from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2880, base_ring=CyclotomicField(24))
M = H._module
chi = DirichletCharacter(H, M([12,9,4,12]))
pari: [g,chi] = znchar(Mod(119,2880))
Basic properties
Modulus: | \(2880\) | |
Conductor: | \(1440\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(24\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{1440}(1379,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | no | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2880.ep
\(\chi_{2880}(119,\cdot)\) \(\chi_{2880}(599,\cdot)\) \(\chi_{2880}(839,\cdot)\) \(\chi_{2880}(1319,\cdot)\) \(\chi_{2880}(1559,\cdot)\) \(\chi_{2880}(2039,\cdot)\) \(\chi_{2880}(2279,\cdot)\) \(\chi_{2880}(2759,\cdot)\)
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: | \(\Q(\zeta_{24})\) |
Fixed field: | 24.24.362906559992367024835248285188899410542592000000000000.1 |
Values on generators
\((2431,901,641,577)\) → \((-1,e\left(\frac{3}{8}\right),e\left(\frac{1}{6}\right),-1)\)
First values
\(a\) | \(-1\) | \(1\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) |
\( \chi_{ 2880 }(119, a) \) | \(1\) | \(1\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{13}{24}\right)\) | \(e\left(\frac{11}{24}\right)\) | \(-1\) | \(e\left(\frac{1}{8}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{7}{24}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{7}{8}\right)\) | \(e\left(\frac{1}{12}\right)\) |
sage: chi.jacobi_sum(n)