Properties

Conductor 473
Order 42
Real No
Primitive No
Parity Even
Orbit Label 8041.cw

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[120]
 
pari: [g,chi] = znchar(Mod(120,8041))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 473
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 42
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.cw
Orbit index = 75

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 ]
 

\(\chi_{8041}(120,\cdot)\) \(\chi_{8041}(1990,\cdot)\) \(\chi_{8041}(2738,\cdot)\) \(\chi_{8041}(3486,\cdot)\) \(\chi_{8041}(3673,\cdot)\) \(\chi_{8041}(3860,\cdot)\) \(\chi_{8041}(4047,\cdot)\) \(\chi_{8041}(4234,\cdot)\) \(\chi_{8041}(5917,\cdot)\) \(\chi_{8041}(6478,\cdot)\) \(\chi_{8041}(7039,\cdot)\) \(\chi_{8041}(7974,\cdot)\)

Inducing primitive character

\(\chi_{473}(120,\cdot)\)

Values on generators

\((6580,2366,562)\) → \((-1,1,e\left(\frac{23}{42}\right))\)

Values

-11234567891012
\(1\)\(1\)\(e\left(\frac{2}{7}\right)\)\(e\left(\frac{23}{42}\right)\)\(e\left(\frac{4}{7}\right)\)\(e\left(\frac{29}{42}\right)\)\(e\left(\frac{5}{6}\right)\)\(e\left(\frac{2}{3}\right)\)\(e\left(\frac{6}{7}\right)\)\(e\left(\frac{2}{21}\right)\)\(e\left(\frac{41}{42}\right)\)\(e\left(\frac{5}{42}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{21})\)