Properties

Conductor 4031
Order 21
Real no
Primitive yes
Minimal yes
Parity even
Orbit label 4031.q

Related objects

Learn more about

Show commands for: Pari/GP / SageMath
sage: from dirichlet_conrey import DirichletGroup_conrey # requires nonstandard Sage package to be installed
 
sage: H = DirichletGroup_conrey(4031)
 
sage: chi = H[181]
 
pari: [g,chi] = znchar(Mod(181,4031))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 4031
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 21
Real = no
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1 \\ if not primitive returns [cond,factorization]
 
Primitive = yes
Minimal = yes
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 
Parity = even
Orbit label = 4031.q
Orbit index = 17

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 ]
 

\(\chi_{4031}(181,\cdot)\) \(\chi_{4031}(459,\cdot)\) \(\chi_{4031}(513,\cdot)\) \(\chi_{4031}(1069,\cdot)\) \(\chi_{4031}(1154,\cdot)\) \(\chi_{4031}(1486,\cdot)\) \(\chi_{4031}(1764,\cdot)\) \(\chi_{4031}(1988,\cdot)\) \(\chi_{4031}(2459,\cdot)\) \(\chi_{4031}(3239,\cdot)\) \(\chi_{4031}(3293,\cdot)\) \(\chi_{4031}(3795,\cdot)\)

Values on generators

\((3337,697)\) → \((e\left(\frac{3}{7}\right),e\left(\frac{2}{3}\right))\)

Values

-11234567891011
\(1\)\(1\)\(e\left(\frac{2}{21}\right)\)\(e\left(\frac{10}{21}\right)\)\(e\left(\frac{4}{21}\right)\)\(e\left(\frac{16}{21}\right)\)\(e\left(\frac{4}{7}\right)\)\(e\left(\frac{10}{21}\right)\)\(e\left(\frac{2}{7}\right)\)\(e\left(\frac{20}{21}\right)\)\(e\left(\frac{6}{7}\right)\)\(e\left(\frac{8}{21}\right)\)
value at  e.g. 2

Related number fields

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