Properties

Label 9295.654
Modulus $9295$
Conductor $715$
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(9295, base_ring=CyclotomicField(30))
 
M = H._module
 
chi = DirichletCharacter(H, M([15,12,5]))
 
pari: [g,chi] = znchar(Mod(654,9295))
 

Basic properties

Modulus: \(9295\)
Conductor: \(715\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(30\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from \(\chi_{715}(654,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: no
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 9295.cv

\(\chi_{9295}(654,\cdot)\) \(\chi_{9295}(1499,\cdot)\) \(\chi_{9295}(1544,\cdot)\) \(\chi_{9295}(4079,\cdot)\) \(\chi_{9295}(5724,\cdot)\) \(\chi_{9295}(5769,\cdot)\) \(\chi_{9295}(6614,\cdot)\) \(\chi_{9295}(8259,\cdot)\)

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

\((7437,4226,6931)\) → \((-1,e\left(\frac{2}{5}\right),e\left(\frac{1}{6}\right))\)

First values

\(a\) \(-1\)\(1\)\(2\)\(3\)\(4\)\(6\)\(7\)\(8\)\(9\)\(12\)\(14\)\(16\)
\( \chi_{ 9295 }(654, a) \) \(1\)\(1\)\(e\left(\frac{1}{15}\right)\)\(e\left(\frac{11}{30}\right)\)\(e\left(\frac{2}{15}\right)\)\(e\left(\frac{13}{30}\right)\)\(e\left(\frac{2}{15}\right)\)\(e\left(\frac{1}{5}\right)\)\(e\left(\frac{11}{15}\right)\)\(-1\)\(e\left(\frac{1}{5}\right)\)\(e\left(\frac{4}{15}\right)\)
sage: chi.jacobi_sum(n)
 
\( \chi_{ 9295 }(654,a) \;\) at \(\;a = \) e.g. 2