Properties

Conductor 731
Order 168
Real No
Primitive No
Parity Even
Orbit Label 8041.es

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[100]
 
pari: [g,chi] = znchar(Mod(100,8041))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 731
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 168
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.es
Orbit index = 123

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 ]
 

\(\chi_{8041}(100,\cdot)\) \(\chi_{8041}(111,\cdot)\) \(\chi_{8041}(144,\cdot)\) \(\chi_{8041}(298,\cdot)\) \(\chi_{8041}(529,\cdot)\) \(\chi_{8041}(705,\cdot)\) \(\chi_{8041}(848,\cdot)\) \(\chi_{8041}(1046,\cdot)\) \(\chi_{8041}(1090,\cdot)\) \(\chi_{8041}(1651,\cdot)\) \(\chi_{8041}(1794,\cdot)\) \(\chi_{8041}(2388,\cdot)\) \(\chi_{8041}(2575,\cdot)\) \(\chi_{8041}(2718,\cdot)\) \(\chi_{8041}(2762,\cdot)\) \(\chi_{8041}(2905,\cdot)\) \(\chi_{8041}(2949,\cdot)\) \(\chi_{8041}(3136,\cdot)\) \(\chi_{8041}(3334,\cdot)\) \(\chi_{8041}(3521,\cdot)\) \(\chi_{8041}(3664,\cdot)\) \(\chi_{8041}(3708,\cdot)\) \(\chi_{8041}(3840,\cdot)\) \(\chi_{8041}(3851,\cdot)\) \(\chi_{8041}(3884,\cdot)\) \(\chi_{8041}(3895,\cdot)\) \(\chi_{8041}(4082,\cdot)\) \(\chi_{8041}(4401,\cdot)\) \(\chi_{8041}(4632,\cdot)\) \(\chi_{8041}(4786,\cdot)\) ...

Inducing primitive character

\(\chi_{731}(100,\cdot)\)

Values on generators

\((6580,2366,562)\) → \((1,e\left(\frac{3}{8}\right),e\left(\frac{10}{21}\right))\)

Values

-11234567891012
\(1\)\(1\)\(e\left(\frac{3}{28}\right)\)\(e\left(\frac{143}{168}\right)\)\(e\left(\frac{3}{14}\right)\)\(e\left(\frac{131}{168}\right)\)\(e\left(\frac{23}{24}\right)\)\(e\left(\frac{19}{24}\right)\)\(e\left(\frac{9}{28}\right)\)\(e\left(\frac{59}{84}\right)\)\(e\left(\frac{149}{168}\right)\)\(e\left(\frac{11}{168}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{168})\)