Properties

Label 9450.2113
Modulus $9450$
Conductor $4725$
Order $180$
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(180))
 
M = H._module
 
chi = DirichletCharacter(H, M([160,171,90]))
 
pari: [g,chi] = znchar(Mod(2113,9450))
 

Basic properties

Modulus: \(9450\)
Conductor: \(4725\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(180\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from \(\chi_{4725}(2113,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 9450.hh

\(\chi_{9450}(13,\cdot)\) \(\chi_{9450}(97,\cdot)\) \(\chi_{9450}(223,\cdot)\) \(\chi_{9450}(517,\cdot)\) \(\chi_{9450}(727,\cdot)\) \(\chi_{9450}(853,\cdot)\) \(\chi_{9450}(1147,\cdot)\) \(\chi_{9450}(1273,\cdot)\) \(\chi_{9450}(1483,\cdot)\) \(\chi_{9450}(1777,\cdot)\) \(\chi_{9450}(1903,\cdot)\) \(\chi_{9450}(1987,\cdot)\) \(\chi_{9450}(2113,\cdot)\) \(\chi_{9450}(2533,\cdot)\) \(\chi_{9450}(2617,\cdot)\) \(\chi_{9450}(3037,\cdot)\) \(\chi_{9450}(3163,\cdot)\) \(\chi_{9450}(3247,\cdot)\) \(\chi_{9450}(3373,\cdot)\) \(\chi_{9450}(3667,\cdot)\) \(\chi_{9450}(3877,\cdot)\) \(\chi_{9450}(4003,\cdot)\) \(\chi_{9450}(4297,\cdot)\) \(\chi_{9450}(4423,\cdot)\) \(\chi_{9450}(4633,\cdot)\) \(\chi_{9450}(4927,\cdot)\) \(\chi_{9450}(5053,\cdot)\) \(\chi_{9450}(5137,\cdot)\) \(\chi_{9450}(5263,\cdot)\) \(\chi_{9450}(5683,\cdot)\) ...

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: $\Q(\zeta_{180})$
Fixed field: Number field defined by a degree 180 polynomial (not computed)

Values on generators

\((9101,6427,6751)\) → \((e\left(\frac{8}{9}\right),e\left(\frac{19}{20}\right),-1)\)

First values

\(a\) \(-1\)\(1\)\(11\)\(13\)\(17\)\(19\)\(23\)\(29\)\(31\)\(37\)\(41\)\(43\)
\( \chi_{ 9450 }(2113, a) \) \(1\)\(1\)\(e\left(\frac{34}{45}\right)\)\(e\left(\frac{119}{180}\right)\)\(e\left(\frac{11}{60}\right)\)\(e\left(\frac{4}{15}\right)\)\(e\left(\frac{41}{180}\right)\)\(e\left(\frac{71}{90}\right)\)\(e\left(\frac{79}{90}\right)\)\(e\left(\frac{53}{60}\right)\)\(e\left(\frac{37}{90}\right)\)\(e\left(\frac{29}{36}\right)\)
sage: chi.jacobi_sum(n)
 
\( \chi_{ 9450 }(2113,a) \;\) at \(\;a = \) e.g. 2