Properties

 Label 1225.43 Modulus $1225$ Conductor $245$ Order $28$ Real no Primitive no Minimal yes Parity odd

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

sage: H = DirichletGroup(1225)

sage: M = H._module

sage: chi = DirichletCharacter(H, M([21,4]))

pari: [g,chi] = znchar(Mod(43,1225))

Basic properties

 Modulus: $$1225$$ Conductor: $$245$$ sage: chi.conductor()  pari: znconreyconductor(g,chi) Order: $$28$$ sage: chi.multiplicative_order()  pari: charorder(g,chi) Real: no Primitive: no, induced from $$\chi_{245}(43,\cdot)$$ sage: chi.is_primitive()  pari: #znconreyconductor(g,chi)==1 Minimal: yes Parity: odd sage: chi.is_odd()  pari: zncharisodd(g,chi)

Galois orbit 1225.y

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

$$(1177,101)$$ → $$(-i,e\left(\frac{1}{7}\right))$$

Values

 $$-1$$ $$1$$ $$2$$ $$3$$ $$4$$ $$6$$ $$8$$ $$9$$ $$11$$ $$12$$ $$13$$ $$16$$ $$-1$$ $$1$$ $$e\left(\frac{13}{28}\right)$$ $$e\left(\frac{11}{28}\right)$$ $$e\left(\frac{13}{14}\right)$$ $$e\left(\frac{6}{7}\right)$$ $$e\left(\frac{11}{28}\right)$$ $$e\left(\frac{11}{14}\right)$$ $$e\left(\frac{5}{7}\right)$$ $$e\left(\frac{9}{28}\right)$$ $$e\left(\frac{27}{28}\right)$$ $$e\left(\frac{6}{7}\right)$$
 value at e.g. 2

Related number fields

 Field of values: $$\Q(\zeta_{28})$$ Fixed field: 28.0.17501529797217428894629579082505064100647449493408203125.1