Basic properties
| Modulus: | \(8085\) | |
| Conductor: | \(8085\) | 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 8085.gd
\(\chi_{8085}(593,\cdot)\) \(\chi_{8085}(857,\cdot)\) \(\chi_{8085}(1088,\cdot)\) \(\chi_{8085}(1517,\cdot)\) \(\chi_{8085}(1748,\cdot)\) \(\chi_{8085}(2012,\cdot)\) \(\chi_{8085}(2243,\cdot)\) \(\chi_{8085}(2672,\cdot)\) \(\chi_{8085}(2903,\cdot)\) \(\chi_{8085}(3398,\cdot)\) \(\chi_{8085}(3827,\cdot)\) \(\chi_{8085}(4058,\cdot)\) \(\chi_{8085}(4322,\cdot)\) \(\chi_{8085}(4553,\cdot)\) \(\chi_{8085}(4982,\cdot)\) \(\chi_{8085}(5477,\cdot)\) \(\chi_{8085}(5708,\cdot)\) \(\chi_{8085}(6137,\cdot)\) \(\chi_{8085}(6368,\cdot)\) \(\chi_{8085}(6632,\cdot)\) \(\chi_{8085}(6863,\cdot)\) \(\chi_{8085}(7292,\cdot)\) \(\chi_{8085}(7523,\cdot)\) \(\chi_{8085}(7787,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{84})$ |
| Fixed field: | Number field defined by a degree 84 polynomial |
Values on generators
\((2696,4852,1816,3676)\) → \((-1,-i,e\left(\frac{29}{42}\right),-1)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(8\) | \(13\) | \(16\) | \(17\) | \(19\) | \(23\) | \(26\) | \(29\) |
| \( \chi_{ 8085 }(593, a) \) | \(1\) | \(1\) | \(e\left(\frac{59}{84}\right)\) | \(e\left(\frac{17}{42}\right)\) | \(e\left(\frac{3}{28}\right)\) | \(e\left(\frac{15}{28}\right)\) | \(e\left(\frac{17}{21}\right)\) | \(e\left(\frac{1}{84}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{83}{84}\right)\) | \(e\left(\frac{5}{21}\right)\) | \(e\left(\frac{13}{14}\right)\) |