Properties

 Label 4830.149 Modulus $4830$ Conductor $2415$ Order $66$ Real no Primitive no Minimal yes Parity even

Related objects

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

sage: H = DirichletGroup(4830, base_ring=CyclotomicField(66))

sage: M = H._module

sage: chi = DirichletCharacter(H, M([33,33,22,27]))

pari: [g,chi] = znchar(Mod(149,4830))

Basic properties

 Modulus: $$4830$$ Conductor: $$2415$$ sage: chi.conductor()  pari: znconreyconductor(g,chi) Order: $$66$$ sage: chi.multiplicative_order()  pari: charorder(g,chi) Real: no Primitive: no, induced from $$\chi_{2415}(149,\cdot)$$ sage: chi.is_primitive()  pari: #znconreyconductor(g,chi)==1 Minimal: yes Parity: even sage: chi.is_odd()  pari: zncharisodd(g,chi)

Galois orbit 4830.dh

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: $$\Q(\zeta_{33})$$ Fixed field: Number field defined by a degree 66 polynomial

Values on generators

$$(3221,967,2761,1891)$$ → $$(-1,-1,e\left(\frac{1}{3}\right),e\left(\frac{9}{22}\right))$$

Values

 $$-1$$ $$1$$ $$11$$ $$13$$ $$17$$ $$19$$ $$29$$ $$31$$ $$37$$ $$41$$ $$43$$ $$47$$ $$1$$ $$1$$ $$e\left(\frac{17}{33}\right)$$ $$e\left(\frac{5}{22}\right)$$ $$e\left(\frac{13}{66}\right)$$ $$e\left(\frac{53}{66}\right)$$ $$e\left(\frac{19}{22}\right)$$ $$e\left(\frac{26}{33}\right)$$ $$e\left(\frac{25}{33}\right)$$ $$e\left(\frac{9}{22}\right)$$ $$e\left(\frac{6}{11}\right)$$ $$e\left(\frac{2}{3}\right)$$
sage: chi.jacobi_sum(n)

$$\chi_{ 4830 }(149,a) \;$$ at $$\;a =$$ e.g. 2