Basic properties
| Modulus: | \(8023\) | |
| Conductor: | \(8023\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(70\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8023.ds
\(\chi_{8023}(7,\cdot)\) \(\chi_{8023}(343,\cdot)\) \(\chi_{8023}(422,\cdot)\) \(\chi_{8023}(459,\cdot)\) \(\chi_{8023}(1360,\cdot)\) \(\chi_{8023}(1554,\cdot)\) \(\chi_{8023}(2232,\cdot)\) \(\chi_{8023}(2324,\cdot)\) \(\chi_{8023}(2456,\cdot)\) \(\chi_{8023}(2696,\cdot)\) \(\chi_{8023}(2908,\cdot)\) \(\chi_{8023}(3713,\cdot)\) \(\chi_{8023}(3736,\cdot)\) \(\chi_{8023}(4810,\cdot)\) \(\chi_{8023}(5069,\cdot)\) \(\chi_{8023}(5168,\cdot)\) \(\chi_{8023}(5431,\cdot)\) \(\chi_{8023}(5622,\cdot)\) \(\chi_{8023}(5940,\cdot)\) \(\chi_{8023}(6445,\cdot)\) \(\chi_{8023}(6526,\cdot)\) \(\chi_{8023}(6877,\cdot)\) \(\chi_{8023}(7801,\cdot)\) \(\chi_{8023}(7974,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{35})$ |
| Fixed field: | Number field defined by a degree 70 polynomial |
Values on generators
\((6894,3054)\) → \((e\left(\frac{1}{70}\right),e\left(\frac{1}{14}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 8023 }(7, a) \) | \(-1\) | \(1\) | \(e\left(\frac{33}{35}\right)\) | \(e\left(\frac{31}{70}\right)\) | \(e\left(\frac{31}{35}\right)\) | \(e\left(\frac{23}{70}\right)\) | \(e\left(\frac{27}{70}\right)\) | \(e\left(\frac{41}{70}\right)\) | \(e\left(\frac{29}{35}\right)\) | \(e\left(\frac{31}{35}\right)\) | \(e\left(\frac{19}{70}\right)\) | \(e\left(\frac{51}{70}\right)\) |