Properties

 Modulus 1157 Conductor 1157 Order 132 Real no Primitive yes Minimal yes Parity odd Orbit label 1157.bv

Related objects

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

sage: H = DirichletGroup(1157)

sage: M = H._module

sage: chi = DirichletCharacter(H, M([77,126]))

pari: [g,chi] = znchar(Mod(11,1157))

Basic properties

 sage: chi.conductor()  pari: znconreyconductor(g,chi) Modulus = 1157 Conductor = 1157 sage: chi.multiplicative_order()  pari: charorder(g,chi) Order = 132 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 = odd Orbit label = 1157.bv Orbit index = 48

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

$$(535,92)$$ → $$(e\left(\frac{7}{12}\right),e\left(\frac{21}{22}\right))$$

Values

 -1 1 2 3 4 5 6 7 8 9 10 11 $$-1$$ $$1$$ $$e\left(\frac{113}{132}\right)$$ $$e\left(\frac{19}{66}\right)$$ $$e\left(\frac{47}{66}\right)$$ $$e\left(\frac{3}{44}\right)$$ $$e\left(\frac{19}{132}\right)$$ $$e\left(\frac{97}{132}\right)$$ $$e\left(\frac{25}{44}\right)$$ $$e\left(\frac{19}{33}\right)$$ $$e\left(\frac{61}{66}\right)$$ $$e\left(\frac{35}{132}\right)$$
value at  e.g. 2

Related number fields

 Field of values $$\Q(\zeta_{132})$$