Properties

Label 9450.2833
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([100,27,150]))
 
pari: [g,chi] = znchar(Mod(2833,9450))
 

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 \(\chi_{4725}(2833,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 9450.hg

\(\chi_{9450}(187,\cdot)\) \(\chi_{9450}(283,\cdot)\) \(\chi_{9450}(313,\cdot)\) \(\chi_{9450}(787,\cdot)\) \(\chi_{9450}(817,\cdot)\) \(\chi_{9450}(913,\cdot)\) \(\chi_{9450}(1417,\cdot)\) \(\chi_{9450}(1447,\cdot)\) \(\chi_{9450}(1573,\cdot)\) \(\chi_{9450}(2047,\cdot)\) \(\chi_{9450}(2077,\cdot)\) \(\chi_{9450}(2173,\cdot)\) \(\chi_{9450}(2203,\cdot)\) \(\chi_{9450}(2677,\cdot)\) \(\chi_{9450}(2803,\cdot)\) \(\chi_{9450}(2833,\cdot)\) \(\chi_{9450}(3337,\cdot)\) \(\chi_{9450}(3433,\cdot)\) \(\chi_{9450}(3463,\cdot)\) \(\chi_{9450}(3937,\cdot)\) \(\chi_{9450}(3967,\cdot)\) \(\chi_{9450}(4063,\cdot)\) \(\chi_{9450}(4567,\cdot)\) \(\chi_{9450}(4597,\cdot)\) \(\chi_{9450}(4723,\cdot)\) \(\chi_{9450}(5197,\cdot)\) \(\chi_{9450}(5227,\cdot)\) \(\chi_{9450}(5323,\cdot)\) \(\chi_{9450}(5353,\cdot)\) \(\chi_{9450}(5827,\cdot)\) ...

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

\((9101,6427,6751)\) → \((e\left(\frac{5}{9}\right),e\left(\frac{3}{20}\right),e\left(\frac{5}{6}\right))\)

First values

\(a\) \(-1\)\(1\)\(11\)\(13\)\(17\)\(19\)\(23\)\(29\)\(31\)\(37\)\(41\)\(43\)
\( \chi_{ 9450 }(2833, a) \) \(1\)\(1\)\(e\left(\frac{43}{45}\right)\)\(e\left(\frac{143}{180}\right)\)\(e\left(\frac{7}{60}\right)\)\(e\left(\frac{8}{15}\right)\)\(e\left(\frac{77}{180}\right)\)\(e\left(\frac{77}{90}\right)\)\(e\left(\frac{13}{90}\right)\)\(e\left(\frac{7}{20}\right)\)\(e\left(\frac{49}{90}\right)\)\(e\left(\frac{17}{36}\right)\)
sage: chi.jacobi_sum(n)
 
\( \chi_{ 9450 }(2833,a) \;\) at \(\;a = \) e.g. 2