Properties

Label 1520.11
Modulus $1520$
Conductor $304$
Order $12$
Real no
Primitive no
Minimal yes
Parity odd

Related objects

Downloads

Learn more

Show commands: PariGP / SageMath
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1520, base_ring=CyclotomicField(12))
 
M = H._module
 
chi = DirichletCharacter(H, M([6,3,0,8]))
 
pari: [g,chi] = znchar(Mod(11,1520))
 

Basic properties

Modulus: \(1520\)
Conductor: \(304\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(12\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from \(\chi_{304}(11,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: odd
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 1520.cv

\(\chi_{1520}(11,\cdot)\) \(\chi_{1520}(691,\cdot)\) \(\chi_{1520}(771,\cdot)\) \(\chi_{1520}(1451,\cdot)\)

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: \(\Q(\zeta_{12})\)
Fixed field: 12.0.145887695661298614272.69

Values on generators

\((191,1141,1217,401)\) → \((-1,i,1,e\left(\frac{2}{3}\right))\)

First values

\(a\) \(-1\)\(1\)\(3\)\(7\)\(9\)\(11\)\(13\)\(17\)\(21\)\(23\)\(27\)\(29\)
\( \chi_{ 1520 }(11, a) \) \(-1\)\(1\)\(e\left(\frac{11}{12}\right)\)\(1\)\(e\left(\frac{5}{6}\right)\)\(-i\)\(e\left(\frac{1}{12}\right)\)\(e\left(\frac{2}{3}\right)\)\(e\left(\frac{11}{12}\right)\)\(e\left(\frac{1}{3}\right)\)\(-i\)\(e\left(\frac{1}{12}\right)\)
sage: chi.jacobi_sum(n)
 
\( \chi_{ 1520 }(11,a) \;\) at \(\;a = \) e.g. 2