index = 15

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 ]
 

\(\chi_{6017}(538,\cdot)\) \(\chi_{6017}(912,\cdot)\) \(\chi_{6017}(1121,\cdot)\) \(\chi_{6017}(2738,\cdot)\) \(\chi_{6017}(4619,\cdot)\) \(\chi_{6017}(5389,\cdot)\)

Values on generators

\((3830,2190)\) → \((-1,e\left(\frac{1}{14}\right))\)

Values

-11234567891012
\(1\)\(1\)\(e\left(\frac{4}{7}\right)\)\(e\left(\frac{9}{14}\right)\)\(e\left(\frac{1}{7}\right)\)\(e\left(\frac{11}{14}\right)\)\(e\left(\frac{3}{14}\right)\)\(e\left(\frac{6}{7}\right)\)\(e\left(\frac{5}{7}\right)\)\(e\left(\frac{2}{7}\right)\)\(e\left(\frac{5}{14}\right)\)\(e\left(\frac{11}{14}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{7})\)