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Properties

Label 640332.bnh
Modulus $640332$
Conductor $160083$
Order $6930$
Real no
Primitive no
Minimal yes
Parity odd

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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([0,2695,165,1323])) chi.galois_orbit()
 
Copy content pari:[g,chi] = znchar(Mod(101,640332)) 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.tr
Copy content sage:chi.is_primitive()
 
Copy content pari:#znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: odd
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 3 of 1440 characters in Galois orbit

Character \(-1\) \(1\) \(5\) \(13\) \(17\) \(19\) \(23\) \(25\) \(29\) \(31\) \(37\) \(41\)
\(\chi_{640332}(101,\cdot)\) \(-1\) \(1\) \(e\left(\frac{2641}{3465}\right)\) \(e\left(\frac{619}{3465}\right)\) \(e\left(\frac{603}{770}\right)\) \(e\left(\frac{19}{55}\right)\) \(e\left(\frac{757}{1386}\right)\) \(e\left(\frac{1817}{3465}\right)\) \(e\left(\frac{218}{3465}\right)\) \(e\left(\frac{359}{990}\right)\) \(e\left(\frac{131}{1155}\right)\) \(e\left(\frac{2489}{6930}\right)\)
\(\chi_{640332}(761,\cdot)\) \(-1\) \(1\) \(e\left(\frac{2141}{3465}\right)\) \(e\left(\frac{3299}{3465}\right)\) \(e\left(\frac{283}{770}\right)\) \(e\left(\frac{34}{55}\right)\) \(e\left(\frac{1361}{1386}\right)\) \(e\left(\frac{817}{3465}\right)\) \(e\left(\frac{283}{3465}\right)\) \(e\left(\frac{709}{990}\right)\) \(e\left(\frac{631}{1155}\right)\) \(e\left(\frac{5059}{6930}\right)\)
\(\chi_{640332}(1361,\cdot)\) \(-1\) \(1\) \(e\left(\frac{1333}{3465}\right)\) \(e\left(\frac{1282}{3465}\right)\) \(e\left(\frac{579}{770}\right)\) \(e\left(\frac{27}{55}\right)\) \(e\left(\frac{1195}{1386}\right)\) \(e\left(\frac{2666}{3465}\right)\) \(e\left(\frac{194}{3465}\right)\) \(e\left(\frac{47}{990}\right)\) \(e\left(\frac{53}{1155}\right)\) \(e\left(\frac{1007}{6930}\right)\)