↑

Properties

Label 1976.do
Modulus $1976$
Conductor $988$
Order $12$
Real no
Primitive no
Minimal no
Parity even

Related objects

Downloads

Learn more

Show commands: Pari/GP / SageMath
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1976, base_ring=CyclotomicField(12)) M = H._module chi = DirichletCharacter(H, M([6,0,11,4])) chi.galois_orbit()
 
Copy content pari:[g,chi] = znchar(Mod(7,1976)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: \(1976\)
Conductor: \(988\)
Copy content sage:chi.conductor()
 
Copy content pari:znconreyconductor(g,chi)
 
Order: \(12\)
Copy content sage:chi.multiplicative_order()
 
Copy content pari:charorder(g,chi)
 
Real: no
Primitive: no, induced from 988.bv
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: \(\Q(\zeta_{12})\)
Fixed field: 12.12.124671053953887395784773632.1

Characters in Galois orbit

Character \(-1\) \(1\) \(3\) \(5\) \(7\) \(9\) \(11\) \(15\) \(17\) \(21\) \(23\) \(25\)
\(\chi_{1976}(7,\cdot)\) \(1\) \(1\) \(-1\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{7}{12}\right)\) \(1\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{6}\right)\)
\(\chi_{1976}(847,\cdot)\) \(1\) \(1\) \(-1\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{5}{12}\right)\) \(1\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{5}{6}\right)\)
\(\chi_{1976}(999,\cdot)\) \(1\) \(1\) \(-1\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{11}{12}\right)\) \(1\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{5}{6}\right)\)
\(\chi_{1976}(1527,\cdot)\) \(1\) \(1\) \(-1\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{1}{12}\right)\) \(1\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{6}\right)\)