Basic properties
| Modulus: | \(6012\) | |
| Conductor: | \(6012\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(498\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6012.z
\(\chi_{6012}(43,\cdot)\) \(\chi_{6012}(67,\cdot)\) \(\chi_{6012}(79,\cdot)\) \(\chi_{6012}(103,\cdot)\) \(\chi_{6012}(139,\cdot)\) \(\chi_{6012}(151,\cdot)\) \(\chi_{6012}(187,\cdot)\) \(\chi_{6012}(247,\cdot)\) \(\chi_{6012}(259,\cdot)\) \(\chi_{6012}(331,\cdot)\) \(\chi_{6012}(403,\cdot)\) \(\chi_{6012}(439,\cdot)\) \(\chi_{6012}(463,\cdot)\) \(\chi_{6012}(499,\cdot)\) \(\chi_{6012}(511,\cdot)\) \(\chi_{6012}(535,\cdot)\) \(\chi_{6012}(547,\cdot)\) \(\chi_{6012}(571,\cdot)\) \(\chi_{6012}(583,\cdot)\) \(\chi_{6012}(607,\cdot)\) \(\chi_{6012}(619,\cdot)\) \(\chi_{6012}(643,\cdot)\) \(\chi_{6012}(691,\cdot)\) \(\chi_{6012}(727,\cdot)\) \(\chi_{6012}(751,\cdot)\) \(\chi_{6012}(763,\cdot)\) \(\chi_{6012}(787,\cdot)\) \(\chi_{6012}(799,\cdot)\) \(\chi_{6012}(823,\cdot)\) \(\chi_{6012}(895,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{249})$ |
| Fixed field: | Number field defined by a degree 498 polynomial (not computed) |
Values on generators
\((3007,3341,4681)\) → \((-1,e\left(\frac{2}{3}\right),e\left(\frac{27}{166}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) |
| \( \chi_{ 6012 }(403, a) \) | \(1\) | \(1\) | \(e\left(\frac{247}{498}\right)\) | \(e\left(\frac{179}{498}\right)\) | \(e\left(\frac{359}{498}\right)\) | \(e\left(\frac{43}{498}\right)\) | \(e\left(\frac{103}{166}\right)\) | \(e\left(\frac{155}{166}\right)\) | \(e\left(\frac{233}{249}\right)\) | \(e\left(\frac{247}{249}\right)\) | \(e\left(\frac{16}{249}\right)\) | \(e\left(\frac{235}{498}\right)\) |