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Properties

Label 1275.ce
Modulus $1275$
Conductor $1275$
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(1275, base_ring=CyclotomicField(40)) M = H._module chi = DirichletCharacter(H, M([20,2,35])) chi.galois_orbit()
 
Copy content pari:[g,chi] = znchar(Mod(2,1275)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: \(1275\)
Conductor: \(1275\)
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 \(-1\) \(1\) \(2\) \(4\) \(7\) \(8\) \(11\) \(13\) \(14\) \(16\) \(19\) \(22\)
\(\chi_{1275}(2,\cdot)\) \(1\) \(1\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{17}{40}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{27}{40}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{9}{40}\right)\)
\(\chi_{1275}(8,\cdot)\) \(1\) \(1\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{11}{40}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{1}{40}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{27}{40}\right)\)
\(\chi_{1275}(128,\cdot)\) \(1\) \(1\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{39}{40}\right)\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{29}{40}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{23}{40}\right)\)
\(\chi_{1275}(263,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{3}{40}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{33}{40}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{11}{40}\right)\)
\(\chi_{1275}(287,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{13}{40}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{23}{40}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{21}{40}\right)\)
\(\chi_{1275}(383,\cdot)\) \(1\) \(1\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{31}{40}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{21}{40}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{7}{40}\right)\)
\(\chi_{1275}(512,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{33}{40}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{3}{40}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{1}{40}\right)\)
\(\chi_{1275}(542,\cdot)\) \(1\) \(1\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{21}{40}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{31}{40}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{37}{40}\right)\)
\(\chi_{1275}(638,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{23}{40}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{13}{40}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{31}{40}\right)\)
\(\chi_{1275}(767,\cdot)\) \(1\) \(1\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{1}{40}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{11}{40}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{17}{40}\right)\)
\(\chi_{1275}(773,\cdot)\) \(1\) \(1\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{27}{40}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{17}{40}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{19}{40}\right)\)
\(\chi_{1275}(797,\cdot)\) \(1\) \(1\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{29}{40}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{39}{40}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{13}{40}\right)\)
\(\chi_{1275}(1022,\cdot)\) \(1\) \(1\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{9}{40}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{19}{40}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{33}{40}\right)\)
\(\chi_{1275}(1028,\cdot)\) \(1\) \(1\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{19}{40}\right)\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{9}{40}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{3}{40}\right)\)
\(\chi_{1275}(1052,\cdot)\) \(1\) \(1\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{37}{40}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{7}{40}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{29}{40}\right)\)
\(\chi_{1275}(1148,\cdot)\) \(1\) \(1\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{7}{40}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{37}{40}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{39}{40}\right)\)