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Properties

Label 5520.gc
Modulus 55205520
Conductor 368368
Order 4444
Real no
Primitive no
Minimal yes
Parity even

Related objects

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Show commands: PariGP / SageMath
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(5520, base_ring=CyclotomicField(44))
 
M = H._module
 
chi = DirichletCharacter(H, M([22,33,0,0,42]))
 
chi.galois_orbit()
 
[g,chi] = znchar(Mod(451,5520))
 
order = charorder(g,chi)
 
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: 55205520
Conductor: 368368
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: 4444
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from 368.x
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Related number fields

Field of values: Q(ζ44)\Q(\zeta_{44})
Fixed field: 44.44.4141890260646712580912980965306954513336276372715662057543551492310346739946349214617837764608.1

Characters in Galois orbit

Character −1-1 11 77 1111 1313 1717 1919 2929 3131 3737 4141 4343
χ5520(451,⋅)\chi_{5520}(451,\cdot) 11 11 e(322)e\left(\frac{3}{22}\right) e(3744)e\left(\frac{37}{44}\right) e(2744)e\left(\frac{27}{44}\right) e(1522)e\left(\frac{15}{22}\right) e(344)e\left(\frac{3}{44}\right) e(1944)e\left(\frac{19}{44}\right) e(522)e\left(\frac{5}{22}\right) e(3544)e\left(\frac{35}{44}\right) e(2122)e\left(\frac{21}{22}\right) e(144)e\left(\frac{1}{44}\right)
χ5520(571,⋅)\chi_{5520}(571,\cdot) 11 11 e(2122)e\left(\frac{21}{22}\right) e(3944)e\left(\frac{39}{44}\right) e(1344)e\left(\frac{13}{44}\right) e(1722)e\left(\frac{17}{22}\right) e(2144)e\left(\frac{21}{44}\right) e(144)e\left(\frac{1}{44}\right) e(1322)e\left(\frac{13}{22}\right) e(2544)e\left(\frac{25}{44}\right) e(1522)e\left(\frac{15}{22}\right) e(744)e\left(\frac{7}{44}\right)
χ5520(931,⋅)\chi_{5520}(931,\cdot) 11 11 e(1722)e\left(\frac{17}{22}\right) e(4144)e\left(\frac{41}{44}\right) e(4344)e\left(\frac{43}{44}\right) e(1922)e\left(\frac{19}{22}\right) e(3944)e\left(\frac{39}{44}\right) e(2744)e\left(\frac{27}{44}\right) e(2122)e\left(\frac{21}{22}\right) e(1544)e\left(\frac{15}{44}\right) e(922)e\left(\frac{9}{22}\right) e(1344)e\left(\frac{13}{44}\right)
χ5520(1171,⋅)\chi_{5520}(1171,\cdot) 11 11 e(522)e\left(\frac{5}{22}\right) e(2544)e\left(\frac{25}{44}\right) e(2344)e\left(\frac{23}{44}\right) e(322)e\left(\frac{3}{22}\right) e(2744)e\left(\frac{27}{44}\right) e(3944)e\left(\frac{39}{44}\right) e(122)e\left(\frac{1}{22}\right) e(744)e\left(\frac{7}{44}\right) e(1322)e\left(\frac{13}{22}\right) e(944)e\left(\frac{9}{44}\right)
χ5520(1891,⋅)\chi_{5520}(1891,\cdot) 11 11 e(1922)e\left(\frac{19}{22}\right) e(2944)e\left(\frac{29}{44}\right) e(3944)e\left(\frac{39}{44}\right) e(722)e\left(\frac{7}{22}\right) e(1944)e\left(\frac{19}{44}\right) e(344)e\left(\frac{3}{44}\right) e(1722)e\left(\frac{17}{22}\right) e(3144)e\left(\frac{31}{44}\right) e(122)e\left(\frac{1}{22}\right) e(2144)e\left(\frac{21}{44}\right)
