↑

Properties

Label 4032.gz
Modulus 40324032
Conductor 13441344
Order 4848
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(4032, base_ring=CyclotomicField(48))
 
M = H._module
 
chi = DirichletCharacter(H, M([24,39,24,16]))
 
chi.galois_orbit()
 
[g,chi] = znchar(Mod(107,4032))
 
order = charorder(g,chi)
 
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: 40324032
Conductor: 13441344
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: 4848
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from 1344.cx
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 55 1111 1313 1717 1919 2323 2525 2929 3131 3737
χ4032(107,⋅)\chi_{4032}(107,\cdot) 11 11 e(4748)e\left(\frac{47}{48}\right) e(1948)e\left(\frac{19}{48}\right) e(316)e\left(\frac{3}{16}\right) e(712)e\left(\frac{7}{12}\right) e(4148)e\left(\frac{41}{48}\right) e(124)e\left(\frac{1}{24}\right) e(2324)e\left(\frac{23}{24}\right) e(716)e\left(\frac{7}{16}\right) e(13)e\left(\frac{1}{3}\right) e(4748)e\left(\frac{47}{48}\right)
χ4032(179,⋅)\chi_{4032}(179,\cdot) 11 11 e(3748)e\left(\frac{37}{48}\right) e(1748)e\left(\frac{17}{48}\right) e(116)e\left(\frac{1}{16}\right) e(512)e\left(\frac{5}{12}\right) e(1948)e\left(\frac{19}{48}\right) e(1124)e\left(\frac{11}{24}\right) e(1324)e\left(\frac{13}{24}\right) e(1316)e\left(\frac{13}{16}\right) e(23)e\left(\frac{2}{3}\right) e(3748)e\left(\frac{37}{48}\right)
χ4032(611,⋅)\chi_{4032}(611,\cdot) 11 11 e(4148)e\left(\frac{41}{48}\right) e(3748)e\left(\frac{37}{48}\right) e(516)e\left(\frac{5}{16}\right) e(112)e\left(\frac{1}{12}\right) e(4748)e\left(\frac{47}{48}\right) e(724)e\left(\frac{7}{24}\right) e(1724)e\left(\frac{17}{24}\right) e(116)e\left(\frac{1}{16}\right) e(13)e\left(\frac{1}{3}\right) e(4148)e\left(\frac{41}{48}\right)
χ4032(683,⋅)\chi_{4032}(683,\cdot) 11 11 e(3148)e\left(\frac{31}{48}\right) e(3548)e\left(\frac{35}{48}\right) e(316)e\left(\frac{3}{16}\right) e(1112)e\left(\frac{11}{12}\right) e(2548)e\left(\frac{25}{48}\right) e(1724)e\left(\frac{17}{24}\right) e(724)e\left(\frac{7}{24}\right) e(716)e\left(\frac{7}{16}\right) e(23)e\left(\frac{2}{3}\right) e(3148)e\left(\frac{31}{48}\right)
χ4032(1115,⋅)\chi_{4032}(1115,\cdot) 11 11 e(3548)e\left(\frac{35}{48}\right) e(748)e\left(\frac{7}{48}\right) e(716)e\left(\frac{7}{16}\right) e(712)e\left(\frac{7}{12}\right) e(548)e\left(\frac{5}{48}\right) e(1324)e\left(\frac{13}{24}\right) e(1124)e\left(\frac{11}{24}\right) e(1116)e\left(\frac{11}{16}\right) e(13)e\left(\frac{1}{3}\right) e(3548)e\left(\frac{35}{48}\right)
χ4032(1187,⋅)\chi_{4032}(1187,\cdot) 11 11 e(2548)e\left(\frac{25}{48}\right) e(548)e\left(\frac{5}{48}\right) e(516)e\left(\frac{5}{16}\right) e(512)e\left(\frac{5}{12}\right) e(3148)e\left(\frac{31}{48}\right) e(2324)e\left(\frac{23}{24}\right) e(124)e\left(\frac{1}{24}\right) e(116)e\left(\frac{1}{16}\right) e(23)e\left(\frac{2}{3}\right) e(2548)e\left(\frac{25}{48}\right)
χ4032(1619,⋅)\chi_{4032}(1619,\cdot) 11 11 e(2948)e\left(\frac{29}{48}\right) e(2548)e\left(\frac{25}{48}\right) e(916)e\left(\frac{9}{16}\right) e(112)e\left(\frac{1}{12}\right) e(1148)e\left(\frac{11}{48}\right) e(1924)e\left(\frac{19}{24}\right) e(524)e\left(\frac{5}{24}\right) e(516)e\left(\frac{5}{16}\right) e(13)e\left(\frac{1}{3}\right) e(2948)e\left(\frac{29}{48}\right)
