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Properties

Label 1300.bx
Modulus $1300$
Conductor $1300$
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(1300, base_ring=CyclotomicField(20)) M = H._module chi = DirichletCharacter(H, M([10,6,15])) chi.galois_orbit()
 
Copy content pari:[g,chi] = znchar(Mod(239,1300)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: \(1300\)
Conductor: \(1300\)
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: 20.20.31241389779108128051757812500000000000000000000.1

Characters in Galois orbit

Character \(-1\) \(1\) \(3\) \(7\) \(9\) \(11\) \(17\) \(19\) \(21\) \(23\) \(27\) \(29\)
\(\chi_{1300}(239,\cdot)\) \(1\) \(1\) \(e\left(\frac{3}{5}\right)\) \(i\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{3}{5}\right)\)
\(\chi_{1300}(359,\cdot)\) \(1\) \(1\) \(e\left(\frac{2}{5}\right)\) \(-i\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{2}{5}\right)\)
\(\chi_{1300}(619,\cdot)\) \(1\) \(1\) \(e\left(\frac{4}{5}\right)\) \(-i\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{4}{5}\right)\)
\(\chi_{1300}(759,\cdot)\) \(1\) \(1\) \(e\left(\frac{2}{5}\right)\) \(i\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{2}{5}\right)\)
\(\chi_{1300}(879,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{5}\right)\) \(-i\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{1}{5}\right)\)
\(\chi_{1300}(1019,\cdot)\) \(1\) \(1\) \(e\left(\frac{4}{5}\right)\) \(i\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{4}{5}\right)\)
\(\chi_{1300}(1139,\cdot)\) \(1\) \(1\) \(e\left(\frac{3}{5}\right)\) \(-i\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{3}{5}\right)\)
\(\chi_{1300}(1279,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{5}\right)\) \(i\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{1}{5}\right)\)