Properties

Label 1792.bo
Modulus $1792$
Conductor $448$
Order $48$
Real no
Primitive no
Minimal no
Parity odd

Related objects

Learn more

Show commands: Pari/GP / SageMath
sage: from sage.modular.dirichlet import DirichletCharacter
 
sage: H = DirichletGroup(1792, base_ring=CyclotomicField(48))
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([0,21,8]))
 
sage: chi.galois_orbit()
 
pari: [g,chi] = znchar(Mod(17,1792))
 
pari: order = charorder(g,chi)
 
pari: [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: \(1792\)
Conductor: \(448\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(48\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from 448.bk
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: no
Parity: odd
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 \(-1\) \(1\) \(3\) \(5\) \(9\) \(11\) \(13\) \(15\) \(17\) \(19\) \(23\) \(25\)
\(\chi_{1792}(17,\cdot)\) \(-1\) \(1\) \(e\left(\frac{23}{48}\right)\) \(e\left(\frac{13}{48}\right)\) \(e\left(\frac{23}{24}\right)\) \(e\left(\frac{41}{48}\right)\) \(e\left(\frac{1}{16}\right)\) \(-i\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{43}{48}\right)\) \(e\left(\frac{11}{24}\right)\) \(e\left(\frac{13}{24}\right)\)
\(\chi_{1792}(145,\cdot)\) \(-1\) \(1\) \(e\left(\frac{31}{48}\right)\) \(e\left(\frac{5}{48}\right)\) \(e\left(\frac{7}{24}\right)\) \(e\left(\frac{1}{48}\right)\) \(e\left(\frac{9}{16}\right)\) \(-i\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{35}{48}\right)\) \(e\left(\frac{19}{24}\right)\) \(e\left(\frac{5}{24}\right)\)
\(\chi_{1792}(241,\cdot)\) \(-1\) \(1\) \(e\left(\frac{41}{48}\right)\) \(e\left(\frac{19}{48}\right)\) \(e\left(\frac{17}{24}\right)\) \(e\left(\frac{23}{48}\right)\) \(e\left(\frac{15}{16}\right)\) \(i\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{37}{48}\right)\) \(e\left(\frac{5}{24}\right)\) \(e\left(\frac{19}{24}\right)\)
\(\chi_{1792}(369,\cdot)\) \(-1\) \(1\) \(e\left(\frac{1}{48}\right)\) \(e\left(\frac{11}{48}\right)\) \(e\left(\frac{1}{24}\right)\) \(e\left(\frac{31}{48}\right)\) \(e\left(\frac{7}{16}\right)\) \(i\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{29}{48}\right)\) \(e\left(\frac{13}{24}\right)\) \(e\left(\frac{11}{24}\right)\)
\(\chi_{1792}(465,\cdot)\) \(-1\) \(1\) \(e\left(\frac{11}{48}\right)\) \(e\left(\frac{25}{48}\right)\) \(e\left(\frac{11}{24}\right)\) \(e\left(\frac{5}{48}\right)\) \(e\left(\frac{13}{16}\right)\) \(-i\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{31}{48}\right)\) \(e\left(\frac{23}{24}\right)\) \(e\left(\frac{1}{24}\right)\)
\(\chi_{1792}(593,\cdot)\) \(-1\) \(1\) \(e\left(\frac{19}{48}\right)\) \(e\left(\frac{17}{48}\right)\) \(e\left(\frac{19}{24}\right)\) \(e\left(\frac{13}{48}\right)\) \(e\left(\frac{5}{16}\right)\) \(-i\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{23}{48}\right)\) \(e\left(\frac{7}{24}\right)\) \(e\left(\frac{17}{24}\right)\)
\(\chi_{1792}(689,\cdot)\) \(-1\) \(1\) \(e\left(\frac{29}{48}\right)\) \(e\left(\frac{31}{48}\right)\) \(e\left(\frac{5}{24}\right)\) \(e\left(\frac{35}{48}\right)\) \(e\left(\frac{11}{16}\right)\) \(i\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{25}{48}\right)\) \(e\left(\frac{17}{24}\right)\) \(e\left(\frac{7}{24}\right)\)
