Properties

Label 2888.1029
Modulus $2888$
Conductor $152$
Order $18$
Real no
Primitive no
Minimal no
Parity odd

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Show commands: Pari/GP / SageMath
sage: from sage.modular.dirichlet import DirichletCharacter
 
sage: H = DirichletGroup(2888, base_ring=CyclotomicField(18))
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([0,9,13]))
 
pari: [g,chi] = znchar(Mod(1029,2888))
 

Basic properties

Modulus: \(2888\)
Conductor: \(152\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(18\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from \(\chi_{152}(117,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: no
Parity: odd
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 2888.s

\(\chi_{2888}(333,\cdot)\) \(\chi_{2888}(477,\cdot)\) \(\chi_{2888}(1021,\cdot)\) \(\chi_{2888}(1029,\cdot)\) \(\chi_{2888}(2293,\cdot)\) \(\chi_{2888}(2789,\cdot)\)

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

Related number fields

Field of values: \(\Q(\zeta_{9})\)
Fixed field: 18.0.735565072612935262326166126592.1

Values on generators

\((2167,1445,2529)\) → \((1,-1,e\left(\frac{13}{18}\right))\)

Values

\(a\) \(-1\)\(1\)\(3\)\(5\)\(7\)\(9\)\(11\)\(13\)\(15\)\(17\)\(21\)\(23\)
\( \chi_{ 2888 }(1029, a) \) \(-1\)\(1\)\(e\left(\frac{8}{9}\right)\)\(e\left(\frac{1}{18}\right)\)\(e\left(\frac{1}{3}\right)\)\(e\left(\frac{7}{9}\right)\)\(e\left(\frac{1}{6}\right)\)\(e\left(\frac{1}{9}\right)\)\(e\left(\frac{17}{18}\right)\)\(e\left(\frac{2}{9}\right)\)\(e\left(\frac{2}{9}\right)\)\(e\left(\frac{4}{9}\right)\)
sage: chi.jacobi_sum(n)
 
\( \chi_{ 2888 }(1029,a) \;\) at \(\;a = \) e.g. 2