Properties

Label 2240.ea
Modulus $2240$
Conductor $2240$
Order $16$
Real no
Primitive yes
Minimal yes
Parity odd

Related objects

Downloads

Learn more

Show commands: PariGP / SageMath
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(2240, base_ring=CyclotomicField(16))
 
M = H._module
 
chi = DirichletCharacter(H, M([0,1,8,8]))
 
chi.galois_orbit()
 
[g,chi] = znchar(Mod(69,2240))
 
order = charorder(g,chi)
 
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: \(2240\)
Conductor: \(2240\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(16\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: yes
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: odd
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Related number fields

Field of values: \(\Q(\zeta_{16})\)
Fixed field: 16.0.1361175151140670679877995724800000000.1

Characters in Galois orbit

Character \(-1\) \(1\) \(3\) \(9\) \(11\) \(13\) \(17\) \(19\) \(23\) \(27\) \(29\) \(31\)
\(\chi_{2240}(69,\cdot)\) \(-1\) \(1\) \(e\left(\frac{3}{16}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{5}{16}\right)\) \(e\left(\frac{15}{16}\right)\) \(-i\) \(e\left(\frac{15}{16}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{9}{16}\right)\) \(e\left(\frac{11}{16}\right)\) \(1\)
\(\chi_{2240}(349,\cdot)\) \(-1\) \(1\) \(e\left(\frac{1}{16}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{7}{16}\right)\) \(e\left(\frac{5}{16}\right)\) \(i\) \(e\left(\frac{5}{16}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{3}{16}\right)\) \(e\left(\frac{9}{16}\right)\) \(1\)
\(\chi_{2240}(629,\cdot)\) \(-1\) \(1\) \(e\left(\frac{15}{16}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{9}{16}\right)\) \(e\left(\frac{11}{16}\right)\) \(-i\) \(e\left(\frac{11}{16}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{13}{16}\right)\) \(e\left(\frac{7}{16}\right)\) \(1\)
\(\chi_{2240}(909,\cdot)\) \(-1\) \(1\) \(e\left(\frac{13}{16}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{11}{16}\right)\) \(e\left(\frac{1}{16}\right)\) \(i\) \(e\left(\frac{1}{16}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{7}{16}\right)\) \(e\left(\frac{5}{16}\right)\) \(1\)
\(\chi_{2240}(1189,\cdot)\) \(-1\) \(1\) \(e\left(\frac{11}{16}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{13}{16}\right)\) \(e\left(\frac{7}{16}\right)\) \(-i\) \(e\left(\frac{7}{16}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{1}{16}\right)\) \(e\left(\frac{3}{16}\right)\) \(1\)
\(\chi_{2240}(1469,\cdot)\) \(-1\) \(1\) \(e\left(\frac{9}{16}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{15}{16}\right)\) \(e\left(\frac{13}{16}\right)\) \(i\) \(e\left(\frac{13}{16}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{11}{16}\right)\) \(e\left(\frac{1}{16}\right)\) \(1\)
\(\chi_{2240}(1749,\cdot)\) \(-1\) \(1\) \(e\left(\frac{7}{16}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{1}{16}\right)\) \(e\left(\frac{3}{16}\right)\) \(-i\) \(e\left(\frac{3}{16}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{5}{16}\right)\) \(e\left(\frac{15}{16}\right)\) \(1\)
\(\chi_{2240}(2029,\cdot)\) \(-1\) \(1\) \(e\left(\frac{5}{16}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{3}{16}\right)\) \(e\left(\frac{9}{16}\right)\) \(i\) \(e\left(\frac{9}{16}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{15}{16}\right)\) \(e\left(\frac{13}{16}\right)\) \(1\)