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Properties

Label 6800.id
Modulus $6800$
Conductor $3400$
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(6800, base_ring=CyclotomicField(40)) M = H._module chi = DirichletCharacter(H, M([0,20,24,35])) chi.galois_orbit()
 
Copy content pari:[g,chi] = znchar(Mod(121,6800)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: \(6800\)
Conductor: \(3400\)
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 3400.ej
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: Number field defined by a degree 40 polynomial

Characters in Galois orbit

Character \(-1\) \(1\) \(3\) \(7\) \(9\) \(11\) \(13\) \(19\) \(21\) \(23\) \(27\) \(29\)
\(\chi_{6800}(121,\cdot)\) \(1\) \(1\) \(e\left(\frac{23}{40}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{9}{40}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{29}{40}\right)\) \(e\left(\frac{29}{40}\right)\) \(e\left(\frac{3}{40}\right)\)
\(\chi_{6800}(281,\cdot)\) \(1\) \(1\) \(e\left(\frac{17}{40}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{31}{40}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{11}{40}\right)\) \(e\left(\frac{11}{40}\right)\) \(e\left(\frac{37}{40}\right)\)
\(\chi_{6800}(841,\cdot)\) \(1\) \(1\) \(e\left(\frac{21}{40}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{3}{40}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{23}{40}\right)\) \(e\left(\frac{23}{40}\right)\) \(e\left(\frac{1}{40}\right)\)
\(\chi_{6800}(1481,\cdot)\) \(1\) \(1\) \(e\left(\frac{7}{40}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{1}{40}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{21}{40}\right)\) \(e\left(\frac{21}{40}\right)\) \(e\left(\frac{27}{40}\right)\)
\(\chi_{6800}(1641,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{40}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{23}{40}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{3}{40}\right)\) \(e\left(\frac{3}{40}\right)\) \(e\left(\frac{21}{40}\right)\)
\(\chi_{6800}(2361,\cdot)\) \(1\) \(1\) \(e\left(\frac{19}{40}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{37}{40}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{17}{40}\right)\) \(e\left(\frac{17}{40}\right)\) \(e\left(\frac{39}{40}\right)\)
\(\chi_{6800}(2841,\cdot)\) \(1\) \(1\) \(e\left(\frac{31}{40}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{33}{40}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{13}{40}\right)\) \(e\left(\frac{13}{40}\right)\) \(e\left(\frac{11}{40}\right)\)
\(\chi_{6800}(3561,\cdot)\) \(1\) \(1\) \(e\left(\frac{29}{40}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{27}{40}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{7}{40}\right)\) \(e\left(\frac{7}{40}\right)\) \(e\left(\frac{9}{40}\right)\)
\(\chi_{6800}(3721,\cdot)\) \(1\) \(1\) \(e\left(\frac{3}{40}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{29}{40}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{9}{40}\right)\) \(e\left(\frac{9}{40}\right)\) \(e\left(\frac{23}{40}\right)\)
\(\chi_{6800}(4361,\cdot)\) \(1\) \(1\) \(e\left(\frac{9}{40}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{7}{40}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{27}{40}\right)\) \(e\left(\frac{27}{40}\right)\) \(e\left(\frac{29}{40}\right)\)
\(\chi_{6800}(4921,\cdot)\) \(1\) \(1\) \(e\left(\frac{13}{40}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{19}{40}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{39}{40}\right)\) \(e\left(\frac{39}{40}\right)\) \(e\left(\frac{33}{40}\right)\)
\(\chi_{6800}(5081,\cdot)\) \(1\) \(1\) \(e\left(\frac{27}{40}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{21}{40}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{1}{40}\right)\) \(e\left(\frac{1}{40}\right)\) \(e\left(\frac{7}{40}\right)\)
\(\chi_{6800}(5561,\cdot)\) \(1\) \(1\) \(e\left(\frac{39}{40}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{17}{40}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{37}{40}\right)\) \(e\left(\frac{37}{40}\right)\) \(e\left(\frac{19}{40}\right)\)
\(\chi_{6800}(5721,\cdot)\) \(1\) \(1\) \(e\left(\frac{33}{40}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{39}{40}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{19}{40}\right)\) \(e\left(\frac{19}{40}\right)\) \(e\left(\frac{13}{40}\right)\)
\(\chi_{6800}(6281,\cdot)\) \(1\) \(1\) \(e\left(\frac{37}{40}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{11}{40}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{31}{40}\right)\) \(e\left(\frac{31}{40}\right)\) \(e\left(\frac{17}{40}\right)\)
\(\chi_{6800}(6441,\cdot)\) \(1\) \(1\) \(e\left(\frac{11}{40}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{13}{40}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{33}{40}\right)\) \(e\left(\frac{33}{40}\right)\) \(e\left(\frac{31}{40}\right)\)