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Show commands for: Pari/GP / SageMath
sage: from dirichlet_conrey import DirichletGroup_conrey # requires nonstandard Sage package to be installed
 
sage: H = DirichletGroup_conrey(27200)
 
sage: chi = H[1]
 
pari: [g,chi] = znchar(Mod(1,27200))
 

Basic properties

Modulus: \(27200\)
Conductor: \(1\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(1\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: yes
Primitive: no, induced from \(\chi_{1}(1,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1 \\ if not primitive returns [cond,factorization]
 
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 27200.None

\(\chi_{27200}(1,\cdot)\)

sage: chi.galois_orbit()
 
pari: order = charorder(g,chi)
 
pari: [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Values on generators

sage: chi(k) for k in H.gens()
 
pari: [ chareval(g,chi,x) | x <- g.gen ] \\ value in Q/Z
 

\((20877,1601,19857,5951)\) → \((1,1,1,1)\)

First values

\(1\)\(3\)\(7\)\(9\)\(11\)\(13\)\(19\)\(21\)\(23\)\(27\)\(29\)\(31\)\(33\)\(37\)\(39\)\(41\)\(43\)\(47\)\(49\)\(53\)\(57\)\(59\)\(61\)\(63\)\(67\)\(69\)\(71\)\(73\)\(77\)\(79\)
111111111111111111111111111111
value at e.g. 2

Related number fields

Field of values: \(\Q\)