Properties

 Label 8034.253 Modulus $8034$ Conductor $1339$ Order $12$ 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(8034)

sage: M = H._module

sage: chi = DirichletCharacter(H, M([0,5,10]))

pari: [g,chi] = znchar(Mod(253,8034))

Basic properties

 Modulus: $$8034$$ Conductor: $$1339$$ sage: chi.conductor()  pari: znconreyconductor(g,chi) Order: $$12$$ sage: chi.multiplicative_order()  pari: charorder(g,chi) Real: no Primitive: no, induced from $$\chi_{1339}(253,\cdot)$$ sage: chi.is_primitive()  pari: #znconreyconductor(g,chi)==1 Minimal: yes Parity: even sage: chi.is_odd()  pari: zncharisodd(g,chi)

Galois orbit 8034.ce

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

$$(5357,1237,5773)$$ → $$(1,e\left(\frac{5}{12}\right),e\left(\frac{5}{6}\right))$$

Values

 $$-1$$ $$1$$ $$5$$ $$7$$ $$11$$ $$17$$ $$19$$ $$23$$ $$25$$ $$29$$ $$31$$ $$35$$ $$1$$ $$1$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$-i$$ $$e\left(\frac{1}{6}\right)$$ $$-i$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$i$$ $$-1$$
 value at e.g. 2

Related number fields

 Field of values: $$\Q(\zeta_{12})$$ Fixed field: Number field defined by a degree 12 polynomial