Properties

 Label 1104.797 Modulus $1104$ Conductor $1104$ Order $44$ Real no Primitive yes Minimal yes Parity even

Related objects

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

sage: H = DirichletGroup(1104, base_ring=CyclotomicField(44))

sage: M = H._module

sage: chi = DirichletCharacter(H, M([0,33,22,34]))

pari: [g,chi] = znchar(Mod(797,1104))

Basic properties

 Modulus: $$1104$$ Conductor: $$1104$$ sage: chi.conductor()  pari: znconreyconductor(g,chi) Order: $$44$$ sage: chi.multiplicative_order()  pari: charorder(g,chi) Real: no Primitive: yes sage: chi.is_primitive()  pari: #znconreyconductor(g,chi)==1 Minimal: yes Parity: even sage: chi.is_odd()  pari: zncharisodd(g,chi)

Galois orbit 1104.bo

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

$$(415,277,737,97)$$ → $$(1,-i,-1,e\left(\frac{17}{22}\right))$$

Values

 $$-1$$ $$1$$ $$5$$ $$7$$ $$11$$ $$13$$ $$17$$ $$19$$ $$25$$ $$29$$ $$31$$ $$35$$ $$1$$ $$1$$ $$e\left(\frac{1}{44}\right)$$ $$e\left(\frac{2}{11}\right)$$ $$e\left(\frac{9}{44}\right)$$ $$e\left(\frac{3}{44}\right)$$ $$e\left(\frac{10}{11}\right)$$ $$e\left(\frac{37}{44}\right)$$ $$e\left(\frac{1}{22}\right)$$ $$e\left(\frac{29}{44}\right)$$ $$e\left(\frac{7}{11}\right)$$ $$e\left(\frac{9}{44}\right)$$
sage: chi.jacobi_sum(n)

$$\chi_{ 1104 }(797,a) \;$$ at $$\;a =$$ e.g. 2