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: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6012.be
\(\chi_{6012}(23,\cdot)\) \(\chi_{6012}(59,\cdot)\) \(\chi_{6012}(83,\cdot)\) \(\chi_{6012}(95,\cdot)\) \(\chi_{6012}(119,\cdot)\) \(\chi_{6012}(131,\cdot)\) \(\chi_{6012}(155,\cdot)\) \(\chi_{6012}(227,\cdot)\) \(\chi_{6012}(347,\cdot)\) \(\chi_{6012}(371,\cdot)\) \(\chi_{6012}(407,\cdot)\) \(\chi_{6012}(443,\cdot)\) \(\chi_{6012}(479,\cdot)\) \(\chi_{6012}(527,\cdot)\) \(\chi_{6012}(587,\cdot)\) \(\chi_{6012}(635,\cdot)\) \(\chi_{6012}(659,\cdot)\) \(\chi_{6012}(707,\cdot)\) \(\chi_{6012}(779,\cdot)\) \(\chi_{6012}(803,\cdot)\) \(\chi_{6012}(875,\cdot)\) \(\chi_{6012}(887,\cdot)\) \(\chi_{6012}(983,\cdot)\) \(\chi_{6012}(995,\cdot)\) \(\chi_{6012}(1019,\cdot)\) \(\chi_{6012}(1055,\cdot)\) \(\chi_{6012}(1103,\cdot)\) \(\chi_{6012}(1127,\cdot)\) \(\chi_{6012}(1163,\cdot)\) \(\chi_{6012}(1199,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{249})$ |
| Fixed field: | Number field defined by a degree 498 polynomial (not computed) |
Values on generators
\((3007,3341,4681)\) → \((-1,e\left(\frac{1}{6}\right),e\left(\frac{43}{166}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) |
| \( \chi_{ 6012 }(83, a) \) | \(-1\) | \(1\) | \(e\left(\frac{23}{249}\right)\) | \(e\left(\frac{365}{498}\right)\) | \(e\left(\frac{229}{249}\right)\) | \(e\left(\frac{7}{498}\right)\) | \(e\left(\frac{19}{83}\right)\) | \(e\left(\frac{87}{166}\right)\) | \(e\left(\frac{487}{498}\right)\) | \(e\left(\frac{46}{249}\right)\) | \(e\left(\frac{11}{498}\right)\) | \(e\left(\frac{73}{498}\right)\) |