![Copy content]()
sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7616, base_ring=CyclotomicField(48))
M = H._module
chi = DirichletCharacter(H, M([0,27,16,3]))
![Copy content]()
pari:[g,chi] = znchar(Mod(37,7616))
| Modulus: | \(7616\) | |
| Conductor: | \(7616\) |
![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: | odd |
![Copy content]()
sage:chi.is_odd()
![Copy content]()
pari:zncharisodd(g,chi)
|
\(\chi_{7616}(37,\cdot)\)
\(\chi_{7616}(277,\cdot)\)
\(\chi_{7616}(1677,\cdot)\)
\(\chi_{7616}(2557,\cdot)\)
\(\chi_{7616}(2613,\cdot)\)
\(\chi_{7616}(2781,\cdot)\)
\(\chi_{7616}(3117,\cdot)\)
\(\chi_{7616}(3301,\cdot)\)
\(\chi_{7616}(3397,\cdot)\)
\(\chi_{7616}(4629,\cdot)\)
\(\chi_{7616}(5821,\cdot)\)
\(\chi_{7616}(5877,\cdot)\)
\(\chi_{7616}(6029,\cdot)\)
\(\chi_{7616}(6045,\cdot)\)
\(\chi_{7616}(6381,\cdot)\)
\(\chi_{7616}(6661,\cdot)\)
![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 ]
\((5951,3333,3265,2689)\) → \((1,e\left(\frac{9}{16}\right),e\left(\frac{1}{3}\right),e\left(\frac{1}{16}\right))\)
| \(a\) |
\(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(13\) | \(15\) | \(19\) | \(23\) | \(25\) | \(27\) |
| \( \chi_{ 7616 }(37, a) \) |
\(-1\) | \(1\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{13}{24}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{11}{16}\right)\) | \(e\left(\frac{5}{8}\right)\) | \(e\left(\frac{23}{48}\right)\) | \(e\left(\frac{23}{48}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(i\) |
![Copy content]()
sage:chi.jacobi_sum(n)
