![Copy content]()
sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1984, base_ring=CyclotomicField(48))
M = H._module
chi = DirichletCharacter(H, M([0,39,32]))
![Copy content]()
pari:[g,chi] = znchar(Mod(1493,1984))
| Modulus: | \(1984\) | |
| Conductor: | \(1984\) |
![Copy content]()
sage:chi.conductor()
![Copy content]()
pari:znconreyconductor(g,chi)
|
| Order: | \(48\) |
![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)
|
\(\chi_{1984}(5,\cdot)\)
\(\chi_{1984}(149,\cdot)\)
\(\chi_{1984}(253,\cdot)\)
\(\chi_{1984}(397,\cdot)\)
\(\chi_{1984}(501,\cdot)\)
\(\chi_{1984}(645,\cdot)\)
\(\chi_{1984}(749,\cdot)\)
\(\chi_{1984}(893,\cdot)\)
\(\chi_{1984}(997,\cdot)\)
\(\chi_{1984}(1141,\cdot)\)
\(\chi_{1984}(1245,\cdot)\)
\(\chi_{1984}(1389,\cdot)\)
\(\chi_{1984}(1493,\cdot)\)
\(\chi_{1984}(1637,\cdot)\)
\(\chi_{1984}(1741,\cdot)\)
\(\chi_{1984}(1885,\cdot)\)
![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 ]
\((63,1861,65)\) → \((1,e\left(\frac{13}{16}\right),e\left(\frac{2}{3}\right))\)
| \(a\) |
\(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
| \( \chi_{ 1984 }(1493, a) \) |
\(1\) | \(1\) | \(e\left(\frac{5}{48}\right)\) | \(e\left(\frac{7}{48}\right)\) | \(e\left(\frac{19}{24}\right)\) | \(e\left(\frac{5}{24}\right)\) | \(e\left(\frac{19}{48}\right)\) | \(e\left(\frac{25}{48}\right)\) | \(i\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{17}{48}\right)\) | \(e\left(\frac{43}{48}\right)\) |
![Copy content]()
sage:chi.jacobi_sum(n)
