![Copy content]()
sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2475, base_ring=CyclotomicField(30))
M = H._module
chi = DirichletCharacter(H, M([25,6,9]))
![Copy content]()
pari:[g,chi] = znchar(Mod(41,2475))
| Modulus: | \(2475\) | |
| Conductor: | \(2475\) |
![Copy content]()
sage:chi.conductor()
![Copy content]()
pari:znconreyconductor(g,chi)
|
| Order: | \(30\) |
![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)
|
\(\chi_{2475}(41,\cdot)\)
\(\chi_{2475}(446,\cdot)\)
\(\chi_{2475}(866,\cdot)\)
\(\chi_{2475}(986,\cdot)\)
\(\chi_{2475}(1256,\cdot)\)
\(\chi_{2475}(1271,\cdot)\)
\(\chi_{2475}(1811,\cdot)\)
\(\chi_{2475}(2081,\cdot)\)
![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 ]
\((551,2377,2026)\) → \((e\left(\frac{5}{6}\right),e\left(\frac{1}{5}\right),e\left(\frac{3}{10}\right))\)
| \(a\) |
\(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(13\) | \(14\) | \(16\) | \(17\) | \(19\) | \(23\) |
| \( \chi_{ 2475 }(41, a) \) |
\(1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{13}{30}\right)\) | \(1\) | \(e\left(\frac{23}{30}\right)\) | \(e\left(\frac{23}{30}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(-1\) | \(e\left(\frac{11}{30}\right)\) |
![Copy content]()
sage:chi.jacobi_sum(n)
