↑

Properties

Label 1309.cj
Modulus $1309$
Conductor $119$
Order $48$
Real no
Primitive no
Minimal yes
Parity even

Related objects

Downloads

Learn more

Show commands: Pari/GP / SageMath
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1309, base_ring=CyclotomicField(48)) M = H._module chi = DirichletCharacter(H, M([40,0,39])) chi.galois_orbit()
 
Copy content pari:[g,chi] = znchar(Mod(12,1309)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: \(1309\)
Conductor: \(119\)
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: no, induced from 119.s
Copy content sage:chi.is_primitive()
 
Copy content pari:#znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
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 \(-1\) \(1\) \(2\) \(3\) \(4\) \(5\) \(6\) \(8\) \(9\) \(10\) \(12\) \(13\)
\(\chi_{1309}(12,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{24}\right)\) \(e\left(\frac{31}{48}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{11}{48}\right)\) \(e\left(\frac{11}{16}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{7}{24}\right)\) \(e\left(\frac{13}{48}\right)\) \(e\left(\frac{35}{48}\right)\) \(-i\)
\(\chi_{1309}(45,\cdot)\) \(1\) \(1\) \(e\left(\frac{11}{24}\right)\) \(e\left(\frac{29}{48}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{1}{48}\right)\) \(e\left(\frac{1}{16}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{5}{24}\right)\) \(e\left(\frac{23}{48}\right)\) \(e\left(\frac{25}{48}\right)\) \(i\)
\(\chi_{1309}(122,\cdot)\) \(1\) \(1\) \(e\left(\frac{5}{24}\right)\) \(e\left(\frac{11}{48}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{7}{48}\right)\) \(e\left(\frac{7}{16}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{11}{24}\right)\) \(e\left(\frac{17}{48}\right)\) \(e\left(\frac{31}{48}\right)\) \(-i\)
\(\chi_{1309}(199,\cdot)\) \(1\) \(1\) \(e\left(\frac{17}{24}\right)\) \(e\left(\frac{47}{48}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{43}{48}\right)\) \(e\left(\frac{11}{16}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{23}{24}\right)\) \(e\left(\frac{29}{48}\right)\) \(e\left(\frac{19}{48}\right)\) \(-i\)
\(\chi_{1309}(243,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{24}\right)\) \(e\left(\frac{7}{48}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{35}{48}\right)\) \(e\left(\frac{3}{16}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{7}{24}\right)\) \(e\left(\frac{37}{48}\right)\) \(e\left(\frac{11}{48}\right)\) \(-i\)
\(\chi_{1309}(320,\cdot)\) \(1\) \(1\) \(e\left(\frac{13}{24}\right)\) \(e\left(\frac{19}{48}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{47}{48}\right)\) \(e\left(\frac{15}{16}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{19}{24}\right)\) \(e\left(\frac{25}{48}\right)\) \(e\left(\frac{23}{48}\right)\) \(-i\)
\(\chi_{1309}(397,\cdot)\) \(1\) \(1\) \(e\left(\frac{19}{24}\right)\) \(e\left(\frac{37}{48}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{41}{48}\right)\) \(e\left(\frac{9}{16}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{13}{24}\right)\) \(e\left(\frac{31}{48}\right)\) \(e\left(\frac{17}{48}\right)\) \(i\)
\(\chi_{1309}(430,\cdot)\) \(1\) \(1\) \(e\left(\frac{17}{24}\right)\) \(e\left(\frac{23}{48}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{19}{48}\right)\) \(e\left(\frac{3}{16}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{23}{24}\right)\) \(e\left(\frac{5}{48}\right)\) \(e\left(\frac{43}{48}\right)\) \(-i\)
\(\chi_{1309}(507,\cdot)\) \(1\) \(1\) \(e\left(\frac{5}{24}\right)\) \(e\left(\frac{35}{48}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{31}{48}\right)\) \(e\left(\frac{15}{16}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{11}{24}\right)\) \(e\left(\frac{41}{48}\right)\) \(e\left(\frac{7}{48}\right)\) \(-i\)
\(\chi_{1309}(551,\cdot)\) \(1\) \(1\) \(e\left(\frac{7}{24}\right)\) \(e\left(\frac{25}{48}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{29}{48}\right)\) \(e\left(\frac{13}{16}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{1}{24}\right)\) \(e\left(\frac{43}{48}\right)\) \(e\left(\frac{5}{48}\right)\) \(i\)
\(\chi_{1309}(584,\cdot)\) \(1\) \(1\) \(e\left(\frac{11}{24}\right)\) \(e\left(\frac{5}{48}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{25}{48}\right)\) \(e\left(\frac{9}{16}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{5}{24}\right)\) \(e\left(\frac{47}{48}\right)\) \(e\left(\frac{1}{48}\right)\) \(i\)
\(\chi_{1309}(738,\cdot)\) \(1\) \(1\) \(e\left(\frac{23}{24}\right)\) \(e\left(\frac{41}{48}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{13}{48}\right)\) \(e\left(\frac{13}{16}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{17}{24}\right)\) \(e\left(\frac{11}{48}\right)\) \(e\left(\frac{37}{48}\right)\) \(i\)
\(\chi_{1309}(1013,\cdot)\) \(1\) \(1\) \(e\left(\frac{7}{24}\right)\) \(e\left(\frac{1}{48}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{5}{48}\right)\) \(e\left(\frac{5}{16}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{1}{24}\right)\) \(e\left(\frac{19}{48}\right)\) \(e\left(\frac{29}{48}\right)\) \(i\)
\(\chi_{1309}(1167,\cdot)\) \(1\) \(1\) \(e\left(\frac{19}{24}\right)\) \(e\left(\frac{13}{48}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{17}{48}\right)\) \(e\left(\frac{1}{16}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{13}{24}\right)\) \(e\left(\frac{7}{48}\right)\) \(e\left(\frac{41}{48}\right)\) \(i\)
\(\chi_{1309}(1200,\cdot)\) \(1\) \(1\) \(e\left(\frac{23}{24}\right)\) \(e\left(\frac{17}{48}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{37}{48}\right)\) \(e\left(\frac{5}{16}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{17}{24}\right)\) \(e\left(\frac{35}{48}\right)\) \(e\left(\frac{13}{48}\right)\) \(i\)
\(\chi_{1309}(1244,\cdot)\) \(1\) \(1\) \(e\left(\frac{13}{24}\right)\) \(e\left(\frac{43}{48}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{23}{48}\right)\) \(e\left(\frac{7}{16}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{19}{24}\right)\) \(e\left(\frac{1}{48}\right)\) \(e\left(\frac{47}{48}\right)\) \(-i\)