Properties

Conductor 473
Order 210
Real No
Primitive No
Parity Even
Orbit Label 8041.fb

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[18]
 
pari: [g,chi] = znchar(Mod(18,8041))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 473
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 210
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.fb
Orbit index = 132

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 ]
 

\(\chi_{8041}(18,\cdot)\) \(\chi_{8041}(205,\cdot)\) \(\chi_{8041}(392,\cdot)\) \(\chi_{8041}(545,\cdot)\) \(\chi_{8041}(579,\cdot)\) \(\chi_{8041}(800,\cdot)\) \(\chi_{8041}(1293,\cdot)\) \(\chi_{8041}(1361,\cdot)\) \(\chi_{8041}(1480,\cdot)\) \(\chi_{8041}(1531,\cdot)\) \(\chi_{8041}(1667,\cdot)\) \(\chi_{8041}(1854,\cdot)\) \(\chi_{8041}(1922,\cdot)\) \(\chi_{8041}(2041,\cdot)\) \(\chi_{8041}(2092,\cdot)\) \(\chi_{8041}(2262,\cdot)\) \(\chi_{8041}(2653,\cdot)\) \(\chi_{8041}(2823,\cdot)\) \(\chi_{8041}(2857,\cdot)\) \(\chi_{8041}(3044,\cdot)\) \(\chi_{8041}(3384,\cdot)\) \(\chi_{8041}(3588,\cdot)\) \(\chi_{8041}(3724,\cdot)\) \(\chi_{8041}(3775,\cdot)\) \(\chi_{8041}(4285,\cdot)\) \(\chi_{8041}(4319,\cdot)\) \(\chi_{8041}(4506,\cdot)\) \(\chi_{8041}(4846,\cdot)\) \(\chi_{8041}(4914,\cdot)\) \(\chi_{8041}(5645,\cdot)\) ...

Inducing primitive character

\(\chi_{473}(18,\cdot)\)

Values on generators

\((6580,2366,562)\) → \((e\left(\frac{7}{10}\right),1,e\left(\frac{29}{42}\right))\)

Values

-11234567891012
\(1\)\(1\)\(e\left(\frac{12}{35}\right)\)\(e\left(\frac{61}{210}\right)\)\(e\left(\frac{24}{35}\right)\)\(e\left(\frac{13}{210}\right)\)\(e\left(\frac{19}{30}\right)\)\(e\left(\frac{1}{15}\right)\)\(e\left(\frac{1}{35}\right)\)\(e\left(\frac{61}{105}\right)\)\(e\left(\frac{17}{42}\right)\)\(e\left(\frac{41}{42}\right)\)
value at  e.g. 2

Related number fields

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