Properties

Label 2835.2339
Modulus 28352835
Conductor 135135
Order 1818
Real no
Primitive no
Minimal no
Parity odd

Related objects

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Show commands: Pari/GP / SageMath
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(2835, base_ring=CyclotomicField(18)) M = H._module chi = DirichletCharacter(H, M([17,9,0]))
 
Copy content pari:[g,chi] = znchar(Mod(2339,2835))
 

Basic properties

Modulus: 28352835
Conductor: 135135
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: no, induced from χ135(14,)\chi_{135}(14,\cdot)
Copy content sage:chi.is_primitive()
 
Copy content pari:#znconreyconductor(g,chi)==1
 
Minimal: no
Parity: odd
Copy content sage:chi.is_odd()
 
Copy content pari:zncharisodd(g,chi)
 

Galois orbit 2835.cn

χ2835(449,)\chi_{2835}(449,\cdot) χ2835(764,)\chi_{2835}(764,\cdot) χ2835(1394,)\chi_{2835}(1394,\cdot) χ2835(1709,)\chi_{2835}(1709,\cdot) χ2835(2339,)\chi_{2835}(2339,\cdot) χ2835(2654,)\chi_{2835}(2654,\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: 18.0.5770142004982097067662109375.1

Values on generators

(1541,1702,2026)(1541,1702,2026)(e(1718),1,1)(e\left(\frac{17}{18}\right),-1,1)

First values

aa 1-1112244881111131316161717191922222323
χ2835(2339,a) \chi_{ 2835 }(2339, a) 1-111e(49)e\left(\frac{4}{9}\right)e(89)e\left(\frac{8}{9}\right)e(13)e\left(\frac{1}{3}\right)e(518)e\left(\frac{5}{18}\right)e(118)e\left(\frac{1}{18}\right)e(79)e\left(\frac{7}{9}\right)e(23)e\left(\frac{2}{3}\right)e(13)e\left(\frac{1}{3}\right)e(1318)e\left(\frac{13}{18}\right)e(89)e\left(\frac{8}{9}\right)
Copy content sage:chi.jacobi_sum(n)
 
χ2835(2339,a)   \chi_{ 2835 }(2339,a) \; at   a=\;a = e.g. 2