Properties

 Label 1815.4 Modulus $1815$ Conductor $605$ Order $110$ Real no Primitive no Minimal yes Parity even

Related objects

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

sage: H = DirichletGroup(1815, base_ring=CyclotomicField(110))

sage: M = H._module

sage: chi = DirichletCharacter(H, M([0,55,2]))

pari: [g,chi] = znchar(Mod(4,1815))

Basic properties

 Modulus: $$1815$$ Conductor: $$605$$ sage: chi.conductor()  pari: znconreyconductor(g,chi) Order: $$110$$ sage: chi.multiplicative_order()  pari: charorder(g,chi) Real: no Primitive: no, induced from $$\chi_{605}(4,\cdot)$$ sage: chi.is_primitive()  pari: #znconreyconductor(g,chi)==1 Minimal: yes Parity: even sage: chi.is_odd()  pari: zncharisodd(g,chi)

Galois orbit 1815.bm

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

$$(1211,727,1696)$$ → $$(1,-1,e\left(\frac{1}{55}\right))$$

Values

 $$-1$$ $$1$$ $$2$$ $$4$$ $$7$$ $$8$$ $$13$$ $$14$$ $$16$$ $$17$$ $$19$$ $$23$$ $$1$$ $$1$$ $$e\left(\frac{57}{110}\right)$$ $$e\left(\frac{2}{55}\right)$$ $$e\left(\frac{69}{110}\right)$$ $$e\left(\frac{61}{110}\right)$$ $$e\left(\frac{37}{110}\right)$$ $$e\left(\frac{8}{55}\right)$$ $$e\left(\frac{4}{55}\right)$$ $$e\left(\frac{43}{110}\right)$$ $$e\left(\frac{28}{55}\right)$$ $$e\left(\frac{17}{22}\right)$$
 value at e.g. 2

Related number fields

 Field of values: $\Q(\zeta_{55})$ Fixed field: Number field defined by a degree 110 polynomial (not computed)