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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(14994)
 
sage: chi = H[1]
 
pari: [g,chi] = znchar(Mod(1,14994))
 

Basic properties

Modulus: \(14994\)
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 14994.None

\(\chi_{14994}(1,\cdot)\)

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
 

\((4511,3841,12545)\) → \((1,1,1)\)

First values

\(1\)\(5\)\(11\)\(13\)\(19\)\(23\)\(25\)\(29\)\(31\)\(37\)\(41\)\(43\)\(47\)\(53\)\(55\)\(59\)\(61\)\(65\)\(67\)\(71\)\(73\)\(79\)\(83\)\(89\)\(95\)\(97\)\(101\)\(103\)\(107\)\(109\)
111111111111111111111111111111
value at e.g. 2

Related number fields

Field of values: \(\Q\)