Properties

 Label 2520.37 Modulus $2520$ Conductor $280$ Order $12$ Real no Primitive no Minimal yes Parity odd

Related objects

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

sage: H = DirichletGroup(2520, base_ring=CyclotomicField(12))

sage: M = H._module

sage: chi = DirichletCharacter(H, M([0,6,0,3,4]))

pari: [g,chi] = znchar(Mod(37,2520))

Basic properties

 Modulus: $$2520$$ Conductor: $$280$$ sage: chi.conductor()  pari: znconreyconductor(g,chi) Order: $$12$$ sage: chi.multiplicative_order()  pari: charorder(g,chi) Real: no Primitive: no, induced from $$\chi_{280}(37,\cdot)$$ sage: chi.is_primitive()  pari: #znconreyconductor(g,chi)==1 Minimal: yes Parity: odd sage: chi.is_odd()  pari: zncharisodd(g,chi)

Galois orbit 2520.ik

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: $$\Q(\zeta_{12})$$ Fixed field: 12.0.2951578112000000000.1

Values on generators

$$(631,1261,281,2017,1081)$$ → $$(1,-1,1,i,e\left(\frac{1}{3}\right))$$

Values

 $$-1$$ $$1$$ $$11$$ $$13$$ $$17$$ $$19$$ $$23$$ $$29$$ $$31$$ $$37$$ $$41$$ $$43$$ $$-1$$ $$1$$ $$e\left(\frac{5}{6}\right)$$ $$i$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$1$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$1$$ $$i$$
sage: chi.jacobi_sum(n)

$$\chi_{ 2520 }(37,a) \;$$ at $$\;a =$$ e.g. 2