Properties

Label 9450.17
Modulus $9450$
Conductor $1575$
Order $60$
Real no
Primitive no
Minimal no
Parity odd

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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([50,39,10]))
 
pari: [g,chi] = znchar(Mod(17,9450))
 

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 \(\chi_{1575}(1067,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: no
Parity: odd
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 9450.gc

\(\chi_{9450}(17,\cdot)\) \(\chi_{9450}(467,\cdot)\) \(\chi_{9450}(773,\cdot)\) \(\chi_{9450}(1223,\cdot)\) \(\chi_{9450}(2663,\cdot)\) \(\chi_{9450}(3113,\cdot)\) \(\chi_{9450}(3797,\cdot)\) \(\chi_{9450}(4247,\cdot)\) \(\chi_{9450}(4553,\cdot)\) \(\chi_{9450}(5003,\cdot)\) \(\chi_{9450}(5687,\cdot)\) \(\chi_{9450}(6137,\cdot)\) \(\chi_{9450}(7577,\cdot)\) \(\chi_{9450}(8027,\cdot)\) \(\chi_{9450}(8333,\cdot)\) \(\chi_{9450}(8783,\cdot)\)

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

\((9101,6427,6751)\) → \((e\left(\frac{5}{6}\right),e\left(\frac{13}{20}\right),e\left(\frac{1}{6}\right))\)

First values

\(a\) \(-1\)\(1\)\(11\)\(13\)\(17\)\(19\)\(23\)\(29\)\(31\)\(37\)\(41\)\(43\)
\( \chi_{ 9450 }(17, a) \) \(-1\)\(1\)\(e\left(\frac{9}{10}\right)\)\(e\left(\frac{31}{60}\right)\)\(e\left(\frac{7}{60}\right)\)\(e\left(\frac{8}{15}\right)\)\(e\left(\frac{13}{20}\right)\)\(e\left(\frac{2}{15}\right)\)\(e\left(\frac{1}{30}\right)\)\(e\left(\frac{11}{60}\right)\)\(e\left(\frac{4}{15}\right)\)\(e\left(\frac{1}{12}\right)\)
sage: chi.jacobi_sum(n)
 
\( \chi_{ 9450 }(17,a) \;\) at \(\;a = \) e.g. 2