χ5520(2011,⋅)\chi_{5520}(2011,\cdot) 11 11 e(1322)e\left(\frac{13}{22}\right) e(4344)e\left(\frac{43}{44}\right) e(2944)e\left(\frac{29}{44}\right) e(2122)e\left(\frac{21}{22}\right) e(1344)e\left(\frac{13}{44}\right) e(944)e\left(\frac{9}{44}\right) e(722)e\left(\frac{7}{22}\right) e(544)e\left(\frac{5}{44}\right) e(322)e\left(\frac{3}{22}\right) e(1944)e\left(\frac{19}{44}\right)
χ5520(2131,⋅)\chi_{5520}(2131,\cdot) 11 11 e(1522)e\left(\frac{15}{22}\right) e(944)e\left(\frac{9}{44}\right) e(344)e\left(\frac{3}{44}\right) e(922)e\left(\frac{9}{22}\right) e(1544)e\left(\frac{15}{44}\right) e(744)e\left(\frac{7}{44}\right) e(322)e\left(\frac{3}{22}\right) e(4344)e\left(\frac{43}{44}\right) e(1722)e\left(\frac{17}{22}\right) e(544)e\left(\frac{5}{44}\right)
χ5520(2251,⋅)\chi_{5520}(2251,\cdot) 11 11 e(722)e\left(\frac{7}{22}\right) e(3544)e\left(\frac{35}{44}\right) e(4144)e\left(\frac{41}{44}\right) e(1322)e\left(\frac{13}{22}\right) e(2944)e\left(\frac{29}{44}\right) e(3744)e\left(\frac{37}{44}\right) e(1922)e\left(\frac{19}{22}\right) e(144)e\left(\frac{1}{44}\right) e(522)e\left(\frac{5}{22}\right) e(3944)e\left(\frac{39}{44}\right)
χ5520(2491,⋅)\chi_{5520}(2491,\cdot) 11 11 e(922)e\left(\frac{9}{22}\right) e(2344)e\left(\frac{23}{44}\right) e(3744)e\left(\frac{37}{44}\right) e(122)e\left(\frac{1}{22}\right) e(944)e\left(\frac{9}{44}\right) e(1344)e\left(\frac{13}{44}\right) e(1522)e\left(\frac{15}{22}\right) e(1744)e\left(\frac{17}{44}\right) e(1922)e\left(\frac{19}{22}\right) e(344)e\left(\frac{3}{44}\right)
χ5520(2731,⋅)\chi_{5520}(2731,\cdot) 11 11 e(122)e\left(\frac{1}{22}\right) e(2744)e\left(\frac{27}{44}\right) e(944)e\left(\frac{9}{44}\right) e(522)e\left(\frac{5}{22}\right) e(144)e\left(\frac{1}{44}\right) e(2144)e\left(\frac{21}{44}\right) e(922)e\left(\frac{9}{22}\right) e(4144)e\left(\frac{41}{44}\right) e(722)e\left(\frac{7}{22}\right) e(1544)e\left(\frac{15}{44}\right)
χ5520(3211,⋅)\chi_{5520}(3211,\cdot) 11 11 e(322)e\left(\frac{3}{22}\right) e(1544)e\left(\frac{15}{44}\right) e(544)e\left(\frac{5}{44}\right) e(1522)e\left(\frac{15}{22}\right) e(2544)e\left(\frac{25}{44}\right) e(4144)e\left(\frac{41}{44}\right) e(522)e\left(\frac{5}{22}\right) e(1344)e\left(\frac{13}{44}\right) e(2122)e\left(\frac{21}{22}\right) e(2344)e\left(\frac{23}{44}\right)
χ5520(3331,⋅)\chi_{5520}(3331,\cdot) 11 11 e(2122)e\left(\frac{21}{22}\right) e(1744)e\left(\frac{17}{44}\right) e(3544)e\left(\frac{35}{44}\right) e(1722)e\left(\frac{17}{22}\right) e(4344)e\left(\frac{43}{44}\right) e(2344)e\left(\frac{23}{44}\right) e(1322)e\left(\frac{13}{22}\right) e(344)e\left(\frac{3}{44}\right) e(1522)e\left(\frac{15}{22}\right) e(2944)e\left(\frac{29}{44}\right)
