Basic properties
| Modulus: | \(8023\) | |
| Conductor: | \(8023\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(56\) | 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.dd
\(\chi_{8023}(375,\cdot)\) \(\chi_{8023}(813,\cdot)\) \(\chi_{8023}(1026,\cdot)\) \(\chi_{8023}(1521,\cdot)\) \(\chi_{8023}(1962,\cdot)\) \(\chi_{8023}(2096,\cdot)\) \(\chi_{8023}(2178,\cdot)\) \(\chi_{8023}(2789,\cdot)\) \(\chi_{8023}(3225,\cdot)\) \(\chi_{8023}(3303,\cdot)\) \(\chi_{8023}(3453,\cdot)\) \(\chi_{8023}(3641,\cdot)\) \(\chi_{8023}(3666,\cdot)\) \(\chi_{8023}(3811,\cdot)\) \(\chi_{8023}(4155,\cdot)\) \(\chi_{8023}(5157,\cdot)\) \(\chi_{8023}(5362,\cdot)\) \(\chi_{8023}(5639,\cdot)\) \(\chi_{8023}(5641,\cdot)\) \(\chi_{8023}(5854,\cdot)\) \(\chi_{8023}(6793,\cdot)\) \(\chi_{8023}(7130,\cdot)\) \(\chi_{8023}(7219,\cdot)\) \(\chi_{8023}(7546,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{56})$ |
| Fixed field: | Number field defined by a degree 56 polynomial |
Values on generators
\((6894,3054)\) → \((e\left(\frac{4}{7}\right),e\left(\frac{13}{56}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 8023 }(375, a) \) | \(1\) | \(1\) | \(e\left(\frac{3}{14}\right)\) | \(e\left(\frac{5}{56}\right)\) | \(e\left(\frac{3}{7}\right)\) | \(e\left(\frac{15}{56}\right)\) | \(e\left(\frac{17}{56}\right)\) | \(e\left(\frac{3}{7}\right)\) | \(e\left(\frac{9}{14}\right)\) | \(e\left(\frac{5}{28}\right)\) | \(e\left(\frac{27}{56}\right)\) | \(e\left(\frac{25}{28}\right)\) |