Properties

Label 2664.733
Modulus 26642664
Conductor 26642664
Order 1818
Real no
Primitive yes
Minimal yes
Parity even

Related objects

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Show commands: Pari/GP / SageMath
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(2664, base_ring=CyclotomicField(18)) M = H._module chi = DirichletCharacter(H, M([0,9,6,7]))
 
Copy content pari:[g,chi] = znchar(Mod(733,2664))
 

Basic properties

Modulus: 26642664
Conductor: 26642664
Copy content sage:chi.conductor()
 
Copy content pari:znconreyconductor(g,chi)
 
Order: 1818
Copy content sage:chi.multiplicative_order()
 
Copy content pari:charorder(g,chi)
 
Real: no
Primitive: yes
Copy content sage:chi.is_primitive()
 
Copy content pari:#znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
Copy content sage:chi.is_odd()
 
Copy content pari:zncharisodd(g,chi)
 

Galois orbit 2664.ev

χ2664(373,)\chi_{2664}(373,\cdot) χ2664(733,)\chi_{2664}(733,\cdot) χ2664(1357,)\chi_{2664}(1357,\cdot) χ2664(1501,)\chi_{2664}(1501,\cdot) χ2664(1669,)\chi_{2664}(1669,\cdot) χ2664(2581,)\chi_{2664}(2581,\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(ζ9)\Q(\zeta_{9})
Fixed field: Number field defined by a degree 18 polynomial

Values on generators

(1999,1333,2369,1297)(1999,1333,2369,1297)(1,1,e(13),e(718))(1,-1,e\left(\frac{1}{3}\right),e\left(\frac{7}{18}\right))

First values

aa 1-111557711111313171719192323252529293131
χ2664(733,a) \chi_{ 2664 }(733, a) 1111e(19)e\left(\frac{1}{9}\right)e(79)e\left(\frac{7}{9}\right)1-1e(49)e\left(\frac{4}{9}\right)e(1318)e\left(\frac{13}{18}\right)e(19)e\left(\frac{1}{9}\right)1-1e(29)e\left(\frac{2}{9}\right)11e(16)e\left(\frac{1}{6}\right)
Copy content sage:chi.jacobi_sum(n)
 
χ2664(733,a)   \chi_{ 2664 }(733,a) \; at   a=\;a = e.g. 2