Properties

Label 9450.4309
Modulus $9450$
Conductor $4725$
Order $90$
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(9450, base_ring=CyclotomicField(90))
 
M = H._module
 
chi = DirichletCharacter(H, M([20,63,60]))
 
pari: [g,chi] = znchar(Mod(4309,9450))
 

Basic properties

Modulus: \(9450\)
Conductor: \(4725\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(90\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from \(\chi_{4725}(4309,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 9450.gu

\(\chi_{9450}(529,\cdot)\) \(\chi_{9450}(1129,\cdot)\) \(\chi_{9450}(1159,\cdot)\) \(\chi_{9450}(1759,\cdot)\) \(\chi_{9450}(1789,\cdot)\) \(\chi_{9450}(2389,\cdot)\) \(\chi_{9450}(2419,\cdot)\) \(\chi_{9450}(3019,\cdot)\) \(\chi_{9450}(3679,\cdot)\) \(\chi_{9450}(4279,\cdot)\) \(\chi_{9450}(4309,\cdot)\) \(\chi_{9450}(4909,\cdot)\) \(\chi_{9450}(4939,\cdot)\) \(\chi_{9450}(5539,\cdot)\) \(\chi_{9450}(5569,\cdot)\) \(\chi_{9450}(6169,\cdot)\) \(\chi_{9450}(6829,\cdot)\) \(\chi_{9450}(7429,\cdot)\) \(\chi_{9450}(7459,\cdot)\) \(\chi_{9450}(8059,\cdot)\) \(\chi_{9450}(8089,\cdot)\) \(\chi_{9450}(8689,\cdot)\) \(\chi_{9450}(8719,\cdot)\) \(\chi_{9450}(9319,\cdot)\)

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: $\Q(\zeta_{45})$
Fixed field: Number field defined by a degree 90 polynomial

Values on generators

\((9101,6427,6751)\) → \((e\left(\frac{2}{9}\right),e\left(\frac{7}{10}\right),e\left(\frac{2}{3}\right))\)

First values

\(a\) \(-1\)\(1\)\(11\)\(13\)\(17\)\(19\)\(23\)\(29\)\(31\)\(37\)\(41\)\(43\)
\( \chi_{ 9450 }(4309, a) \) \(1\)\(1\)\(e\left(\frac{34}{45}\right)\)\(e\left(\frac{7}{90}\right)\)\(e\left(\frac{1}{10}\right)\)\(e\left(\frac{3}{5}\right)\)\(e\left(\frac{43}{90}\right)\)\(e\left(\frac{28}{45}\right)\)\(e\left(\frac{32}{45}\right)\)\(e\left(\frac{29}{30}\right)\)\(e\left(\frac{26}{45}\right)\)\(e\left(\frac{7}{18}\right)\)
sage: chi.jacobi_sum(n)
 
\( \chi_{ 9450 }(4309,a) \;\) at \(\;a = \) e.g. 2