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: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8023.ej
\(\chi_{8023}(855,\cdot)\) \(\chi_{8023}(888,\cdot)\) \(\chi_{8023}(1247,\cdot)\) \(\chi_{8023}(1250,\cdot)\) \(\chi_{8023}(1307,\cdot)\) \(\chi_{8023}(1439,\cdot)\) \(\chi_{8023}(1925,\cdot)\) \(\chi_{8023}(2119,\cdot)\) \(\chi_{8023}(2583,\cdot)\) \(\chi_{8023}(2606,\cdot)\) \(\chi_{8023}(3136,\cdot)\) \(\chi_{8023}(3341,\cdot)\) \(\chi_{8023}(3623,\cdot)\) \(\chi_{8023}(3701,\cdot)\) \(\chi_{8023}(3812,\cdot)\) \(\chi_{8023}(4976,\cdot)\) \(\chi_{8023}(5057,\cdot)\) \(\chi_{8023}(5846,\cdot)\) \(\chi_{8023}(5860,\cdot)\) \(\chi_{8023}(5880,\cdot)\) \(\chi_{8023}(6312,\cdot)\) \(\chi_{8023}(6618,\cdot)\) \(\chi_{8023}(6976,\cdot)\) \(\chi_{8023}(7465,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{35})$ |
| Fixed field: | Number field defined by a degree 70 polynomial |
Values on generators
\((6894,3054)\) → \((e\left(\frac{13}{35}\right),e\left(\frac{9}{14}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 8023 }(855, a) \) | \(1\) | \(1\) | \(e\left(\frac{33}{35}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{31}{35}\right)\) | \(e\left(\frac{53}{70}\right)\) | \(e\left(\frac{17}{70}\right)\) | \(e\left(\frac{18}{35}\right)\) | \(e\left(\frac{29}{35}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{3}{35}\right)\) |