Properties

Label 9450.6793
Modulus $9450$
Conductor $945$
Order $36$
Real no
Primitive no
Minimal no
Parity even

Related objects

Downloads

Learn more

Show commands: PariGP / SageMath
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(9450, base_ring=CyclotomicField(36))
 
M = H._module
 
chi = DirichletCharacter(H, M([8,27,6]))
 
pari: [g,chi] = znchar(Mod(6793,9450))
 

Basic properties

Modulus: \(9450\)
Conductor: \(945\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(36\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from \(\chi_{945}(178,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: no
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 9450.fi

\(\chi_{9450}(493,\cdot)\) \(\chi_{9450}(607,\cdot)\) \(\chi_{9450}(1993,\cdot)\) \(\chi_{9450}(2257,\cdot)\) \(\chi_{9450}(3643,\cdot)\) \(\chi_{9450}(3757,\cdot)\) \(\chi_{9450}(5143,\cdot)\) \(\chi_{9450}(5407,\cdot)\) \(\chi_{9450}(6793,\cdot)\) \(\chi_{9450}(6907,\cdot)\) \(\chi_{9450}(8293,\cdot)\) \(\chi_{9450}(8557,\cdot)\)

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: \(\Q(\zeta_{36})\)
Fixed field: 36.36.162855238472333830516712627682351491853245650503270085805829617553122341632843017578125.2

Values on generators

\((9101,6427,6751)\) → \((e\left(\frac{2}{9}\right),-i,e\left(\frac{1}{6}\right))\)

First values

\(a\) \(-1\)\(1\)\(11\)\(13\)\(17\)\(19\)\(23\)\(29\)\(31\)\(37\)\(41\)\(43\)
\( \chi_{ 9450 }(6793, a) \) \(1\)\(1\)\(e\left(\frac{5}{9}\right)\)\(e\left(\frac{19}{36}\right)\)\(i\)\(1\)\(e\left(\frac{1}{36}\right)\)\(e\left(\frac{13}{18}\right)\)\(e\left(\frac{11}{18}\right)\)\(e\left(\frac{5}{12}\right)\)\(e\left(\frac{5}{18}\right)\)\(e\left(\frac{5}{36}\right)\)
sage: chi.jacobi_sum(n)
 
\( \chi_{ 9450 }(6793,a) \;\) at \(\;a = \) e.g. 2