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Properties

Label 352.bc
Modulus $352$
Conductor $352$
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(352, base_ring=CyclotomicField(40)) M = H._module chi = DirichletCharacter(H, M([20,35,12])) chi.galois_orbit()
 
Copy content pari:[g,chi] = znchar(Mod(19,352)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: \(352\)
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: 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: 40.40.1411841662908675517629776705295515492024702234241930698046194396081616318012166504448.1

Characters in Galois orbit

Character \(-1\) \(1\) \(3\) \(5\) \(7\) \(9\) \(13\) \(15\) \(17\) \(19\) \(21\) \(23\)
\(\chi_{352}(19,\cdot)\) \(1\) \(1\) \(e\left(\frac{21}{40}\right)\) \(e\left(\frac{3}{40}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{17}{40}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{21}{40}\right)\) \(e\left(\frac{7}{8}\right)\) \(-i\)
\(\chi_{352}(35,\cdot)\) \(1\) \(1\) \(e\left(\frac{17}{40}\right)\) \(e\left(\frac{31}{40}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{29}{40}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{17}{40}\right)\) \(e\left(\frac{3}{8}\right)\) \(-i\)
\(\chi_{352}(51,\cdot)\) \(1\) \(1\) \(e\left(\frac{29}{40}\right)\) \(e\left(\frac{27}{40}\right)\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{33}{40}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{29}{40}\right)\) \(e\left(\frac{7}{8}\right)\) \(-i\)
\(\chi_{352}(83,\cdot)\) \(1\) \(1\) \(e\left(\frac{13}{40}\right)\) \(e\left(\frac{19}{40}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{1}{40}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{13}{40}\right)\) \(e\left(\frac{7}{8}\right)\) \(-i\)
\(\chi_{352}(107,\cdot)\) \(1\) \(1\) \(e\left(\frac{31}{40}\right)\) \(e\left(\frac{33}{40}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{27}{40}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{31}{40}\right)\) \(e\left(\frac{5}{8}\right)\) \(i\)
\(\chi_{352}(123,\cdot)\) \(1\) \(1\) \(e\left(\frac{27}{40}\right)\) \(e\left(\frac{21}{40}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{39}{40}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{27}{40}\right)\) \(e\left(\frac{1}{8}\right)\) \(i\)
\(\chi_{352}(139,\cdot)\) \(1\) \(1\) \(e\left(\frac{39}{40}\right)\) \(e\left(\frac{17}{40}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{3}{40}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{39}{40}\right)\) \(e\left(\frac{5}{8}\right)\) \(i\)
\(\chi_{352}(171,\cdot)\) \(1\) \(1\) \(e\left(\frac{23}{40}\right)\) \(e\left(\frac{9}{40}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{11}{40}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{23}{40}\right)\) \(e\left(\frac{5}{8}\right)\) \(i\)
\(\chi_{352}(195,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{40}\right)\) \(e\left(\frac{23}{40}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{37}{40}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{1}{40}\right)\) \(e\left(\frac{3}{8}\right)\) \(-i\)
\(\chi_{352}(211,\cdot)\) \(1\) \(1\) \(e\left(\frac{37}{40}\right)\) \(e\left(\frac{11}{40}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{9}{40}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{37}{40}\right)\) \(e\left(\frac{7}{8}\right)\) \(-i\)
\(\chi_{352}(227,\cdot)\) \(1\) \(1\) \(e\left(\frac{9}{40}\right)\) \(e\left(\frac{7}{40}\right)\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{13}{40}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{9}{40}\right)\) \(e\left(\frac{3}{8}\right)\) \(-i\)
\(\chi_{352}(259,\cdot)\) \(1\) \(1\) \(e\left(\frac{33}{40}\right)\) \(e\left(\frac{39}{40}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{21}{40}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{33}{40}\right)\) \(e\left(\frac{3}{8}\right)\) \(-i\)
\(\chi_{352}(283,\cdot)\) \(1\) \(1\) \(e\left(\frac{11}{40}\right)\) \(e\left(\frac{13}{40}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{7}{40}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{11}{40}\right)\) \(e\left(\frac{1}{8}\right)\) \(i\)
\(\chi_{352}(299,\cdot)\) \(1\) \(1\) \(e\left(\frac{7}{40}\right)\) \(e\left(\frac{1}{40}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{19}{40}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{7}{40}\right)\) \(e\left(\frac{5}{8}\right)\) \(i\)
\(\chi_{352}(315,\cdot)\) \(1\) \(1\) \(e\left(\frac{19}{40}\right)\) \(e\left(\frac{37}{40}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{23}{40}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{19}{40}\right)\) \(e\left(\frac{1}{8}\right)\) \(i\)
\(\chi_{352}(347,\cdot)\) \(1\) \(1\) \(e\left(\frac{3}{40}\right)\) \(e\left(\frac{29}{40}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{31}{40}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{3}{40}\right)\) \(e\left(\frac{1}{8}\right)\) \(i\)