Properties

Label 9450.6241
Modulus $9450$
Conductor $4725$
Order $45$
Real no
Primitive no
Minimal yes
Parity even

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Show commands: PariGP / SageMath
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(9450, base_ring=CyclotomicField(90))
 
M = H._module
 
chi = DirichletCharacter(H, M([10,18,60]))
 
pari: [g,chi] = znchar(Mod(6241,9450))
 

Basic properties

Modulus: \(9450\)
Conductor: \(4725\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(45\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from \(\chi_{4725}(1516,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 9450.fl

\(\chi_{9450}(331,\cdot)\) \(\chi_{9450}(571,\cdot)\) \(\chi_{9450}(961,\cdot)\) \(\chi_{9450}(1591,\cdot)\) \(\chi_{9450}(1831,\cdot)\) \(\chi_{9450}(2221,\cdot)\) \(\chi_{9450}(2461,\cdot)\) \(\chi_{9450}(3091,\cdot)\) \(\chi_{9450}(3481,\cdot)\) \(\chi_{9450}(3721,\cdot)\) \(\chi_{9450}(4111,\cdot)\) \(\chi_{9450}(4741,\cdot)\) \(\chi_{9450}(4981,\cdot)\) \(\chi_{9450}(5371,\cdot)\) \(\chi_{9450}(5611,\cdot)\) \(\chi_{9450}(6241,\cdot)\) \(\chi_{9450}(6631,\cdot)\) \(\chi_{9450}(6871,\cdot)\) \(\chi_{9450}(7261,\cdot)\) \(\chi_{9450}(7891,\cdot)\) \(\chi_{9450}(8131,\cdot)\) \(\chi_{9450}(8521,\cdot)\) \(\chi_{9450}(8761,\cdot)\) \(\chi_{9450}(9391,\cdot)\)

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 45 polynomial

Values on generators

\((9101,6427,6751)\) → \((e\left(\frac{1}{9}\right),e\left(\frac{1}{5}\right),e\left(\frac{2}{3}\right))\)

First values

\(a\) \(-1\)\(1\)\(11\)\(13\)\(17\)\(19\)\(23\)\(29\)\(31\)\(37\)\(41\)\(43\)
\( \chi_{ 9450 }(6241, a) \) \(1\)\(1\)\(e\left(\frac{14}{45}\right)\)\(e\left(\frac{31}{45}\right)\)\(e\left(\frac{14}{15}\right)\)\(e\left(\frac{4}{15}\right)\)\(e\left(\frac{34}{45}\right)\)\(e\left(\frac{23}{45}\right)\)\(e\left(\frac{22}{45}\right)\)\(e\left(\frac{4}{5}\right)\)\(e\left(\frac{31}{45}\right)\)\(e\left(\frac{4}{9}\right)\)
sage: chi.jacobi_sum(n)
 
\( \chi_{ 9450 }(6241,a) \;\) at \(\;a = \) e.g. 2