from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2888, base_ring=CyclotomicField(18))
M = H._module
chi = DirichletCharacter(H, M([0,9,10]))
pari: [g,chi] = znchar(Mod(245,2888))
Basic properties
| Modulus: | \(2888\) | |
| Conductor: | \(152\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(18\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{152}(93,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2888.t
\(\chi_{2888}(245,\cdot)\) \(\chi_{2888}(389,\cdot)\) \(\chi_{2888}(821,\cdot)\) \(\chi_{2888}(1317,\cdot)\) \(\chi_{2888}(2581,\cdot)\) \(\chi_{2888}(2589,\cdot)\)
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: | \(\Q(\zeta_{9})\) |
| Fixed field: | 18.18.38713951190154487490850848768.1 |
Values on generators
\((2167,1445,2529)\) → \((1,-1,e\left(\frac{5}{9}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(21\) | \(23\) |
| \( \chi_{ 2888 }(245, a) \) | \(1\) | \(1\) | \(e\left(\frac{13}{18}\right)\) | \(e\left(\frac{7}{18}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{4}{9}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{5}{18}\right)\) | \(e\left(\frac{1}{9}\right)\) | \(e\left(\frac{5}{9}\right)\) | \(e\left(\frac{1}{18}\right)\) | \(e\left(\frac{1}{9}\right)\) |
sage: chi.jacobi_sum(n)