Properties

Conductor 547
Order 21
Real no
Primitive no
Minimal yes
Parity even
Orbit label 6017.s

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[716]
 
pari: [g,chi] = znchar(Mod(716,6017))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 547
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 21
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.s
Orbit index = 19

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 ]
 

\(\chi_{6017}(716,\cdot)\) \(\chi_{6017}(1211,\cdot)\) \(\chi_{6017}(2146,\cdot)\) \(\chi_{6017}(2201,\cdot)\) \(\chi_{6017}(2311,\cdot)\) \(\chi_{6017}(2366,\cdot)\) \(\chi_{6017}(2696,\cdot)\) \(\chi_{6017}(2861,\cdot)\) \(\chi_{6017}(3642,\cdot)\) \(\chi_{6017}(4390,\cdot)\) \(\chi_{6017}(5666,\cdot)\) \(\chi_{6017}(5897,\cdot)\)

Values on generators

\((3830,2190)\) → \((1,e\left(\frac{1}{21}\right))\)

Values

-11234567891012
\(1\)\(1\)\(e\left(\frac{1}{21}\right)\)\(e\left(\frac{3}{7}\right)\)\(e\left(\frac{2}{21}\right)\)\(e\left(\frac{11}{21}\right)\)\(e\left(\frac{10}{21}\right)\)\(e\left(\frac{19}{21}\right)\)\(e\left(\frac{1}{7}\right)\)\(e\left(\frac{6}{7}\right)\)\(e\left(\frac{4}{7}\right)\)\(e\left(\frac{11}{21}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{21})\)