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Properties

Label 576.bg
Modulus $576$
Conductor $288$
Order $24$
Real no
Primitive no
Minimal no
Parity even

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Show commands: Pari/GP / SageMath
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(576, base_ring=CyclotomicField(24)) M = H._module chi = DirichletCharacter(H, M([0,3,16])) chi.galois_orbit()
 
Copy content pari:[g,chi] = znchar(Mod(25,576)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: \(576\)
Conductor: \(288\)
Copy content sage:chi.conductor()
 
Copy content pari:znconreyconductor(g,chi)
 
Order: \(24\)
Copy content sage:chi.multiplicative_order()
 
Copy content pari:charorder(g,chi)
 
Real: no
Primitive: no, induced from 288.bc
Copy content sage:chi.is_primitive()
 
Copy content pari:#znconreyconductor(g,chi)==1
 
Minimal: no
Parity: even
Copy content sage:chi.is_odd()
 
Copy content pari:zncharisodd(g,chi)
 

Related number fields

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

Characters in Galois orbit

Character \(-1\) \(1\) \(5\) \(7\) \(11\) \(13\) \(17\) \(19\) \(23\) \(25\) \(29\) \(31\)
\(\chi_{576}(25,\cdot)\) \(1\) \(1\) \(e\left(\frac{11}{24}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{7}{24}\right)\) \(e\left(\frac{5}{24}\right)\) \(-1\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{1}{24}\right)\) \(e\left(\frac{1}{3}\right)\)
\(\chi_{576}(121,\cdot)\) \(1\) \(1\) \(e\left(\frac{7}{24}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{11}{24}\right)\) \(e\left(\frac{1}{24}\right)\) \(-1\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{5}{24}\right)\) \(e\left(\frac{2}{3}\right)\)
\(\chi_{576}(169,\cdot)\) \(1\) \(1\) \(e\left(\frac{5}{24}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{1}{24}\right)\) \(e\left(\frac{11}{24}\right)\) \(-1\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{7}{24}\right)\) \(e\left(\frac{1}{3}\right)\)
\(\chi_{576}(265,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{24}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{5}{24}\right)\) \(e\left(\frac{7}{24}\right)\) \(-1\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{11}{24}\right)\) \(e\left(\frac{2}{3}\right)\)
\(\chi_{576}(313,\cdot)\) \(1\) \(1\) \(e\left(\frac{23}{24}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{19}{24}\right)\) \(e\left(\frac{17}{24}\right)\) \(-1\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{13}{24}\right)\) \(e\left(\frac{1}{3}\right)\)
\(\chi_{576}(409,\cdot)\) \(1\) \(1\) \(e\left(\frac{19}{24}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{23}{24}\right)\) \(e\left(\frac{13}{24}\right)\) \(-1\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{17}{24}\right)\) \(e\left(\frac{2}{3}\right)\)
\(\chi_{576}(457,\cdot)\) \(1\) \(1\) \(e\left(\frac{17}{24}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{13}{24}\right)\) \(e\left(\frac{23}{24}\right)\) \(-1\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{19}{24}\right)\) \(e\left(\frac{1}{3}\right)\)
\(\chi_{576}(553,\cdot)\) \(1\) \(1\) \(e\left(\frac{13}{24}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{17}{24}\right)\) \(e\left(\frac{19}{24}\right)\) \(-1\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{23}{24}\right)\) \(e\left(\frac{2}{3}\right)\)