Properties

Conductor 6003
Order 84
Real No
Primitive Yes
Parity Even
Orbit Label 6003.cp

Related objects

Learn more about

Show commands for: SageMath / Pari/GP
sage: from dirichlet_conrey import DirichletGroup_conrey # requires nonstandard Sage package to be installed
 
sage: H = DirichletGroup_conrey(6003)
 
sage: chi = H[160]
 
pari: [g,chi] = znchar(Mod(160,6003))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 6003
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 84
Real = No
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1 \\ if not primitive returns [cond,factorization]
 
Primitive = Yes
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 
Parity = Even
Orbit label = 6003.cp
Orbit index = 68

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 ]
 

\(\chi_{6003}(160,\cdot)\) \(\chi_{6003}(229,\cdot)\) \(\chi_{6003}(367,\cdot)\) \(\chi_{6003}(781,\cdot)\) \(\chi_{6003}(988,\cdot)\) \(\chi_{6003}(1402,\cdot)\) \(\chi_{6003}(1471,\cdot)\) \(\chi_{6003}(1609,\cdot)\) \(\chi_{6003}(1816,\cdot)\) \(\chi_{6003}(2230,\cdot)\) \(\chi_{6003}(2299,\cdot)\) \(\chi_{6003}(3472,\cdot)\) \(\chi_{6003}(3541,\cdot)\) \(\chi_{6003}(3955,\cdot)\) \(\chi_{6003}(4162,\cdot)\) \(\chi_{6003}(4300,\cdot)\) \(\chi_{6003}(4369,\cdot)\) \(\chi_{6003}(4783,\cdot)\) \(\chi_{6003}(4990,\cdot)\) \(\chi_{6003}(5404,\cdot)\) \(\chi_{6003}(5542,\cdot)\) \(\chi_{6003}(5611,\cdot)\) \(\chi_{6003}(5818,\cdot)\) \(\chi_{6003}(5956,\cdot)\)

Values on generators

\((668,3133,4555)\) → \((e\left(\frac{2}{3}\right),-1,e\left(\frac{27}{28}\right))\)

Values

-11245781011131416
\(1\)\(1\)\(e\left(\frac{53}{84}\right)\)\(e\left(\frac{11}{42}\right)\)\(e\left(\frac{1}{21}\right)\)\(e\left(\frac{31}{42}\right)\)\(e\left(\frac{25}{28}\right)\)\(e\left(\frac{19}{28}\right)\)\(e\left(\frac{23}{84}\right)\)\(e\left(\frac{29}{42}\right)\)\(e\left(\frac{31}{84}\right)\)\(e\left(\frac{11}{21}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{84})\)