Properties

 Label 1380.1037 Modulus $1380$ Conductor $345$ Order $44$ 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(1380, base_ring=CyclotomicField(44))

sage: M = H._module

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

pari: [g,chi] = znchar(Mod(1037,1380))

Basic properties

 Modulus: $$1380$$ Conductor: $$345$$ sage: chi.conductor()  pari: znconreyconductor(g,chi) Order: $$44$$ sage: chi.multiplicative_order()  pari: charorder(g,chi) Real: no Primitive: no, induced from $$\chi_{345}(2,\cdot)$$ sage: chi.is_primitive()  pari: #znconreyconductor(g,chi)==1 Minimal: yes Parity: even sage: chi.is_odd()  pari: zncharisodd(g,chi)

Galois orbit 1380.bu

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

$$(691,461,277,1201)$$ → $$(1,-1,i,e\left(\frac{1}{11}\right))$$

Values

 $$-1$$ $$1$$ $$7$$ $$11$$ $$13$$ $$17$$ $$19$$ $$29$$ $$31$$ $$37$$ $$41$$ $$43$$ $$1$$ $$1$$ $$e\left(\frac{43}{44}\right)$$ $$e\left(\frac{7}{22}\right)$$ $$e\left(\frac{1}{44}\right)$$ $$e\left(\frac{17}{44}\right)$$ $$e\left(\frac{19}{22}\right)$$ $$e\left(\frac{7}{11}\right)$$ $$e\left(\frac{6}{11}\right)$$ $$e\left(\frac{7}{44}\right)$$ $$e\left(\frac{13}{22}\right)$$ $$e\left(\frac{9}{44}\right)$$
sage: chi.jacobi_sum(n)

$$\chi_{ 1380 }(1037,a) \;$$ at $$\;a =$$ e.g. 2