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Properties

Label 45120.ep
Modulus 4512045120
Conductor 1504015040
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(45120, base_ring=CyclotomicField(16))
 
M = H._module
 
chi = DirichletCharacter(H, M([0,3,0,4,8]))
 
chi.galois_orbit()
 
[g,chi] = znchar(Mod(1597,45120))
 
order = charorder(g,chi)
 
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: 4512045120
Conductor: 1504015040
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: 1616
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from 15040.ch
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: Number field defined by a degree 16 polynomial

Characters in Galois orbit

Character −1-1 11 77 1111 1313 1717 1919 2323 2929 3131 3737 4141
χ45120(1597,⋅)\chi_{45120}(1597,\cdot) 11 11 e(18)e\left(\frac{1}{8}\right) e(716)e\left(\frac{7}{16}\right) e(116)e\left(\frac{1}{16}\right) −1-1 e(516)e\left(\frac{5}{16}\right) e(78)e\left(\frac{7}{8}\right) e(116)e\left(\frac{1}{16}\right) 11 e(1516)e\left(\frac{15}{16}\right) e(18)e\left(\frac{1}{8}\right)
χ45120(9493,⋅)\chi_{45120}(9493,\cdot) 11 11 e(78)e\left(\frac{7}{8}\right) e(916)e\left(\frac{9}{16}\right) e(1516)e\left(\frac{15}{16}\right) −1-1 e(1116)e\left(\frac{11}{16}\right) e(18)e\left(\frac{1}{8}\right) e(1516)e\left(\frac{15}{16}\right) 11 e(116)e\left(\frac{1}{16}\right) e(78)e\left(\frac{7}{8}\right)
χ45120(12877,⋅)\chi_{45120}(12877,\cdot) 11 11 e(58)e\left(\frac{5}{8}\right) e(316)e\left(\frac{3}{16}\right) e(516)e\left(\frac{5}{16}\right) −1-1 e(916)e\left(\frac{9}{16}\right) e(38)e\left(\frac{3}{8}\right) e(516)e\left(\frac{5}{16}\right) 11 e(1116)e\left(\frac{11}{16}\right) e(58)e\left(\frac{5}{8}\right)
χ45120(20773,⋅)\chi_{45120}(20773,\cdot) 11 11 e(38)e\left(\frac{3}{8}\right) e(516)e\left(\frac{5}{16}\right) e(316)e\left(\frac{3}{16}\right) −1-1 e(1516)e\left(\frac{15}{16}\right) e(58)e\left(\frac{5}{8}\right) e(316)e\left(\frac{3}{16}\right) 11 e(1316)e\left(\frac{13}{16}\right) e(38)e\left(\frac{3}{8}\right)
χ45120(24157,⋅)\chi_{45120}(24157,\cdot) 11 11 e(18)e\left(\frac{1}{8}\right) e(1516)e\left(\frac{15}{16}\right) e(916)e\left(\frac{9}{16}\right) −1-1 e(1316)e\left(\frac{13}{16}\right) e(78)e\left(\frac{7}{8}\right) e(916)e\left(\frac{9}{16}\right) 11 e(716)e\left(\frac{7}{16}\right) e(18)e\left(\frac{1}{8}\right)
χ45120(32053,⋅)\chi_{45120}(32053,\cdot) 11 11 e(78)e\left(\frac{7}{8}\right) e(116)e\left(\frac{1}{16}\right) e(716)e\left(\frac{7}{16}\right) −1-1 e(316)e\left(\frac{3}{16}\right) e(18)e\left(\frac{1}{8}\right) e(716)e\left(\frac{7}{16}\right) 11 e(916)e\left(\frac{9}{16}\right) e(78)e\left(\frac{7}{8}\right)
χ45120(35437,⋅)\chi_{45120}(35437,\cdot) 11 11 e(58)e\left(\frac{5}{8}\right) e(1116)e\left(\frac{11}{16}\right) e(1316)e\left(\frac{13}{16}\right) −1-1 e(116)e\left(\frac{1}{16}\right) e(38)e\left(\frac{3}{8}\right) e(1316)e\left(\frac{13}{16}\right) 11 e(316)e\left(\frac{3}{16}\right) e(58)e\left(\frac{5}{8}\right)
χ45120(43333,⋅)\chi_{45120}(43333,\cdot) 11 11 e(38)e\left(\frac{3}{8}\right) e(1316)e\left(\frac{13}{16}\right) e(1116)e\left(\frac{11}{16}\right) −1-1 e(716)e\left(\frac{7}{16}\right) e(58)e\left(\frac{5}{8}\right) e(1116)e\left(\frac{11}{16}\right) 11 e(516)e\left(\frac{5}{16}\right) e(38)e\left(\frac{3}{8}\right)