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Properties

Label 4675.de
Modulus 46754675
Conductor 8585
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(4675, base_ring=CyclotomicField(16))
 
M = H._module
 
chi = DirichletCharacter(H, M([4,0,9]))
 
chi.galois_orbit()
 
[g,chi] = znchar(Mod(507,4675))
 
order = charorder(g,chi)
 
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: 46754675
Conductor: 8585
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: 1616
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from 85.r
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: 16.16.698833752810013621337890625.1

Characters in Galois orbit

Character −1-1 11 22 33 44 66 77 88 99 1212 1313 1414
χ4675(507,⋅)\chi_{4675}(507,\cdot) 11 11 e(18)e\left(\frac{1}{8}\right) e(516)e\left(\frac{5}{16}\right) ii e(716)e\left(\frac{7}{16}\right) e(716)e\left(\frac{7}{16}\right) e(38)e\left(\frac{3}{8}\right) e(58)e\left(\frac{5}{8}\right) e(916)e\left(\frac{9}{16}\right) 11 e(916)e\left(\frac{9}{16}\right)
χ4675(793,⋅)\chi_{4675}(793,\cdot) 11 11 e(78)e\left(\frac{7}{8}\right) e(1116)e\left(\frac{11}{16}\right) −i-i e(916)e\left(\frac{9}{16}\right) e(916)e\left(\frac{9}{16}\right) e(58)e\left(\frac{5}{8}\right) e(38)e\left(\frac{3}{8}\right) e(716)e\left(\frac{7}{16}\right) 11 e(716)e\left(\frac{7}{16}\right)
χ4675(1057,⋅)\chi_{4675}(1057,\cdot) 11 11 e(18)e\left(\frac{1}{8}\right) e(1316)e\left(\frac{13}{16}\right) ii e(1516)e\left(\frac{15}{16}\right) e(1516)e\left(\frac{15}{16}\right) e(38)e\left(\frac{3}{8}\right) e(58)e\left(\frac{5}{8}\right) e(116)e\left(\frac{1}{16}\right) 11 e(116)e\left(\frac{1}{16}\right)
χ4675(1882,⋅)\chi_{4675}(1882,\cdot) 11 11 e(58)e\left(\frac{5}{8}\right) e(916)e\left(\frac{9}{16}\right) ii e(316)e\left(\frac{3}{16}\right) e(316)e\left(\frac{3}{16}\right) e(78)e\left(\frac{7}{8}\right) e(18)e\left(\frac{1}{8}\right) e(1316)e\left(\frac{13}{16}\right) 11 e(1316)e\left(\frac{13}{16}\right)
χ4675(1893,⋅)\chi_{4675}(1893,\cdot) 11 11 e(78)e\left(\frac{7}{8}\right) e(316)e\left(\frac{3}{16}\right) −i-i e(116)e\left(\frac{1}{16}\right) e(116)e\left(\frac{1}{16}\right) e(58)e\left(\frac{5}{8}\right) e(38)e\left(\frac{3}{8}\right) e(1516)e\left(\frac{15}{16}\right) 11 e(1516)e\left(\frac{15}{16}\right)
χ4675(3543,⋅)\chi_{4675}(3543,\cdot) 11 11 e(38)e\left(\frac{3}{8}\right) e(1516)e\left(\frac{15}{16}\right) −i-i e(516)e\left(\frac{5}{16}\right) e(516)e\left(\frac{5}{16}\right) e(18)e\left(\frac{1}{8}\right) e(78)e\left(\frac{7}{8}\right) e(1116)e\left(\frac{11}{16}\right) 11 e(1116)e\left(\frac{11}{16}\right)
χ4675(3818,⋅)\chi_{4675}(3818,\cdot) 11 11 e(38)e\left(\frac{3}{8}\right) e(716)e\left(\frac{7}{16}\right) −i-i e(1316)e\left(\frac{13}{16}\right) e(1316)e\left(\frac{13}{16}\right) e(18)e\left(\frac{1}{8}\right) e(78)e\left(\frac{7}{8}\right) e(316)e\left(\frac{3}{16}\right) 11 e(316)e\left(\frac{3}{16}\right)
χ4675(4357,⋅)\chi_{4675}(4357,\cdot) 11 11 e(58)e\left(\frac{5}{8}\right) e(116)e\left(\frac{1}{16}\right) ii e(1116)e\left(\frac{11}{16}\right) e(1116)e\left(\frac{11}{16}\right) e(78)e\left(\frac{7}{8}\right) e(18)e\left(\frac{1}{8}\right) e(516)e\left(\frac{5}{16}\right) 11 e(516)e\left(\frac{5}{16}\right)