Properties

Label 5520.983
Modulus $5520$
Conductor $2760$
Order $44$
Real no
Primitive no
Minimal no
Parity even

Related objects

Learn more

Show commands for: Pari/GP / SageMath
sage: from sage.modular.dirichlet import DirichletCharacter
 
sage: H = DirichletGroup(5520, base_ring=CyclotomicField(44))
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([22,22,22,33,14]))
 
pari: [g,chi] = znchar(Mod(983,5520))
 

Basic properties

Modulus: \(5520\)
Conductor: \(2760\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(44\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from \(\chi_{2760}(2363,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: no
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 5520.et

\(\chi_{5520}(263,\cdot)\) \(\chi_{5520}(503,\cdot)\) \(\chi_{5520}(743,\cdot)\) \(\chi_{5520}(983,\cdot)\) \(\chi_{5520}(1367,\cdot)\) \(\chi_{5520}(1463,\cdot)\) \(\chi_{5520}(1607,\cdot)\) \(\chi_{5520}(1847,\cdot)\) \(\chi_{5520}(1943,\cdot)\) \(\chi_{5520}(2087,\cdot)\) \(\chi_{5520}(2183,\cdot)\) \(\chi_{5520}(2567,\cdot)\) \(\chi_{5520}(2903,\cdot)\) \(\chi_{5520}(3047,\cdot)\) \(\chi_{5520}(3143,\cdot)\) \(\chi_{5520}(3287,\cdot)\) \(\chi_{5520}(4007,\cdot)\) \(\chi_{5520}(4247,\cdot)\) \(\chi_{5520}(4343,\cdot)\) \(\chi_{5520}(5447,\cdot)\)

sage: chi.galois_orbit()
 
pari: order = charorder(g,chi)
 
pari: [ 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

\((4831,1381,1841,4417,1201)\) → \((-1,-1,-1,-i,e\left(\frac{7}{22}\right))\)

Values

\(-1\)\(1\)\(7\)\(11\)\(13\)\(17\)\(19\)\(29\)\(31\)\(37\)\(41\)\(43\)
\(1\)\(1\)\(e\left(\frac{13}{44}\right)\)\(e\left(\frac{4}{11}\right)\)\(e\left(\frac{9}{44}\right)\)\(e\left(\frac{21}{44}\right)\)\(e\left(\frac{3}{11}\right)\)\(e\left(\frac{5}{22}\right)\)\(e\left(\frac{9}{22}\right)\)\(e\left(\frac{41}{44}\right)\)\(e\left(\frac{7}{22}\right)\)\(e\left(\frac{37}{44}\right)\)
value at e.g. 2