Properties

 Modulus 9900 Conductor 275 Order 20 Real no Primitive no Minimal yes Parity odd Orbit label 9900.hg

Related objects

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

sage: H = DirichletGroup(9900)

sage: M = H._module

sage: chi = DirichletCharacter(H, M([0,0,9,4]))

pari: [g,chi] = znchar(Mod(37,9900))

Basic properties

 sage: chi.conductor()  pari: znconreyconductor(g,chi) Modulus = 9900 Conductor = 275 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 = no Minimal = yes sage: chi.is_odd()  pari: zncharisodd(g,chi) Parity = odd Orbit label = 9900.hg Orbit index = 189

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

$$(4951,5501,2377,4501)$$ → $$(1,1,e\left(\frac{9}{20}\right),e\left(\frac{1}{5}\right))$$

Values

 -1 1 7 13 17 19 23 29 31 37 41 43 $$-1$$ $$1$$ $$e\left(\frac{13}{20}\right)$$ $$-i$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{9}{20}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$-i$$
value at  e.g. 2

Related number fields

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