Related objects

Learn more about

Show commands for: Pari/GP / SageMath
sage: from dirichlet_conrey import DirichletGroup_conrey # requires nonstandard Sage package to be installed
 
sage: H = DirichletGroup_conrey(53312)
 
sage: chi = H[1]
 
pari: [g,chi] = znchar(Mod(1,53312))
 

Basic properties

Modulus: \(53312\)
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 53312.None

\(\chi_{53312}(1,\cdot)\)

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
 

\((20877,40769,42433,51647)\) → \((1,1,1,1)\)

First values

\(1\)\(3\)\(5\)\(9\)\(11\)\(13\)\(15\)\(19\)\(23\)\(25\)\(27\)\(29\)\(31\)\(33\)\(37\)\(39\)\(41\)\(43\)\(45\)\(47\)\(53\)\(55\)\(57\)\(59\)\(61\)\(65\)\(67\)\(69\)\(71\)\(73\)
111111111111111111111111111111
value at e.g. 2

Related number fields

Field of values: \(\Q\)