Basic properties
| Modulus: | \(833\) | |
| Conductor: | \(833\) | 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 833.bg
\(\chi_{833}(4,\cdot)\) \(\chi_{833}(72,\cdot)\) \(\chi_{833}(81,\cdot)\) \(\chi_{833}(123,\cdot)\) \(\chi_{833}(149,\cdot)\) \(\chi_{833}(191,\cdot)\) \(\chi_{833}(200,\cdot)\) \(\chi_{833}(242,\cdot)\) \(\chi_{833}(268,\cdot)\) \(\chi_{833}(310,\cdot)\) \(\chi_{833}(319,\cdot)\) \(\chi_{833}(387,\cdot)\) \(\chi_{833}(429,\cdot)\) \(\chi_{833}(438,\cdot)\) \(\chi_{833}(480,\cdot)\) \(\chi_{833}(506,\cdot)\) \(\chi_{833}(548,\cdot)\) \(\chi_{833}(599,\cdot)\) \(\chi_{833}(625,\cdot)\) \(\chi_{833}(676,\cdot)\) \(\chi_{833}(718,\cdot)\) \(\chi_{833}(744,\cdot)\) \(\chi_{833}(786,\cdot)\) \(\chi_{833}(795,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{84})$ |
| Fixed field: | Number field defined by a degree 84 polynomial |
Values on generators
\((52,785)\) → \((e\left(\frac{5}{21}\right),-i)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(11\) | \(12\) |
| \( \chi_{ 833 }(4, a) \) | \(1\) | \(1\) | \(e\left(\frac{29}{42}\right)\) | \(e\left(\frac{83}{84}\right)\) | \(e\left(\frac{8}{21}\right)\) | \(e\left(\frac{55}{84}\right)\) | \(e\left(\frac{19}{28}\right)\) | \(e\left(\frac{1}{14}\right)\) | \(e\left(\frac{41}{42}\right)\) | \(e\left(\frac{29}{84}\right)\) | \(e\left(\frac{65}{84}\right)\) | \(e\left(\frac{31}{84}\right)\) |