Properties

 Conductor 89 Order 88 Real no Primitive no Minimal yes Parity odd Orbit label 1157.bq

Related objects

Show commands for: Pari/GP / SageMath
sage: from dirichlet_conrey import DirichletGroup_conrey # requires nonstandard Sage package to be installed

sage: H = DirichletGroup_conrey(1157)

sage: chi = H[27]

pari: [g,chi] = znchar(Mod(27,1157))

Basic properties

 sage: chi.conductor()  pari: znconreyconductor(g,chi) Conductor = 89 sage: chi.multiplicative_order()  pari: charorder(g,chi) Order = 88 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 = 1157.bq Orbit index = 43

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 ]

Values on generators

$$(535,92)$$ → $$(1,e\left(\frac{3}{88}\right))$$

Values

 -1 1 2 3 4 5 6 7 8 9 10 11 $$-1$$ $$1$$ $$e\left(\frac{6}{11}\right)$$ $$e\left(\frac{3}{88}\right)$$ $$e\left(\frac{1}{11}\right)$$ $$e\left(\frac{17}{44}\right)$$ $$e\left(\frac{51}{88}\right)$$ $$e\left(\frac{67}{88}\right)$$ $$e\left(\frac{7}{11}\right)$$ $$e\left(\frac{3}{44}\right)$$ $$e\left(\frac{41}{44}\right)$$ $$e\left(\frac{19}{22}\right)$$
value at  e.g. 2

Related number fields

 Field of values $$\Q(\zeta_{88})$$