Properties

Label 1890.479
Modulus $1890$
Conductor $945$
Order $18$
Real no
Primitive no
Minimal yes
Parity even

Related objects

Downloads

Learn more

Show commands: PariGP / SageMath
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1890, base_ring=CyclotomicField(18))
 
M = H._module
 
chi = DirichletCharacter(H, M([7,9,3]))
 
pari: [g,chi] = znchar(Mod(479,1890))
 

Basic properties

Modulus: \(1890\)
Conductor: \(945\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(18\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from \(\chi_{945}(479,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 1890.cm

\(\chi_{1890}(479,\cdot)\) \(\chi_{1890}(509,\cdot)\) \(\chi_{1890}(1109,\cdot)\) \(\chi_{1890}(1139,\cdot)\) \(\chi_{1890}(1739,\cdot)\) \(\chi_{1890}(1769,\cdot)\)

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: \(\Q(\zeta_{9})\)
Fixed field: 18.18.27394104089758334183232516621303416015625.1

Values on generators

\((1541,757,1081)\) → \((e\left(\frac{7}{18}\right),-1,e\left(\frac{1}{6}\right))\)

First values

\(a\) \(-1\)\(1\)\(11\)\(13\)\(17\)\(19\)\(23\)\(29\)\(31\)\(37\)\(41\)\(43\)
\( \chi_{ 1890 }(479, a) \) \(1\)\(1\)\(e\left(\frac{13}{18}\right)\)\(e\left(\frac{1}{9}\right)\)\(-1\)\(-1\)\(e\left(\frac{1}{9}\right)\)\(e\left(\frac{7}{18}\right)\)\(e\left(\frac{17}{18}\right)\)\(e\left(\frac{1}{6}\right)\)\(e\left(\frac{1}{9}\right)\)\(e\left(\frac{1}{18}\right)\)
sage: chi.jacobi_sum(n)
 
\( \chi_{ 1890 }(479,a) \;\) at \(\;a = \) e.g. 2