from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2873, base_ring=CyclotomicField(16))
M = H._module
chi = DirichletCharacter(H, M([4,7]))
pari: [g,chi] = znchar(Mod(606,2873))
Basic properties
| Modulus: | \(2873\) | |
| Conductor: | \(221\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(16\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{221}(164,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2873.bb
\(\chi_{2873}(606,\cdot)\) \(\chi_{2873}(775,\cdot)\) \(\chi_{2873}(915,\cdot)\) \(\chi_{2873}(1253,\cdot)\) \(\chi_{2873}(1282,\cdot)\) \(\chi_{2873}(1451,\cdot)\) \(\chi_{2873}(2436,\cdot)\) \(\chi_{2873}(2774,\cdot)\)
sage: chi.galois_orbit()
order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
Related number fields
| Field of values: | \(\Q(\zeta_{16})\) |
| Fixed field: | 16.16.66688975910627504451630153142433.2 |
Values on generators
\((171,2536)\) → \((i,e\left(\frac{7}{16}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 2873 }(606, a) \) | \(1\) | \(1\) | \(e\left(\frac{3}{8}\right)\) | \(e\left(\frac{7}{16}\right)\) | \(-i\) | \(e\left(\frac{7}{16}\right)\) | \(e\left(\frac{13}{16}\right)\) | \(e\left(\frac{9}{16}\right)\) | \(e\left(\frac{1}{8}\right)\) | \(e\left(\frac{7}{8}\right)\) | \(e\left(\frac{13}{16}\right)\) | \(e\left(\frac{13}{16}\right)\) |
sage: chi.jacobi_sum(n)