Properties

 Label 1152.19 Modulus $1152$ Conductor $128$ Order $32$ Real no Primitive no Minimal yes Parity odd

Related objects

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

sage: H = DirichletGroup(1152, base_ring=CyclotomicField(32))

sage: M = H._module

sage: chi = DirichletCharacter(H, M([16,23,0]))

pari: [g,chi] = znchar(Mod(19,1152))

Basic properties

 Modulus: $$1152$$ Conductor: $$128$$ sage: chi.conductor()  pari: znconreyconductor(g,chi) Order: $$32$$ sage: chi.multiplicative_order()  pari: charorder(g,chi) Real: no Primitive: no, induced from $$\chi_{128}(19,\cdot)$$ sage: chi.is_primitive()  pari: #znconreyconductor(g,chi)==1 Minimal: yes Parity: odd sage: chi.is_odd()  pari: zncharisodd(g,chi)

Galois orbit 1152.bk

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: $$\Q(\zeta_{32})$$ Fixed field: 32.0.3138550867693340381917894711603833208051177722232017256448.1

Values on generators

$$(127,901,641)$$ → $$(-1,e\left(\frac{23}{32}\right),1)$$

Values

 $$-1$$ $$1$$ $$5$$ $$7$$ $$11$$ $$13$$ $$17$$ $$19$$ $$23$$ $$25$$ $$29$$ $$31$$ $$-1$$ $$1$$ $$e\left(\frac{23}{32}\right)$$ $$e\left(\frac{11}{16}\right)$$ $$e\left(\frac{19}{32}\right)$$ $$e\left(\frac{25}{32}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{1}{32}\right)$$ $$e\left(\frac{9}{16}\right)$$ $$e\left(\frac{7}{16}\right)$$ $$e\left(\frac{13}{32}\right)$$ $$i$$
 value at e.g. 2