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.bd
\(\chi_{6012}(7,\cdot)\) \(\chi_{6012}(31,\cdot)\) \(\chi_{6012}(115,\cdot)\) \(\chi_{6012}(175,\cdot)\) \(\chi_{6012}(211,\cdot)\) \(\chi_{6012}(223,\cdot)\) \(\chi_{6012}(283,\cdot)\) \(\chi_{6012}(295,\cdot)\) \(\chi_{6012}(319,\cdot)\) \(\chi_{6012}(355,\cdot)\) \(\chi_{6012}(367,\cdot)\) \(\chi_{6012}(391,\cdot)\) \(\chi_{6012}(427,\cdot)\) \(\chi_{6012}(475,\cdot)\) \(\chi_{6012}(655,\cdot)\) \(\chi_{6012}(679,\cdot)\) \(\chi_{6012}(715,\cdot)\) \(\chi_{6012}(859,\cdot)\) \(\chi_{6012}(871,\cdot)\) \(\chi_{6012}(907,\cdot)\) \(\chi_{6012}(931,\cdot)\) \(\chi_{6012}(943,\cdot)\) \(\chi_{6012}(967,\cdot)\) \(\chi_{6012}(979,\cdot)\) \(\chi_{6012}(1051,\cdot)\) \(\chi_{6012}(1087,\cdot)\) \(\chi_{6012}(1123,\cdot)\) \(\chi_{6012}(1159,\cdot)\) \(\chi_{6012}(1183,\cdot)\) \(\chi_{6012}(1219,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{249})$ |
| Fixed field: | Number field defined by a degree 498 polynomial (not computed) |
Values on generators
\((3007,3341,4681)\) → \((-1,e\left(\frac{1}{3}\right),e\left(\frac{45}{83}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) |
| \( \chi_{ 6012 }(31, a) \) | \(-1\) | \(1\) | \(e\left(\frac{52}{249}\right)\) | \(e\left(\frac{403}{498}\right)\) | \(e\left(\frac{7}{498}\right)\) | \(e\left(\frac{127}{249}\right)\) | \(e\left(\frac{61}{83}\right)\) | \(e\left(\frac{157}{166}\right)\) | \(e\left(\frac{419}{498}\right)\) | \(e\left(\frac{104}{249}\right)\) | \(e\left(\frac{164}{249}\right)\) | \(e\left(\frac{479}{498}\right)\) |