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Properties

Label 1984.ck
Modulus $1984$
Conductor $1984$
Order $48$
Real no
Primitive yes
Minimal yes
Parity even

Related objects

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Show commands: Pari/GP / SageMath
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1984, base_ring=CyclotomicField(48)) M = H._module chi = DirichletCharacter(H, M([0,3,32])) chi.galois_orbit()
 
Copy content pari:[g,chi] = znchar(Mod(5,1984)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: \(1984\)
Conductor: \(1984\)
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: 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 \(-1\) \(1\) \(3\) \(5\) \(7\) \(9\) \(11\) \(13\) \(15\) \(17\) \(19\) \(21\)
\(\chi_{1984}(5,\cdot)\) \(1\) \(1\) \(e\left(\frac{41}{48}\right)\) \(e\left(\frac{19}{48}\right)\) \(e\left(\frac{7}{24}\right)\) \(e\left(\frac{17}{24}\right)\) \(e\left(\frac{31}{48}\right)\) \(e\left(\frac{13}{48}\right)\) \(i\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{5}{48}\right)\) \(e\left(\frac{7}{48}\right)\)
\(\chi_{1984}(149,\cdot)\) \(1\) \(1\) \(e\left(\frac{37}{48}\right)\) \(e\left(\frac{23}{48}\right)\) \(e\left(\frac{11}{24}\right)\) \(e\left(\frac{13}{24}\right)\) \(e\left(\frac{35}{48}\right)\) \(e\left(\frac{41}{48}\right)\) \(i\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{1}{48}\right)\) \(e\left(\frac{11}{48}\right)\)
\(\chi_{1984}(253,\cdot)\) \(1\) \(1\) \(e\left(\frac{11}{48}\right)\) \(e\left(\frac{25}{48}\right)\) \(e\left(\frac{13}{24}\right)\) \(e\left(\frac{11}{24}\right)\) \(e\left(\frac{13}{48}\right)\) \(e\left(\frac{7}{48}\right)\) \(-i\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{47}{48}\right)\) \(e\left(\frac{37}{48}\right)\)
\(\chi_{1984}(397,\cdot)\) \(1\) \(1\) \(e\left(\frac{7}{48}\right)\) \(e\left(\frac{29}{48}\right)\) \(e\left(\frac{17}{24}\right)\) \(e\left(\frac{7}{24}\right)\) \(e\left(\frac{17}{48}\right)\) \(e\left(\frac{35}{48}\right)\) \(-i\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{43}{48}\right)\) \(e\left(\frac{41}{48}\right)\)
\(\chi_{1984}(501,\cdot)\) \(1\) \(1\) \(e\left(\frac{29}{48}\right)\) \(e\left(\frac{31}{48}\right)\) \(e\left(\frac{19}{24}\right)\) \(e\left(\frac{5}{24}\right)\) \(e\left(\frac{43}{48}\right)\) \(e\left(\frac{1}{48}\right)\) \(i\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{41}{48}\right)\) \(e\left(\frac{19}{48}\right)\)
\(\chi_{1984}(645,\cdot)\) \(1\) \(1\) \(e\left(\frac{25}{48}\right)\) \(e\left(\frac{35}{48}\right)\) \(e\left(\frac{23}{24}\right)\) \(e\left(\frac{1}{24}\right)\) \(e\left(\frac{47}{48}\right)\) \(e\left(\frac{29}{48}\right)\) \(i\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{37}{48}\right)\) \(e\left(\frac{23}{48}\right)\)
\(\chi_{1984}(749,\cdot)\) \(1\) \(1\) \(e\left(\frac{47}{48}\right)\) \(e\left(\frac{37}{48}\right)\) \(e\left(\frac{1}{24}\right)\) \(e\left(\frac{23}{24}\right)\) \(e\left(\frac{25}{48}\right)\) \(e\left(\frac{43}{48}\right)\) \(-i\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{35}{48}\right)\) \(e\left(\frac{1}{48}\right)\)
