Properties

Label 1444.423
Modulus 14441444
Conductor 7676
Order 1818
Real no
Primitive no
Minimal no
Parity odd

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Show commands: PariGP / SageMath
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1444, base_ring=CyclotomicField(18))
 
M = H._module
 
chi = DirichletCharacter(H, M([9,16]))
 
pari: [g,chi] = znchar(Mod(423,1444))
 

Basic properties

Modulus: 14441444
Conductor: 7676
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: 1818
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from χ76(43,)\chi_{76}(43,\cdot)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: no
Parity: odd
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 1444.l

χ1444(99,)\chi_{1444}(99,\cdot) χ1444(415,)\chi_{1444}(415,\cdot) χ1444(423,)\chi_{1444}(423,\cdot) χ1444(595,)\chi_{1444}(595,\cdot) χ1444(967,)\chi_{1444}(967,\cdot) χ1444(1111,)\chi_{1444}(1111,\cdot)

sage: chi.galois_orbit()
 
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: 18.0.75613185918270483380568064.1

Values on generators

(723,1085)(723,1085)(1,e(89))(-1,e\left(\frac{8}{9}\right))

First values

aa 1-11133557799111113131515171721212323
χ1444(423,a) \chi_{ 1444 }(423, a) 1-111e(118)e\left(\frac{1}{18}\right)e(29)e\left(\frac{2}{9}\right)e(56)e\left(\frac{5}{6}\right)e(19)e\left(\frac{1}{9}\right)e(16)e\left(\frac{1}{6}\right)e(49)e\left(\frac{4}{9}\right)e(518)e\left(\frac{5}{18}\right)e(89)e\left(\frac{8}{9}\right)e(89)e\left(\frac{8}{9}\right)e(518)e\left(\frac{5}{18}\right)
sage: chi.jacobi_sum(n)
 
χ1444(423,a)   \chi_{ 1444 }(423,a) \; at   a=\;a = e.g. 2