Properties

Label 5520.3163
Modulus $5520$
Conductor $1840$
Order $44$
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(5520, base_ring=CyclotomicField(44))
 
M = H._module
 
chi = DirichletCharacter(H, M([22,11,0,33,40]))
 
pari: [g,chi] = znchar(Mod(3163,5520))
 

Basic properties

Modulus: \(5520\)
Conductor: \(1840\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(44\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from \(\chi_{1840}(1323,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 5520.fd

\(\chi_{5520}(307,\cdot)\) \(\chi_{5520}(547,\cdot)\) \(\chi_{5520}(763,\cdot)\) \(\chi_{5520}(1267,\cdot)\) \(\chi_{5520}(1507,\cdot)\) \(\chi_{5520}(1963,\cdot)\) \(\chi_{5520}(1987,\cdot)\) \(\chi_{5520}(2203,\cdot)\) \(\chi_{5520}(2467,\cdot)\) \(\chi_{5520}(2707,\cdot)\) \(\chi_{5520}(2923,\cdot)\) \(\chi_{5520}(2947,\cdot)\) \(\chi_{5520}(3163,\cdot)\) \(\chi_{5520}(3187,\cdot)\) \(\chi_{5520}(3643,\cdot)\) \(\chi_{5520}(4123,\cdot)\) \(\chi_{5520}(4363,\cdot)\) \(\chi_{5520}(4603,\cdot)\) \(\chi_{5520}(4627,\cdot)\) \(\chi_{5520}(4843,\cdot)\)

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: \(\Q(\zeta_{44})\)
Fixed field: Number field defined by a degree 44 polynomial

Values on generators

\((4831,1381,1841,4417,1201)\) → \((-1,i,1,-i,e\left(\frac{10}{11}\right))\)

First values

\(a\) \(-1\)\(1\)\(7\)\(11\)\(13\)\(17\)\(19\)\(29\)\(31\)\(37\)\(41\)\(43\)
\( \chi_{ 5520 }(3163, a) \) \(1\)\(1\)\(e\left(\frac{1}{44}\right)\)\(e\left(\frac{41}{44}\right)\)\(e\left(\frac{8}{11}\right)\)\(e\left(\frac{5}{44}\right)\)\(e\left(\frac{17}{44}\right)\)\(e\left(\frac{27}{44}\right)\)\(e\left(\frac{21}{22}\right)\)\(e\left(\frac{1}{11}\right)\)\(e\left(\frac{9}{22}\right)\)\(e\left(\frac{6}{11}\right)\)
sage: chi.jacobi_sum(n)
 
\( \chi_{ 5520 }(3163,a) \;\) at \(\;a = \) e.g. 2