Properties

Label 9450.4337
Modulus $9450$
Conductor $1575$
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([50,27,40]))
 
pari: [g,chi] = znchar(Mod(4337,9450))
 

Basic properties

Modulus: \(9450\)
Conductor: \(1575\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(60\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from \(\chi_{1575}(662,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 9450.gb

\(\chi_{9450}(737,\cdot)\) \(\chi_{9450}(1313,\cdot)\) \(\chi_{9450}(2447,\cdot)\) \(\chi_{9450}(2627,\cdot)\) \(\chi_{9450}(3203,\cdot)\) \(\chi_{9450}(3383,\cdot)\) \(\chi_{9450}(4337,\cdot)\) \(\chi_{9450}(4517,\cdot)\) \(\chi_{9450}(5273,\cdot)\) \(\chi_{9450}(6227,\cdot)\) \(\chi_{9450}(6983,\cdot)\) \(\chi_{9450}(7163,\cdot)\) \(\chi_{9450}(8117,\cdot)\) \(\chi_{9450}(8297,\cdot)\) \(\chi_{9450}(8873,\cdot)\) \(\chi_{9450}(9053,\cdot)\)

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

\((9101,6427,6751)\) → \((e\left(\frac{5}{6}\right),e\left(\frac{9}{20}\right),e\left(\frac{2}{3}\right))\)

First values

\(a\) \(-1\)\(1\)\(11\)\(13\)\(17\)\(19\)\(23\)\(29\)\(31\)\(37\)\(41\)\(43\)
\( \chi_{ 9450 }(4337, a) \) \(1\)\(1\)\(e\left(\frac{7}{10}\right)\)\(e\left(\frac{13}{60}\right)\)\(e\left(\frac{1}{60}\right)\)\(e\left(\frac{13}{30}\right)\)\(e\left(\frac{9}{20}\right)\)\(e\left(\frac{11}{15}\right)\)\(e\left(\frac{14}{15}\right)\)\(e\left(\frac{23}{60}\right)\)\(e\left(\frac{29}{30}\right)\)\(e\left(\frac{1}{12}\right)\)
sage: chi.jacobi_sum(n)
 
\( \chi_{ 9450 }(4337,a) \;\) at \(\;a = \) e.g. 2