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Properties

Label 30345.ce
Modulus $30345$
Conductor $595$
Order $8$
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(30345, base_ring=CyclotomicField(8)) M = H._module chi = DirichletCharacter(H, M([0,6,4,5])) chi.galois_orbit()
 
Copy content pari:[g,chi] = znchar(Mod(9358,30345)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: \(30345\)
Conductor: \(595\)
Copy content sage:chi.conductor()
 
Copy content pari:znconreyconductor(g,chi)
 
Order: \(8\)
Copy content sage:chi.multiplicative_order()
 
Copy content pari:charorder(g,chi)
 
Real: no
Primitive: no, induced from 595.bd
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: \(\Q(\zeta_{8})\)
Fixed field: 8.8.15394111779265625.2

Characters in Galois orbit

Character \(-1\) \(1\) \(2\) \(4\) \(8\) \(11\) \(13\) \(16\) \(19\) \(22\) \(23\) \(26\)
\(\chi_{30345}(9358,\cdot)\) \(1\) \(1\) \(-1\) \(1\) \(-1\) \(e\left(\frac{3}{8}\right)\) \(i\) \(1\) \(-i\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{5}{8}\right)\) \(-i\)
\(\chi_{30345}(18052,\cdot)\) \(1\) \(1\) \(-1\) \(1\) \(-1\) \(e\left(\frac{5}{8}\right)\) \(-i\) \(1\) \(i\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{3}{8}\right)\) \(i\)
\(\chi_{30345}(20698,\cdot)\) \(1\) \(1\) \(-1\) \(1\) \(-1\) \(e\left(\frac{7}{8}\right)\) \(i\) \(1\) \(-i\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{1}{8}\right)\) \(-i\)
\(\chi_{30345}(24142,\cdot)\) \(1\) \(1\) \(-1\) \(1\) \(-1\) \(e\left(\frac{1}{8}\right)\) \(-i\) \(1\) \(i\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{7}{8}\right)\) \(i\)