Properties

Label 5520.149
Modulus $5520$
Conductor $5520$
Order $44$
Real no
Primitive yes
Minimal yes
Parity even

Related objects

Learn more about

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([0,11,22,22,18]))
 
pari: [g,chi] = znchar(Mod(149,5520))
 

Basic properties

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

Galois orbit 5520.gb

\(\chi_{5520}(149,\cdot)\) \(\chi_{5520}(389,\cdot)\) \(\chi_{5520}(1109,\cdot)\) \(\chi_{5520}(1229,\cdot)\) \(\chi_{5520}(1349,\cdot)\) \(\chi_{5520}(1469,\cdot)\) \(\chi_{5520}(1709,\cdot)\) \(\chi_{5520}(1949,\cdot)\) \(\chi_{5520}(2429,\cdot)\) \(\chi_{5520}(2549,\cdot)\) \(\chi_{5520}(2909,\cdot)\) \(\chi_{5520}(3149,\cdot)\) \(\chi_{5520}(3869,\cdot)\) \(\chi_{5520}(3989,\cdot)\) \(\chi_{5520}(4109,\cdot)\) \(\chi_{5520}(4229,\cdot)\) \(\chi_{5520}(4469,\cdot)\) \(\chi_{5520}(4709,\cdot)\) \(\chi_{5520}(5189,\cdot)\) \(\chi_{5520}(5309,\cdot)\)

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

\((4831,1381,1841,4417,1201)\) → \((1,i,-1,-1,e\left(\frac{9}{22}\right))\)

Values

\(-1\)\(1\)\(7\)\(11\)\(13\)\(17\)\(19\)\(29\)\(31\)\(37\)\(41\)\(43\)
\(1\)\(1\)\(e\left(\frac{17}{22}\right)\)\(e\left(\frac{19}{44}\right)\)\(e\left(\frac{43}{44}\right)\)\(e\left(\frac{19}{22}\right)\)\(e\left(\frac{39}{44}\right)\)\(e\left(\frac{27}{44}\right)\)\(e\left(\frac{5}{11}\right)\)\(e\left(\frac{15}{44}\right)\)\(e\left(\frac{10}{11}\right)\)\(e\left(\frac{35}{44}\right)\)
value at e.g. 2