Properties

Label 8664.7465
Modulus $8664$
Conductor $19$
Order $9$
Real no
Primitive no
Minimal no
Parity even

Related objects

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Show commands: Pari/GP / SageMath
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(8664, base_ring=CyclotomicField(18)) M = H._module chi = DirichletCharacter(H, M([0,0,0,10]))
 
Copy content pari:[g,chi] = znchar(Mod(7465,8664))
 

Basic properties

Modulus: \(8664\)
Conductor: \(19\)
Copy content sage:chi.conductor()
 
Copy content pari:znconreyconductor(g,chi)
 
Order: \(9\)
Copy content sage:chi.multiplicative_order()
 
Copy content pari:charorder(g,chi)
 
Real: no
Primitive: no, induced from \(\chi_{19}(17,\cdot)\)
Copy content sage:chi.is_primitive()
 
Copy content pari:#znconreyconductor(g,chi)==1
 
Minimal: no
Parity: even
Copy content sage:chi.is_odd()
 
Copy content pari:zncharisodd(g,chi)
 

Galois orbit 8664.bg

\(\chi_{8664}(2761,\cdot)\) \(\chi_{8664}(4033,\cdot)\) \(\chi_{8664}(6913,\cdot)\) \(\chi_{8664}(7465,\cdot)\) \(\chi_{8664}(7609,\cdot)\) \(\chi_{8664}(8041,\cdot)\)

Copy content sage:chi.galois_orbit()
 
Copy content pari:order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Related number fields

Field of values: \(\Q(\zeta_{9})\)
Fixed field: \(\Q(\zeta_{19})^+\)

Values on generators

\((2167,4333,5777,8305)\) → \((1,1,1,e\left(\frac{5}{9}\right))\)

First values

\(a\) \(-1\)\(1\)\(5\)\(7\)\(11\)\(13\)\(17\)\(23\)\(25\)\(29\)\(31\)\(35\)
\( \chi_{ 8664 }(7465, a) \) \(1\)\(1\)\(e\left(\frac{8}{9}\right)\)\(e\left(\frac{1}{3}\right)\)\(e\left(\frac{2}{3}\right)\)\(e\left(\frac{7}{9}\right)\)\(e\left(\frac{5}{9}\right)\)\(e\left(\frac{1}{9}\right)\)\(e\left(\frac{7}{9}\right)\)\(e\left(\frac{4}{9}\right)\)\(e\left(\frac{1}{3}\right)\)\(e\left(\frac{2}{9}\right)\)
Copy content sage:chi.jacobi_sum(n)
 
\( \chi_{ 8664 }(7465,a) \;\) at \(\;a = \) e.g. 2