Basic properties
| Modulus: | \(8023\) | |
| Conductor: | \(8023\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(35\) | 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.cq
\(\chi_{8023}(242,\cdot)\) \(\chi_{8023}(445,\cdot)\) \(\chi_{8023}(819,\cdot)\) \(\chi_{8023}(1271,\cdot)\) \(\chi_{8023}(1744,\cdot)\) \(\chi_{8023}(2276,\cdot)\) \(\chi_{8023}(2403,\cdot)\) \(\chi_{8023}(2422,\cdot)\) \(\chi_{8023}(2708,\cdot)\) \(\chi_{8023}(2818,\cdot)\) \(\chi_{8023}(3420,\cdot)\) \(\chi_{8023}(3870,\cdot)\) \(\chi_{8023}(3985,\cdot)\) \(\chi_{8023}(4516,\cdot)\) \(\chi_{8023}(4852,\cdot)\) \(\chi_{8023}(5341,\cdot)\) \(\chi_{8023}(5473,\cdot)\) \(\chi_{8023}(5553,\cdot)\) \(\chi_{8023}(5565,\cdot)\) \(\chi_{8023}(5872,\cdot)\) \(\chi_{8023}(5982,\cdot)\) \(\chi_{8023}(6377,\cdot)\) \(\chi_{8023}(6889,\cdot)\) \(\chi_{8023}(7813,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{35})$ |
| Fixed field: | Number field defined by a degree 35 polynomial |
Values on generators
\((6894,3054)\) → \((e\left(\frac{34}{35}\right),e\left(\frac{3}{7}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 8023 }(242, a) \) | \(1\) | \(1\) | \(e\left(\frac{34}{35}\right)\) | \(e\left(\frac{24}{35}\right)\) | \(e\left(\frac{33}{35}\right)\) | \(e\left(\frac{27}{35}\right)\) | \(e\left(\frac{23}{35}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{32}{35}\right)\) | \(e\left(\frac{13}{35}\right)\) | \(e\left(\frac{26}{35}\right)\) | \(e\left(\frac{29}{35}\right)\) |