Properties

Label 2240.ej
Modulus $2240$
Conductor $224$
Order $24$
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(2240, base_ring=CyclotomicField(24))
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([12,9,0,4]))
 
sage: chi.galois_orbit()
 
pari: [g,chi] = znchar(Mod(311,2240))
 
pari: order = charorder(g,chi)
 
pari: [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: \(2240\)
Conductor: \(224\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(24\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from 224.be
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: no
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Related number fields

Field of values: \(\Q(\zeta_{24})\)
Fixed field: 24.24.790224330201082600125157415256880139617697792.1

Characters in Galois orbit

Character \(-1\) \(1\) \(3\) \(9\) \(11\) \(13\) \(17\) \(19\) \(23\) \(27\) \(29\) \(31\)
\(\chi_{2240}(311,\cdot)\) \(1\) \(1\) \(e\left(\frac{19}{24}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{1}{24}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{23}{24}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{2}{3}\right)\)
\(\chi_{2240}(551,\cdot)\) \(1\) \(1\) \(e\left(\frac{17}{24}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{11}{24}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{13}{24}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{1}{3}\right)\)
\(\chi_{2240}(871,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{24}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{19}{24}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{5}{24}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{2}{3}\right)\)
\(\chi_{2240}(1111,\cdot)\) \(1\) \(1\) \(e\left(\frac{23}{24}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{5}{24}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{19}{24}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{1}{3}\right)\)
\(\chi_{2240}(1431,\cdot)\) \(1\) \(1\) \(e\left(\frac{7}{24}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{13}{24}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{11}{24}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{2}{3}\right)\)
\(\chi_{2240}(1671,\cdot)\) \(1\) \(1\) \(e\left(\frac{5}{24}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{23}{24}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{24}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{1}{3}\right)\)
\(\chi_{2240}(1991,\cdot)\) \(1\) \(1\) \(e\left(\frac{13}{24}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{7}{24}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{17}{24}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{2}{3}\right)\)
\(\chi_{2240}(2231,\cdot)\) \(1\) \(1\) \(e\left(\frac{11}{24}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{17}{24}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{7}{24}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{1}{3}\right)\)