Basic properties
| Modulus: | \(8085\) | |
| Conductor: | \(2695\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(210\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{2695}(4,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8085.gx
\(\chi_{8085}(4,\cdot)\) \(\chi_{8085}(289,\cdot)\) \(\chi_{8085}(394,\cdot)\) \(\chi_{8085}(499,\cdot)\) \(\chi_{8085}(709,\cdot)\) \(\chi_{8085}(1054,\cdot)\) \(\chi_{8085}(1159,\cdot)\) \(\chi_{8085}(1369,\cdot)\) \(\chi_{8085}(1444,\cdot)\) \(\chi_{8085}(1654,\cdot)\) \(\chi_{8085}(1864,\cdot)\) \(\chi_{8085}(2104,\cdot)\) \(\chi_{8085}(2209,\cdot)\) \(\chi_{8085}(2314,\cdot)\) \(\chi_{8085}(2524,\cdot)\) \(\chi_{8085}(2599,\cdot)\) \(\chi_{8085}(2704,\cdot)\) \(\chi_{8085}(2809,\cdot)\) \(\chi_{8085}(3259,\cdot)\) \(\chi_{8085}(3364,\cdot)\) \(\chi_{8085}(3469,\cdot)\) \(\chi_{8085}(3679,\cdot)\) \(\chi_{8085}(3859,\cdot)\) \(\chi_{8085}(3964,\cdot)\) \(\chi_{8085}(4174,\cdot)\) \(\chi_{8085}(4414,\cdot)\) \(\chi_{8085}(4519,\cdot)\) \(\chi_{8085}(4834,\cdot)\) \(\chi_{8085}(4909,\cdot)\) \(\chi_{8085}(5014,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{105})$ |
| Fixed field: | Number field defined by a degree 210 polynomial (not computed) |
Values on generators
\((2696,4852,1816,3676)\) → \((1,-1,e\left(\frac{5}{21}\right),e\left(\frac{1}{5}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(8\) | \(13\) | \(16\) | \(17\) | \(19\) | \(23\) | \(26\) | \(29\) |
| \( \chi_{ 8085 }(4, a) \) | \(1\) | \(1\) | \(e\left(\frac{187}{210}\right)\) | \(e\left(\frac{82}{105}\right)\) | \(e\left(\frac{47}{70}\right)\) | \(e\left(\frac{39}{70}\right)\) | \(e\left(\frac{59}{105}\right)\) | \(e\left(\frac{53}{210}\right)\) | \(e\left(\frac{14}{15}\right)\) | \(e\left(\frac{23}{42}\right)\) | \(e\left(\frac{47}{105}\right)\) | \(e\left(\frac{24}{35}\right)\) |