from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2888, base_ring=CyclotomicField(38))
M = H._module
chi = DirichletCharacter(H, M([19,19,20]))
pari: [g,chi] = znchar(Mod(571,2888))
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.bb
\(\chi_{2888}(115,\cdot)\) \(\chi_{2888}(267,\cdot)\) \(\chi_{2888}(419,\cdot)\) \(\chi_{2888}(571,\cdot)\) \(\chi_{2888}(875,\cdot)\) \(\chi_{2888}(1027,\cdot)\) \(\chi_{2888}(1179,\cdot)\) \(\chi_{2888}(1331,\cdot)\) \(\chi_{2888}(1483,\cdot)\) \(\chi_{2888}(1635,\cdot)\) \(\chi_{2888}(1787,\cdot)\) \(\chi_{2888}(1939,\cdot)\) \(\chi_{2888}(2091,\cdot)\) \(\chi_{2888}(2243,\cdot)\) \(\chi_{2888}(2395,\cdot)\) \(\chi_{2888}(2547,\cdot)\) \(\chi_{2888}(2699,\cdot)\) \(\chi_{2888}(2851,\cdot)\)
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: | Number field defined by a degree 38 polynomial |
Values on generators
\((2167,1445,2529)\) → \((-1,-1,e\left(\frac{10}{19}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(21\) | \(23\) |
\( \chi_{ 2888 }(571, a) \) | \(-1\) | \(1\) | \(e\left(\frac{3}{19}\right)\) | \(e\left(\frac{23}{38}\right)\) | \(e\left(\frac{17}{38}\right)\) | \(e\left(\frac{6}{19}\right)\) | \(e\left(\frac{13}{19}\right)\) | \(e\left(\frac{25}{38}\right)\) | \(e\left(\frac{29}{38}\right)\) | \(e\left(\frac{18}{19}\right)\) | \(e\left(\frac{23}{38}\right)\) | \(e\left(\frac{13}{38}\right)\) |
sage: chi.jacobi_sum(n)