Properties

Label 9464.463
Modulus $9464$
Conductor $676$
Order $52$
Real no
Primitive no
Minimal no
Parity even

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Show commands: PariGP / SageMath
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(9464, base_ring=CyclotomicField(52))
 
M = H._module
 
chi = DirichletCharacter(H, M([26,0,0,9]))
 
pari: [g,chi] = znchar(Mod(463,9464))
 

Basic properties

Modulus: \(9464\)
Conductor: \(676\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(52\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from \(\chi_{676}(463,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: no
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 9464.fr

\(\chi_{9464}(463,\cdot)\) \(\chi_{9464}(967,\cdot)\) \(\chi_{9464}(1191,\cdot)\) \(\chi_{9464}(1695,\cdot)\) \(\chi_{9464}(1919,\cdot)\) \(\chi_{9464}(2423,\cdot)\) \(\chi_{9464}(2647,\cdot)\) \(\chi_{9464}(3151,\cdot)\) \(\chi_{9464}(3375,\cdot)\) \(\chi_{9464}(3879,\cdot)\) \(\chi_{9464}(4103,\cdot)\) \(\chi_{9464}(4607,\cdot)\) \(\chi_{9464}(5335,\cdot)\) \(\chi_{9464}(5559,\cdot)\) \(\chi_{9464}(6063,\cdot)\) \(\chi_{9464}(6287,\cdot)\) \(\chi_{9464}(6791,\cdot)\) \(\chi_{9464}(7015,\cdot)\) \(\chi_{9464}(7519,\cdot)\) \(\chi_{9464}(7743,\cdot)\) \(\chi_{9464}(8247,\cdot)\) \(\chi_{9464}(8471,\cdot)\) \(\chi_{9464}(8975,\cdot)\) \(\chi_{9464}(9199,\cdot)\)

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: $\Q(\zeta_{52})$
Fixed field: Number field defined by a degree 52 polynomial

Values on generators

\((2367,4733,2705,9297)\) → \((-1,1,1,e\left(\frac{9}{52}\right))\)

First values

\(a\) \(-1\)\(1\)\(3\)\(5\)\(9\)\(11\)\(15\)\(17\)\(19\)\(23\)\(25\)\(27\)
\( \chi_{ 9464 }(463, a) \) \(1\)\(1\)\(e\left(\frac{25}{26}\right)\)\(e\left(\frac{29}{52}\right)\)\(e\left(\frac{12}{13}\right)\)\(e\left(\frac{17}{52}\right)\)\(e\left(\frac{27}{52}\right)\)\(e\left(\frac{7}{26}\right)\)\(-i\)\(1\)\(e\left(\frac{3}{26}\right)\)\(e\left(\frac{23}{26}\right)\)
sage: chi.jacobi_sum(n)
 
\( \chi_{ 9464 }(463,a) \;\) at \(\;a = \) e.g. 2