Properties

 Label 3549.211 Modulus $3549$ Conductor $169$ Order $39$ 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(3549, base_ring=CyclotomicField(78))

sage: M = H._module

sage: chi = DirichletCharacter(H, M([0,0,38]))

pari: [g,chi] = znchar(Mod(211,3549))

Basic properties

 Modulus: $$3549$$ Conductor: $$169$$ sage: chi.conductor()  pari: znconreyconductor(g,chi) Order: $$39$$ sage: chi.multiplicative_order()  pari: charorder(g,chi) Real: no Primitive: no, induced from $$\chi_{169}(42,\cdot)$$ sage: chi.is_primitive()  pari: #znconreyconductor(g,chi)==1 Minimal: yes Parity: even sage: chi.is_odd()  pari: zncharisodd(g,chi)

Galois orbit 3549.cr

sage: chi.galois_orbit()

pari: order = charorder(g,chi)

pari: [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Related number fields

 Field of values: $\Q(\zeta_{39})$ Fixed field: 39.39.27027636582498189040621249864144468324898507852136260989871841246090732111847218889.1

Values on generators

$$(1184,1522,3382)$$ → $$(1,1,e\left(\frac{19}{39}\right))$$

Values

 $$-1$$ $$1$$ $$2$$ $$4$$ $$5$$ $$8$$ $$10$$ $$11$$ $$16$$ $$17$$ $$19$$ $$20$$ $$1$$ $$1$$ $$e\left(\frac{19}{39}\right)$$ $$e\left(\frac{38}{39}\right)$$ $$e\left(\frac{5}{13}\right)$$ $$e\left(\frac{6}{13}\right)$$ $$e\left(\frac{34}{39}\right)$$ $$e\left(\frac{7}{39}\right)$$ $$e\left(\frac{37}{39}\right)$$ $$e\left(\frac{5}{39}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{14}{39}\right)$$
 value at e.g. 2