from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2888, base_ring=CyclotomicField(38))
M = H._module
chi = DirichletCharacter(H, M([0,19,5]))
pari: [g,chi] = znchar(Mod(37,2888))
Basic properties
| Modulus: | \(2888\) | |
| Conductor: | \(2888\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(38\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2888.ba
\(\chi_{2888}(37,\cdot)\) \(\chi_{2888}(189,\cdot)\) \(\chi_{2888}(341,\cdot)\) \(\chi_{2888}(493,\cdot)\) \(\chi_{2888}(645,\cdot)\) \(\chi_{2888}(797,\cdot)\) \(\chi_{2888}(949,\cdot)\) \(\chi_{2888}(1101,\cdot)\) \(\chi_{2888}(1253,\cdot)\) \(\chi_{2888}(1405,\cdot)\) \(\chi_{2888}(1557,\cdot)\) \(\chi_{2888}(1709,\cdot)\) \(\chi_{2888}(1861,\cdot)\) \(\chi_{2888}(2013,\cdot)\) \(\chi_{2888}(2317,\cdot)\) \(\chi_{2888}(2469,\cdot)\) \(\chi_{2888}(2621,\cdot)\) \(\chi_{2888}(2773,\cdot)\)
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: | \(\Q(\zeta_{19})\) |
| Fixed field: | 38.0.321901219811890081790219546628722051791865953039568238015939027374467326085267423464178688376545784307644366848.1 |
Values on generators
\((2167,1445,2529)\) → \((1,-1,e\left(\frac{5}{38}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(21\) | \(23\) |
| \( \chi_{ 2888 }(37, a) \) | \(-1\) | \(1\) | \(e\left(\frac{15}{19}\right)\) | \(e\left(\frac{1}{38}\right)\) | \(e\left(\frac{14}{19}\right)\) | \(e\left(\frac{11}{19}\right)\) | \(e\left(\frac{35}{38}\right)\) | \(e\left(\frac{15}{19}\right)\) | \(e\left(\frac{31}{38}\right)\) | \(e\left(\frac{14}{19}\right)\) | \(e\left(\frac{10}{19}\right)\) | \(e\left(\frac{4}{19}\right)\) |
sage: chi.jacobi_sum(n)