![Copy content]()
sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1300, base_ring=CyclotomicField(60))
M = H._module
chi = DirichletCharacter(H, M([30,21,10]))
![Copy content]()
pari:[g,chi] = znchar(Mod(303,1300))
| Modulus: | \(1300\) | |
| Conductor: | \(1300\) |
![Copy content]()
sage:chi.conductor()
![Copy content]()
pari:znconreyconductor(g,chi)
|
| Order: | \(60\) |
![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)
|
\(\chi_{1300}(23,\cdot)\)
\(\chi_{1300}(127,\cdot)\)
\(\chi_{1300}(147,\cdot)\)
\(\chi_{1300}(283,\cdot)\)
\(\chi_{1300}(303,\cdot)\)
\(\chi_{1300}(387,\cdot)\)
\(\chi_{1300}(563,\cdot)\)
\(\chi_{1300}(647,\cdot)\)
\(\chi_{1300}(667,\cdot)\)
\(\chi_{1300}(803,\cdot)\)
\(\chi_{1300}(823,\cdot)\)
\(\chi_{1300}(927,\cdot)\)
\(\chi_{1300}(1063,\cdot)\)
\(\chi_{1300}(1083,\cdot)\)
\(\chi_{1300}(1167,\cdot)\)
\(\chi_{1300}(1187,\cdot)\)
![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 ]
\((651,677,301)\) → \((-1,e\left(\frac{7}{20}\right),e\left(\frac{1}{6}\right))\)
| \(a\) |
\(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) | \(29\) |
| \( \chi_{ 1300 }(303, a) \) |
\(1\) | \(1\) | \(e\left(\frac{37}{60}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{7}{30}\right)\) | \(e\left(\frac{4}{15}\right)\) | \(e\left(\frac{53}{60}\right)\) | \(e\left(\frac{19}{30}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{1}{60}\right)\) | \(e\left(\frac{17}{20}\right)\) | \(e\left(\frac{11}{30}\right)\) |
![Copy content]()
sage:chi.jacobi_sum(n)
