Properties

Label 9464.41
Modulus $9464$
Conductor $1183$
Order $156$
Real no
Primitive no
Minimal yes
Parity even

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Show commands: PariGP / SageMath
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(9464, base_ring=CyclotomicField(156))
 
M = H._module
 
chi = DirichletCharacter(H, M([0,0,78,85]))
 
pari: [g,chi] = znchar(Mod(41,9464))
 

Basic properties

Modulus: \(9464\)
Conductor: \(1183\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(156\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from \(\chi_{1183}(41,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 9464.in

\(\chi_{9464}(41,\cdot)\) \(\chi_{9464}(97,\cdot)\) \(\chi_{9464}(713,\cdot)\) \(\chi_{9464}(769,\cdot)\) \(\chi_{9464}(825,\cdot)\) \(\chi_{9464}(1385,\cdot)\) \(\chi_{9464}(1497,\cdot)\) \(\chi_{9464}(1553,\cdot)\) \(\chi_{9464}(2113,\cdot)\) \(\chi_{9464}(2169,\cdot)\) \(\chi_{9464}(2225,\cdot)\) \(\chi_{9464}(2281,\cdot)\) \(\chi_{9464}(2841,\cdot)\) \(\chi_{9464}(2897,\cdot)\) \(\chi_{9464}(3009,\cdot)\) \(\chi_{9464}(3569,\cdot)\) \(\chi_{9464}(3625,\cdot)\) \(\chi_{9464}(3681,\cdot)\) \(\chi_{9464}(4297,\cdot)\) \(\chi_{9464}(4353,\cdot)\) \(\chi_{9464}(4409,\cdot)\) \(\chi_{9464}(4465,\cdot)\) \(\chi_{9464}(5025,\cdot)\) \(\chi_{9464}(5081,\cdot)\) \(\chi_{9464}(5137,\cdot)\) \(\chi_{9464}(5193,\cdot)\) \(\chi_{9464}(5753,\cdot)\) \(\chi_{9464}(5809,\cdot)\) \(\chi_{9464}(5865,\cdot)\) \(\chi_{9464}(5921,\cdot)\) ...

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: $\Q(\zeta_{156})$
Fixed field: Number field defined by a degree 156 polynomial (not computed)

Values on generators

\((2367,4733,2705,9297)\) → \((1,1,-1,e\left(\frac{85}{156}\right))\)

First values

\(a\) \(-1\)\(1\)\(3\)\(5\)\(9\)\(11\)\(15\)\(17\)\(19\)\(23\)\(25\)\(27\)
\( \chi_{ 9464 }(41, a) \) \(1\)\(1\)\(e\left(\frac{5}{78}\right)\)\(e\left(\frac{21}{52}\right)\)\(e\left(\frac{5}{39}\right)\)\(e\left(\frac{19}{156}\right)\)\(e\left(\frac{73}{156}\right)\)\(e\left(\frac{2}{39}\right)\)\(e\left(\frac{11}{12}\right)\)\(e\left(\frac{5}{6}\right)\)\(e\left(\frac{21}{26}\right)\)\(e\left(\frac{5}{26}\right)\)
sage: chi.jacobi_sum(n)
 
\( \chi_{ 9464 }(41,a) \;\) at \(\;a = \) e.g. 2