χ4032(1691,⋅)\chi_{4032}(1691,\cdot) 11 11 e(1948)e\left(\frac{19}{48}\right) e(2348)e\left(\frac{23}{48}\right) e(716)e\left(\frac{7}{16}\right) e(1112)e\left(\frac{11}{12}\right) e(3748)e\left(\frac{37}{48}\right) e(524)e\left(\frac{5}{24}\right) e(1924)e\left(\frac{19}{24}\right) e(1116)e\left(\frac{11}{16}\right) e(23)e\left(\frac{2}{3}\right) e(1948)e\left(\frac{19}{48}\right)
χ4032(2123,⋅)\chi_{4032}(2123,\cdot) 11 11 e(2348)e\left(\frac{23}{48}\right) e(4348)e\left(\frac{43}{48}\right) e(1116)e\left(\frac{11}{16}\right) e(712)e\left(\frac{7}{12}\right) e(1748)e\left(\frac{17}{48}\right) e(124)e\left(\frac{1}{24}\right) e(2324)e\left(\frac{23}{24}\right) e(1516)e\left(\frac{15}{16}\right) e(13)e\left(\frac{1}{3}\right) e(2348)e\left(\frac{23}{48}\right)
χ4032(2195,⋅)\chi_{4032}(2195,\cdot) 11 11 e(1348)e\left(\frac{13}{48}\right) e(4148)e\left(\frac{41}{48}\right) e(916)e\left(\frac{9}{16}\right) e(512)e\left(\frac{5}{12}\right) e(4348)e\left(\frac{43}{48}\right) e(1124)e\left(\frac{11}{24}\right) e(1324)e\left(\frac{13}{24}\right) e(516)e\left(\frac{5}{16}\right) e(23)e\left(\frac{2}{3}\right) e(1348)e\left(\frac{13}{48}\right)
χ4032(2627,⋅)\chi_{4032}(2627,\cdot) 11 11 e(1748)e\left(\frac{17}{48}\right) e(1348)e\left(\frac{13}{48}\right) e(1316)e\left(\frac{13}{16}\right) e(112)e\left(\frac{1}{12}\right) e(2348)e\left(\frac{23}{48}\right) e(724)e\left(\frac{7}{24}\right) e(1724)e\left(\frac{17}{24}\right) e(916)e\left(\frac{9}{16}\right) e(13)e\left(\frac{1}{3}\right) e(1748)e\left(\frac{17}{48}\right)
χ4032(2699,⋅)\chi_{4032}(2699,\cdot) 11 11 e(748)e\left(\frac{7}{48}\right) e(1148)e\left(\frac{11}{48}\right) e(1116)e\left(\frac{11}{16}\right) e(1112)e\left(\frac{11}{12}\right) e(148)e\left(\frac{1}{48}\right) e(1724)e\left(\frac{17}{24}\right) e(724)e\left(\frac{7}{24}\right) e(1516)e\left(\frac{15}{16}\right) e(23)e\left(\frac{2}{3}\right) e(748)e\left(\frac{7}{48}\right)
χ4032(3131,⋅)\chi_{4032}(3131,\cdot) 11 11 e(1148)e\left(\frac{11}{48}\right) e(3148)e\left(\frac{31}{48}\right) e(1516)e\left(\frac{15}{16}\right) e(712)e\left(\frac{7}{12}\right) e(2948)e\left(\frac{29}{48}\right) e(1324)e\left(\frac{13}{24}\right) e(1124)e\left(\frac{11}{24}\right) e(316)e\left(\frac{3}{16}\right) e(13)e\left(\frac{1}{3}\right) e(1148)e\left(\frac{11}{48}\right)
χ4032(3203,⋅)\chi_{4032}(3203,\cdot) 11 11 e(148)e\left(\frac{1}{48}\right) e(2948)e\left(\frac{29}{48}\right) e(1316)e\left(\frac{13}{16}\right) e(512)e\left(\frac{5}{12}\right) e(748)e\left(\frac{7}{48}\right) e(2324)e\left(\frac{23}{24}\right) e(124)e\left(\frac{1}{24}\right) e(916)e\left(\frac{9}{16}\right) e(23)e\left(\frac{2}{3}\right) e(148)e\left(\frac{1}{48}\right)
χ4032(3635,⋅)\chi_{4032}(3635,\cdot) 11 11 e(548)e\left(\frac{5}{48}\right) e(148)e\left(\frac{1}{48}\right) e(116)e\left(\frac{1}{16}\right) e(112)e\left(\frac{1}{12}\right) e(3548)e\left(\frac{35}{48}\right) e(1924)e\left(\frac{19}{24}\right) e(524)e\left(\frac{5}{24}\right) e(1316)e\left(\frac{13}{16}\right) e(13)e\left(\frac{1}{3}\right) e(548)e\left(\frac{5}{48}\right)
χ4032(3707,⋅)\chi_{4032}(3707,\cdot) 11 11 e(4348)e\left(\frac{43}{48}\right) e(4748)e\left(\frac{47}{48}\right) e(1516)e\left(\frac{15}{16}\right) e(1112)e\left(\frac{11}{12}\right) e(1348)e\left(\frac{13}{48}\right) e(524)e\left(\frac{5}{24}\right) e(1924)e\left(\frac{19}{24}\right) e(316)e\left(\frac{3}{16}\right) e(23)e\left(\frac{2}{3}\right) e(4348)e\left(\frac{43}{48}\right)