Properties

Conductor 175
Order 15
Real no
Primitive no
Minimal yes
Parity even
Orbit label 9450.cu

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(9450)
 
sage: chi = H[541]
 
pari: [g,chi] = znchar(Mod(541,9450))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 175
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 = 9450.cu
Orbit index = 73

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 ]
 

\(\chi_{9450}(541,\cdot)\) \(\chi_{9450}(1621,\cdot)\) \(\chi_{9450}(2431,\cdot)\) \(\chi_{9450}(3511,\cdot)\) \(\chi_{9450}(4321,\cdot)\) \(\chi_{9450}(6211,\cdot)\) \(\chi_{9450}(7291,\cdot)\) \(\chi_{9450}(9181,\cdot)\)

Values on generators

\((9101,6427,6751)\) → \((1,e\left(\frac{1}{5}\right),e\left(\frac{1}{3}\right))\)

Values

-1111131719232931374143
\(1\)\(1\)\(e\left(\frac{8}{15}\right)\)\(e\left(\frac{4}{5}\right)\)\(e\left(\frac{14}{15}\right)\)\(e\left(\frac{4}{15}\right)\)\(e\left(\frac{13}{15}\right)\)\(e\left(\frac{2}{5}\right)\)\(e\left(\frac{14}{15}\right)\)\(e\left(\frac{7}{15}\right)\)\(e\left(\frac{4}{5}\right)\)\(1\)
value at  e.g. 2

Related number fields

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