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Properties

Label 1216.bp
Modulus $1216$
Conductor $608$
Order $24$
Real no
Primitive no
Minimal no
Parity odd

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Show commands: Pari/GP / SageMath
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1216, base_ring=CyclotomicField(24)) M = H._module chi = DirichletCharacter(H, M([0,3,4])) chi.galois_orbit()
 
Copy content pari:[g,chi] = znchar(Mod(217,1216)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: \(1216\)
Conductor: \(608\)
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 608.bl
Copy content sage:chi.is_primitive()
 
Copy content pari:#znconreyconductor(g,chi)==1
 
Minimal: no
Parity: odd
Copy content sage:chi.is_odd()
 
Copy content pari:zncharisodd(g,chi)
 

Related number fields

Field of values: \(\Q(\zeta_{24})\)
Fixed field: 24.0.372273065750166762311522006998539295982015765641428992.1

Characters in Galois orbit

Character \(-1\) \(1\) \(3\) \(5\) \(7\) \(9\) \(11\) \(13\) \(15\) \(17\) \(21\) \(23\)
\(\chi_{1216}(217,\cdot)\) \(-1\) \(1\) \(e\left(\frac{13}{24}\right)\) \(e\left(\frac{19}{24}\right)\) \(i\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{17}{24}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{19}{24}\right)\) \(e\left(\frac{1}{12}\right)\)
\(\chi_{1216}(297,\cdot)\) \(-1\) \(1\) \(e\left(\frac{11}{24}\right)\) \(e\left(\frac{5}{24}\right)\) \(-i\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{7}{24}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{5}{24}\right)\) \(e\left(\frac{11}{12}\right)\)
\(\chi_{1216}(521,\cdot)\) \(-1\) \(1\) \(e\left(\frac{7}{24}\right)\) \(e\left(\frac{1}{24}\right)\) \(-i\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{11}{24}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{24}\right)\) \(e\left(\frac{7}{12}\right)\)
\(\chi_{1216}(601,\cdot)\) \(-1\) \(1\) \(e\left(\frac{5}{24}\right)\) \(e\left(\frac{11}{24}\right)\) \(i\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{1}{24}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{11}{24}\right)\) \(e\left(\frac{5}{12}\right)\)
\(\chi_{1216}(825,\cdot)\) \(-1\) \(1\) \(e\left(\frac{1}{24}\right)\) \(e\left(\frac{7}{24}\right)\) \(i\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{5}{24}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{7}{24}\right)\) \(e\left(\frac{1}{12}\right)\)
\(\chi_{1216}(905,\cdot)\) \(-1\) \(1\) \(e\left(\frac{23}{24}\right)\) \(e\left(\frac{17}{24}\right)\) \(-i\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{19}{24}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{17}{24}\right)\) \(e\left(\frac{11}{12}\right)\)
\(\chi_{1216}(1129,\cdot)\) \(-1\) \(1\) \(e\left(\frac{19}{24}\right)\) \(e\left(\frac{13}{24}\right)\) \(-i\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{23}{24}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{13}{24}\right)\) \(e\left(\frac{7}{12}\right)\)
\(\chi_{1216}(1209,\cdot)\) \(-1\) \(1\) \(e\left(\frac{17}{24}\right)\) \(e\left(\frac{23}{24}\right)\) \(i\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{13}{24}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{23}{24}\right)\) \(e\left(\frac{5}{12}\right)\)