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.dv
\(\chi_{8023}(196,\cdot)\) \(\chi_{8023}(309,\cdot)\) \(\chi_{8023}(1780,\cdot)\) \(\chi_{8023}(2490,\cdot)\) \(\chi_{8023}(2684,\cdot)\) \(\chi_{8023}(3058,\cdot)\) \(\chi_{8023}(3249,\cdot)\) \(\chi_{8023}(3362,\cdot)\) \(\chi_{8023}(3394,\cdot)\) \(\chi_{8023}(3959,\cdot)\) \(\chi_{8023}(3962,\cdot)\) \(\chi_{8023}(4052,\cdot)\) \(\chi_{8023}(4072,\cdot)\) \(\chi_{8023}(4527,\cdot)\) \(\chi_{8023}(4640,\cdot)\) \(\chi_{8023}(4956,\cdot)\) \(\chi_{8023}(5521,\cdot)\) \(\chi_{8023}(5634,\cdot)\) \(\chi_{8023}(5827,\cdot)\) \(\chi_{8023}(6731,\cdot)\) \(\chi_{8023}(6750,\cdot)\) \(\chi_{8023}(7296,\cdot)\) \(\chi_{8023}(7409,\cdot)\) \(\chi_{8023}(7654,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{35})$ |
| Fixed field: | Number field defined by a degree 70 polynomial |
Values on generators
\((6894,3054)\) → \((e\left(\frac{1}{5}\right),e\left(\frac{5}{14}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 8023 }(196, a) \) | \(1\) | \(1\) | \(e\left(\frac{17}{35}\right)\) | \(e\left(\frac{39}{70}\right)\) | \(e\left(\frac{34}{35}\right)\) | \(e\left(\frac{17}{70}\right)\) | \(e\left(\frac{3}{70}\right)\) | \(e\left(\frac{2}{35}\right)\) | \(e\left(\frac{16}{35}\right)\) | \(e\left(\frac{4}{35}\right)\) | \(e\left(\frac{51}{70}\right)\) | \(e\left(\frac{22}{35}\right)\) |