Basic properties
| Modulus: | \(8085\) | |
| Conductor: | \(1617\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(70\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1617}(281,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8085.fs
\(\chi_{8085}(281,\cdot)\) \(\chi_{8085}(596,\cdot)\) \(\chi_{8085}(701,\cdot)\) \(\chi_{8085}(1436,\cdot)\) \(\chi_{8085}(1646,\cdot)\) \(\chi_{8085}(1751,\cdot)\) \(\chi_{8085}(1856,\cdot)\) \(\chi_{8085}(2591,\cdot)\) \(\chi_{8085}(2801,\cdot)\) \(\chi_{8085}(2906,\cdot)\) \(\chi_{8085}(3011,\cdot)\) \(\chi_{8085}(3746,\cdot)\) \(\chi_{8085}(3956,\cdot)\) \(\chi_{8085}(4061,\cdot)\) \(\chi_{8085}(5111,\cdot)\) \(\chi_{8085}(5216,\cdot)\) \(\chi_{8085}(5321,\cdot)\) \(\chi_{8085}(6056,\cdot)\) \(\chi_{8085}(6266,\cdot)\) \(\chi_{8085}(6476,\cdot)\) \(\chi_{8085}(7211,\cdot)\) \(\chi_{8085}(7421,\cdot)\) \(\chi_{8085}(7526,\cdot)\) \(\chi_{8085}(7631,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{35})$ |
| Fixed field: | Number field defined by a degree 70 polynomial |
Values on generators
\((2696,4852,1816,3676)\) → \((-1,1,e\left(\frac{2}{7}\right),e\left(\frac{9}{10}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(8\) | \(13\) | \(16\) | \(17\) | \(19\) | \(23\) | \(26\) | \(29\) |
| \( \chi_{ 8085 }(281, a) \) | \(1\) | \(1\) | \(e\left(\frac{29}{35}\right)\) | \(e\left(\frac{23}{35}\right)\) | \(e\left(\frac{17}{35}\right)\) | \(e\left(\frac{23}{70}\right)\) | \(e\left(\frac{11}{35}\right)\) | \(e\left(\frac{26}{35}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{5}{14}\right)\) | \(e\left(\frac{11}{70}\right)\) | \(e\left(\frac{33}{35}\right)\) |