Properties

 Label 5520.1451 Modulus $5520$ Conductor $1104$ Order $44$ Real no Primitive no Minimal yes Parity even

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

sage: H = DirichletGroup(5520, base_ring=CyclotomicField(44))

sage: M = H._module

sage: chi = DirichletCharacter(H, M([22,11,22,0,4]))

pari: [g,chi] = znchar(Mod(1451,5520))

Basic properties

 Modulus: $$5520$$ Conductor: $$1104$$ sage: chi.conductor()  pari: znconreyconductor(g,chi) Order: $$44$$ sage: chi.multiplicative_order()  pari: charorder(g,chi) Real: no Primitive: no, induced from $$\chi_{1104}(347,\cdot)$$ sage: chi.is_primitive()  pari: #znconreyconductor(g,chi)==1 Minimal: yes Parity: even sage: chi.is_odd()  pari: zncharisodd(g,chi)

Galois orbit 5520.ep

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: $$\Q(\zeta_{44})$$ Fixed field: Number field defined by a degree 44 polynomial

Values on generators

$$(4831,1381,1841,4417,1201)$$ → $$(-1,i,-1,1,e\left(\frac{1}{11}\right))$$

Values

 $$-1$$ $$1$$ $$7$$ $$11$$ $$13$$ $$17$$ $$19$$ $$29$$ $$31$$ $$37$$ $$41$$ $$43$$ $$1$$ $$1$$ $$e\left(\frac{8}{11}\right)$$ $$e\left(\frac{3}{44}\right)$$ $$e\left(\frac{1}{44}\right)$$ $$e\left(\frac{3}{22}\right)$$ $$e\left(\frac{27}{44}\right)$$ $$e\left(\frac{39}{44}\right)$$ $$e\left(\frac{1}{22}\right)$$ $$e\left(\frac{7}{44}\right)$$ $$e\left(\frac{1}{11}\right)$$ $$e\left(\frac{9}{44}\right)$$
 value at e.g. 2