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Properties

Label 3825.db
Modulus $3825$
Conductor $765$
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(3825, base_ring=CyclotomicField(24)) M = H._module chi = DirichletCharacter(H, M([8,12,9])) chi.galois_orbit()
 
Copy content pari:[g,chi] = znchar(Mod(49,3825)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: \(3825\)
Conductor: \(765\)
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 765.cg
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: Number field defined by a degree 24 polynomial

Characters in Galois orbit

Character \(-1\) \(1\) \(2\) \(4\) \(7\) \(8\) \(11\) \(13\) \(14\) \(16\) \(19\) \(22\)
\(\chi_{3825}(49,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{23}{24}\right)\) \(i\) \(e\left(\frac{23}{24}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{24}\right)\) \(e\left(\frac{1}{3}\right)\) \(i\) \(e\left(\frac{1}{24}\right)\)
\(\chi_{3825}(274,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{11}{24}\right)\) \(i\) \(e\left(\frac{11}{24}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{13}{24}\right)\) \(e\left(\frac{1}{3}\right)\) \(i\) \(e\left(\frac{13}{24}\right)\)
\(\chi_{3825}(349,\cdot)\) \(1\) \(1\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{13}{24}\right)\) \(-i\) \(e\left(\frac{13}{24}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{11}{24}\right)\) \(e\left(\frac{2}{3}\right)\) \(-i\) \(e\left(\frac{11}{24}\right)\)
\(\chi_{3825}(1249,\cdot)\) \(1\) \(1\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{24}\right)\) \(-i\) \(e\left(\frac{1}{24}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{23}{24}\right)\) \(e\left(\frac{2}{3}\right)\) \(-i\) \(e\left(\frac{23}{24}\right)\)
\(\chi_{3825}(1624,\cdot)\) \(1\) \(1\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{5}{24}\right)\) \(-i\) \(e\left(\frac{5}{24}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{19}{24}\right)\) \(e\left(\frac{1}{3}\right)\) \(-i\) \(e\left(\frac{19}{24}\right)\)
\(\chi_{3825}(2524,\cdot)\) \(1\) \(1\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{17}{24}\right)\) \(-i\) \(e\left(\frac{17}{24}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{7}{24}\right)\) \(e\left(\frac{1}{3}\right)\) \(-i\) \(e\left(\frac{7}{24}\right)\)
\(\chi_{3825}(2599,\cdot)\) \(1\) \(1\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{7}{24}\right)\) \(i\) \(e\left(\frac{7}{24}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{17}{24}\right)\) \(e\left(\frac{2}{3}\right)\) \(i\) \(e\left(\frac{17}{24}\right)\)
\(\chi_{3825}(2824,\cdot)\) \(1\) \(1\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{19}{24}\right)\) \(i\) \(e\left(\frac{19}{24}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{5}{24}\right)\) \(e\left(\frac{2}{3}\right)\) \(i\) \(e\left(\frac{5}{24}\right)\)