Properties

Label 2925.17
Modulus $2925$
Conductor $975$
Order $60$
Real no
Primitive no
Minimal no
Parity even

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Show commands: PariGP / SageMath
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(2925, base_ring=CyclotomicField(60))
 
M = H._module
 
chi = DirichletCharacter(H, M([30,39,10]))
 
pari: [g,chi] = znchar(Mod(17,2925))
 

Basic properties

Modulus: \(2925\)
Conductor: \(975\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(60\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from \(\chi_{975}(17,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: no
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 2925.gw

\(\chi_{2925}(17,\cdot)\) \(\chi_{2925}(62,\cdot)\) \(\chi_{2925}(413,\cdot)\) \(\chi_{2925}(602,\cdot)\) \(\chi_{2925}(647,\cdot)\) \(\chi_{2925}(953,\cdot)\) \(\chi_{2925}(998,\cdot)\) \(\chi_{2925}(1187,\cdot)\) \(\chi_{2925}(1538,\cdot)\) \(\chi_{2925}(1583,\cdot)\) \(\chi_{2925}(1772,\cdot)\) \(\chi_{2925}(1817,\cdot)\) \(\chi_{2925}(2123,\cdot)\) \(\chi_{2925}(2402,\cdot)\) \(\chi_{2925}(2708,\cdot)\) \(\chi_{2925}(2753,\cdot)\)

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

\((326,352,2251)\) → \((-1,e\left(\frac{13}{20}\right),e\left(\frac{1}{6}\right))\)

First values

\(a\) \(-1\)\(1\)\(2\)\(4\)\(7\)\(8\)\(11\)\(14\)\(16\)\(17\)\(19\)\(22\)
\( \chi_{ 2925 }(17, a) \) \(1\)\(1\)\(e\left(\frac{19}{60}\right)\)\(e\left(\frac{19}{30}\right)\)\(e\left(\frac{1}{12}\right)\)\(e\left(\frac{19}{20}\right)\)\(e\left(\frac{1}{15}\right)\)\(e\left(\frac{2}{5}\right)\)\(e\left(\frac{4}{15}\right)\)\(e\left(\frac{17}{60}\right)\)\(e\left(\frac{8}{15}\right)\)\(e\left(\frac{23}{60}\right)\)
sage: chi.jacobi_sum(n)
 
\( \chi_{ 2925 }(17,a) \;\) at \(\;a = \) e.g. 2