Basic properties
| Modulus: | \(812\) | |
| Conductor: | \(812\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(84\) | 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 812.bu
\(\chi_{812}(3,\cdot)\) \(\chi_{812}(19,\cdot)\) \(\chi_{812}(31,\cdot)\) \(\chi_{812}(47,\cdot)\) \(\chi_{812}(131,\cdot)\) \(\chi_{812}(143,\cdot)\) \(\chi_{812}(159,\cdot)\) \(\chi_{812}(171,\cdot)\) \(\chi_{812}(243,\cdot)\) \(\chi_{812}(271,\cdot)\) \(\chi_{812}(311,\cdot)\) \(\chi_{812}(327,\cdot)\) \(\chi_{812}(367,\cdot)\) \(\chi_{812}(395,\cdot)\) \(\chi_{812}(467,\cdot)\) \(\chi_{812}(479,\cdot)\) \(\chi_{812}(495,\cdot)\) \(\chi_{812}(507,\cdot)\) \(\chi_{812}(591,\cdot)\) \(\chi_{812}(607,\cdot)\) \(\chi_{812}(619,\cdot)\) \(\chi_{812}(635,\cdot)\) \(\chi_{812}(675,\cdot)\) \(\chi_{812}(775,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{84})$ |
| Fixed field: | Number field defined by a degree 84 polynomial |
Values on generators
\((407,465,785)\) → \((-1,e\left(\frac{1}{6}\right),e\left(\frac{9}{28}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) |
| \( \chi_{ 812 }(367, a) \) | \(-1\) | \(1\) | \(e\left(\frac{23}{84}\right)\) | \(e\left(\frac{19}{21}\right)\) | \(e\left(\frac{23}{42}\right)\) | \(e\left(\frac{17}{84}\right)\) | \(e\left(\frac{2}{7}\right)\) | \(e\left(\frac{5}{28}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{19}{84}\right)\) | \(e\left(\frac{11}{42}\right)\) | \(e\left(\frac{17}{21}\right)\) |