Properties

Conductor 3004
Order 10
Real no
Primitive yes
Minimal yes
Parity even
Orbit label 3004.j

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(3004)
 
sage: chi = H[359]
 
pari: [g,chi] = znchar(Mod(359,3004))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 3004
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 10
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 = 3004.j
Orbit index = 10

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 ]
 

\(\chi_{3004}(291,\cdot)\) \(\chi_{3004}(359,\cdot)\) \(\chi_{3004}(671,\cdot)\) \(\chi_{3004}(2435,\cdot)\)

Values on generators

\((1503,1505)\) → \((-1,e\left(\frac{9}{10}\right))\)

Values

-113579111315171921
\(1\)\(1\)\(e\left(\frac{2}{5}\right)\)\(e\left(\frac{2}{5}\right)\)\(e\left(\frac{2}{5}\right)\)\(e\left(\frac{4}{5}\right)\)\(1\)\(e\left(\frac{1}{5}\right)\)\(e\left(\frac{4}{5}\right)\)\(e\left(\frac{1}{10}\right)\)\(e\left(\frac{7}{10}\right)\)\(e\left(\frac{4}{5}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{5})\)