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Properties

Label 4032.fb
Modulus 40324032
Conductor 448448
Order 1616
Real no
Primitive no
Minimal yes
Parity even

Related objects

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Show commands: PariGP / SageMath
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(4032, base_ring=CyclotomicField(16))
 
M = H._module
 
chi = DirichletCharacter(H, M([8,15,0,8]))
 
chi.galois_orbit()
 
[g,chi] = znchar(Mod(307,4032))
 
order = charorder(g,chi)
 
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: 40324032
Conductor: 448448
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: 1616
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from 448.bd
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Related number fields

Field of values: Q(ζ16)\Q(\zeta_{16})
Fixed field: 16.16.3484608386920116940487669055488.4

Characters in Galois orbit

Character −1-1 11 55 1111 1313 1717 1919 2323 2525 2929 3131 3737
χ4032(307,⋅)\chi_{4032}(307,\cdot) 11 11 e(716)e\left(\frac{7}{16}\right) e(316)e\left(\frac{3}{16}\right) e(916)e\left(\frac{9}{16}\right) −i-i e(916)e\left(\frac{9}{16}\right) e(58)e\left(\frac{5}{8}\right) e(78)e\left(\frac{7}{8}\right) e(516)e\left(\frac{5}{16}\right) −1-1 e(716)e\left(\frac{7}{16}\right)
χ4032(811,⋅)\chi_{4032}(811,\cdot) 11 11 e(516)e\left(\frac{5}{16}\right) e(916)e\left(\frac{9}{16}\right) e(1116)e\left(\frac{11}{16}\right) ii e(1116)e\left(\frac{11}{16}\right) e(78)e\left(\frac{7}{8}\right) e(58)e\left(\frac{5}{8}\right) e(1516)e\left(\frac{15}{16}\right) −1-1 e(516)e\left(\frac{5}{16}\right)
χ4032(1315,⋅)\chi_{4032}(1315,\cdot) 11 11 e(316)e\left(\frac{3}{16}\right) e(1516)e\left(\frac{15}{16}\right) e(1316)e\left(\frac{13}{16}\right) −i-i e(1316)e\left(\frac{13}{16}\right) e(18)e\left(\frac{1}{8}\right) e(38)e\left(\frac{3}{8}\right) e(916)e\left(\frac{9}{16}\right) −1-1 e(316)e\left(\frac{3}{16}\right)
χ4032(1819,⋅)\chi_{4032}(1819,\cdot) 11 11 e(116)e\left(\frac{1}{16}\right) e(516)e\left(\frac{5}{16}\right) e(1516)e\left(\frac{15}{16}\right) ii e(1516)e\left(\frac{15}{16}\right) e(38)e\left(\frac{3}{8}\right) e(18)e\left(\frac{1}{8}\right) e(316)e\left(\frac{3}{16}\right) −1-1 e(116)e\left(\frac{1}{16}\right)
χ4032(2323,⋅)\chi_{4032}(2323,\cdot) 11 11 e(1516)e\left(\frac{15}{16}\right) e(1116)e\left(\frac{11}{16}\right) e(116)e\left(\frac{1}{16}\right) −i-i e(116)e\left(\frac{1}{16}\right) e(58)e\left(\frac{5}{8}\right) e(78)e\left(\frac{7}{8}\right) e(1316)e\left(\frac{13}{16}\right) −1-1 e(1516)e\left(\frac{15}{16}\right)
χ4032(2827,⋅)\chi_{4032}(2827,\cdot) 11 11 e(1316)e\left(\frac{13}{16}\right) e(116)e\left(\frac{1}{16}\right) e(316)e\left(\frac{3}{16}\right) ii e(316)e\left(\frac{3}{16}\right) e(78)e\left(\frac{7}{8}\right) e(58)e\left(\frac{5}{8}\right) e(716)e\left(\frac{7}{16}\right) −1-1 e(1316)e\left(\frac{13}{16}\right)
χ4032(3331,⋅)\chi_{4032}(3331,\cdot) 11 11 e(1116)e\left(\frac{11}{16}\right) e(716)e\left(\frac{7}{16}\right) e(516)e\left(\frac{5}{16}\right) −i-i e(516)e\left(\frac{5}{16}\right) e(18)e\left(\frac{1}{8}\right) e(38)e\left(\frac{3}{8}\right) e(116)e\left(\frac{1}{16}\right) −1-1 e(1116)e\left(\frac{11}{16}\right)
χ4032(3835,⋅)\chi_{4032}(3835,\cdot) 11 11 e(916)e\left(\frac{9}{16}\right) e(1316)e\left(\frac{13}{16}\right) e(716)e\left(\frac{7}{16}\right) ii e(716)e\left(\frac{7}{16}\right) e(38)e\left(\frac{3}{8}\right) e(18)e\left(\frac{1}{8}\right) e(1116)e\left(\frac{11}{16}\right) −1-1 e(916)e\left(\frac{9}{16}\right)