↑

Properties

Label 8007.cy
Modulus $8007$
Conductor $2669$
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(8007, base_ring=CyclotomicField(48)) M = H._module chi = DirichletCharacter(H, M([0,15,4])) chi.galois_orbit()
 
Copy content pari:[g,chi] = znchar(Mod(22,8007)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: \(8007\)
Conductor: \(2669\)
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 2669.bn
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 \(-1\) \(1\) \(2\) \(4\) \(5\) \(7\) \(8\) \(10\) \(11\) \(13\) \(14\) \(16\)
\(\chi_{8007}(22,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{8}\right)\) \(i\) \(e\left(\frac{31}{48}\right)\) \(e\left(\frac{11}{16}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{37}{48}\right)\) \(e\left(\frac{25}{48}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{13}{16}\right)\) \(-1\)
\(\chi_{8007}(364,\cdot)\) \(1\) \(1\) \(e\left(\frac{7}{8}\right)\) \(-i\) \(e\left(\frac{17}{48}\right)\) \(e\left(\frac{5}{16}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{11}{48}\right)\) \(e\left(\frac{23}{48}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{3}{16}\right)\) \(-1\)
\(\chi_{8007}(964,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{8}\right)\) \(i\) \(e\left(\frac{7}{48}\right)\) \(e\left(\frac{3}{16}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{13}{48}\right)\) \(e\left(\frac{1}{48}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{5}{16}\right)\) \(-1\)
\(\chi_{8007}(1234,\cdot)\) \(1\) \(1\) \(e\left(\frac{7}{8}\right)\) \(-i\) \(e\left(\frac{25}{48}\right)\) \(e\left(\frac{13}{16}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{19}{48}\right)\) \(e\left(\frac{31}{48}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{11}{16}\right)\) \(-1\)
\(\chi_{8007}(1363,\cdot)\) \(1\) \(1\) \(e\left(\frac{5}{8}\right)\) \(i\) \(e\left(\frac{35}{48}\right)\) \(e\left(\frac{15}{16}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{17}{48}\right)\) \(e\left(\frac{5}{48}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{9}{16}\right)\) \(-1\)
\(\chi_{8007}(2377,\cdot)\) \(1\) \(1\) \(e\left(\frac{5}{8}\right)\) \(i\) \(e\left(\frac{43}{48}\right)\) \(e\left(\frac{7}{16}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{25}{48}\right)\) \(e\left(\frac{13}{48}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{1}{16}\right)\) \(-1\)
\(\chi_{8007}(2776,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{8}\right)\) \(i\) \(e\left(\frac{47}{48}\right)\) \(e\left(\frac{11}{16}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{5}{48}\right)\) \(e\left(\frac{41}{48}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{13}{16}\right)\) \(-1\)
\(\chi_{8007}(3118,\cdot)\) \(1\) \(1\) \(e\left(\frac{7}{8}\right)\) \(-i\) \(e\left(\frac{1}{48}\right)\) \(e\left(\frac{5}{16}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{43}{48}\right)\) \(e\left(\frac{7}{48}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{3}{16}\right)\) \(-1\)
\(\chi_{8007}(3190,\cdot)\) \(1\) \(1\) \(e\left(\frac{3}{8}\right)\) \(-i\) \(e\left(\frac{5}{48}\right)\) \(e\left(\frac{9}{16}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{23}{48}\right)\) \(e\left(\frac{35}{48}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{15}{16}\right)\) \(-1\)
\(\chi_{8007}(3661,\cdot)\) \(1\) \(1\) \(e\left(\frac{3}{8}\right)\) \(-i\) \(e\left(\frac{29}{48}\right)\) \(e\left(\frac{1}{16}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{47}{48}\right)\) \(e\left(\frac{11}{48}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{7}{16}\right)\) \(-1\)
\(\chi_{8007}(3718,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{8}\right)\) \(i\) \(e\left(\frac{23}{48}\right)\) \(e\left(\frac{3}{16}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{29}{48}\right)\) \(e\left(\frac{17}{48}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{5}{16}\right)\) \(-1\)
\(\chi_{8007}(5131,\cdot)\) \(1\) \(1\) \(e\left(\frac{5}{8}\right)\) \(i\) \(e\left(\frac{11}{48}\right)\) \(e\left(\frac{7}{16}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{41}{48}\right)\) \(e\left(\frac{29}{48}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{1}{16}\right)\) \(-1\)
\(\chi_{8007}(5944,\cdot)\) \(1\) \(1\) \(e\left(\frac{3}{8}\right)\) \(-i\) \(e\left(\frac{37}{48}\right)\) \(e\left(\frac{9}{16}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{7}{48}\right)\) \(e\left(\frac{19}{48}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{15}{16}\right)\) \(-1\)
\(\chi_{8007}(6415,\cdot)\) \(1\) \(1\) \(e\left(\frac{3}{8}\right)\) \(-i\) \(e\left(\frac{13}{48}\right)\) \(e\left(\frac{1}{16}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{31}{48}\right)\) \(e\left(\frac{43}{48}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{7}{16}\right)\) \(-1\)
\(\chi_{8007}(6487,\cdot)\) \(1\) \(1\) \(e\left(\frac{7}{8}\right)\) \(-i\) \(e\left(\frac{41}{48}\right)\) \(e\left(\frac{13}{16}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{35}{48}\right)\) \(e\left(\frac{47}{48}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{11}{16}\right)\) \(-1\)
\(\chi_{8007}(6616,\cdot)\) \(1\) \(1\) \(e\left(\frac{5}{8}\right)\) \(i\) \(e\left(\frac{19}{48}\right)\) \(e\left(\frac{15}{16}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{1}{48}\right)\) \(e\left(\frac{37}{48}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{9}{16}\right)\) \(-1\)