Basic properties
| Modulus: | \(8085\) | |
| Conductor: | \(8085\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(140\) | 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.gm
\(\chi_{8085}(62,\cdot)\) \(\chi_{8085}(83,\cdot)\) \(\chi_{8085}(167,\cdot)\) \(\chi_{8085}(272,\cdot)\) \(\chi_{8085}(398,\cdot)\) \(\chi_{8085}(503,\cdot)\) \(\chi_{8085}(1007,\cdot)\) \(\chi_{8085}(1217,\cdot)\) \(\chi_{8085}(1238,\cdot)\) \(\chi_{8085}(1427,\cdot)\) \(\chi_{8085}(1448,\cdot)\) \(\chi_{8085}(1553,\cdot)\) \(\chi_{8085}(1658,\cdot)\) \(\chi_{8085}(2162,\cdot)\) \(\chi_{8085}(2372,\cdot)\) \(\chi_{8085}(2393,\cdot)\) \(\chi_{8085}(2477,\cdot)\) \(\chi_{8085}(2582,\cdot)\) \(\chi_{8085}(2603,\cdot)\) \(\chi_{8085}(2708,\cdot)\) \(\chi_{8085}(2813,\cdot)\) \(\chi_{8085}(3317,\cdot)\) \(\chi_{8085}(3548,\cdot)\) \(\chi_{8085}(3632,\cdot)\) \(\chi_{8085}(3737,\cdot)\) \(\chi_{8085}(3758,\cdot)\) \(\chi_{8085}(3863,\cdot)\) \(\chi_{8085}(4472,\cdot)\) \(\chi_{8085}(4682,\cdot)\) \(\chi_{8085}(4787,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{140})$ |
| Fixed field: | Number field defined by a degree 140 polynomial (not computed) |
Values on generators
\((2696,4852,1816,3676)\) → \((-1,i,e\left(\frac{11}{14}\right),e\left(\frac{7}{10}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(8\) | \(13\) | \(16\) | \(17\) | \(19\) | \(23\) | \(26\) | \(29\) |
| \( \chi_{ 8085 }(62, a) \) | \(1\) | \(1\) | \(e\left(\frac{123}{140}\right)\) | \(e\left(\frac{53}{70}\right)\) | \(e\left(\frac{89}{140}\right)\) | \(e\left(\frac{53}{140}\right)\) | \(e\left(\frac{18}{35}\right)\) | \(e\left(\frac{97}{140}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{3}{28}\right)\) | \(e\left(\frac{9}{35}\right)\) | \(e\left(\frac{3}{70}\right)\) |