Properties

Label 1224.cw
Modulus $1224$
Conductor $153$
Order $48$
Real no
Primitive no
Minimal yes
Parity even

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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: \(1224\)
Conductor: \(153\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(48\)
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: \(\Q(\zeta_{48})\)
Fixed field: Number field defined by a degree 48 polynomial

Characters in Galois orbit

Character \(-1\) \(1\) \(5\) \(7\) \(11\) \(13\) \(19\) \(23\) \(25\) \(29\) \(31\) \(35\)
\(\chi_{1224}(41,\cdot)\) \(1\) \(1\) \(e\left(\frac{29}{48}\right)\) \(e\left(\frac{43}{48}\right)\) \(e\left(\frac{31}{48}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{23}{48}\right)\) \(e\left(\frac{5}{24}\right)\) \(e\left(\frac{37}{48}\right)\) \(e\left(\frac{41}{48}\right)\) \(-1\)
\(\chi_{1224}(65,\cdot)\) \(1\) \(1\) \(e\left(\frac{31}{48}\right)\) \(e\left(\frac{41}{48}\right)\) \(e\left(\frac{5}{48}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{13}{48}\right)\) \(e\left(\frac{7}{24}\right)\) \(e\left(\frac{23}{48}\right)\) \(e\left(\frac{19}{48}\right)\) \(-1\)
\(\chi_{1224}(113,\cdot)\) \(1\) \(1\) \(e\left(\frac{17}{48}\right)\) \(e\left(\frac{7}{48}\right)\) \(e\left(\frac{43}{48}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{35}{48}\right)\) \(e\left(\frac{17}{24}\right)\) \(e\left(\frac{25}{48}\right)\) \(e\left(\frac{29}{48}\right)\) \(-1\)
\(\chi_{1224}(209,\cdot)\) \(1\) \(1\) \(e\left(\frac{19}{48}\right)\) \(e\left(\frac{5}{48}\right)\) \(e\left(\frac{17}{48}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{25}{48}\right)\) \(e\left(\frac{19}{24}\right)\) \(e\left(\frac{11}{48}\right)\) \(e\left(\frac{7}{48}\right)\) \(-1\)
\(\chi_{1224}(329,\cdot)\) \(1\) \(1\) \(e\left(\frac{41}{48}\right)\) \(e\left(\frac{31}{48}\right)\) \(e\left(\frac{19}{48}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{11}{48}\right)\) \(e\left(\frac{17}{24}\right)\) \(e\left(\frac{1}{48}\right)\) \(e\left(\frac{5}{48}\right)\) \(-1\)
\(\chi_{1224}(401,\cdot)\) \(1\) \(1\) \(e\left(\frac{5}{48}\right)\) \(e\left(\frac{19}{48}\right)\) \(e\left(\frac{7}{48}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{47}{48}\right)\) \(e\left(\frac{5}{24}\right)\) \(e\left(\frac{13}{48}\right)\) \(e\left(\frac{17}{48}\right)\) \(-1\)
\(\chi_{1224}(473,\cdot)\) \(1\) \(1\) \(e\left(\frac{47}{48}\right)\) \(e\left(\frac{25}{48}\right)\) \(e\left(\frac{37}{48}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{29}{48}\right)\) \(e\left(\frac{23}{24}\right)\) \(e\left(\frac{7}{48}\right)\) \(e\left(\frac{35}{48}\right)\) \(-1\)
\(\chi_{1224}(617,\cdot)\) \(1\) \(1\) \(e\left(\frac{35}{48}\right)\) \(e\left(\frac{37}{48}\right)\) \(e\left(\frac{1}{48}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{41}{48}\right)\) \(e\left(\frac{11}{24}\right)\) \(e\left(\frac{43}{48}\right)\) \(e\left(\frac{23}{48}\right)\) \(-1\)
\(\chi_{1224}(641,\cdot)\) \(1\) \(1\) \(e\left(\frac{43}{48}\right)\) \(e\left(\frac{29}{48}\right)\) \(e\left(\frac{41}{48}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{1}{48}\right)\) \(e\left(\frac{19}{24}\right)\) \(e\left(\frac{35}{48}\right)\) \(e\left(\frac{31}{48}\right)\) \(-1\)
\(\chi_{1224}(785,\cdot)\) \(1\) \(1\) \(e\left(\frac{7}{48}\right)\) \(e\left(\frac{17}{48}\right)\) \(e\left(\frac{29}{48}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{37}{48}\right)\) \(e\left(\frac{7}{24}\right)\) \(e\left(\frac{47}{48}\right)\) \(e\left(\frac{43}{48}\right)\) \(-1\)
\(\chi_{1224}(857,\cdot)\) \(1\) \(1\) \(e\left(\frac{13}{48}\right)\) \(e\left(\frac{11}{48}\right)\) \(e\left(\frac{47}{48}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{7}{48}\right)\) \(e\left(\frac{13}{24}\right)\) \(e\left(\frac{5}{48}\right)\) \(e\left(\frac{25}{48}\right)\) \(-1\)
\(\chi_{1224}(929,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{48}\right)\) \(e\left(\frac{23}{48}\right)\) \(e\left(\frac{11}{48}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{19}{48}\right)\) \(e\left(\frac{1}{24}\right)\) \(e\left(\frac{41}{48}\right)\) \(e\left(\frac{13}{48}\right)\) \(-1\)
\(\chi_{1224}(1049,\cdot)\) \(1\) \(1\) \(e\left(\frac{11}{48}\right)\) \(e\left(\frac{13}{48}\right)\) \(e\left(\frac{25}{48}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{17}{48}\right)\) \(e\left(\frac{11}{24}\right)\) \(e\left(\frac{19}{48}\right)\) \(e\left(\frac{47}{48}\right)\) \(-1\)
\(\chi_{1224}(1145,\cdot)\) \(1\) \(1\) \(e\left(\frac{25}{48}\right)\) \(e\left(\frac{47}{48}\right)\) \(e\left(\frac{35}{48}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{43}{48}\right)\) \(e\left(\frac{1}{24}\right)\) \(e\left(\frac{17}{48}\right)\) \(e\left(\frac{37}{48}\right)\) \(-1\)
\(\chi_{1224}(1193,\cdot)\) \(1\) \(1\) \(e\left(\frac{23}{48}\right)\) \(e\left(\frac{1}{48}\right)\) \(e\left(\frac{13}{48}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{5}{48}\right)\) \(e\left(\frac{23}{24}\right)\) \(e\left(\frac{31}{48}\right)\) \(e\left(\frac{11}{48}\right)\) \(-1\)
\(\chi_{1224}(1217,\cdot)\) \(1\) \(1\) \(e\left(\frac{37}{48}\right)\) \(e\left(\frac{35}{48}\right)\) \(e\left(\frac{23}{48}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{31}{48}\right)\) \(e\left(\frac{13}{24}\right)\) \(e\left(\frac{29}{48}\right)\) \(e\left(\frac{1}{48}\right)\) \(-1\)