Properties

Label 9464.727
Modulus $9464$
Conductor $4732$
Order $26$
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(9464, base_ring=CyclotomicField(26))
 
M = H._module
 
chi = DirichletCharacter(H, M([13,0,13,19]))
 
pari: [g,chi] = znchar(Mod(727,9464))
 

Basic properties

Modulus: \(9464\)
Conductor: \(4732\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(26\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from \(\chi_{4732}(727,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: no
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 9464.er

\(\chi_{9464}(727,\cdot)\) \(\chi_{9464}(1455,\cdot)\) \(\chi_{9464}(2183,\cdot)\) \(\chi_{9464}(2911,\cdot)\) \(\chi_{9464}(3639,\cdot)\) \(\chi_{9464}(4367,\cdot)\) \(\chi_{9464}(5095,\cdot)\) \(\chi_{9464}(5823,\cdot)\) \(\chi_{9464}(6551,\cdot)\) \(\chi_{9464}(7279,\cdot)\) \(\chi_{9464}(8007,\cdot)\) \(\chi_{9464}(8735,\cdot)\)

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: \(\Q(\zeta_{13})\)
Fixed field: 26.26.24904548371754690207828206084673035814148045702609536001608390487104815104.1

Values on generators

\((2367,4733,2705,9297)\) → \((-1,1,-1,e\left(\frac{19}{26}\right))\)

First values

\(a\) \(-1\)\(1\)\(3\)\(5\)\(9\)\(11\)\(15\)\(17\)\(19\)\(23\)\(25\)\(27\)
\( \chi_{ 9464 }(727, a) \) \(1\)\(1\)\(e\left(\frac{8}{13}\right)\)\(e\left(\frac{1}{13}\right)\)\(e\left(\frac{3}{13}\right)\)\(e\left(\frac{10}{13}\right)\)\(e\left(\frac{9}{13}\right)\)\(e\left(\frac{5}{26}\right)\)\(-1\)\(-1\)\(e\left(\frac{2}{13}\right)\)\(e\left(\frac{11}{13}\right)\)
sage: chi.jacobi_sum(n)
 
\( \chi_{ 9464 }(727,a) \;\) at \(\;a = \) e.g. 2