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Properties

Label 4160.jp
Modulus 41604160
Conductor 41604160
Order 4848
Real no
Primitive yes
Minimal yes
Parity even

Related objects

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Show commands: PariGP / SageMath
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(4160, base_ring=CyclotomicField(48))
 
M = H._module
 
chi = DirichletCharacter(H, M([0,33,24,16]))
 
chi.galois_orbit()
 
[g,chi] = znchar(Mod(29,4160))
 
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: 4848
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(ζ48)\Q(\zeta_{48})
Fixed field: Number field defined by a degree 48 polynomial

Characters in Galois orbit

Character −1-1 11 33 77 99 1111 1717 1919 2121 2323 2727 2929
χ4160(29,⋅)\chi_{4160}(29,\cdot) 11 11 e(4348)e\left(\frac{43}{48}\right) e(124)e\left(\frac{1}{24}\right) e(1924)e\left(\frac{19}{24}\right) e(3748)e\left(\frac{37}{48}\right) e(512)e\left(\frac{5}{12}\right) e(2348)e\left(\frac{23}{48}\right) e(1516)e\left(\frac{15}{16}\right) e(1124)e\left(\frac{11}{24}\right) e(1116)e\left(\frac{11}{16}\right) e(4348)e\left(\frac{43}{48}\right)
χ4160(269,⋅)\chi_{4160}(269,\cdot) 11 11 e(4748)e\left(\frac{47}{48}\right) e(524)e\left(\frac{5}{24}\right) e(2324)e\left(\frac{23}{24}\right) e(1748)e\left(\frac{17}{48}\right) e(112)e\left(\frac{1}{12}\right) e(4348)e\left(\frac{43}{48}\right) e(316)e\left(\frac{3}{16}\right) e(724)e\left(\frac{7}{24}\right) e(1516)e\left(\frac{15}{16}\right) e(4748)e\left(\frac{47}{48}\right)
χ4160(549,⋅)\chi_{4160}(549,\cdot) 11 11 e(2548)e\left(\frac{25}{48}\right) e(1924)e\left(\frac{19}{24}\right) e(124)e\left(\frac{1}{24}\right) e(748)e\left(\frac{7}{48}\right) e(1112)e\left(\frac{11}{12}\right) e(2948)e\left(\frac{29}{48}\right) e(516)e\left(\frac{5}{16}\right) e(1724)e\left(\frac{17}{24}\right) e(916)e\left(\frac{9}{16}\right) e(2548)e\left(\frac{25}{48}\right)
χ4160(789,⋅)\chi_{4160}(789,\cdot) 11 11 e(2948)e\left(\frac{29}{48}\right) e(2324)e\left(\frac{23}{24}\right) e(524)e\left(\frac{5}{24}\right) e(3548)e\left(\frac{35}{48}\right) e(712)e\left(\frac{7}{12}\right) e(148)e\left(\frac{1}{48}\right) e(916)e\left(\frac{9}{16}\right) e(1324)e\left(\frac{13}{24}\right) e(1316)e\left(\frac{13}{16}\right) e(2948)e\left(\frac{29}{48}\right)
χ4160(1069,⋅)\chi_{4160}(1069,\cdot) 11 11 e(748)e\left(\frac{7}{48}\right) e(1324)e\left(\frac{13}{24}\right) e(724)e\left(\frac{7}{24}\right) e(2548)e\left(\frac{25}{48}\right) e(512)e\left(\frac{5}{12}\right) e(3548)e\left(\frac{35}{48}\right) e(1116)e\left(\frac{11}{16}\right) e(2324)e\left(\frac{23}{24}\right) e(716)e\left(\frac{7}{16}\right) e(748)e\left(\frac{7}{48}\right)
χ4160(1309,⋅)\chi_{4160}(1309,\cdot) 11 11 e(1148)e\left(\frac{11}{48}\right) e(1724)e\left(\frac{17}{24}\right) e(1124)e\left(\frac{11}{24}\right) e(548)e\left(\frac{5}{48}\right) e(112)e\left(\frac{1}{12}\right) e(748)e\left(\frac{7}{48}\right) e(1516)e\left(\frac{15}{16}\right) e(1924)e\left(\frac{19}{24}\right) e(1116)e\left(\frac{11}{16}\right) e(1148)e\left(\frac{11}{48}\right)
χ4160(1589,⋅)\chi_{4160}(1589,\cdot) 11 11 e(3748)e\left(\frac{37}{48}\right) e(724)e\left(\frac{7}{24}\right) e(1324)e\left(\frac{13}{24}\right) e(4348)e\left(\frac{43}{48}\right) e(1112)e\left(\frac{11}{12}\right) e(4148)e\left(\frac{41}{48}\right) e(116)e\left(\frac{1}{16}\right) e(524)e\left(\frac{5}{24}\right) e(516)e\left(\frac{5}{16}\right) e(3748)e\left(\frac{37}{48}\right)
