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Properties

Label 288.bc
Modulus 288288
Conductor 288288
Order 2424
Real no
Primitive yes
Minimal yes
Parity even

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Show commands: Pari/GP / SageMath
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(288, base_ring=CyclotomicField(24)) M = H._module chi = DirichletCharacter(H, M([0,21,8])) chi.galois_orbit()
 
Copy content pari:[g,chi] = znchar(Mod(13,288)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: 288288
Conductor: 288288
Copy content sage:chi.conductor()
 
Copy content pari:znconreyconductor(g,chi)
 
Order: 2424
Copy content sage:chi.multiplicative_order()
 
Copy content pari:charorder(g,chi)
 
Real: no
Primitive: yes
Copy content sage:chi.is_primitive()
 
Copy content pari:#znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
Copy content sage:chi.is_odd()
 
Copy content pari:zncharisodd(g,chi)
 

Related number fields

Field of values: Q(ζ24)\Q(\zeta_{24})
Fixed field: 24.24.18351423083070806589199715754737431920771072.1

Characters in Galois orbit

Character −1-1 11 55 77 1111 1313 1717 1919 2323 2525 2929 3131
χ288(13,⋅)\chi_{288}(13,\cdot) 11 11 e(1324)e\left(\frac{13}{24}\right) e(112)e\left(\frac{1}{12}\right) e(1724)e\left(\frac{17}{24}\right) e(1924)e\left(\frac{19}{24}\right) −1-1 e(18)e\left(\frac{1}{8}\right) e(1112)e\left(\frac{11}{12}\right) e(112)e\left(\frac{1}{12}\right) e(2324)e\left(\frac{23}{24}\right) e(23)e\left(\frac{2}{3}\right)
χ288(61,⋅)\chi_{288}(61,\cdot) 11 11 e(1724)e\left(\frac{17}{24}\right) e(512)e\left(\frac{5}{12}\right) e(1324)e\left(\frac{13}{24}\right) e(2324)e\left(\frac{23}{24}\right) −1-1 e(58)e\left(\frac{5}{8}\right) e(712)e\left(\frac{7}{12}\right) e(512)e\left(\frac{5}{12}\right) e(1924)e\left(\frac{19}{24}\right) e(13)e\left(\frac{1}{3}\right)
χ288(85,⋅)\chi_{288}(85,\cdot) 11 11 e(724)e\left(\frac{7}{24}\right) e(712)e\left(\frac{7}{12}\right) e(1124)e\left(\frac{11}{24}\right) e(124)e\left(\frac{1}{24}\right) −1-1 e(38)e\left(\frac{3}{8}\right) e(512)e\left(\frac{5}{12}\right) e(712)e\left(\frac{7}{12}\right) e(524)e\left(\frac{5}{24}\right) e(23)e\left(\frac{2}{3}\right)
χ288(133,⋅)\chi_{288}(133,\cdot) 11 11 e(1124)e\left(\frac{11}{24}\right) e(1112)e\left(\frac{11}{12}\right) e(724)e\left(\frac{7}{24}\right) e(524)e\left(\frac{5}{24}\right) −1-1 e(78)e\left(\frac{7}{8}\right) e(112)e\left(\frac{1}{12}\right) e(1112)e\left(\frac{11}{12}\right) e(124)e\left(\frac{1}{24}\right) e(13)e\left(\frac{1}{3}\right)
χ288(157,⋅)\chi_{288}(157,\cdot) 11 11 e(124)e\left(\frac{1}{24}\right) e(112)e\left(\frac{1}{12}\right) e(524)e\left(\frac{5}{24}\right) e(724)e\left(\frac{7}{24}\right) −1-1 e(58)e\left(\frac{5}{8}\right) e(1112)e\left(\frac{11}{12}\right) e(112)e\left(\frac{1}{12}\right) e(1124)e\left(\frac{11}{24}\right) e(23)e\left(\frac{2}{3}\right)
χ288(205,⋅)\chi_{288}(205,\cdot) 11 11 e(524)e\left(\frac{5}{24}\right) e(512)e\left(\frac{5}{12}\right) e(124)e\left(\frac{1}{24}\right) e(1124)e\left(\frac{11}{24}\right) −1-1 e(18)e\left(\frac{1}{8}\right) e(712)e\left(\frac{7}{12}\right) e(512)e\left(\frac{5}{12}\right) e(724)e\left(\frac{7}{24}\right) e(13)e\left(\frac{1}{3}\right)
χ288(229,⋅)\chi_{288}(229,\cdot) 11 11 e(1924)e\left(\frac{19}{24}\right) e(712)e\left(\frac{7}{12}\right) e(2324)e\left(\frac{23}{24}\right) e(1324)e\left(\frac{13}{24}\right) −1-1 e(78)e\left(\frac{7}{8}\right) e(512)e\left(\frac{5}{12}\right) e(712)e\left(\frac{7}{12}\right) e(1724)e\left(\frac{17}{24}\right) e(23)e\left(\frac{2}{3}\right)
χ288(277,⋅)\chi_{288}(277,\cdot) 11 11 e(2324)e\left(\frac{23}{24}\right) e(1112)e\left(\frac{11}{12}\right) e(1924)e\left(\frac{19}{24}\right) e(1724)e\left(\frac{17}{24}\right) −1-1 e(38)e\left(\frac{3}{8}\right) e(112)e\left(\frac{1}{12}\right) e(1112)e\left(\frac{11}{12}\right) e(1324)e\left(\frac{13}{24}\right) e(13)e\left(\frac{1}{3}\right)