Properties

Label 3744.ja
Modulus $3744$
Conductor $288$
Order $24$
Real no
Primitive no
Minimal yes
Parity odd

Related objects

Learn more

Show commands: Pari/GP / SageMath
sage: from sage.modular.dirichlet import DirichletCharacter
 
sage: H = DirichletGroup(3744, base_ring=CyclotomicField(24))
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([12,9,16,0]))
 
sage: chi.galois_orbit()
 
pari: [g,chi] = znchar(Mod(547,3744))
 
pari: order = charorder(g,chi)
 
pari: [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: \(3744\)
Conductor: \(288\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(24\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from 288.bd
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: odd
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Related number fields

Field of values: \(\Q(\zeta_{24})\)
Fixed field: 24.0.18351423083070806589199715754737431920771072.1

Characters in Galois orbit

Character \(-1\) \(1\) \(5\) \(7\) \(11\) \(17\) \(19\) \(23\) \(25\) \(29\) \(31\) \(35\)
\(\chi_{3744}(547,\cdot)\) \(-1\) \(1\) \(e\left(\frac{17}{24}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{1}{24}\right)\) \(-1\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{19}{24}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{5}{8}\right)\)
\(\chi_{3744}(859,\cdot)\) \(-1\) \(1\) \(e\left(\frac{19}{24}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{11}{24}\right)\) \(-1\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{17}{24}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{7}{8}\right)\)
\(\chi_{3744}(1483,\cdot)\) \(-1\) \(1\) \(e\left(\frac{23}{24}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{7}{24}\right)\) \(-1\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{13}{24}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{3}{8}\right)\)
\(\chi_{3744}(1795,\cdot)\) \(-1\) \(1\) \(e\left(\frac{1}{24}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{17}{24}\right)\) \(-1\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{11}{24}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{5}{8}\right)\)
\(\chi_{3744}(2419,\cdot)\) \(-1\) \(1\) \(e\left(\frac{5}{24}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{13}{24}\right)\) \(-1\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{7}{24}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{8}\right)\)
\(\chi_{3744}(2731,\cdot)\) \(-1\) \(1\) \(e\left(\frac{7}{24}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{23}{24}\right)\) \(-1\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{5}{24}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{3}{8}\right)\)
\(\chi_{3744}(3355,\cdot)\) \(-1\) \(1\) \(e\left(\frac{11}{24}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{19}{24}\right)\) \(-1\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{1}{24}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{7}{8}\right)\)
\(\chi_{3744}(3667,\cdot)\) \(-1\) \(1\) \(e\left(\frac{13}{24}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{5}{24}\right)\) \(-1\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{23}{24}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{8}\right)\)