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Properties

Label 8925.fd
Modulus $8925$
Conductor $175$
Order $20$
Real no
Primitive no
Minimal yes
Parity even

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Show commands: Pari/GP / SageMath
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(8925, base_ring=CyclotomicField(20)) M = H._module chi = DirichletCharacter(H, M([0,7,10,0])) chi.galois_orbit()
 
Copy content pari:[g,chi] = znchar(Mod(1378,8925)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: \(8925\)
Conductor: \(175\)
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 175.s
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: \(\Q(\zeta_{20})\)
Fixed field: 20.20.822111175511963665485382080078125.1

Characters in Galois orbit

Character \(-1\) \(1\) \(2\) \(4\) \(8\) \(11\) \(13\) \(16\) \(19\) \(22\) \(23\) \(26\)
\(\chi_{8925}(1378,\cdot)\) \(1\) \(1\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{17}{20}\right)\) \(-1\)
\(\chi_{8925}(2092,\cdot)\) \(1\) \(1\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{3}{20}\right)\) \(-1\)
\(\chi_{8925}(3163,\cdot)\) \(1\) \(1\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{9}{20}\right)\) \(-1\)
\(\chi_{8925}(3877,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{11}{20}\right)\) \(-1\)
\(\chi_{8925}(4948,\cdot)\) \(1\) \(1\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{1}{20}\right)\) \(-1\)
\(\chi_{8925}(5662,\cdot)\) \(1\) \(1\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{19}{20}\right)\) \(-1\)
\(\chi_{8925}(6733,\cdot)\) \(1\) \(1\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{13}{20}\right)\) \(-1\)
\(\chi_{8925}(7447,\cdot)\) \(1\) \(1\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{7}{20}\right)\) \(-1\)