![Copy content]()
sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2600, base_ring=CyclotomicField(20))
M = H._module
chi = DirichletCharacter(H, M([0,10,7,5]))
![Copy content]()
pari:[g,chi] = znchar(Mod(853,2600))
| Modulus: | \(2600\) | |
| Conductor: | \(2600\) |
![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)
|
\(\chi_{2600}(317,\cdot)\)
\(\chi_{2600}(333,\cdot)\)
\(\chi_{2600}(837,\cdot)\)
\(\chi_{2600}(853,\cdot)\)
\(\chi_{2600}(1373,\cdot)\)
\(\chi_{2600}(1877,\cdot)\)
\(\chi_{2600}(2397,\cdot)\)
\(\chi_{2600}(2413,\cdot)\)
![Copy content]()
sage:chi.galois_orbit()
![Copy content]()
pari:order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
\((1951,1301,1977,1601)\) → \((1,-1,e\left(\frac{7}{20}\right),i)\)
| \(a\) |
\(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) | \(29\) |
| \( \chi_{ 2600 }(853, a) \) |
\(1\) | \(1\) | \(e\left(\frac{19}{20}\right)\) | \(-1\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{17}{20}\right)\) | \(e\left(\frac{1}{20}\right)\) | \(e\left(\frac{1}{20}\right)\) | \(e\left(\frac{9}{20}\right)\) | \(e\left(\frac{7}{20}\right)\) | \(e\left(\frac{17}{20}\right)\) | \(e\left(\frac{1}{5}\right)\) |
![Copy content]()
sage:chi.jacobi_sum(n)
