from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2880, base_ring=CyclotomicField(48))
M = H._module
chi = DirichletCharacter(H, M([0,33,8,24]))
pari: [g,chi] = znchar(Mod(29,2880))
Basic properties
| Modulus: | \(2880\) | |
| Conductor: | \(2880\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(48\) | 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 2880.fh
\(\chi_{2880}(29,\cdot)\) \(\chi_{2880}(149,\cdot)\) \(\chi_{2880}(389,\cdot)\) \(\chi_{2880}(509,\cdot)\) \(\chi_{2880}(749,\cdot)\) \(\chi_{2880}(869,\cdot)\) \(\chi_{2880}(1109,\cdot)\) \(\chi_{2880}(1229,\cdot)\) \(\chi_{2880}(1469,\cdot)\) \(\chi_{2880}(1589,\cdot)\) \(\chi_{2880}(1829,\cdot)\) \(\chi_{2880}(1949,\cdot)\) \(\chi_{2880}(2189,\cdot)\) \(\chi_{2880}(2309,\cdot)\) \(\chi_{2880}(2549,\cdot)\) \(\chi_{2880}(2669,\cdot)\)
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: | \(\Q(\zeta_{48})\) |
| Fixed field: | Number field defined by a degree 48 polynomial |
Values on generators
\((2431,901,641,577)\) → \((1,e\left(\frac{11}{16}\right),e\left(\frac{1}{6}\right),-1)\)
First values
| \(a\) | \(-1\) | \(1\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) |
| \( \chi_{ 2880 }(29, a) \) | \(-1\) | \(1\) | \(e\left(\frac{1}{24}\right)\) | \(e\left(\frac{29}{48}\right)\) | \(e\left(\frac{7}{48}\right)\) | \(i\) | \(e\left(\frac{13}{16}\right)\) | \(e\left(\frac{23}{24}\right)\) | \(e\left(\frac{35}{48}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{11}{16}\right)\) | \(e\left(\frac{11}{24}\right)\) |
sage: chi.jacobi_sum(n)