Properties

Label 4650.269
Modulus $4650$
Conductor $2325$
Order $30$
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(4650, base_ring=CyclotomicField(30))
 
M = H._module
 
chi = DirichletCharacter(H, M([15,27,29]))
 
pari: [g,chi] = znchar(Mod(269,4650))
 

Basic properties

Modulus: \(4650\)
Conductor: \(2325\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(30\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from \(\chi_{2325}(269,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 4650.ep

\(\chi_{4650}(269,\cdot)\) \(\chi_{4650}(1469,\cdot)\) \(\chi_{4650}(2039,\cdot)\) \(\chi_{4650}(3959,\cdot)\) \(\chi_{4650}(4109,\cdot)\) \(\chi_{4650}(4229,\cdot)\) \(\chi_{4650}(4289,\cdot)\) \(\chi_{4650}(4529,\cdot)\)

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: \(\Q(\zeta_{15})\)
Fixed field: Number field defined by a degree 30 polynomial

Values on generators

\((3101,2977,1801)\) → \((-1,e\left(\frac{9}{10}\right),e\left(\frac{29}{30}\right))\)

First values

\(a\) \(-1\)\(1\)\(7\)\(11\)\(13\)\(17\)\(19\)\(23\)\(29\)\(37\)\(41\)\(43\)
\( \chi_{ 4650 }(269, a) \) \(1\)\(1\)\(e\left(\frac{17}{30}\right)\)\(e\left(\frac{2}{15}\right)\)\(e\left(\frac{11}{15}\right)\)\(e\left(\frac{29}{30}\right)\)\(e\left(\frac{1}{15}\right)\)\(-1\)\(1\)\(e\left(\frac{4}{15}\right)\)\(e\left(\frac{19}{30}\right)\)\(e\left(\frac{13}{15}\right)\)
sage: chi.jacobi_sum(n)
 
\( \chi_{ 4650 }(269,a) \;\) at \(\;a = \) e.g. 2