↑

Properties

Label 7225.s
Modulus 72257225
Conductor 8585
Order 1616
Real no
Primitive no
Minimal yes
Parity even

Related objects

Downloads

Learn more

Show commands: PariGP / SageMath
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(7225, base_ring=CyclotomicField(16))
 
M = H._module
 
chi = DirichletCharacter(H, M([12,9]))
 
chi.galois_orbit()
 
[g,chi] = znchar(Mod(643,7225))
 
order = charorder(g,chi)
 
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: 72257225
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.o
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: 16.16.698833752810013621337890625.2

Characters in Galois orbit

Character −1-1 11 22 33 44 66 77 88 99 1111 1212 1313
χ7225(643,⋅)\chi_{7225}(643,\cdot) 11 11 e(58)e\left(\frac{5}{8}\right) e(1316)e\left(\frac{13}{16}\right) ii e(716)e\left(\frac{7}{16}\right) e(1516)e\left(\frac{15}{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) e(116)e\left(\frac{1}{16}\right) −1-1
χ7225(907,⋅)\chi_{7225}(907,\cdot) 11 11 e(38)e\left(\frac{3}{8}\right) e(1116)e\left(\frac{11}{16}\right) −i-i e(116)e\left(\frac{1}{16}\right) e(916)e\left(\frac{9}{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) e(716)e\left(\frac{7}{16}\right) −1-1
χ7225(2443,⋅)\chi_{7225}(2443,\cdot) 11 11 e(18)e\left(\frac{1}{8}\right) e(116)e\left(\frac{1}{16}\right) ii e(316)e\left(\frac{3}{16}\right) e(1116)e\left(\frac{11}{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) e(516)e\left(\frac{5}{16}\right) −1-1
χ7225(3682,⋅)\chi_{7225}(3682,\cdot) 11 11 e(78)e\left(\frac{7}{8}\right) e(1516)e\left(\frac{15}{16}\right) −i-i e(1316)e\left(\frac{13}{16}\right) e(516)e\left(\frac{5}{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) e(1116)e\left(\frac{11}{16}\right) −1-1
χ7225(3832,⋅)\chi_{7225}(3832,\cdot) 11 11 e(78)e\left(\frac{7}{8}\right) e(716)e\left(\frac{7}{16}\right) −i-i e(516)e\left(\frac{5}{16}\right) e(1316)e\left(\frac{13}{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) e(316)e\left(\frac{3}{16}\right) −1-1
χ7225(4493,⋅)\chi_{7225}(4493,\cdot) 11 11 e(18)e\left(\frac{1}{8}\right) e(916)e\left(\frac{9}{16}\right) ii e(1116)e\left(\frac{11}{16}\right) e(316)e\left(\frac{3}{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) e(1316)e\left(\frac{13}{16}\right) −1-1
χ7225(6293,⋅)\chi_{7225}(6293,\cdot) 11 11 e(58)e\left(\frac{5}{8}\right) e(516)e\left(\frac{5}{16}\right) ii e(1516)e\left(\frac{15}{16}\right) e(716)e\left(\frac{7}{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) e(916)e\left(\frac{9}{16}\right) −1-1
χ7225(6607,⋅)\chi_{7225}(6607,\cdot) 11 11 e(38)e\left(\frac{3}{8}\right) e(316)e\left(\frac{3}{16}\right) −i-i e(916)e\left(\frac{9}{16}\right) e(116)e\left(\frac{1}{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) e(1516)e\left(\frac{15}{16}\right) −1-1