Properties

 Modulus 2100 Conductor 2100 Order 20 Real no Primitive yes Minimal yes Parity even Orbit label 2100.cp

Related objects

Show commands for: Pari/GP / SageMath
sage: from sage.modular.dirichlet import DirichletCharacter

sage: H = DirichletGroup(2100)

sage: M = H._module

sage: chi = DirichletCharacter(H, M([10,10,3,10]))

pari: [g,chi] = znchar(Mod(83,2100))

Basic properties

 sage: chi.conductor()  pari: znconreyconductor(g,chi) Modulus = 2100 Conductor = 2100 sage: chi.multiplicative_order()  pari: charorder(g,chi) Order = 20 Real = no sage: chi.is_primitive()  pari: #znconreyconductor(g,chi)==1 \\ if not primitive returns [cond,factorization] Primitive = yes Minimal = yes sage: chi.is_odd()  pari: zncharisodd(g,chi) Parity = even Orbit label = 2100.cp Orbit index = 68

Galois orbit

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

$$(1051,701,1177,1501)$$ → $$(-1,-1,e\left(\frac{3}{20}\right),-1)$$

Values

 -1 1 11 13 17 19 23 29 31 37 41 43 $$1$$ $$1$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$-i$$
value at  e.g. 2

Related number fields

 Field of values $$\Q(\zeta_{20})$$