Basic properties
| Modulus: | \(8085\) | |
| Conductor: | \(539\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(105\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{539}(16,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8085.ge
\(\chi_{8085}(16,\cdot)\) \(\chi_{8085}(256,\cdot)\) \(\chi_{8085}(466,\cdot)\) \(\chi_{8085}(676,\cdot)\) \(\chi_{8085}(751,\cdot)\) \(\chi_{8085}(856,\cdot)\) \(\chi_{8085}(1171,\cdot)\) \(\chi_{8085}(1411,\cdot)\) \(\chi_{8085}(1516,\cdot)\) \(\chi_{8085}(1621,\cdot)\) \(\chi_{8085}(1906,\cdot)\) \(\chi_{8085}(2011,\cdot)\) \(\chi_{8085}(2116,\cdot)\) \(\chi_{8085}(2326,\cdot)\) \(\chi_{8085}(2671,\cdot)\) \(\chi_{8085}(2776,\cdot)\) \(\chi_{8085}(2986,\cdot)\) \(\chi_{8085}(3061,\cdot)\) \(\chi_{8085}(3271,\cdot)\) \(\chi_{8085}(3481,\cdot)\) \(\chi_{8085}(3721,\cdot)\) \(\chi_{8085}(3826,\cdot)\) \(\chi_{8085}(3931,\cdot)\) \(\chi_{8085}(4141,\cdot)\) \(\chi_{8085}(4216,\cdot)\) \(\chi_{8085}(4321,\cdot)\) \(\chi_{8085}(4426,\cdot)\) \(\chi_{8085}(4876,\cdot)\) \(\chi_{8085}(4981,\cdot)\) \(\chi_{8085}(5086,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{105})$ |
| Fixed field: | Number field defined by a degree 105 polynomial (not computed) |
Values on generators
\((2696,4852,1816,3676)\) → \((1,1,e\left(\frac{10}{21}\right),e\left(\frac{2}{5}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(8\) | \(13\) | \(16\) | \(17\) | \(19\) | \(23\) | \(26\) | \(29\) |
| \( \chi_{ 8085 }(16, a) \) | \(1\) | \(1\) | \(e\left(\frac{82}{105}\right)\) | \(e\left(\frac{59}{105}\right)\) | \(e\left(\frac{12}{35}\right)\) | \(e\left(\frac{4}{35}\right)\) | \(e\left(\frac{13}{105}\right)\) | \(e\left(\frac{53}{105}\right)\) | \(e\left(\frac{13}{15}\right)\) | \(e\left(\frac{2}{21}\right)\) | \(e\left(\frac{94}{105}\right)\) | \(e\left(\frac{13}{35}\right)\) |