↑

Properties

Label 640332.bls
Modulus $640332$
Conductor $160083$
Order $6930$
Real no
Primitive no
Minimal yes
Parity even

Related objects

Downloads

Learn more

Show commands: Pari/GP / SageMath
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(640332, base_ring=CyclotomicField(6930)) M = H._module chi = DirichletCharacter(H, M([0,1925,4785,4662])) chi.galois_orbit()
 
Copy content pari:[g,chi] = znchar(Mod(5,640332)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: \(640332\)
Conductor: \(160083\)
Copy content sage:chi.conductor()
 
Copy content pari:znconreyconductor(g,chi)
 
Order: \(6930\)
Copy content sage:chi.multiplicative_order()
 
Copy content pari:charorder(g,chi)
 
Real: no
Primitive: no, induced from 160083.sx
Copy content sage:chi.is_primitive()
 
Copy content pari:#znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
Copy content sage:chi.is_odd()
 
Copy content pari:zncharisodd(g,chi)
 

Related number fields

Field of values: $\Q(\zeta_{3465})$
Fixed field: Number field defined by a degree 6930 polynomial (not computed)

First 2 of 1440 characters in Galois orbit

Character \(-1\) \(1\) \(5\) \(13\) \(17\) \(19\) \(23\) \(25\) \(29\) \(31\) \(37\) \(41\)
\(\chi_{640332}(5,\cdot)\) \(1\) \(1\) \(e\left(\frac{674}{3465}\right)\) \(e\left(\frac{6607}{6930}\right)\) \(e\left(\frac{151}{385}\right)\) \(e\left(\frac{37}{110}\right)\) \(e\left(\frac{533}{1386}\right)\) \(e\left(\frac{1348}{3465}\right)\) \(e\left(\frac{989}{6930}\right)\) \(e\left(\frac{241}{990}\right)\) \(e\left(\frac{19}{1155}\right)\) \(e\left(\frac{1913}{3465}\right)\)
\(\chi_{640332}(257,\cdot)\) \(1\) \(1\) \(e\left(\frac{1037}{3465}\right)\) \(e\left(\frac{6541}{6930}\right)\) \(e\left(\frac{338}{385}\right)\) \(e\left(\frac{81}{110}\right)\) \(e\left(\frac{599}{1386}\right)\) \(e\left(\frac{2074}{3465}\right)\) \(e\left(\frac{4817}{6930}\right)\) \(e\left(\frac{373}{990}\right)\) \(e\left(\frac{1042}{1155}\right)\) \(e\left(\frac{2969}{3465}\right)\)