↑

Properties

Label 8640.gt
Modulus $8640$
Conductor $576$
Order $48$
Real no
Primitive no
Minimal no
Parity even

Related objects

Downloads

Learn more

Show commands: Magma / Pari/GP / SageMath
Copy content comment:Define the Dirichlet character orbit
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(8640, base_ring=CyclotomicField(48)) M = H._module chi = DirichletCharacter(H, M([24,3,8,0])) chi.galois_orbit()
 
Copy content gp:[g,chi] = znchar(Mod(251, 8640)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 
Copy content magma:// Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("8640.251"); order := Order(chi); { chi^k : k in [1..order-1] | GCD(k,order) eq 1 };
 

Basic properties

Modulus: \(8640\)
Copy content comment:Modulus
 
Copy content sage:chi.modulus()
 
Copy content gp:g[1][1]
 
Copy content magma:Modulus(chi);
 
Conductor: \(576\)
Copy content comment:Conductor
 
Copy content sage:chi.conductor()
 
Copy content gp:znconreyconductor(g,chi)
 
Copy content magma:Conductor(chi);
 
Order: \(48\)
Copy content comment:Order
 
Copy content sage:chi.multiplicative_order()
 
Copy content gp:charorder(g,chi)
 
Copy content magma:Order(chi);
 
Real: no
Copy content comment:Whether the character is real
 
Copy content sage:chi.multiplicative_order() <= 2
 
Copy content gp:charorder(g,chi) <= 2
 
Copy content magma:Order(chi) le 2;
 
Primitive: no, induced from 576.bl
Copy content comment:If the character is primitive
 
Copy content sage:chi.is_primitive()
 
Copy content gp:#znconreyconductor(g,chi)==1
 
Copy content magma:IsPrimitive(chi);
 
Minimal: no
Parity: even
Copy content comment:Parity
 
Copy content sage:chi.is_odd()
 
Copy content gp:zncharisodd(g,chi)
 
