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Properties

Label 1200.db
Modulus $1200$
Conductor $1200$
Order $20$
Real no
Primitive yes
Minimal yes
Parity even

Related objects

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Show commands: Pari/GP / SageMath
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1200, base_ring=CyclotomicField(20)) M = H._module chi = DirichletCharacter(H, M([10,5,10,16])) chi.galois_orbit()
 
Copy content pari:[g,chi] = znchar(Mod(11,1200)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: \(1200\)
Conductor: \(1200\)
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: 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: \(\Q(\zeta_{20})\)
Fixed field: Number field defined by a degree 20 polynomial

Characters in Galois orbit

Character \(-1\) \(1\) \(7\) \(11\) \(13\) \(17\) \(19\) \(23\) \(29\) \(31\) \(37\) \(41\)
\(\chi_{1200}(11,\cdot)\) \(1\) \(1\) \(1\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{1}{5}\right)\)
\(\chi_{1200}(131,\cdot)\) \(1\) \(1\) \(1\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{3}{5}\right)\)
\(\chi_{1200}(371,\cdot)\) \(1\) \(1\) \(1\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{2}{5}\right)\)
\(\chi_{1200}(491,\cdot)\) \(1\) \(1\) \(1\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{4}{5}\right)\)
\(\chi_{1200}(611,\cdot)\) \(1\) \(1\) \(1\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{1}{5}\right)\)
\(\chi_{1200}(731,\cdot)\) \(1\) \(1\) \(1\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{3}{5}\right)\)
\(\chi_{1200}(971,\cdot)\) \(1\) \(1\) \(1\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{2}{5}\right)\)
\(\chi_{1200}(1091,\cdot)\) \(1\) \(1\) \(1\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{4}{5}\right)\)