\(\chi_{1792}(817,\cdot)\) \(-1\) \(1\) \(e\left(\frac{37}{48}\right)\) \(e\left(\frac{23}{48}\right)\) \(e\left(\frac{13}{24}\right)\) \(e\left(\frac{43}{48}\right)\) \(e\left(\frac{3}{16}\right)\) \(i\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{17}{48}\right)\) \(e\left(\frac{1}{24}\right)\) \(e\left(\frac{23}{24}\right)\)
\(\chi_{1792}(913,\cdot)\) \(-1\) \(1\) \(e\left(\frac{47}{48}\right)\) \(e\left(\frac{37}{48}\right)\) \(e\left(\frac{23}{24}\right)\) \(e\left(\frac{17}{48}\right)\) \(e\left(\frac{9}{16}\right)\) \(-i\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{19}{48}\right)\) \(e\left(\frac{11}{24}\right)\) \(e\left(\frac{13}{24}\right)\)
\(\chi_{1792}(1041,\cdot)\) \(-1\) \(1\) \(e\left(\frac{7}{48}\right)\) \(e\left(\frac{29}{48}\right)\) \(e\left(\frac{7}{24}\right)\) \(e\left(\frac{25}{48}\right)\) \(e\left(\frac{1}{16}\right)\) \(-i\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{11}{48}\right)\) \(e\left(\frac{19}{24}\right)\) \(e\left(\frac{5}{24}\right)\)
\(\chi_{1792}(1137,\cdot)\) \(-1\) \(1\) \(e\left(\frac{17}{48}\right)\) \(e\left(\frac{43}{48}\right)\) \(e\left(\frac{17}{24}\right)\) \(e\left(\frac{47}{48}\right)\) \(e\left(\frac{7}{16}\right)\) \(i\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{13}{48}\right)\) \(e\left(\frac{5}{24}\right)\) \(e\left(\frac{19}{24}\right)\)
\(\chi_{1792}(1265,\cdot)\) \(-1\) \(1\) \(e\left(\frac{25}{48}\right)\) \(e\left(\frac{35}{48}\right)\) \(e\left(\frac{1}{24}\right)\) \(e\left(\frac{7}{48}\right)\) \(e\left(\frac{15}{16}\right)\) \(i\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{5}{48}\right)\) \(e\left(\frac{13}{24}\right)\) \(e\left(\frac{11}{24}\right)\)
\(\chi_{1792}(1361,\cdot)\) \(-1\) \(1\) \(e\left(\frac{35}{48}\right)\) \(e\left(\frac{1}{48}\right)\) \(e\left(\frac{11}{24}\right)\) \(e\left(\frac{29}{48}\right)\) \(e\left(\frac{5}{16}\right)\) \(-i\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{7}{48}\right)\) \(e\left(\frac{23}{24}\right)\) \(e\left(\frac{1}{24}\right)\)
\(\chi_{1792}(1489,\cdot)\) \(-1\) \(1\) \(e\left(\frac{43}{48}\right)\) \(e\left(\frac{41}{48}\right)\) \(e\left(\frac{19}{24}\right)\) \(e\left(\frac{37}{48}\right)\) \(e\left(\frac{13}{16}\right)\) \(-i\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{47}{48}\right)\) \(e\left(\frac{7}{24}\right)\) \(e\left(\frac{17}{24}\right)\)
\(\chi_{1792}(1585,\cdot)\) \(-1\) \(1\) \(e\left(\frac{5}{48}\right)\) \(e\left(\frac{7}{48}\right)\) \(e\left(\frac{5}{24}\right)\) \(e\left(\frac{11}{48}\right)\) \(e\left(\frac{3}{16}\right)\) \(i\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{1}{48}\right)\) \(e\left(\frac{17}{24}\right)\) \(e\left(\frac{7}{24}\right)\)
\(\chi_{1792}(1713,\cdot)\) \(-1\) \(1\) \(e\left(\frac{13}{48}\right)\) \(e\left(\frac{47}{48}\right)\) \(e\left(\frac{13}{24}\right)\) \(e\left(\frac{19}{48}\right)\) \(e\left(\frac{11}{16}\right)\) \(i\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{41}{48}\right)\) \(e\left(\frac{1}{24}\right)\) \(e\left(\frac{23}{24}\right)\)