![Copy content]()
sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4225, base_ring=CyclotomicField(780))
M = H._module
chi = DirichletCharacter(H, M([507,640]))
![Copy content]()
pari:[g,chi] = znchar(Mod(217,4225))
| Modulus: | \(4225\) | |
| Conductor: | \(4225\) |
![Copy content]()
sage:chi.conductor()
![Copy content]()
pari:znconreyconductor(g,chi)
|
| Order: | \(780\) |
![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: | odd |
![Copy content]()
sage:chi.is_odd()
![Copy content]()
pari:zncharisodd(g,chi)
|
\(\chi_{4225}(3,\cdot)\)
\(\chi_{4225}(42,\cdot)\)
\(\chi_{4225}(48,\cdot)\)
\(\chi_{4225}(87,\cdot)\)
\(\chi_{4225}(113,\cdot)\)
\(\chi_{4225}(133,\cdot)\)
\(\chi_{4225}(152,\cdot)\)
\(\chi_{4225}(172,\cdot)\)
\(\chi_{4225}(178,\cdot)\)
\(\chi_{4225}(198,\cdot)\)
\(\chi_{4225}(217,\cdot)\)
\(\chi_{4225}(237,\cdot)\)
\(\chi_{4225}(263,\cdot)\)
\(\chi_{4225}(302,\cdot)\)
\(\chi_{4225}(308,\cdot)\)
\(\chi_{4225}(328,\cdot)\)
\(\chi_{4225}(347,\cdot)\)
\(\chi_{4225}(367,\cdot)\)
\(\chi_{4225}(373,\cdot)\)
\(\chi_{4225}(412,\cdot)\)
\(\chi_{4225}(438,\cdot)\)
\(\chi_{4225}(458,\cdot)\)
\(\chi_{4225}(477,\cdot)\)
\(\chi_{4225}(497,\cdot)\)
\(\chi_{4225}(503,\cdot)\)
\(\chi_{4225}(523,\cdot)\)
\(\chi_{4225}(542,\cdot)\)
\(\chi_{4225}(562,\cdot)\)
\(\chi_{4225}(588,\cdot)\)
\(\chi_{4225}(627,\cdot)\)
...
![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 ]
\((677,3551)\) → \((e\left(\frac{13}{20}\right),e\left(\frac{32}{39}\right))\)
| \(a\) |
\(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(11\) | \(12\) | \(14\) |
| \( \chi_{ 4225 }(217, a) \) |
\(-1\) | \(1\) | \(e\left(\frac{367}{780}\right)\) | \(e\left(\frac{229}{780}\right)\) | \(e\left(\frac{367}{390}\right)\) | \(e\left(\frac{149}{195}\right)\) | \(e\left(\frac{7}{156}\right)\) | \(e\left(\frac{107}{260}\right)\) | \(e\left(\frac{229}{390}\right)\) | \(e\left(\frac{178}{195}\right)\) | \(e\left(\frac{61}{260}\right)\) | \(e\left(\frac{67}{130}\right)\) |
![Copy content]()
sage:chi.jacobi_sum(n)
