Properties

Conductor 261
Order 84
Real No
Primitive No
Parity Even
Orbit Label 6003.cq

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[47]
 
pari: [g,chi] = znchar(Mod(47,6003))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 261
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 = No
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 
Parity = Even
Orbit label = 6003.cq
Orbit index = 69

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 ]
 

\(\chi_{6003}(47,\cdot)\) \(\chi_{6003}(185,\cdot)\) \(\chi_{6003}(392,\cdot)\) \(\chi_{6003}(461,\cdot)\) \(\chi_{6003}(599,\cdot)\) \(\chi_{6003}(1013,\cdot)\) \(\chi_{6003}(1220,\cdot)\) \(\chi_{6003}(1634,\cdot)\) \(\chi_{6003}(1703,\cdot)\) \(\chi_{6003}(1841,\cdot)\) \(\chi_{6003}(2048,\cdot)\) \(\chi_{6003}(2462,\cdot)\) \(\chi_{6003}(2531,\cdot)\) \(\chi_{6003}(3704,\cdot)\) \(\chi_{6003}(3773,\cdot)\) \(\chi_{6003}(4187,\cdot)\) \(\chi_{6003}(4394,\cdot)\) \(\chi_{6003}(4532,\cdot)\) \(\chi_{6003}(4601,\cdot)\) \(\chi_{6003}(5015,\cdot)\) \(\chi_{6003}(5222,\cdot)\) \(\chi_{6003}(5636,\cdot)\) \(\chi_{6003}(5774,\cdot)\) \(\chi_{6003}(5843,\cdot)\)

Inducing primitive character

\(\chi_{261}(47,\cdot)\)

Values on generators

\((668,3133,4555)\) → \((e\left(\frac{1}{6}\right),1,e\left(\frac{11}{28}\right))\)

Values

-11245781011131416
\(1\)\(1\)\(e\left(\frac{47}{84}\right)\)\(e\left(\frac{5}{42}\right)\)\(e\left(\frac{10}{21}\right)\)\(e\left(\frac{8}{21}\right)\)\(e\left(\frac{19}{28}\right)\)\(e\left(\frac{1}{28}\right)\)\(e\left(\frac{83}{84}\right)\)\(e\left(\frac{17}{42}\right)\)\(e\left(\frac{79}{84}\right)\)\(e\left(\frac{5}{21}\right)\)
value at  e.g. 2

Related number fields

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