Properties

Label 5520.313
Modulus $5520$
Conductor $920$
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([0,22,0,33,42]))
 
pari: [g,chi] = znchar(Mod(313,5520))
 

Basic properties

Modulus: \(5520\)
Conductor: \(920\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(44\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from \(\chi_{920}(773,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: no
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 5520.eu

\(\chi_{5520}(217,\cdot)\) \(\chi_{5520}(313,\cdot)\) \(\chi_{5520}(457,\cdot)\) \(\chi_{5520}(697,\cdot)\) \(\chi_{5520}(793,\cdot)\) \(\chi_{5520}(937,\cdot)\) \(\chi_{5520}(1033,\cdot)\) \(\chi_{5520}(1417,\cdot)\) \(\chi_{5520}(1753,\cdot)\) \(\chi_{5520}(1897,\cdot)\) \(\chi_{5520}(1993,\cdot)\) \(\chi_{5520}(2137,\cdot)\) \(\chi_{5520}(2857,\cdot)\) \(\chi_{5520}(3097,\cdot)\) \(\chi_{5520}(3193,\cdot)\) \(\chi_{5520}(4297,\cdot)\) \(\chi_{5520}(4633,\cdot)\) \(\chi_{5520}(4873,\cdot)\) \(\chi_{5520}(5113,\cdot)\) \(\chi_{5520}(5353,\cdot)\)

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: 44.44.13383169230192059253459701104387771124501004765020501667165784506368000000000000000000000000000000000.1

Values on generators

\((4831,1381,1841,4417,1201)\) → \((1,-1,1,-i,e\left(\frac{21}{22}\right))\)

Values

\(-1\)\(1\)\(7\)\(11\)\(13\)\(17\)\(19\)\(29\)\(31\)\(37\)\(41\)\(43\)
\(1\)\(1\)\(e\left(\frac{39}{44}\right)\)\(e\left(\frac{1}{11}\right)\)\(e\left(\frac{5}{44}\right)\)\(e\left(\frac{19}{44}\right)\)\(e\left(\frac{7}{22}\right)\)\(e\left(\frac{2}{11}\right)\)\(e\left(\frac{8}{11}\right)\)\(e\left(\frac{13}{44}\right)\)\(e\left(\frac{5}{11}\right)\)\(e\left(\frac{23}{44}\right)\)
value at e.g. 2