χ5520(3691,⋅)\chi_{5520}(3691,\cdot) 11 11 e(1722)e\left(\frac{17}{22}\right) e(1944)e\left(\frac{19}{44}\right) e(2144)e\left(\frac{21}{44}\right) e(1922)e\left(\frac{19}{22}\right) e(1744)e\left(\frac{17}{44}\right) e(544)e\left(\frac{5}{44}\right) e(2122)e\left(\frac{21}{22}\right) e(3744)e\left(\frac{37}{44}\right) e(922)e\left(\frac{9}{22}\right) e(3544)e\left(\frac{35}{44}\right)
χ5520(3931,⋅)\chi_{5520}(3931,\cdot) 11 11 e(522)e\left(\frac{5}{22}\right) e(344)e\left(\frac{3}{44}\right) e(144)e\left(\frac{1}{44}\right) e(322)e\left(\frac{3}{22}\right) e(544)e\left(\frac{5}{44}\right) e(1744)e\left(\frac{17}{44}\right) e(122)e\left(\frac{1}{22}\right) e(2944)e\left(\frac{29}{44}\right) e(1322)e\left(\frac{13}{22}\right) e(3144)e\left(\frac{31}{44}\right)
χ5520(4651,⋅)\chi_{5520}(4651,\cdot) 11 11 e(1922)e\left(\frac{19}{22}\right) e(744)e\left(\frac{7}{44}\right) e(1744)e\left(\frac{17}{44}\right) e(722)e\left(\frac{7}{22}\right) e(4144)e\left(\frac{41}{44}\right) e(2544)e\left(\frac{25}{44}\right) e(1722)e\left(\frac{17}{22}\right) e(944)e\left(\frac{9}{44}\right) e(122)e\left(\frac{1}{22}\right) e(4344)e\left(\frac{43}{44}\right)
χ5520(4771,⋅)\chi_{5520}(4771,\cdot) 11 11 e(1322)e\left(\frac{13}{22}\right) e(2144)e\left(\frac{21}{44}\right) e(744)e\left(\frac{7}{44}\right) e(2122)e\left(\frac{21}{22}\right) e(3544)e\left(\frac{35}{44}\right) e(3144)e\left(\frac{31}{44}\right) e(722)e\left(\frac{7}{22}\right) e(2744)e\left(\frac{27}{44}\right) e(322)e\left(\frac{3}{22}\right) e(4144)e\left(\frac{41}{44}\right)
χ5520(4891,⋅)\chi_{5520}(4891,\cdot) 11 11 e(1522)e\left(\frac{15}{22}\right) e(3144)e\left(\frac{31}{44}\right) e(2544)e\left(\frac{25}{44}\right) e(922)e\left(\frac{9}{22}\right) e(3744)e\left(\frac{37}{44}\right) e(2944)e\left(\frac{29}{44}\right) e(322)e\left(\frac{3}{22}\right) e(2144)e\left(\frac{21}{44}\right) e(1722)e\left(\frac{17}{22}\right) e(2744)e\left(\frac{27}{44}\right)
χ5520(5011,⋅)\chi_{5520}(5011,\cdot) 11 11 e(722)e\left(\frac{7}{22}\right) e(1344)e\left(\frac{13}{44}\right) e(1944)e\left(\frac{19}{44}\right) e(1322)e\left(\frac{13}{22}\right) e(744)e\left(\frac{7}{44}\right) e(1544)e\left(\frac{15}{44}\right) e(1922)e\left(\frac{19}{22}\right) e(2344)e\left(\frac{23}{44}\right) e(522)e\left(\frac{5}{22}\right) e(1744)e\left(\frac{17}{44}\right)
χ5520(5251,⋅)\chi_{5520}(5251,\cdot) 11 11 e(922)e\left(\frac{9}{22}\right) e(144)e\left(\frac{1}{44}\right) e(1544)e\left(\frac{15}{44}\right) e(122)e\left(\frac{1}{22}\right) e(3144)e\left(\frac{31}{44}\right) e(3544)e\left(\frac{35}{44}\right) e(1522)e\left(\frac{15}{22}\right) e(3944)e\left(\frac{39}{44}\right) e(1922)e\left(\frac{19}{22}\right) e(2544)e\left(\frac{25}{44}\right)
χ5520(5491,⋅)\chi_{5520}(5491,\cdot) 11 11 e(122)e\left(\frac{1}{22}\right) e(544)e\left(\frac{5}{44}\right) e(3144)e\left(\frac{31}{44}\right) e(522)e\left(\frac{5}{22}\right) e(2344)e\left(\frac{23}{44}\right) e(4344)e\left(\frac{43}{44}\right) e(922)e\left(\frac{9}{22}\right) e(1944)e\left(\frac{19}{44}\right) e(722)e\left(\frac{7}{22}\right) e(3744)e\left(\frac{37}{44}\right)