Properties

Conductor 473
Order 30
Real no
Primitive no
Minimal yes
Parity even
Orbit label 4730.ca

Related objects

Learn more about

Show commands for: SageMath / Pari/GP
sage: from dirichlet_conrey import DirichletGroup_conrey # requires nonstandard Sage package to be installed
 
sage: H = DirichletGroup_conrey(4730)
 
sage: chi = H[4681]
 
pari: [g,chi] = znchar(Mod(4681,4730))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 473
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 30
Real = no
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1 \\ if not primitive returns [cond,factorization]
 
Primitive = no
Minimal = yes
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 
Parity = even
Orbit label = 4730.ca
Orbit index = 53

Galois orbit

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

\(\chi_{4730}(381,\cdot)\) \(\chi_{4730}(811,\cdot)\) \(\chi_{4730}(1641,\cdot)\) \(\chi_{4730}(2961,\cdot)\) \(\chi_{4730}(3361,\cdot)\) \(\chi_{4730}(3791,\cdot)\) \(\chi_{4730}(4221,\cdot)\) \(\chi_{4730}(4681,\cdot)\)

Values on generators

\((947,431,1981)\) → \((1,e\left(\frac{9}{10}\right),e\left(\frac{1}{6}\right))\)

Values

-1137913171921232729
\(1\)\(1\)\(e\left(\frac{11}{30}\right)\)\(e\left(\frac{2}{15}\right)\)\(e\left(\frac{11}{15}\right)\)\(e\left(\frac{7}{30}\right)\)\(e\left(\frac{13}{30}\right)\)\(e\left(\frac{13}{15}\right)\)\(-1\)\(e\left(\frac{2}{3}\right)\)\(e\left(\frac{1}{10}\right)\)\(e\left(\frac{2}{15}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{15})\)