sage: from sage.modular.dirichlet import DirichletCharacter
sage: H = DirichletGroup(6025, base_ring=CyclotomicField(30))
sage: M = H._module
sage: chi = DirichletCharacter(H, M([15,26]))
pari: [g,chi] = znchar(Mod(5774,6025))
Basic properties
| Modulus: | \(6025\) | |
| Conductor: | \(1205\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(30\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1205}(954,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6025.ek
\(\chi_{6025}(24,\cdot)\) \(\chi_{6025}(424,\cdot)\) \(\chi_{6025}(1124,\cdot)\) \(\chi_{6025}(1299,\cdot)\) \(\chi_{6025}(1324,\cdot)\) \(\chi_{6025}(3474,\cdot)\) \(\chi_{6025}(4874,\cdot)\) \(\chi_{6025}(5774,\cdot)\)
sage: chi.galois_orbit()
pari: order = charorder(g,chi)
pari: [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
Values on generators
\((2652,2176)\) → \((-1,e\left(\frac{13}{15}\right))\)
Values
| \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) |
| \(1\) | \(1\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{7}{30}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{11}{30}\right)\) | \(-1\) | \(e\left(\frac{7}{15}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{17}{30}\right)\) | \(e\left(\frac{7}{30}\right)\) |
Related number fields
| Field of values: | \(\Q(\zeta_{15})\) |
| Fixed field: | Number field defined by a degree 30 polynomial |