Copy content magma:IsOdd(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 \(-1\) \(1\) \(7\) \(11\) \(13\) \(17\) \(19\) \(23\) \(29\) \(31\) \(37\) \(41\)
\(\chi_{8640}(251,\cdot)\) \(1\) \(1\) \(e\left(\frac{19}{24}\right)\) \(e\left(\frac{47}{48}\right)\) \(e\left(\frac{13}{48}\right)\) \(i\) \(e\left(\frac{15}{16}\right)\) \(e\left(\frac{5}{24}\right)\) \(e\left(\frac{41}{48}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{9}{16}\right)\) \(e\left(\frac{17}{24}\right)\)
\(\chi_{8640}(611,\cdot)\) \(1\) \(1\) \(e\left(\frac{17}{24}\right)\) \(e\left(\frac{37}{48}\right)\) \(e\left(\frac{47}{48}\right)\) \(-i\) \(e\left(\frac{5}{16}\right)\) \(e\left(\frac{7}{24}\right)\) \(e\left(\frac{19}{48}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{3}{16}\right)\) \(e\left(\frac{19}{24}\right)\)
\(\chi_{8640}(1331,\cdot)\) \(1\) \(1\) \(e\left(\frac{13}{24}\right)\) \(e\left(\frac{17}{48}\right)\) \(e\left(\frac{19}{48}\right)\) \(-i\) \(e\left(\frac{1}{16}\right)\) \(e\left(\frac{11}{24}\right)\) \(e\left(\frac{23}{48}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{7}{16}\right)\) \(e\left(\frac{23}{24}\right)\)
\(\chi_{8640}(1691,\cdot)\) \(1\) \(1\) \(e\left(\frac{11}{24}\right)\) \(e\left(\frac{7}{48}\right)\) \(e\left(\frac{5}{48}\right)\) \(i\) \(e\left(\frac{7}{16}\right)\) \(e\left(\frac{13}{24}\right)\) \(e\left(\frac{1}{48}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{16}\right)\) \(e\left(\frac{1}{24}\right)\)
\(\chi_{8640}(2411,\cdot)\) \(1\) \(1\) \(e\left(\frac{7}{24}\right)\) \(e\left(\frac{35}{48}\right)\) \(e\left(\frac{25}{48}\right)\) \(i\) \(e\left(\frac{3}{16}\right)\) \(e\left(\frac{17}{24}\right)\) \(e\left(\frac{5}{48}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{5}{16}\right)\) \(e\left(\frac{5}{24}\right)\)
\(\chi_{8640}(2771,\cdot)\) \(1\) \(1\) \(e\left(\frac{5}{24}\right)\) \(e\left(\frac{25}{48}\right)\) \(e\left(\frac{11}{48}\right)\) \(-i\) \(e\left(\frac{9}{16}\right)\) \(e\left(\frac{19}{24}\right)\) \(e\left(\frac{31}{48}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{15}{16}\right)\) \(e\left(\frac{7}{24}\right)\)
\(\chi_{8640}(3491,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{24}\right)\) \(e\left(\frac{5}{48}\right)\) \(e\left(\frac{31}{48}\right)\) \(-i\) \(e\left(\frac{5}{16}\right)\) \(e\left(\frac{23}{24}\right)\) \(e\left(\frac{35}{48}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{3}{16}\right)\) \(e\left(\frac{11}{24}\right)\)
\(\chi_{8640}(3851,\cdot)\) \(1\) \(1\) \(e\left(\frac{23}{24}\right)\) \(e\left(\frac{43}{48}\right)\) \(e\left(\frac{17}{48}\right)\) \(i\) \(e\left(\frac{11}{16}\right)\) \(e\left(\frac{1}{24}\right)\) \(e\left(\frac{13}{48}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{13}{16}\right)\) \(e\left(\frac{13}{24}\right)\)
\(\chi_{8640}(4571,\cdot)\) \(1\) \(1\) \(e\left(\frac{19}{24}\right)\) \(e\left(\frac{23}{48}\right)\) \(e\left(\frac{37}{48}\right)\) \(i\) \(e\left(\frac{7}{16}\right)\) \(e\left(\frac{5}{24}\right)\) \(e\left(\frac{17}{48}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{16}\right)\) \(e\left(\frac{17}{24}\right)\)
\(\chi_{8640}(4931,\cdot)\) \(1\) \(1\) \(e\left(\frac{17}{24}\right)\) \(e\left(\frac{13}{48}\right)\) \(e\left(\frac{23}{48}\right)\) \(-i\) \(e\left(\frac{13}{16}\right)\) \(e\left(\frac{7}{24}\right)\) \(e\left(\frac{43}{48}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{11}{16}\right)\) \(e\left(\frac{19}{24}\right)\)
\(\chi_{8640}(5651,\cdot)\) \(1\) \(1\) \(e\left(\frac{13}{24}\right)\) \(e\left(\frac{41}{48}\right)\) \(e\left(\frac{43}{48}\right)\) \(-i\) \(e\left(\frac{9}{16}\right)\) \(e\left(\frac{11}{24}\right)\) \(e\left(\frac{47}{48}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{15}{16}\right)\) \(e\left(\frac{23}{24}\right)\)
\(\chi_{8640}(6011,\cdot)\) \(1\) \(1\) \(e\left(\frac{11}{24}\right)\) \(e\left(\frac{31}{48}\right)\) \(e\left(\frac{29}{48}\right)\) \(i\) \(e\left(\frac{15}{16}\right)\) \(e\left(\frac{13}{24}\right)\) \(e\left(\frac{25}{48}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{9}{16}\right)\) \(e\left(\frac{1}{24}\right)\)
\(\chi_{8640}(6731,\cdot)\) \(1\) \(1\) \(e\left(\frac{7}{24}\right)\) \(e\left(\frac{11}{48}\right)\) \(e\left(\frac{1}{48}\right)\) \(i\) \(e\left(\frac{11}{16}\right)\) \(e\left(\frac{17}{24}\right)\) \(e\left(\frac{29}{48}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{13}{16}\right)\) \(e\left(\frac{5}{24}\right)\)
\(\chi_{8640}(7091,\cdot)\) \(1\) \(1\) \(e\left(\frac{5}{24}\right)\) \(e\left(\frac{1}{48}\right)\) \(e\left(\frac{35}{48}\right)\) \(-i\) \(e\left(\frac{1}{16}\right)\) \(e\left(\frac{19}{24}\right)\) \(e\left(\frac{7}{48}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{7}{16}\right)\) \(e\left(\frac{7}{24}\right)\)
\(\chi_{8640}(7811,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{24}\right)\) \(e\left(\frac{29}{48}\right)\) \(e\left(\frac{7}{48}\right)\) \(-i\) \(e\left(\frac{13}{16}\right)\) \(e\left(\frac{23}{24}\right)\) \(e\left(\frac{11}{48}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{11}{16}\right)\) \(e\left(\frac{11}{24}\right)\)
\(\chi_{8640}(8171,\cdot)\) \(1\) \(1\) \(e\left(\frac{23}{24}\right)\) \(e\left(\frac{19}{48}\right)\) \(e\left(\frac{41}{48}\right)\) \(i\) \(e\left(\frac{3}{16}\right)\) \(e\left(\frac{1}{24}\right)\) \(e\left(\frac{37}{48}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{5}{16}\right)\) \(e\left(\frac{13}{24}\right)\)