↑

Properties

Label 5712.jw
Modulus $5712$
Conductor $5712$
Order $48$
Real no
Primitive yes
Minimal yes
Parity odd

Related objects

Downloads

Learn more

Show commands: Pari/GP / SageMath
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(5712, base_ring=CyclotomicField(48)) M = H._module chi = DirichletCharacter(H, M([24,12,24,32,21])) chi.galois_orbit()
 
Copy content pari:[g,chi] = znchar(Mod(11,5712)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: \(5712\)
Conductor: \(5712\)
Copy content sage:chi.conductor()
 
Copy content pari:znconreyconductor(g,chi)
 
Order: \(48\)
Copy content sage:chi.multiplicative_order()
 
Copy content pari:charorder(g,chi)
 
Real: no
Primitive: yes
Copy content sage:chi.is_primitive()
 
Copy content pari:#znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: odd
Copy content sage:chi.is_odd()
 
Copy content 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 \(-1\) \(1\) \(5\) \(11\) \(13\) \(19\) \(23\) \(25\) \(29\) \(31\) \(37\) \(41\)
\(\chi_{5712}(11,\cdot)\) \(-1\) \(1\) \(e\left(\frac{13}{48}\right)\) \(e\left(\frac{47}{48}\right)\) \(-1\) \(e\left(\frac{17}{24}\right)\) \(e\left(\frac{19}{48}\right)\) \(e\left(\frac{13}{24}\right)\) \(e\left(\frac{15}{16}\right)\) \(e\left(\frac{5}{48}\right)\) \(e\left(\frac{1}{48}\right)\) \(e\left(\frac{13}{16}\right)\)
\(\chi_{5712}(275,\cdot)\) \(-1\) \(1\) \(e\left(\frac{11}{48}\right)\) \(e\left(\frac{25}{48}\right)\) \(-1\) \(e\left(\frac{7}{24}\right)\) \(e\left(\frac{5}{48}\right)\) \(e\left(\frac{11}{24}\right)\) \(e\left(\frac{9}{16}\right)\) \(e\left(\frac{19}{48}\right)\) \(e\left(\frac{23}{48}\right)\) \(e\left(\frac{11}{16}\right)\)
\(\chi_{5712}(347,\cdot)\) \(-1\) \(1\) \(e\left(\frac{25}{48}\right)\) \(e\left(\frac{35}{48}\right)\) \(-1\) \(e\left(\frac{5}{24}\right)\) \(e\left(\frac{7}{48}\right)\) \(e\left(\frac{1}{24}\right)\) \(e\left(\frac{3}{16}\right)\) \(e\left(\frac{17}{48}\right)\) \(e\left(\frac{13}{48}\right)\) \(e\left(\frac{9}{16}\right)\)
\(\chi_{5712}(515,\cdot)\) \(-1\) \(1\) \(e\left(\frac{7}{48}\right)\) \(e\left(\frac{29}{48}\right)\) \(-1\) \(e\left(\frac{11}{24}\right)\) \(e\left(\frac{25}{48}\right)\) \(e\left(\frac{7}{24}\right)\) \(e\left(\frac{13}{16}\right)\) \(e\left(\frac{47}{48}\right)\) \(e\left(\frac{19}{48}\right)\) \(e\left(\frac{7}{16}\right)\)
\(\chi_{5712}(947,\cdot)\) \(-1\) \(1\) \(e\left(\frac{47}{48}\right)\) \(e\left(\frac{37}{48}\right)\) \(-1\) \(e\left(\frac{19}{24}\right)\) \(e\left(\frac{17}{48}\right)\) \(e\left(\frac{23}{24}\right)\) \(e\left(\frac{5}{16}\right)\) \(e\left(\frac{7}{48}\right)\) \(e\left(\frac{11}{48}\right)\) \(e\left(\frac{15}{16}\right)\)
\(\chi_{5712}(1115,\cdot)\) \(-1\) \(1\) \(e\left(\frac{17}{48}\right)\) \(e\left(\frac{43}{48}\right)\) \(-1\) \(e\left(\frac{13}{24}\right)\) \(e\left(\frac{47}{48}\right)\) \(e\left(\frac{17}{24}\right)\) \(e\left(\frac{11}{16}\right)\) \(e\left(\frac{25}{48}\right)\) \(e\left(\frac{5}{48}\right)\) \(e\left(\frac{1}{16}\right)\)
