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Properties

Label 352.ba
Modulus $352$
Conductor $176$
Order $20$
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(352, base_ring=CyclotomicField(20)) M = H._module chi = DirichletCharacter(H, M([0,15,12])) chi.galois_orbit()
 
Copy content pari:[g,chi] = znchar(Mod(9,352)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: \(352\)
Conductor: \(176\)
Copy content sage:chi.conductor()
 
Copy content pari:znconreyconductor(g,chi)
 
Order: \(20\)
Copy content sage:chi.multiplicative_order()
 
Copy content pari:charorder(g,chi)
 
Real: no
Primitive: no, induced from 176.w
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: \(\Q(\zeta_{20})\)
Fixed field: 20.20.1655513490330868290261743826894848.1

Characters in Galois orbit

Character \(-1\) \(1\) \(3\) \(5\) \(7\) \(9\) \(13\) \(15\) \(17\) \(19\) \(21\) \(23\)
\(\chi_{352}(9,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{1}{20}\right)\) \(-i\) \(-1\)
\(\chi_{352}(25,\cdot)\) \(1\) \(1\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{3}{20}\right)\) \(i\) \(-1\)
\(\chi_{352}(137,\cdot)\) \(1\) \(1\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{9}{20}\right)\) \(-i\) \(-1\)
\(\chi_{352}(169,\cdot)\) \(1\) \(1\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{17}{20}\right)\) \(-i\) \(-1\)
\(\chi_{352}(185,\cdot)\) \(1\) \(1\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{11}{20}\right)\) \(i\) \(-1\)
\(\chi_{352}(201,\cdot)\) \(1\) \(1\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{13}{20}\right)\) \(-i\) \(-1\)
\(\chi_{352}(313,\cdot)\) \(1\) \(1\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{19}{20}\right)\) \(i\) \(-1\)
\(\chi_{352}(345,\cdot)\) \(1\) \(1\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{7}{20}\right)\) \(i\) \(-1\)