↑

Properties

Label 305760.cof
Modulus $305760$
Conductor $14560$
Order $24$
Real no
Primitive no
Minimal no
Parity odd

Related objects

Downloads

Learn more

Show commands: Pari/GP / SageMath
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(305760, base_ring=CyclotomicField(24)) M = H._module chi = DirichletCharacter(H, M([12,21,0,12,20,10])) chi.galois_orbit()
 
Copy content pari:[g,chi] = znchar(Mod(19,305760)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: \(305760\)
Conductor: \(14560\)
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 14560.bfu
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: Number field defined by a degree 24 polynomial

Characters in Galois orbit

Character \(-1\) \(1\) \(11\) \(17\) \(19\) \(23\) \(29\) \(31\) \(37\) \(41\) \(43\) \(47\)
\(\chi_{305760}(19,\cdot)\) \(-1\) \(1\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{7}{24}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{23}{24}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{5}{24}\right)\) \(e\left(\frac{11}{12}\right)\)
\(\chi_{305760}(24139,\cdot)\) \(-1\) \(1\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{5}{24}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{13}{24}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{7}{24}\right)\) \(e\left(\frac{1}{12}\right)\)
\(\chi_{305760}(30019,\cdot)\) \(-1\) \(1\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{11}{24}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{19}{24}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{24}\right)\) \(e\left(\frac{7}{12}\right)\)
\(\chi_{305760}(135259,\cdot)\) \(-1\) \(1\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{1}{24}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{17}{24}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{11}{24}\right)\) \(e\left(\frac{5}{12}\right)\)
\(\chi_{305760}(152899,\cdot)\) \(-1\) \(1\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{19}{24}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{11}{24}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{17}{24}\right)\) \(e\left(\frac{11}{12}\right)\)
\(\chi_{305760}(177019,\cdot)\) \(-1\) \(1\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{17}{24}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{1}{24}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{19}{24}\right)\) \(e\left(\frac{1}{12}\right)\)
\(\chi_{305760}(182899,\cdot)\) \(-1\) \(1\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{23}{24}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{7}{24}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{13}{24}\right)\) \(e\left(\frac{7}{12}\right)\)
\(\chi_{305760}(288139,\cdot)\) \(-1\) \(1\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{13}{24}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{5}{24}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{23}{24}\right)\) \(e\left(\frac{5}{12}\right)\)