Properties

 Label 6025.781 Modulus $6025$ Conductor $6025$ Order $30$ Real no Primitive yes Minimal yes Parity even

Related objects

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

sage: H = DirichletGroup(6025)

sage: M = H._module

sage: chi = DirichletCharacter(H, M([12,13]))

pari: [g,chi] = znchar(Mod(781,6025))

Basic properties

 Modulus: $$6025$$ Conductor: $$6025$$ sage: chi.conductor()  pari: znconreyconductor(g,chi) Order: $$30$$ sage: chi.multiplicative_order()  pari: charorder(g,chi) Real: no Primitive: yes sage: chi.is_primitive()  pari: #znconreyconductor(g,chi)==1 Minimal: yes Parity: even sage: chi.is_odd()  pari: zncharisodd(g,chi)

Galois orbit 6025.ef

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

$$(2652,2176)$$ → $$(e\left(\frac{2}{5}\right),e\left(\frac{13}{30}\right))$$

Values

 $$-1$$ $$1$$ $$2$$ $$3$$ $$4$$ $$6$$ $$7$$ $$8$$ $$9$$ $$11$$ $$12$$ $$13$$ $$1$$ $$1$$ $$e\left(\frac{11}{15}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{7}{15}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{13}{30}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{7}{30}\right)$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{29}{30}\right)$$
 value at e.g. 2

Related number fields

 Field of values: $$\Q(\zeta_{15})$$ Fixed field: Number field defined by a degree 30 polynomial