Properties

Label 1295.t
Modulus 12951295
Conductor 55
Order 44
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(1295, base_ring=CyclotomicField(4)) M = H._module chi = DirichletCharacter(H, M([3,0,0])) chi.galois_orbit()
 
Copy content pari:[g,chi] = znchar(Mod(778,1295)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: 12951295
Conductor: 55
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 5.c
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(i)\mathbb{Q}(i)
Fixed field: Q(ζ5)\Q(\zeta_{5})

Characters in Galois orbit

Character 1-1 11 22 33 44 66 88 99 1111 1212 1313 1616
χ1295(778,)\chi_{1295}(778,\cdot) 1-1 11 i-i ii 1-1 11 ii 1-1 11 i-i ii 11
χ1295(1037,)\chi_{1295}(1037,\cdot) 1-1 11 ii i-i 1-1 11 i-i 1-1 11 ii i-i 11