↑

Properties

Label 4160.hv
Modulus 41604160
Conductor 41604160
Order 1616
Real no
Primitive yes
Minimal yes
Parity even

Related objects

Downloads

Learn more

Show commands: PariGP / SageMath
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(4160, base_ring=CyclotomicField(16))
 
M = H._module
 
chi = DirichletCharacter(H, M([0,3,4,12]))
 
chi.galois_orbit()
 
[g,chi] = znchar(Mod(317,4160))
 
order = charorder(g,chi)
 
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: 41604160
Conductor: 41604160
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: 1616
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)
 

Related number fields

Field of values: Q(ζ16)\Q(\zeta_{16})
Fixed field: 16.16.3438190509295256478027799611834368000000000000.4

Characters in Galois orbit

Character −1-1 11 33 77 99 1111 1717 1919 2121 2323 2727 2929
χ4160(317,⋅)\chi_{4160}(317,\cdot) 11 11 e(516)e\left(\frac{5}{16}\right) e(38)e\left(\frac{3}{8}\right) e(58)e\left(\frac{5}{8}\right) e(316)e\left(\frac{3}{16}\right) 11 e(916)e\left(\frac{9}{16}\right) e(1116)e\left(\frac{11}{16}\right) e(78)e\left(\frac{7}{8}\right) e(1516)e\left(\frac{15}{16}\right) e(916)e\left(\frac{9}{16}\right)
χ4160(853,⋅)\chi_{4160}(853,\cdot) 11 11 e(1116)e\left(\frac{11}{16}\right) e(58)e\left(\frac{5}{8}\right) e(38)e\left(\frac{3}{8}\right) e(1316)e\left(\frac{13}{16}\right) 11 e(716)e\left(\frac{7}{16}\right) e(516)e\left(\frac{5}{16}\right) e(18)e\left(\frac{1}{8}\right) e(116)e\left(\frac{1}{16}\right) e(716)e\left(\frac{7}{16}\right)
χ4160(1357,⋅)\chi_{4160}(1357,\cdot) 11 11 e(916)e\left(\frac{9}{16}\right) e(78)e\left(\frac{7}{8}\right) e(18)e\left(\frac{1}{8}\right) e(1516)e\left(\frac{15}{16}\right) 11 e(1316)e\left(\frac{13}{16}\right) e(716)e\left(\frac{7}{16}\right) e(38)e\left(\frac{3}{8}\right) e(1116)e\left(\frac{11}{16}\right) e(1316)e\left(\frac{13}{16}\right)
χ4160(1893,⋅)\chi_{4160}(1893,\cdot) 11 11 e(1516)e\left(\frac{15}{16}\right) e(18)e\left(\frac{1}{8}\right) e(78)e\left(\frac{7}{8}\right) e(916)e\left(\frac{9}{16}\right) 11 e(1116)e\left(\frac{11}{16}\right) e(116)e\left(\frac{1}{16}\right) e(58)e\left(\frac{5}{8}\right) e(1316)e\left(\frac{13}{16}\right) e(1116)e\left(\frac{11}{16}\right)
χ4160(2397,⋅)\chi_{4160}(2397,\cdot) 11 11 e(1316)e\left(\frac{13}{16}\right) e(38)e\left(\frac{3}{8}\right) e(58)e\left(\frac{5}{8}\right) e(1116)e\left(\frac{11}{16}\right) 11 e(116)e\left(\frac{1}{16}\right) e(316)e\left(\frac{3}{16}\right) e(78)e\left(\frac{7}{8}\right) e(716)e\left(\frac{7}{16}\right) e(116)e\left(\frac{1}{16}\right)
χ4160(2933,⋅)\chi_{4160}(2933,\cdot) 11 11 e(316)e\left(\frac{3}{16}\right) e(58)e\left(\frac{5}{8}\right) e(38)e\left(\frac{3}{8}\right) e(516)e\left(\frac{5}{16}\right) 11 e(1516)e\left(\frac{15}{16}\right) e(1316)e\left(\frac{13}{16}\right) e(18)e\left(\frac{1}{8}\right) e(916)e\left(\frac{9}{16}\right) e(1516)e\left(\frac{15}{16}\right)
χ4160(3437,⋅)\chi_{4160}(3437,\cdot) 11 11 e(116)e\left(\frac{1}{16}\right) e(78)e\left(\frac{7}{8}\right) e(18)e\left(\frac{1}{8}\right) e(716)e\left(\frac{7}{16}\right) 11 e(516)e\left(\frac{5}{16}\right) e(1516)e\left(\frac{15}{16}\right) e(38)e\left(\frac{3}{8}\right) e(316)e\left(\frac{3}{16}\right) e(516)e\left(\frac{5}{16}\right)
χ4160(3973,⋅)\chi_{4160}(3973,\cdot) 11 11 e(716)e\left(\frac{7}{16}\right) e(18)e\left(\frac{1}{8}\right) e(78)e\left(\frac{7}{8}\right) e(116)e\left(\frac{1}{16}\right) 11 e(316)e\left(\frac{3}{16}\right) e(916)e\left(\frac{9}{16}\right) e(58)e\left(\frac{5}{8}\right) e(516)e\left(\frac{5}{16}\right) e(316)e\left(\frac{3}{16}\right)