Properties

Label 2240.251
Modulus $2240$
Conductor $448$
Order $16$
Real no
Primitive no
Minimal yes
Parity even

Related objects

Learn more

Show commands for: Pari/GP / SageMath
sage: from sage.modular.dirichlet import DirichletCharacter
 
sage: H = DirichletGroup(2240, base_ring=CyclotomicField(16))
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([8,1,0,8]))
 
pari: [g,chi] = znchar(Mod(251,2240))
 

Basic properties

Modulus: \(2240\)
Conductor: \(448\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(16\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from \(\chi_{448}(251,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 2240.dy

\(\chi_{2240}(251,\cdot)\) \(\chi_{2240}(531,\cdot)\) \(\chi_{2240}(811,\cdot)\) \(\chi_{2240}(1091,\cdot)\) \(\chi_{2240}(1371,\cdot)\) \(\chi_{2240}(1651,\cdot)\) \(\chi_{2240}(1931,\cdot)\) \(\chi_{2240}(2211,\cdot)\)

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: \(\Q(\zeta_{16})\)
Fixed field: 16.16.3484608386920116940487669055488.4

Values on generators

\((1471,1541,897,1921)\) → \((-1,e\left(\frac{1}{16}\right),1,-1)\)

Values

\(-1\)\(1\)\(3\)\(9\)\(11\)\(13\)\(17\)\(19\)\(23\)\(27\)\(29\)\(31\)
\(1\)\(1\)\(e\left(\frac{3}{16}\right)\)\(e\left(\frac{3}{8}\right)\)\(e\left(\frac{13}{16}\right)\)\(e\left(\frac{7}{16}\right)\)\(i\)\(e\left(\frac{7}{16}\right)\)\(e\left(\frac{3}{8}\right)\)\(e\left(\frac{9}{16}\right)\)\(e\left(\frac{11}{16}\right)\)\(-1\)
value at e.g. 2