from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6027, base_ring=CyclotomicField(24))
M = H._module
chi = DirichletCharacter(H, M([0,20,15]))
pari: [g,chi] = znchar(Mod(3253,6027))
Basic properties
| Modulus: | \(6027\) | |
| Conductor: | \(287\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(24\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{287}(96,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6027.cb
\(\chi_{6027}(178,\cdot)\) \(\chi_{6027}(325,\cdot)\) \(\chi_{6027}(1930,\cdot)\) \(\chi_{6027}(2077,\cdot)\) \(\chi_{6027}(3253,\cdot)\) \(\chi_{6027}(3400,\cdot)\) \(\chi_{6027}(4882,\cdot)\) \(\chi_{6027}(5029,\cdot)\)
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: | \(\Q(\zeta_{24})\) |
| Fixed field: | 24.24.589415824352273084266952490343550409844469452348841.1 |
Values on generators
\((4019,493,2794)\) → \((1,e\left(\frac{5}{6}\right),e\left(\frac{5}{8}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) |
| \( \chi_{ 6027 }(3253, a) \) | \(1\) | \(1\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(-i\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{5}{24}\right)\) | \(e\left(\frac{7}{8}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{11}{24}\right)\) | \(e\left(\frac{19}{24}\right)\) |
sage: chi.jacobi_sum(n)