Properties

 Label 2850.83 Modulus $2850$ Conductor $1425$ Order $60$ 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(2850, base_ring=CyclotomicField(60))

sage: M = H._module

sage: chi = DirichletCharacter(H, M([30,9,20]))

pari: [g,chi] = znchar(Mod(83,2850))

Basic properties

 Modulus: $$2850$$ Conductor: $$1425$$ sage: chi.conductor()  pari: znconreyconductor(g,chi) Order: $$60$$ sage: chi.multiplicative_order()  pari: charorder(g,chi) Real: no Primitive: no, induced from $$\chi_{1425}(83,\cdot)$$ sage: chi.is_primitive()  pari: #znconreyconductor(g,chi)==1 Minimal: yes Parity: even sage: chi.is_odd()  pari: zncharisodd(g,chi)

Galois orbit 2850.ci

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: $$\Q(\zeta_{60})$$ Fixed field: Number field defined by a degree 60 polynomial

Values on generators

$$(1901,1027,1351)$$ → $$(-1,e\left(\frac{3}{20}\right),e\left(\frac{1}{3}\right))$$

Values

 $$-1$$ $$1$$ $$7$$ $$11$$ $$13$$ $$17$$ $$23$$ $$29$$ $$31$$ $$37$$ $$41$$ $$43$$ $$1$$ $$1$$ $$-i$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{31}{60}\right)$$ $$e\left(\frac{47}{60}\right)$$ $$e\left(\frac{49}{60}\right)$$ $$e\left(\frac{7}{15}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{13}{30}\right)$$ $$e\left(\frac{7}{12}\right)$$
 value at e.g. 2