Properties

Conductor 473
Order 105
Real No
Primitive No
Parity Even
Orbit Label 8041.ee

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[103]
 
pari: [g,chi] = znchar(Mod(103,8041))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 473
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 105
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.ee
Orbit index = 109

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 ]
 

\(\chi_{8041}(103,\cdot)\) \(\chi_{8041}(273,\cdot)\) \(\chi_{8041}(324,\cdot)\) \(\chi_{8041}(443,\cdot)\) \(\chi_{8041}(511,\cdot)\) \(\chi_{8041}(698,\cdot)\) \(\chi_{8041}(834,\cdot)\) \(\chi_{8041}(885,\cdot)\) \(\chi_{8041}(1004,\cdot)\) \(\chi_{8041}(1072,\cdot)\) \(\chi_{8041}(1565,\cdot)\) \(\chi_{8041}(1786,\cdot)\) \(\chi_{8041}(1820,\cdot)\) \(\chi_{8041}(1973,\cdot)\) \(\chi_{8041}(2160,\cdot)\) \(\chi_{8041}(2347,\cdot)\) \(\chi_{8041}(2517,\cdot)\) \(\chi_{8041}(2534,\cdot)\) \(\chi_{8041}(2568,\cdot)\) \(\chi_{8041}(2704,\cdot)\) \(\chi_{8041}(2891,\cdot)\) \(\chi_{8041}(3078,\cdot)\) \(\chi_{8041}(3248,\cdot)\) \(\chi_{8041}(3265,\cdot)\) \(\chi_{8041}(3282,\cdot)\) \(\chi_{8041}(3435,\cdot)\) \(\chi_{8041}(3622,\cdot)\) \(\chi_{8041}(3809,\cdot)\) \(\chi_{8041}(3996,\cdot)\) \(\chi_{8041}(4013,\cdot)\) ...

Inducing primitive character

\(\chi_{473}(103,\cdot)\)

Values on generators

\((6580,2366,562)\) → \((e\left(\frac{1}{5}\right),1,e\left(\frac{19}{21}\right))\)

Values

-11234567891012
\(1\)\(1\)\(e\left(\frac{22}{35}\right)\)\(e\left(\frac{53}{105}\right)\)\(e\left(\frac{9}{35}\right)\)\(e\left(\frac{44}{105}\right)\)\(e\left(\frac{2}{15}\right)\)\(e\left(\frac{1}{15}\right)\)\(e\left(\frac{31}{35}\right)\)\(e\left(\frac{1}{105}\right)\)\(e\left(\frac{1}{21}\right)\)\(e\left(\frac{16}{21}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{105})\)