Properties

Conductor 8041
Order 420
Real No
Primitive Yes
Parity Even
Orbit Label 8041.fp

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[30]
 
pari: [g,chi] = znchar(Mod(30,8041))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 8041
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 420
Real = No
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1 \\ if not primitive returns [cond,factorization]
 
Primitive = Yes
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 
Parity = Even
Orbit label = 8041.fp
Orbit index = 146

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 ]
 

\(\chi_{8041}(30,\cdot)\) \(\chi_{8041}(72,\cdot)\) \(\chi_{8041}(106,\cdot)\) \(\chi_{8041}(149,\cdot)\) \(\chi_{8041}(200,\cdot)\) \(\chi_{8041}(327,\cdot)\) \(\chi_{8041}(370,\cdot)\) \(\chi_{8041}(761,\cdot)\) \(\chi_{8041}(820,\cdot)\) \(\chi_{8041}(888,\cdot)\) \(\chi_{8041}(931,\cdot)\) \(\chi_{8041}(965,\cdot)\) \(\chi_{8041}(1007,\cdot)\) \(\chi_{8041}(1058,\cdot)\) \(\chi_{8041}(1152,\cdot)\) \(\chi_{8041}(1194,\cdot)\) \(\chi_{8041}(1381,\cdot)\) \(\chi_{8041}(1449,\cdot)\) \(\chi_{8041}(1492,\cdot)\) \(\chi_{8041}(1568,\cdot)\) \(\chi_{8041}(1619,\cdot)\) \(\chi_{8041}(1696,\cdot)\) \(\chi_{8041}(1789,\cdot)\) \(\chi_{8041}(1832,\cdot)\) \(\chi_{8041}(1883,\cdot)\) \(\chi_{8041}(2180,\cdot)\) \(\chi_{8041}(2350,\cdot)\) \(\chi_{8041}(2384,\cdot)\) \(\chi_{8041}(2393,\cdot)\) \(\chi_{8041}(2427,\cdot)\) ...

Values on generators

\((6580,2366,562)\) → \((e\left(\frac{3}{10}\right),i,e\left(\frac{11}{42}\right))\)

Values

-11234567891012
\(1\)\(1\)\(e\left(\frac{61}{70}\right)\)\(e\left(\frac{383}{420}\right)\)\(e\left(\frac{26}{35}\right)\)\(e\left(\frac{419}{420}\right)\)\(e\left(\frac{47}{60}\right)\)\(e\left(\frac{1}{60}\right)\)\(e\left(\frac{43}{70}\right)\)\(e\left(\frac{173}{210}\right)\)\(e\left(\frac{73}{84}\right)\)\(e\left(\frac{55}{84}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{420})\)