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Properties

Label 1224.cw
Modulus 12241224
Conductor 153153
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(1224, base_ring=CyclotomicField(48))
 
M = H._module
 
chi = DirichletCharacter(H, M([0,0,40,33]))
 
chi.galois_orbit()
 
[g,chi] = znchar(Mod(41,1224))
 
order = charorder(g,chi)
 
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: 12241224
Conductor: 153153
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: 4848
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from 153.s
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 77 1111 1313 1919 2323 2525 2929 3131 3535
χ1224(41,⋅)\chi_{1224}(41,\cdot) 11 11 e(2948)e\left(\frac{29}{48}\right) e(4348)e\left(\frac{43}{48}\right) e(3148)e\left(\frac{31}{48}\right) e(512)e\left(\frac{5}{12}\right) e(58)e\left(\frac{5}{8}\right) e(2348)e\left(\frac{23}{48}\right) e(524)e\left(\frac{5}{24}\right) e(3748)e\left(\frac{37}{48}\right) e(4148)e\left(\frac{41}{48}\right) −1-1
χ1224(65,⋅)\chi_{1224}(65,\cdot) 11 11 e(3148)e\left(\frac{31}{48}\right) e(4148)e\left(\frac{41}{48}\right) e(548)e\left(\frac{5}{48}\right) e(712)e\left(\frac{7}{12}\right) e(78)e\left(\frac{7}{8}\right) e(1348)e\left(\frac{13}{48}\right) e(724)e\left(\frac{7}{24}\right) e(2348)e\left(\frac{23}{48}\right) e(1948)e\left(\frac{19}{48}\right) −1-1
χ1224(113,⋅)\chi_{1224}(113,\cdot) 11 11 e(1748)e\left(\frac{17}{48}\right) e(748)e\left(\frac{7}{48}\right) e(4348)e\left(\frac{43}{48}\right) e(512)e\left(\frac{5}{12}\right) e(18)e\left(\frac{1}{8}\right) e(3548)e\left(\frac{35}{48}\right) e(1724)e\left(\frac{17}{24}\right) e(2548)e\left(\frac{25}{48}\right) e(2948)e\left(\frac{29}{48}\right) −1-1
χ1224(209,⋅)\chi_{1224}(209,\cdot) 11 11 e(1948)e\left(\frac{19}{48}\right) e(548)e\left(\frac{5}{48}\right) e(1748)e\left(\frac{17}{48}\right) e(712)e\left(\frac{7}{12}\right) e(38)e\left(\frac{3}{8}\right) e(2548)e\left(\frac{25}{48}\right) e(1924)e\left(\frac{19}{24}\right) e(1148)e\left(\frac{11}{48}\right) e(748)e\left(\frac{7}{48}\right) −1-1
χ1224(329,⋅)\chi_{1224}(329,\cdot) 11 11 e(4148)e\left(\frac{41}{48}\right) e(3148)e\left(\frac{31}{48}\right) e(1948)e\left(\frac{19}{48}\right) e(512)e\left(\frac{5}{12}\right) e(18)e\left(\frac{1}{8}\right) e(1148)e\left(\frac{11}{48}\right) e(1724)e\left(\frac{17}{24}\right) e(148)e\left(\frac{1}{48}\right) e(548)e\left(\frac{5}{48}\right) −1-1
χ1224(401,⋅)\chi_{1224}(401,\cdot) 11 11 e(548)e\left(\frac{5}{48}\right) e(1948)e\left(\frac{19}{48}\right) e(748)e\left(\frac{7}{48}\right) e(512)e\left(\frac{5}{12}\right) e(58)e\left(\frac{5}{8}\right) e(4748)e\left(\frac{47}{48}\right) e(524)e\left(\frac{5}{24}\right) e(1348)e\left(\frac{13}{48}\right) e(1748)e\left(\frac{17}{48}\right) −1-1
χ1224(473,⋅)\chi_{1224}(473,\cdot) 11 11 e(4748)e\left(\frac{47}{48}\right) e(2548)e\left(\frac{25}{48}\right) e(3748)e\left(\frac{37}{48}\right) e(1112)e\left(\frac{11}{12}\right) e(78)e\left(\frac{7}{8}\right) e(2948)e\left(\frac{29}{48}\right) e(2324)e\left(\frac{23}{24}\right) e(748)e\left(\frac{7}{48}\right) e(3548)e\left(\frac{35}{48}\right) −1-1
