Properties

Label 2240.67
Modulus $2240$
Conductor $2240$
Order $48$
Real no
Primitive yes
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(48))
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([24,9,12,32]))
 
pari: [g,chi] = znchar(Mod(67,2240))
 

Basic properties

Modulus: \(2240\)
Conductor: \(2240\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(48\)
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 2240.fk

\(\chi_{2240}(67,\cdot)\) \(\chi_{2240}(123,\cdot)\) \(\chi_{2240}(387,\cdot)\) \(\chi_{2240}(443,\cdot)\) \(\chi_{2240}(627,\cdot)\) \(\chi_{2240}(683,\cdot)\) \(\chi_{2240}(947,\cdot)\) \(\chi_{2240}(1003,\cdot)\) \(\chi_{2240}(1187,\cdot)\) \(\chi_{2240}(1243,\cdot)\) \(\chi_{2240}(1507,\cdot)\) \(\chi_{2240}(1563,\cdot)\) \(\chi_{2240}(1747,\cdot)\) \(\chi_{2240}(1803,\cdot)\) \(\chi_{2240}(2067,\cdot)\) \(\chi_{2240}(2123,\cdot)\)

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: \(\Q(\zeta_{48})\)
Fixed field: Number field defined by a degree 48 polynomial

Values on generators

\((1471,1541,897,1921)\) → \((-1,e\left(\frac{3}{16}\right),i,e\left(\frac{2}{3}\right))\)

Values

\(-1\)\(1\)\(3\)\(9\)\(11\)\(13\)\(17\)\(19\)\(23\)\(27\)\(29\)\(31\)
\(1\)\(1\)\(e\left(\frac{23}{48}\right)\)\(e\left(\frac{23}{24}\right)\)\(e\left(\frac{5}{48}\right)\)\(e\left(\frac{9}{16}\right)\)\(e\left(\frac{1}{6}\right)\)\(e\left(\frac{31}{48}\right)\)\(e\left(\frac{5}{24}\right)\)\(e\left(\frac{7}{16}\right)\)\(e\left(\frac{9}{16}\right)\)\(e\left(\frac{2}{3}\right)\)
value at e.g. 2