from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1480, base_ring=CyclotomicField(36))
M = H._module
chi = DirichletCharacter(H, M([0,0,27,23]))
pari: [g,chi] = znchar(Mod(153,1480))
Basic properties
| Modulus: | \(1480\) | |
| Conductor: | \(185\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(36\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{185}(153,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1480.eo
\(\chi_{1480}(57,\cdot)\) \(\chi_{1480}(153,\cdot)\) \(\chi_{1480}(217,\cdot)\) \(\chi_{1480}(313,\cdot)\) \(\chi_{1480}(553,\cdot)\) \(\chi_{1480}(753,\cdot)\) \(\chi_{1480}(833,\cdot)\) \(\chi_{1480}(873,\cdot)\) \(\chi_{1480}(977,\cdot)\) \(\chi_{1480}(1017,\cdot)\) \(\chi_{1480}(1097,\cdot)\) \(\chi_{1480}(1297,\cdot)\)
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: | \(\Q(\zeta_{36})\) |
| Fixed field: | 36.36.57444765302724909954814307473256133361395843470561362005770206451416015625.1 |
Values on generators
\((1111,741,297,1001)\) → \((1,1,-i,e\left(\frac{23}{36}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) |
| \( \chi_{ 1480 }(153, a) \) | \(1\) | \(1\) | \(e\left(\frac{31}{36}\right)\) | \(e\left(\frac{7}{36}\right)\) | \(e\left(\frac{13}{18}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{5}{18}\right)\) | \(e\left(\frac{2}{9}\right)\) | \(e\left(\frac{31}{36}\right)\) | \(e\left(\frac{1}{18}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{7}{12}\right)\) |
sage: chi.jacobi_sum(n)