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Properties

Label 456.bv
Modulus 456456
Conductor 7676
Order 1818
Real no
Primitive no
Minimal no
Parity odd

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Show commands: Pari/GP / SageMath
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(456, base_ring=CyclotomicField(18)) M = H._module chi = DirichletCharacter(H, M([9,0,0,10])) chi.galois_orbit()
 
Copy content pari:[g,chi] = znchar(Mod(55,456)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: 456456
Conductor: 7676
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 76.l
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)
 

Related number fields

Field of values: Q(ζ9)\Q(\zeta_{9})
Fixed field: 18.0.75613185918270483380568064.1

Characters in Galois orbit

Character −1-1 11 55 77 1111 1313 1717 2323 2525 2929 3131 3535
χ456(55,⋅)\chi_{456}(55,\cdot) −1-1 11 e(89)e\left(\frac{8}{9}\right) e(56)e\left(\frac{5}{6}\right) e(16)e\left(\frac{1}{6}\right) e(79)e\left(\frac{7}{9}\right) e(59)e\left(\frac{5}{9}\right) e(1118)e\left(\frac{11}{18}\right) e(79)e\left(\frac{7}{9}\right) e(49)e\left(\frac{4}{9}\right) e(56)e\left(\frac{5}{6}\right) e(1318)e\left(\frac{13}{18}\right)
χ456(175,⋅)\chi_{456}(175,\cdot) −1-1 11 e(79)e\left(\frac{7}{9}\right) e(16)e\left(\frac{1}{6}\right) e(56)e\left(\frac{5}{6}\right) e(59)e\left(\frac{5}{9}\right) e(19)e\left(\frac{1}{9}\right) e(1318)e\left(\frac{13}{18}\right) e(59)e\left(\frac{5}{9}\right) e(89)e\left(\frac{8}{9}\right) e(16)e\left(\frac{1}{6}\right) e(1718)e\left(\frac{17}{18}\right)
χ456(199,⋅)\chi_{456}(199,\cdot) −1-1 11 e(19)e\left(\frac{1}{9}\right) e(16)e\left(\frac{1}{6}\right) e(56)e\left(\frac{5}{6}\right) e(29)e\left(\frac{2}{9}\right) e(49)e\left(\frac{4}{9}\right) e(718)e\left(\frac{7}{18}\right) e(29)e\left(\frac{2}{9}\right) e(59)e\left(\frac{5}{9}\right) e(16)e\left(\frac{1}{6}\right) e(518)e\left(\frac{5}{18}\right)
χ456(271,⋅)\chi_{456}(271,\cdot) −1-1 11 e(29)e\left(\frac{2}{9}\right) e(56)e\left(\frac{5}{6}\right) e(16)e\left(\frac{1}{6}\right) e(49)e\left(\frac{4}{9}\right) e(89)e\left(\frac{8}{9}\right) e(518)e\left(\frac{5}{18}\right) e(49)e\left(\frac{4}{9}\right) e(19)e\left(\frac{1}{9}\right) e(56)e\left(\frac{5}{6}\right) e(118)e\left(\frac{1}{18}\right)
χ456(367,⋅)\chi_{456}(367,\cdot) −1-1 11 e(49)e\left(\frac{4}{9}\right) e(16)e\left(\frac{1}{6}\right) e(56)e\left(\frac{5}{6}\right) e(89)e\left(\frac{8}{9}\right) e(79)e\left(\frac{7}{9}\right) e(118)e\left(\frac{1}{18}\right) e(89)e\left(\frac{8}{9}\right) e(29)e\left(\frac{2}{9}\right) e(16)e\left(\frac{1}{6}\right) e(1118)e\left(\frac{11}{18}\right)
χ456(415,⋅)\chi_{456}(415,\cdot) −1-1 11 e(59)e\left(\frac{5}{9}\right) e(56)e\left(\frac{5}{6}\right) e(16)e\left(\frac{1}{6}\right) e(19)e\left(\frac{1}{9}\right) e(29)e\left(\frac{2}{9}\right) e(1718)e\left(\frac{17}{18}\right) e(19)e\left(\frac{1}{9}\right) e(79)e\left(\frac{7}{9}\right) e(56)e\left(\frac{5}{6}\right) e(718)e\left(\frac{7}{18}\right)