\(\chi_{5712}(1187,\cdot)\) \(-1\) \(1\) \(e\left(\frac{19}{48}\right)\) \(e\left(\frac{17}{48}\right)\) \(-1\) \(e\left(\frac{23}{24}\right)\) \(e\left(\frac{13}{48}\right)\) \(e\left(\frac{19}{24}\right)\) \(e\left(\frac{1}{16}\right)\) \(e\left(\frac{11}{48}\right)\) \(e\left(\frac{31}{48}\right)\) \(e\left(\frac{3}{16}\right)\)
\(\chi_{5712}(1451,\cdot)\) \(-1\) \(1\) \(e\left(\frac{5}{48}\right)\) \(e\left(\frac{7}{48}\right)\) \(-1\) \(e\left(\frac{1}{24}\right)\) \(e\left(\frac{11}{48}\right)\) \(e\left(\frac{5}{24}\right)\) \(e\left(\frac{7}{16}\right)\) \(e\left(\frac{13}{48}\right)\) \(e\left(\frac{41}{48}\right)\) \(e\left(\frac{5}{16}\right)\)
\(\chi_{5712}(2459,\cdot)\) \(-1\) \(1\) \(e\left(\frac{29}{48}\right)\) \(e\left(\frac{31}{48}\right)\) \(-1\) \(e\left(\frac{1}{24}\right)\) \(e\left(\frac{35}{48}\right)\) \(e\left(\frac{5}{24}\right)\) \(e\left(\frac{15}{16}\right)\) \(e\left(\frac{37}{48}\right)\) \(e\left(\frac{17}{48}\right)\) \(e\left(\frac{13}{16}\right)\)
\(\chi_{5712}(2795,\cdot)\) \(-1\) \(1\) \(e\left(\frac{41}{48}\right)\) \(e\left(\frac{19}{48}\right)\) \(-1\) \(e\left(\frac{13}{24}\right)\) \(e\left(\frac{23}{48}\right)\) \(e\left(\frac{17}{24}\right)\) \(e\left(\frac{3}{16}\right)\) \(e\left(\frac{1}{48}\right)\) \(e\left(\frac{29}{48}\right)\) \(e\left(\frac{9}{16}\right)\)
\(\chi_{5712}(2963,\cdot)\) \(-1\) \(1\) \(e\left(\frac{23}{48}\right)\) \(e\left(\frac{13}{48}\right)\) \(-1\) \(e\left(\frac{19}{24}\right)\) \(e\left(\frac{41}{48}\right)\) \(e\left(\frac{23}{24}\right)\) \(e\left(\frac{13}{16}\right)\) \(e\left(\frac{31}{48}\right)\) \(e\left(\frac{35}{48}\right)\) \(e\left(\frac{7}{16}\right)\)
\(\chi_{5712}(3539,\cdot)\) \(-1\) \(1\) \(e\left(\frac{43}{48}\right)\) \(e\left(\frac{41}{48}\right)\) \(-1\) \(e\left(\frac{23}{24}\right)\) \(e\left(\frac{37}{48}\right)\) \(e\left(\frac{19}{24}\right)\) \(e\left(\frac{9}{16}\right)\) \(e\left(\frac{35}{48}\right)\) \(e\left(\frac{7}{48}\right)\) \(e\left(\frac{11}{16}\right)\)
\(\chi_{5712}(3635,\cdot)\) \(-1\) \(1\) \(e\left(\frac{35}{48}\right)\) \(e\left(\frac{1}{48}\right)\) \(-1\) \(e\left(\frac{7}{24}\right)\) \(e\left(\frac{29}{48}\right)\) \(e\left(\frac{11}{24}\right)\) \(e\left(\frac{1}{16}\right)\) \(e\left(\frac{43}{48}\right)\) \(e\left(\frac{47}{48}\right)\) \(e\left(\frac{3}{16}\right)\)
\(\chi_{5712}(4211,\cdot)\) \(-1\) \(1\) \(e\left(\frac{31}{48}\right)\) \(e\left(\frac{5}{48}\right)\) \(-1\) \(e\left(\frac{11}{24}\right)\) \(e\left(\frac{1}{48}\right)\) \(e\left(\frac{7}{24}\right)\) \(e\left(\frac{5}{16}\right)\) \(e\left(\frac{23}{48}\right)\) \(e\left(\frac{43}{48}\right)\) \(e\left(\frac{15}{16}\right)\)
\(\chi_{5712}(4379,\cdot)\) \(-1\) \(1\) \(e\left(\frac{1}{48}\right)\) \(e\left(\frac{11}{48}\right)\) \(-1\) \(e\left(\frac{5}{24}\right)\) \(e\left(\frac{31}{48}\right)\) \(e\left(\frac{1}{24}\right)\) \(e\left(\frac{11}{16}\right)\) \(e\left(\frac{41}{48}\right)\) \(e\left(\frac{37}{48}\right)\) \(e\left(\frac{1}{16}\right)\)
\(\chi_{5712}(4715,\cdot)\) \(-1\) \(1\) \(e\left(\frac{37}{48}\right)\) \(e\left(\frac{23}{48}\right)\) \(-1\) \(e\left(\frac{17}{24}\right)\) \(e\left(\frac{43}{48}\right)\) \(e\left(\frac{13}{24}\right)\) \(e\left(\frac{7}{16}\right)\) \(e\left(\frac{29}{48}\right)\) \(e\left(\frac{25}{48}\right)\) \(e\left(\frac{5}{16}\right)\)