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Properties

Label 6336.ek
Modulus $6336$
Conductor $352$
Order $40$
Real no
Primitive no
Minimal no
Parity even

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Show commands: Pari/GP / SageMath
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(6336, base_ring=CyclotomicField(40)) M = H._module chi = DirichletCharacter(H, M([20,35,0,4])) chi.galois_orbit()
 
Copy content pari:[g,chi] = znchar(Mod(343,6336)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: \(6336\)
Conductor: \(352\)
Copy content sage:chi.conductor()
 
Copy content pari:znconreyconductor(g,chi)
 
Order: \(40\)
Copy content sage:chi.multiplicative_order()
 
Copy content pari:charorder(g,chi)
 
Real: no
Primitive: no, induced from 352.bc
Copy content sage:chi.is_primitive()
 
Copy content pari:#znconreyconductor(g,chi)==1
 
Minimal: no
Parity: even
Copy content sage:chi.is_odd()
 
Copy content pari:zncharisodd(g,chi)
 

Related number fields

Field of values: \(\Q(\zeta_{40})\)
Fixed field: 40.40.1411841662908675517629776705295515492024702234241930698046194396081616318012166504448.1

Characters in Galois orbit

Character \(-1\) \(1\) \(5\) \(7\) \(13\) \(17\) \(19\) \(23\) \(25\) \(29\) \(31\) \(35\)
\(\chi_{6336}(343,\cdot)\) \(1\) \(1\) \(e\left(\frac{11}{40}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{9}{40}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{37}{40}\right)\) \(-i\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{13}{40}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{9}{40}\right)\)
\(\chi_{6336}(919,\cdot)\) \(1\) \(1\) \(e\left(\frac{19}{40}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{1}{40}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{13}{40}\right)\) \(-i\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{37}{40}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{1}{40}\right)\)
\(\chi_{6336}(1063,\cdot)\) \(1\) \(1\) \(e\left(\frac{37}{40}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{23}{40}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{19}{40}\right)\) \(i\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{11}{40}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{23}{40}\right)\)
\(\chi_{6336}(1207,\cdot)\) \(1\) \(1\) \(e\left(\frac{23}{40}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{37}{40}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{1}{40}\right)\) \(-i\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{9}{40}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{37}{40}\right)\)
\(\chi_{6336}(1927,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{40}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{19}{40}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{7}{40}\right)\) \(i\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{23}{40}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{19}{40}\right)\)
\(\chi_{6336}(2503,\cdot)\) \(1\) \(1\) \(e\left(\frac{9}{40}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{11}{40}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{23}{40}\right)\) \(i\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{7}{40}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{11}{40}\right)\)
\(\chi_{6336}(2647,\cdot)\) \(1\) \(1\) \(e\left(\frac{27}{40}\right)\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{33}{40}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{29}{40}\right)\) \(-i\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{21}{40}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{33}{40}\right)\)
\(\chi_{6336}(2791,\cdot)\) \(1\) \(1\) \(e\left(\frac{13}{40}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{7}{40}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{11}{40}\right)\) \(i\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{19}{40}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{7}{40}\right)\)
\(\chi_{6336}(3511,\cdot)\) \(1\) \(1\) \(e\left(\frac{31}{40}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{29}{40}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{17}{40}\right)\) \(-i\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{33}{40}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{29}{40}\right)\)
\(\chi_{6336}(4087,\cdot)\) \(1\) \(1\) \(e\left(\frac{39}{40}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{21}{40}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{33}{40}\right)\) \(-i\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{17}{40}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{21}{40}\right)\)
\(\chi_{6336}(4231,\cdot)\) \(1\) \(1\) \(e\left(\frac{17}{40}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{3}{40}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{39}{40}\right)\) \(i\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{31}{40}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{3}{40}\right)\)
\(\chi_{6336}(4375,\cdot)\) \(1\) \(1\) \(e\left(\frac{3}{40}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{17}{40}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{21}{40}\right)\) \(-i\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{29}{40}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{17}{40}\right)\)
\(\chi_{6336}(5095,\cdot)\) \(1\) \(1\) \(e\left(\frac{21}{40}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{39}{40}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{27}{40}\right)\) \(i\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{3}{40}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{39}{40}\right)\)
\(\chi_{6336}(5671,\cdot)\) \(1\) \(1\) \(e\left(\frac{29}{40}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{31}{40}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{3}{40}\right)\) \(i\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{27}{40}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{31}{40}\right)\)
\(\chi_{6336}(5815,\cdot)\) \(1\) \(1\) \(e\left(\frac{7}{40}\right)\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{13}{40}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{9}{40}\right)\) \(-i\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{1}{40}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{13}{40}\right)\)
\(\chi_{6336}(5959,\cdot)\) \(1\) \(1\) \(e\left(\frac{33}{40}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{27}{40}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{31}{40}\right)\) \(i\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{39}{40}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{27}{40}\right)\)