χ1224(617,⋅)\chi_{1224}(617,\cdot) 11 11 e(3548)e\left(\frac{35}{48}\right) e(3748)e\left(\frac{37}{48}\right) e(148)e\left(\frac{1}{48}\right) e(1112)e\left(\frac{11}{12}\right) e(38)e\left(\frac{3}{8}\right) e(4148)e\left(\frac{41}{48}\right) e(1124)e\left(\frac{11}{24}\right) e(4348)e\left(\frac{43}{48}\right) e(2348)e\left(\frac{23}{48}\right) −1-1
χ1224(641,⋅)\chi_{1224}(641,\cdot) 11 11 e(4348)e\left(\frac{43}{48}\right) e(2948)e\left(\frac{29}{48}\right) e(4148)e\left(\frac{41}{48}\right) e(712)e\left(\frac{7}{12}\right) e(38)e\left(\frac{3}{8}\right) e(148)e\left(\frac{1}{48}\right) e(1924)e\left(\frac{19}{24}\right) e(3548)e\left(\frac{35}{48}\right) e(3148)e\left(\frac{31}{48}\right) −1-1
χ1224(785,⋅)\chi_{1224}(785,\cdot) 11 11 e(748)e\left(\frac{7}{48}\right) e(1748)e\left(\frac{17}{48}\right) e(2948)e\left(\frac{29}{48}\right) e(712)e\left(\frac{7}{12}\right) e(78)e\left(\frac{7}{8}\right) e(3748)e\left(\frac{37}{48}\right) e(724)e\left(\frac{7}{24}\right) e(4748)e\left(\frac{47}{48}\right) e(4348)e\left(\frac{43}{48}\right) −1-1
χ1224(857,⋅)\chi_{1224}(857,\cdot) 11 11 e(1348)e\left(\frac{13}{48}\right) e(1148)e\left(\frac{11}{48}\right) e(4748)e\left(\frac{47}{48}\right) e(112)e\left(\frac{1}{12}\right) e(58)e\left(\frac{5}{8}\right) e(748)e\left(\frac{7}{48}\right) e(1324)e\left(\frac{13}{24}\right) e(548)e\left(\frac{5}{48}\right) e(2548)e\left(\frac{25}{48}\right) −1-1
χ1224(929,⋅)\chi_{1224}(929,\cdot) 11 11 e(148)e\left(\frac{1}{48}\right) e(2348)e\left(\frac{23}{48}\right) e(1148)e\left(\frac{11}{48}\right) e(112)e\left(\frac{1}{12}\right) e(18)e\left(\frac{1}{8}\right) e(1948)e\left(\frac{19}{48}\right) e(124)e\left(\frac{1}{24}\right) e(4148)e\left(\frac{41}{48}\right) e(1348)e\left(\frac{13}{48}\right) −1-1
χ1224(1049,⋅)\chi_{1224}(1049,\cdot) 11 11 e(1148)e\left(\frac{11}{48}\right) e(1348)e\left(\frac{13}{48}\right) e(2548)e\left(\frac{25}{48}\right) e(1112)e\left(\frac{11}{12}\right) e(38)e\left(\frac{3}{8}\right) e(1748)e\left(\frac{17}{48}\right) e(1124)e\left(\frac{11}{24}\right) e(1948)e\left(\frac{19}{48}\right) e(4748)e\left(\frac{47}{48}\right) −1-1
χ1224(1145,⋅)\chi_{1224}(1145,\cdot) 11 11 e(2548)e\left(\frac{25}{48}\right) e(4748)e\left(\frac{47}{48}\right) e(3548)e\left(\frac{35}{48}\right) e(112)e\left(\frac{1}{12}\right) e(18)e\left(\frac{1}{8}\right) e(4348)e\left(\frac{43}{48}\right) e(124)e\left(\frac{1}{24}\right) e(1748)e\left(\frac{17}{48}\right) e(3748)e\left(\frac{37}{48}\right) −1-1
χ1224(1193,⋅)\chi_{1224}(1193,\cdot) 11 11 e(2348)e\left(\frac{23}{48}\right) e(148)e\left(\frac{1}{48}\right) e(1348)e\left(\frac{13}{48}\right) e(1112)e\left(\frac{11}{12}\right) e(78)e\left(\frac{7}{8}\right) e(548)e\left(\frac{5}{48}\right) e(2324)e\left(\frac{23}{24}\right) e(3148)e\left(\frac{31}{48}\right) e(1148)e\left(\frac{11}{48}\right) −1-1
χ1224(1217,⋅)\chi_{1224}(1217,\cdot) 11 11 e(3748)e\left(\frac{37}{48}\right) e(3548)e\left(\frac{35}{48}\right) e(2348)e\left(\frac{23}{48}\right) e(112)e\left(\frac{1}{12}\right) e(58)e\left(\frac{5}{8}\right) e(3148)e\left(\frac{31}{48}\right) e(1324)e\left(\frac{13}{24}\right) e(2948)e\left(\frac{29}{48}\right) e(148)e\left(\frac{1}{48}\right) −1-1