Properties

Conductor 1575
Order 15
Real no
Primitive no
Minimal yes
Parity even
Orbit label 3150.ct

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(3150)
 
sage: chi = H[121]
 
pari: [g,chi] = znchar(Mod(121,3150))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 1575
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 15
Real = no
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1 \\ if not primitive returns [cond,factorization]
 
Primitive = no
Minimal = yes
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 
Parity = even
Orbit label = 3150.ct
Orbit index = 72

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 ]
 

\(\chi_{3150}(121,\cdot)\) \(\chi_{3150}(781,\cdot)\) \(\chi_{3150}(1381,\cdot)\) \(\chi_{3150}(1411,\cdot)\) \(\chi_{3150}(2011,\cdot)\) \(\chi_{3150}(2041,\cdot)\) \(\chi_{3150}(2641,\cdot)\) \(\chi_{3150}(2671,\cdot)\)

Values on generators

\((2801,127,451)\) → \((e\left(\frac{1}{3}\right),e\left(\frac{3}{5}\right),e\left(\frac{1}{3}\right))\)

Values

-1111131719232931374143
\(1\)\(1\)\(e\left(\frac{4}{15}\right)\)\(e\left(\frac{1}{15}\right)\)\(e\left(\frac{2}{15}\right)\)\(e\left(\frac{7}{15}\right)\)\(e\left(\frac{14}{15}\right)\)\(e\left(\frac{8}{15}\right)\)\(e\left(\frac{4}{5}\right)\)\(e\left(\frac{1}{15}\right)\)\(e\left(\frac{1}{15}\right)\)\(e\left(\frac{1}{3}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{15})\)