Properties

Label 5265.94
Modulus $5265$
Conductor $5265$
Order $54$
Real no
Primitive yes
Minimal yes
Parity even

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Show commands: PariGP / SageMath
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(5265, base_ring=CyclotomicField(54))
 
M = H._module
 
chi = DirichletCharacter(H, M([8,27,18]))
 
pari: [g,chi] = znchar(Mod(94,5265))
 

Basic properties

Modulus: \(5265\)
Conductor: \(5265\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(54\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: yes
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 5265.gk

\(\chi_{5265}(94,\cdot)\) \(\chi_{5265}(529,\cdot)\) \(\chi_{5265}(679,\cdot)\) \(\chi_{5265}(1114,\cdot)\) \(\chi_{5265}(1264,\cdot)\) \(\chi_{5265}(1699,\cdot)\) \(\chi_{5265}(1849,\cdot)\) \(\chi_{5265}(2284,\cdot)\) \(\chi_{5265}(2434,\cdot)\) \(\chi_{5265}(2869,\cdot)\) \(\chi_{5265}(3019,\cdot)\) \(\chi_{5265}(3454,\cdot)\) \(\chi_{5265}(3604,\cdot)\) \(\chi_{5265}(4039,\cdot)\) \(\chi_{5265}(4189,\cdot)\) \(\chi_{5265}(4624,\cdot)\) \(\chi_{5265}(4774,\cdot)\) \(\chi_{5265}(5209,\cdot)\)

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: \(\Q(\zeta_{27})\)
Fixed field: Number field defined by a degree 54 polynomial

Values on generators

\((326,2107,2836)\) → \((e\left(\frac{4}{27}\right),-1,e\left(\frac{1}{3}\right))\)

First values

\(a\) \(-1\)\(1\)\(2\)\(4\)\(7\)\(8\)\(11\)\(14\)\(16\)\(17\)\(19\)\(22\)
\( \chi_{ 5265 }(94, a) \) \(1\)\(1\)\(e\left(\frac{53}{54}\right)\)\(e\left(\frac{26}{27}\right)\)\(e\left(\frac{29}{54}\right)\)\(e\left(\frac{17}{18}\right)\)\(e\left(\frac{7}{27}\right)\)\(e\left(\frac{14}{27}\right)\)\(e\left(\frac{25}{27}\right)\)\(e\left(\frac{1}{18}\right)\)\(e\left(\frac{7}{9}\right)\)\(e\left(\frac{13}{54}\right)\)
sage: chi.jacobi_sum(n)
 
\( \chi_{ 5265 }(94,a) \;\) at \(\;a = \) e.g. 2