↑

Properties

Label 820.cc
Modulus $820$
Conductor $820$
Order $40$
Real no
Primitive yes
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(820, base_ring=CyclotomicField(40)) M = H._module chi = DirichletCharacter(H, M([20,20,9])) chi.galois_orbit()
 
Copy content pari:[g,chi] = znchar(Mod(19,820)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: \(820\)
Conductor: \(820\)
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: 40.40.83017628936247865363646717578368932999206418219130479061598801598873600000000000000000000.1

Characters in Galois orbit

Character \(-1\) \(1\) \(3\) \(7\) \(9\) \(11\) \(13\) \(17\) \(19\) \(21\) \(23\) \(27\)
\(\chi_{820}(19,\cdot)\) \(1\) \(1\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{31}{40}\right)\) \(-i\) \(e\left(\frac{7}{40}\right)\) \(e\left(\frac{19}{40}\right)\) \(e\left(\frac{37}{40}\right)\) \(e\left(\frac{21}{40}\right)\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{1}{8}\right)\)
\(\chi_{820}(99,\cdot)\) \(1\) \(1\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{7}{40}\right)\) \(-i\) \(e\left(\frac{39}{40}\right)\) \(e\left(\frac{3}{40}\right)\) \(e\left(\frac{29}{40}\right)\) \(e\left(\frac{37}{40}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{1}{8}\right)\)
\(\chi_{820}(179,\cdot)\) \(1\) \(1\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{3}{40}\right)\) \(-i\) \(e\left(\frac{11}{40}\right)\) \(e\left(\frac{7}{40}\right)\) \(e\left(\frac{1}{40}\right)\) \(e\left(\frac{33}{40}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{5}{8}\right)\)
\(\chi_{820}(199,\cdot)\) \(1\) \(1\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{19}{40}\right)\) \(-i\) \(e\left(\frac{3}{40}\right)\) \(e\left(\frac{31}{40}\right)\) \(e\left(\frac{33}{40}\right)\) \(e\left(\frac{9}{40}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{5}{8}\right)\)
\(\chi_{820}(239,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{21}{40}\right)\) \(i\) \(e\left(\frac{37}{40}\right)\) \(e\left(\frac{9}{40}\right)\) \(e\left(\frac{7}{40}\right)\) \(e\left(\frac{31}{40}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{3}{8}\right)\)
\(\chi_{820}(259,\cdot)\) \(1\) \(1\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{9}{40}\right)\) \(i\) \(e\left(\frac{33}{40}\right)\) \(e\left(\frac{21}{40}\right)\) \(e\left(\frac{3}{40}\right)\) \(e\left(\frac{19}{40}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{7}{8}\right)\)
\(\chi_{820}(299,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{13}{40}\right)\) \(i\) \(e\left(\frac{21}{40}\right)\) \(e\left(\frac{17}{40}\right)\) \(e\left(\frac{31}{40}\right)\) \(e\left(\frac{23}{40}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{3}{8}\right)\)
\(\chi_{820}(339,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{37}{40}\right)\) \(i\) \(e\left(\frac{29}{40}\right)\) \(e\left(\frac{33}{40}\right)\) \(e\left(\frac{39}{40}\right)\) \(e\left(\frac{7}{40}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{3}{8}\right)\)
\(\chi_{820}(399,\cdot)\) \(1\) \(1\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{17}{40}\right)\) \(i\) \(e\left(\frac{9}{40}\right)\) \(e\left(\frac{13}{40}\right)\) \(e\left(\frac{19}{40}\right)\) \(e\left(\frac{27}{40}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{7}{8}\right)\)
\(\chi_{820}(439,\cdot)\) \(1\) \(1\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{33}{40}\right)\) \(i\) \(e\left(\frac{1}{40}\right)\) \(e\left(\frac{37}{40}\right)\) \(e\left(\frac{11}{40}\right)\) \(e\left(\frac{3}{40}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{7}{8}\right)\)
\(\chi_{820}(479,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{29}{40}\right)\) \(i\) \(e\left(\frac{13}{40}\right)\) \(e\left(\frac{1}{40}\right)\) \(e\left(\frac{23}{40}\right)\) \(e\left(\frac{39}{40}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{3}{8}\right)\)
\(\chi_{820}(499,\cdot)\) \(1\) \(1\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{1}{40}\right)\) \(i\) \(e\left(\frac{17}{40}\right)\) \(e\left(\frac{29}{40}\right)\) \(e\left(\frac{27}{40}\right)\) \(e\left(\frac{11}{40}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{7}{8}\right)\)
\(\chi_{820}(539,\cdot)\) \(1\) \(1\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{39}{40}\right)\) \(-i\) \(e\left(\frac{23}{40}\right)\) \(e\left(\frac{11}{40}\right)\) \(e\left(\frac{13}{40}\right)\) \(e\left(\frac{29}{40}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{1}{8}\right)\)
\(\chi_{820}(559,\cdot)\) \(1\) \(1\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{23}{40}\right)\) \(-i\) \(e\left(\frac{31}{40}\right)\) \(e\left(\frac{27}{40}\right)\) \(e\left(\frac{21}{40}\right)\) \(e\left(\frac{13}{40}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{1}{8}\right)\)
\(\chi_{820}(639,\cdot)\) \(1\) \(1\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{27}{40}\right)\) \(-i\) \(e\left(\frac{19}{40}\right)\) \(e\left(\frac{23}{40}\right)\) \(e\left(\frac{9}{40}\right)\) \(e\left(\frac{17}{40}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{5}{8}\right)\)
\(\chi_{820}(719,\cdot)\) \(1\) \(1\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{11}{40}\right)\) \(-i\) \(e\left(\frac{27}{40}\right)\) \(e\left(\frac{39}{40}\right)\) \(e\left(\frac{17}{40}\right)\) \(e\left(\frac{1}{40}\right)\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{5}{8}\right)\)