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Properties

Label 5520.dm
Modulus 55205520
Conductor 27602760
Order 2222
Real no
Primitive no
Minimal no
Parity even

Related objects

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Show commands: PariGP / SageMath
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(5520, base_ring=CyclotomicField(22))
 
M = H._module
 
chi = DirichletCharacter(H, M([0,11,11,11,5]))
 
chi.galois_orbit()
 
[g,chi] = znchar(Mod(89,5520))
 
order = charorder(g,chi)
 
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: 55205520
Conductor: 27602760
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: 2222
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from 2760.cg
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(ζ11)\Q(\zeta_{11})
Fixed field: Number field defined by a degree 22 polynomial

Characters in Galois orbit

Character −1-1 11 77 1111 1313 1717 1919 2929 3131 3737 4141 4343
χ5520(89,⋅)\chi_{5520}(89,\cdot) 11 11 e(911)e\left(\frac{9}{11}\right) e(122)e\left(\frac{1}{22}\right) e(211)e\left(\frac{2}{11}\right) e(1322)e\left(\frac{13}{22}\right) e(1011)e\left(\frac{10}{11}\right) e(111)e\left(\frac{1}{11}\right) e(411)e\left(\frac{4}{11}\right) e(1722)e\left(\frac{17}{22}\right) e(522)e\left(\frac{5}{22}\right) e(322)e\left(\frac{3}{22}\right)
χ5520(329,⋅)\chi_{5520}(329,\cdot) 11 11 e(1011)e\left(\frac{10}{11}\right) e(1722)e\left(\frac{17}{22}\right) e(111)e\left(\frac{1}{11}\right) e(122)e\left(\frac{1}{22}\right) e(511)e\left(\frac{5}{11}\right) e(611)e\left(\frac{6}{11}\right) e(211)e\left(\frac{2}{11}\right) e(322)e\left(\frac{3}{22}\right) e(1922)e\left(\frac{19}{22}\right) e(722)e\left(\frac{7}{22}\right)
χ5520(569,⋅)\chi_{5520}(569,\cdot) 11 11 e(611)e\left(\frac{6}{11}\right) e(1922)e\left(\frac{19}{22}\right) e(511)e\left(\frac{5}{11}\right) e(522)e\left(\frac{5}{22}\right) e(311)e\left(\frac{3}{11}\right) e(811)e\left(\frac{8}{11}\right) e(1011)e\left(\frac{10}{11}\right) e(1522)e\left(\frac{15}{22}\right) e(722)e\left(\frac{7}{22}\right) e(1322)e\left(\frac{13}{22}\right)
χ5520(1049,⋅)\chi_{5520}(1049,\cdot) 11 11 e(711)e\left(\frac{7}{11}\right) e(1322)e\left(\frac{13}{22}\right) e(411)e\left(\frac{4}{11}\right) e(1522)e\left(\frac{15}{22}\right) e(911)e\left(\frac{9}{11}\right) e(211)e\left(\frac{2}{11}\right) e(811)e\left(\frac{8}{11}\right) e(122)e\left(\frac{1}{22}\right) e(2122)e\left(\frac{21}{22}\right) e(1722)e\left(\frac{17}{22}\right)
χ5520(1529,⋅)\chi_{5520}(1529,\cdot) 11 11 e(311)e\left(\frac{3}{11}\right) e(1522)e\left(\frac{15}{22}\right) e(811)e\left(\frac{8}{11}\right) e(1922)e\left(\frac{19}{22}\right) e(711)e\left(\frac{7}{11}\right) e(411)e\left(\frac{4}{11}\right) e(511)e\left(\frac{5}{11}\right) e(1322)e\left(\frac{13}{22}\right) e(922)e\left(\frac{9}{22}\right) e(122)e\left(\frac{1}{22}\right)
χ5520(1769,⋅)\chi_{5520}(1769,\cdot) 11 11 e(811)e\left(\frac{8}{11}\right) e(722)e\left(\frac{7}{22}\right) e(311)e\left(\frac{3}{11}\right) e(322)e\left(\frac{3}{22}\right) e(411)e\left(\frac{4}{11}\right) e(711)e\left(\frac{7}{11}\right) e(611)e\left(\frac{6}{11}\right) e(922)e\left(\frac{9}{22}\right) e(1322)e\left(\frac{13}{22}\right) e(2122)e\left(\frac{21}{22}\right)
χ5520(2489,⋅)\chi_{5520}(2489,\cdot) 11 11 e(411)e\left(\frac{4}{11}\right) e(922)e\left(\frac{9}{22}\right) e(711)e\left(\frac{7}{11}\right) e(722)e\left(\frac{7}{22}\right) e(211)e\left(\frac{2}{11}\right) e(911)e\left(\frac{9}{11}\right) e(311)e\left(\frac{3}{11}\right) e(2122)e\left(\frac{21}{22}\right) e(122)e\left(\frac{1}{22}\right) e(522)e\left(\frac{5}{22}\right)
χ5520(2729,⋅)\chi_{5520}(2729,\cdot) 11 11 e(211)e\left(\frac{2}{11}\right) e(2122)e\left(\frac{21}{22}\right) e(911)e\left(\frac{9}{11}\right) e(922)e\left(\frac{9}{22}\right) e(111)e\left(\frac{1}{11}\right) e(1011)e\left(\frac{10}{11}\right) e(711)e\left(\frac{7}{11}\right) e(522)e\left(\frac{5}{22}\right) e(1722)e\left(\frac{17}{22}\right) e(1922)e\left(\frac{19}{22}\right)
χ5520(3929,⋅)\chi_{5520}(3929,\cdot) 11 11 e(511)e\left(\frac{5}{11}\right) e(322)e\left(\frac{3}{22}\right) e(611)e\left(\frac{6}{11}\right) e(1722)e\left(\frac{17}{22}\right) e(811)e\left(\frac{8}{11}\right) e(311)e\left(\frac{3}{11}\right) e(111)e\left(\frac{1}{11}\right) e(722)e\left(\frac{7}{22}\right) e(1522)e\left(\frac{15}{22}\right) e(922)e\left(\frac{9}{22}\right)
χ5520(5369,⋅)\chi_{5520}(5369,\cdot) 11 11 e(111)e\left(\frac{1}{11}\right) e(522)e\left(\frac{5}{22}\right) e(1011)e\left(\frac{10}{11}\right) e(2122)e\left(\frac{21}{22}\right) e(611)e\left(\frac{6}{11}\right) e(511)e\left(\frac{5}{11}\right) e(911)e\left(\frac{9}{11}\right) e(1922)e\left(\frac{19}{22}\right) e(322)e\left(\frac{3}{22}\right) e(1522)e\left(\frac{15}{22}\right)