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Properties

Label 6800.iv
Modulus $6800$
Conductor $6800$
Order $40$
Real no
Primitive yes
Minimal yes
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([0,30,32,35])) chi.galois_orbit()
 
Copy content pari:[g,chi] = znchar(Mod(461,6800)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: \(6800\)
Conductor: \(6800\)
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: 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: \(\Q(\zeta_{40})\)
Fixed field: Number field defined by a degree 40 polynomial

Characters in Galois orbit

Character \(-1\) \(1\) \(3\) \(7\) \(9\) \(11\) \(13\) \(19\) \(21\) \(23\) \(27\) \(29\)
\(\chi_{6800}(461,\cdot)\) \(1\) \(1\) \(e\left(\frac{29}{40}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{27}{40}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{17}{40}\right)\) \(e\left(\frac{7}{40}\right)\) \(e\left(\frac{9}{40}\right)\)
\(\chi_{6800}(1341,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{40}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{23}{40}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{13}{40}\right)\) \(e\left(\frac{3}{40}\right)\) \(e\left(\frac{21}{40}\right)\)
\(\chi_{6800}(1821,\cdot)\) \(1\) \(1\) \(e\left(\frac{13}{40}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{19}{40}\right)\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{9}{40}\right)\) \(e\left(\frac{39}{40}\right)\) \(e\left(\frac{33}{40}\right)\)
\(\chi_{6800}(1861,\cdot)\) \(1\) \(1\) \(e\left(\frac{39}{40}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{17}{40}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{27}{40}\right)\) \(e\left(\frac{37}{40}\right)\) \(e\left(\frac{19}{40}\right)\)
\(\chi_{6800}(2661,\cdot)\) \(1\) \(1\) \(e\left(\frac{19}{40}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{37}{40}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{7}{40}\right)\) \(e\left(\frac{17}{40}\right)\) \(e\left(\frac{39}{40}\right)\)
\(\chi_{6800}(3181,\cdot)\) \(1\) \(1\) \(e\left(\frac{37}{40}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{11}{40}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{1}{40}\right)\) \(e\left(\frac{31}{40}\right)\) \(e\left(\frac{17}{40}\right)\)
\(\chi_{6800}(3221,\cdot)\) \(1\) \(1\) \(e\left(\frac{23}{40}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{9}{40}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{19}{40}\right)\) \(e\left(\frac{29}{40}\right)\) \(e\left(\frac{3}{40}\right)\)
\(\chi_{6800}(4021,\cdot)\) \(1\) \(1\) \(e\left(\frac{3}{40}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{29}{40}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{39}{40}\right)\) \(e\left(\frac{9}{40}\right)\) \(e\left(\frac{23}{40}\right)\)
\(\chi_{6800}(4061,\cdot)\) \(1\) \(1\) \(e\left(\frac{9}{40}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{7}{40}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{37}{40}\right)\) \(e\left(\frac{27}{40}\right)\) \(e\left(\frac{29}{40}\right)\)
\(\chi_{6800}(4541,\cdot)\) \(1\) \(1\) \(e\left(\frac{21}{40}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{3}{40}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{33}{40}\right)\) \(e\left(\frac{23}{40}\right)\) \(e\left(\frac{1}{40}\right)\)
\(\chi_{6800}(4581,\cdot)\) \(1\) \(1\) \(e\left(\frac{7}{40}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{1}{40}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{11}{40}\right)\) \(e\left(\frac{21}{40}\right)\) \(e\left(\frac{27}{40}\right)\)
\(\chi_{6800}(5381,\cdot)\) \(1\) \(1\) \(e\left(\frac{27}{40}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{21}{40}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{31}{40}\right)\) \(e\left(\frac{1}{40}\right)\) \(e\left(\frac{7}{40}\right)\)
\(\chi_{6800}(5421,\cdot)\) \(1\) \(1\) \(e\left(\frac{33}{40}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{39}{40}\right)\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{29}{40}\right)\) \(e\left(\frac{19}{40}\right)\) \(e\left(\frac{13}{40}\right)\)
\(\chi_{6800}(5941,\cdot)\) \(1\) \(1\) \(e\left(\frac{31}{40}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{33}{40}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{3}{40}\right)\) \(e\left(\frac{13}{40}\right)\) \(e\left(\frac{11}{40}\right)\)
\(\chi_{6800}(6741,\cdot)\) \(1\) \(1\) \(e\left(\frac{11}{40}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{13}{40}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{23}{40}\right)\) \(e\left(\frac{33}{40}\right)\) \(e\left(\frac{31}{40}\right)\)
\(\chi_{6800}(6781,\cdot)\) \(1\) \(1\) \(e\left(\frac{17}{40}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{31}{40}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{21}{40}\right)\) \(e\left(\frac{11}{40}\right)\) \(e\left(\frac{37}{40}\right)\)