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Properties

Label 4032.he
Modulus 40324032
Conductor 448448
Order 4848
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(4032, base_ring=CyclotomicField(48))
 
M = H._module
 
chi = DirichletCharacter(H, M([24,21,0,40]))
 
chi.galois_orbit()
 
[g,chi] = znchar(Mod(19,4032))
 
order = charorder(g,chi)
 
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: 40324032
Conductor: 448448
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: 4848
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from 448.bm
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(19,⋅)\chi_{4032}(19,\cdot) 11 11 e(2948)e\left(\frac{29}{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(724)e\left(\frac{7}{24}\right) e(524)e\left(\frac{5}{24}\right) e(1316)e\left(\frac{13}{16}\right) e(56)e\left(\frac{5}{6}\right) e(2948)e\left(\frac{29}{48}\right)
χ4032(451,⋅)\chi_{4032}(451,\cdot) 11 11 e(148)e\left(\frac{1}{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(1124)e\left(\frac{11}{24}\right) e(124)e\left(\frac{1}{24}\right) e(116)e\left(\frac{1}{16}\right) e(16)e\left(\frac{1}{6}\right) e(148)e\left(\frac{1}{48}\right)
χ4032(523,⋅)\chi_{4032}(523,\cdot) 11 11 e(2348)e\left(\frac{23}{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(1324)e\left(\frac{13}{24}\right) e(2324)e\left(\frac{23}{24}\right) e(716)e\left(\frac{7}{16}\right) e(56)e\left(\frac{5}{6}\right) e(2348)e\left(\frac{23}{48}\right)
χ4032(955,⋅)\chi_{4032}(955,\cdot) 11 11 e(4348)e\left(\frac{43}{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(1724)e\left(\frac{17}{24}\right) e(1924)e\left(\frac{19}{24}\right) e(1116)e\left(\frac{11}{16}\right) e(16)e\left(\frac{1}{6}\right) e(4348)e\left(\frac{43}{48}\right)
χ4032(1027,⋅)\chi_{4032}(1027,\cdot) 11 11 e(1748)e\left(\frac{17}{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(1924)e\left(\frac{19}{24}\right) e(1724)e\left(\frac{17}{24}\right) e(116)e\left(\frac{1}{16}\right) e(56)e\left(\frac{5}{6}\right) e(1748)e\left(\frac{17}{48}\right)
χ4032(1459,⋅)\chi_{4032}(1459,\cdot) 11 11 e(3748)e\left(\frac{37}{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(2324)e\left(\frac{23}{24}\right) e(1324)e\left(\frac{13}{24}\right) e(516)e\left(\frac{5}{16}\right) e(16)e\left(\frac{1}{6}\right) e(3748)e\left(\frac{37}{48}\right)
χ4032(1531,⋅)\chi_{4032}(1531,\cdot) 11 11 e(1148)e\left(\frac{11}{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(124)e\left(\frac{1}{24}\right) e(1124)e\left(\frac{11}{24}\right) e(1116)e\left(\frac{11}{16}\right) e(56)e\left(\frac{5}{6}\right) e(1148)e\left(\frac{11}{48}\right)
χ4032(1963,⋅)\chi_{4032}(1963,\cdot) 11 11 e(3148)e\left(\frac{31}{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(524)e\left(\frac{5}{24}\right) e(724)e\left(\frac{7}{24}\right) e(1516)e\left(\frac{15}{16}\right) e(16)e\left(\frac{1}{6}\right) e(3148)e\left(\frac{31}{48}\right)
χ4032(2035,⋅)\chi_{4032}(2035,\cdot) 11 11 e(548)e\left(\frac{5}{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(724)e\left(\frac{7}{24}\right) e(524)e\left(\frac{5}{24}\right) e(516)e\left(\frac{5}{16}\right) e(56)e\left(\frac{5}{6}\right) e(548)e\left(\frac{5}{48}\right)
χ4032(2467,⋅)\chi_{4032}(2467,\cdot) 11 11 e(2548)e\left(\frac{25}{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(1124)e\left(\frac{11}{24}\right) e(124)e\left(\frac{1}{24}\right) e(916)e\left(\frac{9}{16}\right) e(16)e\left(\frac{1}{6}\right) e(2548)e\left(\frac{25}{48}\right)
χ4032(2539,⋅)\chi_{4032}(2539,\cdot) 11 11 e(4748)e\left(\frac{47}{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(1324)e\left(\frac{13}{24}\right) e(2324)e\left(\frac{23}{24}\right) e(1516)e\left(\frac{15}{16}\right) e(56)e\left(\frac{5}{6}\right) e(4748)e\left(\frac{47}{48}\right)
χ4032(2971,⋅)\chi_{4032}(2971,\cdot) 11 11 e(1948)e\left(\frac{19}{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(1724)e\left(\frac{17}{24}\right) e(1924)e\left(\frac{19}{24}\right) e(316)e\left(\frac{3}{16}\right) e(16)e\left(\frac{1}{6}\right) e(1948)e\left(\frac{19}{48}\right)
χ4032(3043,⋅)\chi_{4032}(3043,\cdot) 11 11 e(4148)e\left(\frac{41}{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(1924)e\left(\frac{19}{24}\right) e(1724)e\left(\frac{17}{24}\right) e(916)e\left(\frac{9}{16}\right) e(56)e\left(\frac{5}{6}\right) e(4148)e\left(\frac{41}{48}\right)
χ4032(3475,⋅)\chi_{4032}(3475,\cdot) 11 11 e(1348)e\left(\frac{13}{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(2324)e\left(\frac{23}{24}\right) e(1324)e\left(\frac{13}{24}\right) e(1316)e\left(\frac{13}{16}\right) e(16)e\left(\frac{1}{6}\right) e(1348)e\left(\frac{13}{48}\right)
χ4032(3547,⋅)\chi_{4032}(3547,\cdot) 11 11 e(3548)e\left(\frac{35}{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(124)e\left(\frac{1}{24}\right) e(1124)e\left(\frac{11}{24}\right) e(316)e\left(\frac{3}{16}\right) e(56)e\left(\frac{5}{6}\right) e(3548)e\left(\frac{35}{48}\right)
χ4032(3979,⋅)\chi_{4032}(3979,\cdot) 11 11 e(748)e\left(\frac{7}{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(524)e\left(\frac{5}{24}\right) e(724)e\left(\frac{7}{24}\right) e(716)e\left(\frac{7}{16}\right) e(16)e\left(\frac{1}{6}\right) e(748)e\left(\frac{7}{48}\right)