χ4160(1829,⋅)\chi_{4160}(1829,\cdot) 11 11 e(4148)e\left(\frac{41}{48}\right) e(1124)e\left(\frac{11}{24}\right) e(1724)e\left(\frac{17}{24}\right) e(2348)e\left(\frac{23}{48}\right) e(712)e\left(\frac{7}{12}\right) e(1348)e\left(\frac{13}{48}\right) e(516)e\left(\frac{5}{16}\right) e(124)e\left(\frac{1}{24}\right) e(916)e\left(\frac{9}{16}\right) e(4148)e\left(\frac{41}{48}\right)
χ4160(2109,⋅)\chi_{4160}(2109,\cdot) 11 11 e(1948)e\left(\frac{19}{48}\right) e(124)e\left(\frac{1}{24}\right) e(1924)e\left(\frac{19}{24}\right) e(1348)e\left(\frac{13}{48}\right) e(512)e\left(\frac{5}{12}\right) e(4748)e\left(\frac{47}{48}\right) e(716)e\left(\frac{7}{16}\right) e(1124)e\left(\frac{11}{24}\right) e(316)e\left(\frac{3}{16}\right) e(1948)e\left(\frac{19}{48}\right)
χ4160(2349,⋅)\chi_{4160}(2349,\cdot) 11 11 e(2348)e\left(\frac{23}{48}\right) e(524)e\left(\frac{5}{24}\right) e(2324)e\left(\frac{23}{24}\right) e(4148)e\left(\frac{41}{48}\right) e(112)e\left(\frac{1}{12}\right) e(1948)e\left(\frac{19}{48}\right) e(1116)e\left(\frac{11}{16}\right) e(724)e\left(\frac{7}{24}\right) e(716)e\left(\frac{7}{16}\right) e(2348)e\left(\frac{23}{48}\right)
χ4160(2629,⋅)\chi_{4160}(2629,\cdot) 11 11 e(148)e\left(\frac{1}{48}\right) e(1924)e\left(\frac{19}{24}\right) e(124)e\left(\frac{1}{24}\right) e(3148)e\left(\frac{31}{48}\right) e(1112)e\left(\frac{11}{12}\right) e(548)e\left(\frac{5}{48}\right) e(1316)e\left(\frac{13}{16}\right) e(1724)e\left(\frac{17}{24}\right) e(116)e\left(\frac{1}{16}\right) e(148)e\left(\frac{1}{48}\right)
χ4160(2869,⋅)\chi_{4160}(2869,\cdot) 11 11 e(548)e\left(\frac{5}{48}\right) e(2324)e\left(\frac{23}{24}\right) e(524)e\left(\frac{5}{24}\right) e(1148)e\left(\frac{11}{48}\right) e(712)e\left(\frac{7}{12}\right) e(2548)e\left(\frac{25}{48}\right) e(116)e\left(\frac{1}{16}\right) e(1324)e\left(\frac{13}{24}\right) e(516)e\left(\frac{5}{16}\right) e(548)e\left(\frac{5}{48}\right)
χ4160(3149,⋅)\chi_{4160}(3149,\cdot) 11 11 e(3148)e\left(\frac{31}{48}\right) e(1324)e\left(\frac{13}{24}\right) e(724)e\left(\frac{7}{24}\right) e(148)e\left(\frac{1}{48}\right) e(512)e\left(\frac{5}{12}\right) e(1148)e\left(\frac{11}{48}\right) e(316)e\left(\frac{3}{16}\right) e(2324)e\left(\frac{23}{24}\right) e(1516)e\left(\frac{15}{16}\right) e(3148)e\left(\frac{31}{48}\right)
χ4160(3389,⋅)\chi_{4160}(3389,\cdot) 11 11 e(3548)e\left(\frac{35}{48}\right) e(1724)e\left(\frac{17}{24}\right) e(1124)e\left(\frac{11}{24}\right) e(2948)e\left(\frac{29}{48}\right) e(112)e\left(\frac{1}{12}\right) e(3148)e\left(\frac{31}{48}\right) e(716)e\left(\frac{7}{16}\right) e(1924)e\left(\frac{19}{24}\right) e(316)e\left(\frac{3}{16}\right) e(3548)e\left(\frac{35}{48}\right)
χ4160(3669,⋅)\chi_{4160}(3669,\cdot) 11 11 e(1348)e\left(\frac{13}{48}\right) e(724)e\left(\frac{7}{24}\right) e(1324)e\left(\frac{13}{24}\right) e(1948)e\left(\frac{19}{48}\right) e(1112)e\left(\frac{11}{12}\right) e(1748)e\left(\frac{17}{48}\right) e(916)e\left(\frac{9}{16}\right) e(524)e\left(\frac{5}{24}\right) e(1316)e\left(\frac{13}{16}\right) e(1348)e\left(\frac{13}{48}\right)
χ4160(3909,⋅)\chi_{4160}(3909,\cdot) 11 11 e(1748)e\left(\frac{17}{48}\right) e(1124)e\left(\frac{11}{24}\right) e(1724)e\left(\frac{17}{24}\right) e(4748)e\left(\frac{47}{48}\right) e(712)e\left(\frac{7}{12}\right) e(3748)e\left(\frac{37}{48}\right) e(1316)e\left(\frac{13}{16}\right) e(124)e\left(\frac{1}{24}\right) e(116)e\left(\frac{1}{16}\right) e(1748)e\left(\frac{17}{48}\right)