Properties

Label 9450.4483
Modulus $9450$
Conductor $175$
Order $60$
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(60))
 
M = H._module
 
chi = DirichletCharacter(H, M([0,9,10]))
 
pari: [g,chi] = znchar(Mod(4483,9450))
 

Basic properties

Modulus: \(9450\)
Conductor: \(175\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(60\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from \(\chi_{175}(108,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 9450.fz

\(\chi_{9450}(703,\cdot)\) \(\chi_{9450}(1027,\cdot)\) \(\chi_{9450}(1783,\cdot)\) \(\chi_{9450}(1837,\cdot)\) \(\chi_{9450}(2917,\cdot)\) \(\chi_{9450}(3673,\cdot)\) \(\chi_{9450}(3727,\cdot)\) \(\chi_{9450}(4483,\cdot)\) \(\chi_{9450}(5563,\cdot)\) \(\chi_{9450}(5617,\cdot)\) \(\chi_{9450}(6373,\cdot)\) \(\chi_{9450}(6697,\cdot)\) \(\chi_{9450}(7453,\cdot)\) \(\chi_{9450}(8263,\cdot)\) \(\chi_{9450}(8587,\cdot)\) \(\chi_{9450}(9397,\cdot)\)

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: \(\Q(\zeta_{60})\)
Fixed field: Number field defined by a degree 60 polynomial

Values on generators

\((9101,6427,6751)\) → \((1,e\left(\frac{3}{20}\right),e\left(\frac{1}{6}\right))\)

First values

\(a\) \(-1\)\(1\)\(11\)\(13\)\(17\)\(19\)\(23\)\(29\)\(31\)\(37\)\(41\)\(43\)
\( \chi_{ 9450 }(4483, a) \) \(1\)\(1\)\(e\left(\frac{1}{15}\right)\)\(e\left(\frac{7}{20}\right)\)\(e\left(\frac{7}{60}\right)\)\(e\left(\frac{8}{15}\right)\)\(e\left(\frac{59}{60}\right)\)\(e\left(\frac{3}{10}\right)\)\(e\left(\frac{11}{30}\right)\)\(e\left(\frac{41}{60}\right)\)\(e\left(\frac{1}{10}\right)\)\(i\)
sage: chi.jacobi_sum(n)
 
\( \chi_{ 9450 }(4483,a) \;\) at \(\;a = \) e.g. 2