Properties

Conductor 731
Order 336
Real No
Primitive No
Parity Even
Orbit Label 8041.fk

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(8041)
 
sage: chi = H[12]
 
pari: [g,chi] = znchar(Mod(12,8041))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 731
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 336
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 = 8041.fk
Orbit index = 141

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 ]
 

\(\chi_{8041}(12,\cdot)\) \(\chi_{8041}(177,\cdot)\) \(\chi_{8041}(243,\cdot)\) \(\chi_{8041}(320,\cdot)\) \(\chi_{8041}(364,\cdot)\) \(\chi_{8041}(507,\cdot)\) \(\chi_{8041}(760,\cdot)\) \(\chi_{8041}(793,\cdot)\) \(\chi_{8041}(804,\cdot)\) \(\chi_{8041}(958,\cdot)\) \(\chi_{8041}(980,\cdot)\) \(\chi_{8041}(1431,\cdot)\) \(\chi_{8041}(1508,\cdot)\) \(\chi_{8041}(1574,\cdot)\) \(\chi_{8041}(1695,\cdot)\) \(\chi_{8041}(1706,\cdot)\) \(\chi_{8041}(1739,\cdot)\) \(\chi_{8041}(1882,\cdot)\) \(\chi_{8041}(1926,\cdot)\) \(\chi_{8041}(2047,\cdot)\) \(\chi_{8041}(2069,\cdot)\) \(\chi_{8041}(2135,\cdot)\) \(\chi_{8041}(2179,\cdot)\) \(\chi_{8041}(2256,\cdot)\) \(\chi_{8041}(2377,\cdot)\) \(\chi_{8041}(2454,\cdot)\) \(\chi_{8041}(2608,\cdot)\) \(\chi_{8041}(2641,\cdot)\) \(\chi_{8041}(2696,\cdot)\) \(\chi_{8041}(2828,\cdot)\) ...

Inducing primitive character

\(\chi_{731}(12,\cdot)\)

Values on generators

\((6580,2366,562)\) → \((1,e\left(\frac{13}{16}\right),e\left(\frac{13}{42}\right))\)

Values

-11234567891012
\(1\)\(1\)\(e\left(\frac{41}{56}\right)\)\(e\left(\frac{41}{336}\right)\)\(e\left(\frac{13}{28}\right)\)\(e\left(\frac{269}{336}\right)\)\(e\left(\frac{41}{48}\right)\)\(e\left(\frac{37}{48}\right)\)\(e\left(\frac{11}{56}\right)\)\(e\left(\frac{41}{168}\right)\)\(e\left(\frac{179}{336}\right)\)\(e\left(\frac{197}{336}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{336})\)