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Properties

Label 135.n
Modulus 135135
Conductor 135135
Order 1818
Real no
Primitive yes
Minimal yes
Parity odd

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Show commands: Pari/GP / SageMath
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(135, base_ring=CyclotomicField(18)) M = H._module chi = DirichletCharacter(H, M([17,9])) chi.galois_orbit()
 
Copy content pari:[g,chi] = znchar(Mod(14,135)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: 135135
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: yes
Copy content sage:chi.is_primitive()
 
Copy content pari:#znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: odd
Copy content sage:chi.is_odd()
 
Copy content pari:zncharisodd(g,chi)
 

Related number fields

Field of values: Q(ζ9)\Q(\zeta_{9})
Fixed field: 18.0.5770142004982097067662109375.1

Characters in Galois orbit

Character −1-1 11 22 44 77 88 1111 1313 1414 1616 1717 1919
χ135(14,⋅)\chi_{135}(14,\cdot) −1-1 11 e(49)e\left(\frac{4}{9}\right) e(89)e\left(\frac{8}{9}\right) e(1118)e\left(\frac{11}{18}\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(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)
χ135(29,⋅)\chi_{135}(29,\cdot) −1-1 11 e(59)e\left(\frac{5}{9}\right) e(19)e\left(\frac{1}{9}\right) e(718)e\left(\frac{7}{18}\right) e(23)e\left(\frac{2}{3}\right) e(1318)e\left(\frac{13}{18}\right) e(1718)e\left(\frac{17}{18}\right) e(1718)e\left(\frac{17}{18}\right) e(29)e\left(\frac{2}{9}\right) e(13)e\left(\frac{1}{3}\right) e(23)e\left(\frac{2}{3}\right)
χ135(59,⋅)\chi_{135}(59,\cdot) −1-1 11 e(79)e\left(\frac{7}{9}\right) e(59)e\left(\frac{5}{9}\right) e(1718)e\left(\frac{17}{18}\right) e(13)e\left(\frac{1}{3}\right) e(1118)e\left(\frac{11}{18}\right) e(1318)e\left(\frac{13}{18}\right) e(1318)e\left(\frac{13}{18}\right) e(19)e\left(\frac{1}{9}\right) e(23)e\left(\frac{2}{3}\right) e(13)e\left(\frac{1}{3}\right)
χ135(74,⋅)\chi_{135}(74,\cdot) −1-1 11 e(89)e\left(\frac{8}{9}\right) e(79)e\left(\frac{7}{9}\right) e(1318)e\left(\frac{13}{18}\right) e(23)e\left(\frac{2}{3}\right) e(118)e\left(\frac{1}{18}\right) e(1118)e\left(\frac{11}{18}\right) e(1118)e\left(\frac{11}{18}\right) e(59)e\left(\frac{5}{9}\right) e(13)e\left(\frac{1}{3}\right) e(23)e\left(\frac{2}{3}\right)
χ135(104,⋅)\chi_{135}(104,\cdot) −1-1 11 e(19)e\left(\frac{1}{9}\right) e(29)e\left(\frac{2}{9}\right) e(518)e\left(\frac{5}{18}\right) e(13)e\left(\frac{1}{3}\right) e(1718)e\left(\frac{17}{18}\right) e(718)e\left(\frac{7}{18}\right) e(718)e\left(\frac{7}{18}\right) e(49)e\left(\frac{4}{9}\right) e(23)e\left(\frac{2}{3}\right) e(13)e\left(\frac{1}{3}\right)
χ135(119,⋅)\chi_{135}(119,\cdot) −1-1 11 e(29)e\left(\frac{2}{9}\right) e(49)e\left(\frac{4}{9}\right) e(118)e\left(\frac{1}{18}\right) e(23)e\left(\frac{2}{3}\right) e(718)e\left(\frac{7}{18}\right) e(518)e\left(\frac{5}{18}\right) e(518)e\left(\frac{5}{18}\right) e(89)e\left(\frac{8}{9}\right) e(13)e\left(\frac{1}{3}\right) e(23)e\left(\frac{2}{3}\right)