\(\chi_{1984}(893,\cdot)\) \(1\) \(1\) \(e\left(\frac{43}{48}\right)\) \(e\left(\frac{41}{48}\right)\) \(e\left(\frac{5}{24}\right)\) \(e\left(\frac{19}{24}\right)\) \(e\left(\frac{29}{48}\right)\) \(e\left(\frac{23}{48}\right)\) \(-i\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{31}{48}\right)\) \(e\left(\frac{5}{48}\right)\)
\(\chi_{1984}(997,\cdot)\) \(1\) \(1\) \(e\left(\frac{17}{48}\right)\) \(e\left(\frac{43}{48}\right)\) \(e\left(\frac{7}{24}\right)\) \(e\left(\frac{17}{24}\right)\) \(e\left(\frac{7}{48}\right)\) \(e\left(\frac{37}{48}\right)\) \(i\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{29}{48}\right)\) \(e\left(\frac{31}{48}\right)\)
\(\chi_{1984}(1141,\cdot)\) \(1\) \(1\) \(e\left(\frac{13}{48}\right)\) \(e\left(\frac{47}{48}\right)\) \(e\left(\frac{11}{24}\right)\) \(e\left(\frac{13}{24}\right)\) \(e\left(\frac{11}{48}\right)\) \(e\left(\frac{17}{48}\right)\) \(i\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{25}{48}\right)\) \(e\left(\frac{35}{48}\right)\)
\(\chi_{1984}(1245,\cdot)\) \(1\) \(1\) \(e\left(\frac{35}{48}\right)\) \(e\left(\frac{1}{48}\right)\) \(e\left(\frac{13}{24}\right)\) \(e\left(\frac{11}{24}\right)\) \(e\left(\frac{37}{48}\right)\) \(e\left(\frac{31}{48}\right)\) \(-i\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{23}{48}\right)\) \(e\left(\frac{13}{48}\right)\)
\(\chi_{1984}(1389,\cdot)\) \(1\) \(1\) \(e\left(\frac{31}{48}\right)\) \(e\left(\frac{5}{48}\right)\) \(e\left(\frac{17}{24}\right)\) \(e\left(\frac{7}{24}\right)\) \(e\left(\frac{41}{48}\right)\) \(e\left(\frac{11}{48}\right)\) \(-i\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{19}{48}\right)\) \(e\left(\frac{17}{48}\right)\)
\(\chi_{1984}(1493,\cdot)\) \(1\) \(1\) \(e\left(\frac{5}{48}\right)\) \(e\left(\frac{7}{48}\right)\) \(e\left(\frac{19}{24}\right)\) \(e\left(\frac{5}{24}\right)\) \(e\left(\frac{19}{48}\right)\) \(e\left(\frac{25}{48}\right)\) \(i\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{17}{48}\right)\) \(e\left(\frac{43}{48}\right)\)
\(\chi_{1984}(1637,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{48}\right)\) \(e\left(\frac{11}{48}\right)\) \(e\left(\frac{23}{24}\right)\) \(e\left(\frac{1}{24}\right)\) \(e\left(\frac{23}{48}\right)\) \(e\left(\frac{5}{48}\right)\) \(i\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{13}{48}\right)\) \(e\left(\frac{47}{48}\right)\)
\(\chi_{1984}(1741,\cdot)\) \(1\) \(1\) \(e\left(\frac{23}{48}\right)\) \(e\left(\frac{13}{48}\right)\) \(e\left(\frac{1}{24}\right)\) \(e\left(\frac{23}{24}\right)\) \(e\left(\frac{1}{48}\right)\) \(e\left(\frac{19}{48}\right)\) \(-i\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{11}{48}\right)\) \(e\left(\frac{25}{48}\right)\)
\(\chi_{1984}(1885,\cdot)\) \(1\) \(1\) \(e\left(\frac{19}{48}\right)\) \(e\left(\frac{17}{48}\right)\) \(e\left(\frac{5}{24}\right)\) \(e\left(\frac{19}{24}\right)\) \(e\left(\frac{5}{48}\right)\) \(e\left(\frac{47}{48}\right)\) \(-i\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{7}{48}\right)\) \(e\left(\frac{29}{48}\right)\)