Properties

Label 624.z
Modulus 624624
Conductor 104104
Order 44
Real no
Primitive no
Minimal no
Parity odd

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Show commands: Pari/GP / SageMath
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(624, base_ring=CyclotomicField(4)) M = H._module chi = DirichletCharacter(H, M([0,2,0,1])) chi.galois_orbit()
 
Copy content pari:[g,chi] = znchar(Mod(73,624)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: 624624
Conductor: 104104
Copy content sage:chi.conductor()
 
Copy content pari:znconreyconductor(g,chi)
 
Order: 44
Copy content sage:chi.multiplicative_order()
 
Copy content pari:charorder(g,chi)
 
Real: no
Primitive: no, induced from 104.j
Copy content sage:chi.is_primitive()
 
Copy content pari:#znconreyconductor(g,chi)==1
 
Minimal: no
Parity: odd
Copy content sage:chi.is_odd()
 
Copy content pari:zncharisodd(g,chi)
 

Related number fields

Field of values: Q(i)\mathbb{Q}(i)
Fixed field: 4.0.140608.2

Characters in Galois orbit

Character 1-1 11 55 77 1111 1717 1919 2323 2525 2929 3131 3535
χ624(73,)\chi_{624}(73,\cdot) 1-1 11 i-i i-i ii 1-1 i-i 1-1 1-1 1-1 ii 1-1
χ624(265,)\chi_{624}(265,\cdot) 1-1 11 ii ii i-i 1-1 ii 1-1 1-1 1-1 i-i 1-1