Properties

Label 4730.1011
Modulus $4730$
Conductor $473$
Order $14$
Real no
Primitive no
Minimal yes
Parity even

Related objects

Downloads

Learn more

Show commands: PariGP / SageMath
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(4730, base_ring=CyclotomicField(14))
 
M = H._module
 
chi = DirichletCharacter(H, M([0,7,5]))
 
pari: [g,chi] = znchar(Mod(1011,4730))
 

Basic properties

Modulus: \(4730\)
Conductor: \(473\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(14\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from \(\chi_{473}(65,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 4730.bn

\(\chi_{4730}(131,\cdot)\) \(\chi_{4730}(1011,\cdot)\) \(\chi_{4730}(1231,\cdot)\) \(\chi_{4730}(1341,\cdot)\) \(\chi_{4730}(1451,\cdot)\) \(\chi_{4730}(3651,\cdot)\)

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: \(\Q(\zeta_{7})\)
Fixed field: 14.14.33484106813054252803754617553.1

Values on generators

\((947,431,1981)\) → \((1,-1,e\left(\frac{5}{14}\right))\)

First values

\(a\) \(-1\)\(1\)\(3\)\(7\)\(9\)\(13\)\(17\)\(19\)\(21\)\(23\)\(27\)\(29\)
\( \chi_{ 4730 }(1011, a) \) \(1\)\(1\)\(e\left(\frac{5}{14}\right)\)\(1\)\(e\left(\frac{5}{7}\right)\)\(e\left(\frac{13}{14}\right)\)\(e\left(\frac{1}{14}\right)\)\(e\left(\frac{2}{7}\right)\)\(e\left(\frac{5}{14}\right)\)\(e\left(\frac{5}{7}\right)\)\(e\left(\frac{1}{14}\right)\)\(e\left(\frac{1}{7}\right)\)
sage: chi.jacobi_sum(n)
 
\( \chi_{ 4730 }(1011,a) \;\) at \(\;a = \) e.g. 2