Basic properties
| Modulus: | \(784\) | |
| Conductor: | \(784\) | 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: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 784.bu
\(\chi_{784}(3,\cdot)\) \(\chi_{784}(59,\cdot)\) \(\chi_{784}(75,\cdot)\) \(\chi_{784}(115,\cdot)\) \(\chi_{784}(131,\cdot)\) \(\chi_{784}(171,\cdot)\) \(\chi_{784}(187,\cdot)\) \(\chi_{784}(243,\cdot)\) \(\chi_{784}(283,\cdot)\) \(\chi_{784}(299,\cdot)\) \(\chi_{784}(339,\cdot)\) \(\chi_{784}(355,\cdot)\) \(\chi_{784}(395,\cdot)\) \(\chi_{784}(451,\cdot)\) \(\chi_{784}(467,\cdot)\) \(\chi_{784}(507,\cdot)\) \(\chi_{784}(523,\cdot)\) \(\chi_{784}(563,\cdot)\) \(\chi_{784}(579,\cdot)\) \(\chi_{784}(635,\cdot)\) \(\chi_{784}(675,\cdot)\) \(\chi_{784}(691,\cdot)\) \(\chi_{784}(731,\cdot)\) \(\chi_{784}(747,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{84})$ |
| Fixed field: | Number field defined by a degree 84 polynomial |
Values on generators
\((687,197,689)\) → \((-1,-i,e\left(\frac{11}{42}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) |
| \( \chi_{ 784 }(355, a) \) | \(1\) | \(1\) | \(e\left(\frac{1}{84}\right)\) | \(e\left(\frac{29}{84}\right)\) | \(e\left(\frac{1}{42}\right)\) | \(e\left(\frac{61}{84}\right)\) | \(e\left(\frac{25}{28}\right)\) | \(e\left(\frac{5}{14}\right)\) | \(e\left(\frac{23}{42}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{20}{21}\right)\) | \(e\left(\frac{29}{42}\right)\) |