Properties

 Modulus 2100 Conductor 700 Order 30 Real no Primitive no Minimal yes Parity even Orbit label 2100.cy

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([15,0,27,25]))

pari: [g,chi] = znchar(Mod(19,2100))

Basic properties

 sage: chi.conductor()  pari: znconreyconductor(g,chi) Modulus = 2100 Conductor = 700 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 = 2100.cy Orbit index = 77

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

$$(1051,701,1177,1501)$$ → $$(-1,1,e\left(\frac{9}{10}\right),e\left(\frac{5}{6}\right))$$

Values

 -1 1 11 13 17 19 23 29 31 37 41 43 $$1$$ $$1$$ $$e\left(\frac{7}{30}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{13}{15}\right)$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{23}{30}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$1$$
value at  e.g. 2

Related number fields

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