Properties

Label 2280.1259
Modulus $2280$
Conductor $2280$
Order $18$
Real no
Primitive yes
Minimal yes
Parity even

Related objects

Learn more

Show commands: Pari/GP / SageMath
sage: from sage.modular.dirichlet import DirichletCharacter
 
sage: H = DirichletGroup(2280, base_ring=CyclotomicField(18))
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([9,9,9,9,16]))
 
pari: [g,chi] = znchar(Mod(1259,2280))
 

Basic properties

Modulus: \(2280\)
Conductor: \(2280\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(18\)
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 2280.eg

\(\chi_{2280}(899,\cdot)\) \(\chi_{2280}(1259,\cdot)\) \(\chi_{2280}(1499,\cdot)\) \(\chi_{2280}(1619,\cdot)\) \(\chi_{2280}(1859,\cdot)\) \(\chi_{2280}(2099,\cdot)\)

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: Number field defined by a degree 18 polynomial

Values on generators

\((1711,1141,761,457,1921)\) → \((-1,-1,-1,-1,e\left(\frac{8}{9}\right))\)

Values

\(-1\)\(1\)\(7\)\(11\)\(13\)\(17\)\(23\)\(29\)\(31\)\(37\)\(41\)\(43\)
\(1\)\(1\)\(e\left(\frac{1}{3}\right)\)\(e\left(\frac{1}{6}\right)\)\(e\left(\frac{4}{9}\right)\)\(e\left(\frac{8}{9}\right)\)\(e\left(\frac{5}{18}\right)\)\(e\left(\frac{1}{9}\right)\)\(e\left(\frac{5}{6}\right)\)\(1\)\(e\left(\frac{1}{18}\right)\)\(e\left(\frac{13}{18}\right)\)
sage: chi.jacobi_sum(n)
 
\( \chi_{ 2280 }(1259,a) \;\) at \(\;a = \) e.g. 2