Properties

Label 5520.4339
Modulus $5520$
Conductor $1840$
Order $44$
Real no
Primitive no
Minimal yes
Parity even

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Show commands: PariGP / SageMath
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(5520, base_ring=CyclotomicField(44))
 
M = H._module
 
chi = DirichletCharacter(H, M([22,33,0,22,34]))
 
pari: [g,chi] = znchar(Mod(4339,5520))
 

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 \(\chi_{1840}(659,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 5520.el

\(\chi_{5520}(19,\cdot)\) \(\chi_{5520}(379,\cdot)\) \(\chi_{5520}(619,\cdot)\) \(\chi_{5520}(1339,\cdot)\) \(\chi_{5520}(1459,\cdot)\) \(\chi_{5520}(1579,\cdot)\) \(\chi_{5520}(1699,\cdot)\) \(\chi_{5520}(1939,\cdot)\) \(\chi_{5520}(2179,\cdot)\) \(\chi_{5520}(2659,\cdot)\) \(\chi_{5520}(2779,\cdot)\) \(\chi_{5520}(3139,\cdot)\) \(\chi_{5520}(3379,\cdot)\) \(\chi_{5520}(4099,\cdot)\) \(\chi_{5520}(4219,\cdot)\) \(\chi_{5520}(4339,\cdot)\) \(\chi_{5520}(4459,\cdot)\) \(\chi_{5520}(4699,\cdot)\) \(\chi_{5520}(4939,\cdot)\) \(\chi_{5520}(5419,\cdot)\)

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

\((4831,1381,1841,4417,1201)\) → \((-1,-i,1,-1,e\left(\frac{17}{22}\right))\)

First values

\(a\) \(-1\)\(1\)\(7\)\(11\)\(13\)\(17\)\(19\)\(29\)\(31\)\(37\)\(41\)\(43\)
\( \chi_{ 5520 }(4339, a) \) \(1\)\(1\)\(e\left(\frac{2}{11}\right)\)\(e\left(\frac{9}{44}\right)\)\(e\left(\frac{25}{44}\right)\)\(e\left(\frac{10}{11}\right)\)\(e\left(\frac{15}{44}\right)\)\(e\left(\frac{7}{44}\right)\)\(e\left(\frac{3}{22}\right)\)\(e\left(\frac{21}{44}\right)\)\(e\left(\frac{17}{22}\right)\)\(e\left(\frac{27}{44}\right)\)
sage: chi.jacobi_sum(n)
 
\( \chi_{ 5520 }(4339,a) \;\) at \(\;a = \) e.g. 2