Properties

Label 9450.3439
Modulus $9450$
Conductor $1575$
Order $30$
Real no
Primitive no
Minimal no
Parity even

Related objects

Downloads

Learn more

Show commands: PariGP / SageMath
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(9450, base_ring=CyclotomicField(30))
 
M = H._module
 
chi = DirichletCharacter(H, M([10,9,10]))
 
pari: [g,chi] = znchar(Mod(3439,9450))
 

Basic properties

Modulus: \(9450\)
Conductor: \(1575\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(30\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from \(\chi_{1575}(814,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: no
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 9450.en

\(\chi_{9450}(1369,\cdot)\) \(\chi_{9450}(3259,\cdot)\) \(\chi_{9450}(3439,\cdot)\) \(\chi_{9450}(5329,\cdot)\) \(\chi_{9450}(7039,\cdot)\) \(\chi_{9450}(7219,\cdot)\) \(\chi_{9450}(8929,\cdot)\) \(\chi_{9450}(9109,\cdot)\)

sage: chi.galois_orbit()
 
order = charorder(g,chi)
 
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Related number fields

Field of values: \(\Q(\zeta_{15})\)
Fixed field: Number field defined by a degree 30 polynomial

Values on generators

\((9101,6427,6751)\) → \((e\left(\frac{1}{3}\right),e\left(\frac{3}{10}\right),e\left(\frac{1}{3}\right))\)

First values

\(a\) \(-1\)\(1\)\(11\)\(13\)\(17\)\(19\)\(23\)\(29\)\(31\)\(37\)\(41\)\(43\)
\( \chi_{ 9450 }(3439, a) \) \(1\)\(1\)\(e\left(\frac{7}{15}\right)\)\(e\left(\frac{11}{30}\right)\)\(e\left(\frac{7}{30}\right)\)\(e\left(\frac{1}{15}\right)\)\(e\left(\frac{19}{30}\right)\)\(e\left(\frac{14}{15}\right)\)\(e\left(\frac{2}{5}\right)\)\(e\left(\frac{11}{30}\right)\)\(e\left(\frac{13}{15}\right)\)\(e\left(\frac{5}{6}\right)\)
sage: chi.jacobi_sum(n)
 
\( \chi_{ 9450 }(3439,a) \;\) at \(\;a = \) e.g. 2