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Properties

Label 912.ck
Modulus 912912
Conductor 456456
Order 1818
Real no
Primitive no
Minimal no
Parity even

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Show commands: PariGP / SageMath
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(912, base_ring=CyclotomicField(18))
 
M = H._module
 
chi = DirichletCharacter(H, M([9,9,9,2]))
 
chi.galois_orbit()
 
[g,chi] = znchar(Mod(23,912))
 
order = charorder(g,chi)
 
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: 912912
Conductor: 456456
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: 1818
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from 456.bu
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: no
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Related number fields

Field of values: Q(ζ9)\Q(\zeta_{9})
Fixed field: Number field defined by a degree 18 polynomial

Characters in Galois orbit

Character −1-1 11 55 77 1111 1313 1717 2323 2525 2929 3131 3535
χ912(23,⋅)\chi_{912}(23,\cdot) 11 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(118)e\left(\frac{1}{18}\right) e(1118)e\left(\frac{11}{18}\right) e(29)e\left(\frac{2}{9}\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)
χ912(119,⋅)\chi_{912}(119,\cdot) 11 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(1718)e\left(\frac{17}{18}\right) e(718)e\left(\frac{7}{18}\right) e(79)e\left(\frac{7}{9}\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)
χ912(215,⋅)\chi_{912}(215,\cdot) 11 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(718)e\left(\frac{7}{18}\right) e(518)e\left(\frac{5}{18}\right) e(59)e\left(\frac{5}{9}\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)
χ912(263,⋅)\chi_{912}(263,\cdot) 11 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(1118)e\left(\frac{11}{18}\right) e(1318)e\left(\frac{13}{18}\right) e(49)e\left(\frac{4}{9}\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)
χ912(359,⋅)\chi_{912}(359,\cdot) 11 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(518)e\left(\frac{5}{18}\right) e(118)e\left(\frac{1}{18}\right) e(19)e\left(\frac{1}{9}\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)
χ912(503,⋅)\chi_{912}(503,\cdot) 11 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(1318)e\left(\frac{13}{18}\right) e(1718)e\left(\frac{17}{18}\right) e(89)e\left(\frac{8}{9}\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)