from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7440, base_ring=CyclotomicField(30))
M = H._module
chi = DirichletCharacter(H, M([0,15,0,0,16]))
pari: [g,chi] = znchar(Mod(121,7440))
Basic properties
Modulus: | \(7440\) | |
Conductor: | \(248\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(30\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{248}(245,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | no | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 7440.jz
\(\chi_{7440}(121,\cdot)\) \(\chi_{7440}(361,\cdot)\) \(\chi_{7440}(1321,\cdot)\) \(\chi_{7440}(2281,\cdot)\) \(\chi_{7440}(2521,\cdot)\) \(\chi_{7440}(3481,\cdot)\) \(\chi_{7440}(5401,\cdot)\) \(\chi_{7440}(6121,\cdot)\)
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: | \(\Q(\zeta_{15})\) |
Fixed field: | 30.30.20159382829191092591451779536401274948781988965475418112.1 |
Values on generators
\((6511,1861,4961,2977,5521)\) → \((1,-1,1,1,e\left(\frac{8}{15}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(37\) | \(41\) | \(43\) |
\( \chi_{ 7440 }(121, a) \) | \(1\) | \(1\) | \(e\left(\frac{14}{15}\right)\) | \(e\left(\frac{23}{30}\right)\) | \(e\left(\frac{11}{30}\right)\) | \(e\left(\frac{11}{15}\right)\) | \(e\left(\frac{19}{30}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{7}{15}\right)\) | \(e\left(\frac{19}{30}\right)\) |
sage: chi.jacobi_sum(n)