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Properties

Label 171.u
Modulus 171171
Conductor 1919
Order 99
Real no
Primitive no
Minimal yes
Parity even

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Show commands: Pari/GP / SageMath
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(171, base_ring=CyclotomicField(18)) M = H._module chi = DirichletCharacter(H, M([0,8])) chi.galois_orbit()
 
Copy content pari:[g,chi] = znchar(Mod(28,171)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: 171171
Conductor: 1919
Copy content sage:chi.conductor()
 
Copy content pari:znconreyconductor(g,chi)
 
Order: 99
Copy content sage:chi.multiplicative_order()
 
Copy content pari:charorder(g,chi)
 
Real: no
Primitive: no, induced from 19.e
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)
 

Related number fields

Field of values: Q(ζ9)\Q(\zeta_{9})
Fixed field: Q(ζ19)+\Q(\zeta_{19})^+

Characters in Galois orbit

Character −1-1 11 22 44 55 77 88 1010 1111 1313 1414 1616
χ171(28,⋅)\chi_{171}(28,\cdot) 11 11 e(49)e\left(\frac{4}{9}\right) e(89)e\left(\frac{8}{9}\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) e(59)e\left(\frac{5}{9}\right) e(13)e\left(\frac{1}{3}\right) e(29)e\left(\frac{2}{9}\right) e(19)e\left(\frac{1}{9}\right) e(79)e\left(\frac{7}{9}\right)
χ171(55,⋅)\chi_{171}(55,\cdot) 11 11 e(59)e\left(\frac{5}{9}\right) e(19)e\left(\frac{1}{9}\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) e(49)e\left(\frac{4}{9}\right) e(23)e\left(\frac{2}{3}\right) e(79)e\left(\frac{7}{9}\right) e(89)e\left(\frac{8}{9}\right) e(29)e\left(\frac{2}{9}\right)
χ171(73,⋅)\chi_{171}(73,\cdot) 11 11 e(29)e\left(\frac{2}{9}\right) e(49)e\left(\frac{4}{9}\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) e(79)e\left(\frac{7}{9}\right) e(23)e\left(\frac{2}{3}\right) e(19)e\left(\frac{1}{9}\right) e(59)e\left(\frac{5}{9}\right) e(89)e\left(\frac{8}{9}\right)
χ171(82,⋅)\chi_{171}(82,\cdot) 11 11 e(79)e\left(\frac{7}{9}\right) e(59)e\left(\frac{5}{9}\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) e(29)e\left(\frac{2}{9}\right) e(13)e\left(\frac{1}{3}\right) e(89)e\left(\frac{8}{9}\right) e(49)e\left(\frac{4}{9}\right) e(19)e\left(\frac{1}{9}\right)
χ171(100,⋅)\chi_{171}(100,\cdot) 11 11 e(89)e\left(\frac{8}{9}\right) e(79)e\left(\frac{7}{9}\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) e(19)e\left(\frac{1}{9}\right) e(23)e\left(\frac{2}{3}\right) e(49)e\left(\frac{4}{9}\right) e(29)e\left(\frac{2}{9}\right) e(59)e\left(\frac{5}{9}\right)
χ171(118,⋅)\chi_{171}(118,\cdot) 11 11 e(19)e\left(\frac{1}{9}\right) e(29)e\left(\frac{2}{9}\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(89)e\left(\frac{8}{9}\right) e(13)e\left(\frac{1}{3}\right) e(59)e\left(\frac{5}{9}\right) e(79)e\left(\frac{7}{9}\right) e(49)e\left(\frac{4}{9}\right)