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Properties

Label 1650.cx
Modulus $1650$
Conductor $825$
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(1650, base_ring=CyclotomicField(20)) M = H._module chi = DirichletCharacter(H, M([10,17,16])) chi.galois_orbit()
 
Copy content pari:[g,chi] = znchar(Mod(47,1650)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: \(1650\)
Conductor: \(825\)
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 825.df
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: 20.20.7896700404567156612433609552681446075439453125.4

Characters in Galois orbit

Character \(-1\) \(1\) \(7\) \(13\) \(17\) \(19\) \(23\) \(29\) \(31\) \(37\) \(41\) \(43\)
\(\chi_{1650}(47,\cdot)\) \(1\) \(1\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{19}{20}\right)\) \(-i\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{3}{5}\right)\) \(i\) \(e\left(\frac{3}{10}\right)\) \(-i\)
\(\chi_{1650}(713,\cdot)\) \(1\) \(1\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{13}{20}\right)\) \(i\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{1}{5}\right)\) \(-i\) \(e\left(\frac{1}{10}\right)\) \(i\)
\(\chi_{1650}(917,\cdot)\) \(1\) \(1\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{11}{20}\right)\) \(-i\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{2}{5}\right)\) \(i\) \(e\left(\frac{7}{10}\right)\) \(-i\)
\(\chi_{1650}(983,\cdot)\) \(1\) \(1\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{1}{20}\right)\) \(i\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{2}{5}\right)\) \(-i\) \(e\left(\frac{7}{10}\right)\) \(i\)
\(\chi_{1650}(1103,\cdot)\) \(1\) \(1\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{9}{20}\right)\) \(i\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{3}{5}\right)\) \(-i\) \(e\left(\frac{3}{10}\right)\) \(i\)
\(\chi_{1650}(1127,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{7}{20}\right)\) \(-i\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{4}{5}\right)\) \(i\) \(e\left(\frac{9}{10}\right)\) \(-i\)
\(\chi_{1650}(1523,\cdot)\) \(1\) \(1\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{17}{20}\right)\) \(i\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{4}{5}\right)\) \(-i\) \(e\left(\frac{9}{10}\right)\) \(i\)
\(\chi_{1650}(1637,\cdot)\) \(1\) \(1\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{3}{20}\right)\) \(-i\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{1}{5}\right)\) \(i\) \(e\left(\frac{1}{10}\right)\) \(-i\)