Properties

Label 2541.1976
Modulus $2541$
Conductor $231$
Order $30$
Real no
Primitive no
Minimal no
Parity even

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Show commands: PariGP / SageMath
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(2541, base_ring=CyclotomicField(30))
 
M = H._module
 
chi = DirichletCharacter(H, M([15,10,21]))
 
pari: [g,chi] = znchar(Mod(1976,2541))
 

Basic properties

Modulus: \(2541\)
Conductor: \(231\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(30\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from \(\chi_{231}(128,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: no
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 2541.bm

\(\chi_{2541}(233,\cdot)\) \(\chi_{2541}(578,\cdot)\) \(\chi_{2541}(1250,\cdot)\) \(\chi_{2541}(1304,\cdot)\) \(\chi_{2541}(1691,\cdot)\) \(\chi_{2541}(1976,\cdot)\) \(\chi_{2541}(2048,\cdot)\) \(\chi_{2541}(2417,\cdot)\)

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: \(\Q(\zeta_{15})\)
Fixed field: Number field defined by a degree 30 polynomial

Values on generators

\((848,1816,2059)\) → \((-1,e\left(\frac{1}{3}\right),e\left(\frac{7}{10}\right))\)

First values

\(a\) \(-1\)\(1\)\(2\)\(4\)\(5\)\(8\)\(10\)\(13\)\(16\)\(17\)\(19\)\(20\)
\( \chi_{ 2541 }(1976, a) \) \(1\)\(1\)\(e\left(\frac{13}{15}\right)\)\(e\left(\frac{11}{15}\right)\)\(e\left(\frac{29}{30}\right)\)\(e\left(\frac{3}{5}\right)\)\(e\left(\frac{5}{6}\right)\)\(e\left(\frac{7}{10}\right)\)\(e\left(\frac{7}{15}\right)\)\(e\left(\frac{2}{15}\right)\)\(e\left(\frac{23}{30}\right)\)\(e\left(\frac{7}{10}\right)\)
sage: chi.jacobi_sum(n)
 
\( \chi_{ 2541 }(1976,a) \;\) at \(\;a = \) e.g. 2