Basic properties
| Modulus: | \(8036\) | |
| Conductor: | \(8036\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(840\) | 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 8036.eu
\(\chi_{8036}(47,\cdot)\) \(\chi_{8036}(75,\cdot)\) \(\chi_{8036}(171,\cdot)\) \(\chi_{8036}(199,\cdot)\) \(\chi_{8036}(299,\cdot)\) \(\chi_{8036}(311,\cdot)\) \(\chi_{8036}(339,\cdot)\) \(\chi_{8036}(395,\cdot)\) \(\chi_{8036}(439,\cdot)\) \(\chi_{8036}(479,\cdot)\) \(\chi_{8036}(507,\cdot)\) \(\chi_{8036}(563,\cdot)\) \(\chi_{8036}(591,\cdot)\) \(\chi_{8036}(663,\cdot)\) \(\chi_{8036}(675,\cdot)\) \(\chi_{8036}(691,\cdot)\) \(\chi_{8036}(703,\cdot)\) \(\chi_{8036}(719,\cdot)\) \(\chi_{8036}(731,\cdot)\) \(\chi_{8036}(831,\cdot)\) \(\chi_{8036}(887,\cdot)\) \(\chi_{8036}(915,\cdot)\) \(\chi_{8036}(955,\cdot)\) \(\chi_{8036}(971,\cdot)\) \(\chi_{8036}(1055,\cdot)\) \(\chi_{8036}(1083,\cdot)\) \(\chi_{8036}(1095,\cdot)\) \(\chi_{8036}(1167,\cdot)\) \(\chi_{8036}(1223,\cdot)\) \(\chi_{8036}(1319,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{840})$ |
| Fixed field: | Number field defined by a degree 840 polynomial (not computed) |
Values on generators
\((4019,493,785)\) → \((-1,e\left(\frac{25}{42}\right),e\left(\frac{1}{40}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) |
| \( \chi_{ 8036 }(703, a) \) | \(-1\) | \(1\) | \(e\left(\frac{79}{168}\right)\) | \(e\left(\frac{341}{420}\right)\) | \(e\left(\frac{79}{84}\right)\) | \(e\left(\frac{323}{840}\right)\) | \(e\left(\frac{117}{280}\right)\) | \(e\left(\frac{79}{280}\right)\) | \(e\left(\frac{593}{840}\right)\) | \(e\left(\frac{67}{120}\right)\) | \(e\left(\frac{2}{105}\right)\) | \(e\left(\frac{131}{210}\right)\) |