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.cz
\(\chi_{8023}(321,\cdot)\) \(\chi_{8023}(747,\cdot)\) \(\chi_{8023}(1965,\cdot)\) \(\chi_{8023}(2304,\cdot)\) \(\chi_{8023}(2391,\cdot)\) \(\chi_{8023}(2530,\cdot)\) \(\chi_{8023}(2730,\cdot)\) \(\chi_{8023}(2956,\cdot)\) \(\chi_{8023}(3598,\cdot)\) \(\chi_{8023}(3937,\cdot)\) \(\chi_{8023}(4024,\cdot)\) \(\chi_{8023}(4163,\cdot)\) \(\chi_{8023}(4363,\cdot)\) \(\chi_{8023}(4564,\cdot)\) \(\chi_{8023}(4589,\cdot)\) \(\chi_{8023}(4990,\cdot)\) \(\chi_{8023}(5355,\cdot)\) \(\chi_{8023}(5781,\cdot)\) \(\chi_{8023}(6197,\cdot)\) \(\chi_{8023}(6623,\cdot)\) \(\chi_{8023}(6711,\cdot)\) \(\chi_{8023}(6988,\cdot)\) \(\chi_{8023}(7137,\cdot)\) \(\chi_{8023}(7414,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{56})$ |
| Fixed field: | Number field defined by a degree 56 polynomial |
Values on generators
\((6894,3054)\) → \((e\left(\frac{2}{7}\right),e\left(\frac{5}{8}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 8023 }(321, a) \) | \(1\) | \(1\) | \(e\left(\frac{3}{14}\right)\) | \(e\left(\frac{3}{56}\right)\) | \(e\left(\frac{3}{7}\right)\) | \(e\left(\frac{7}{8}\right)\) | \(e\left(\frac{15}{56}\right)\) | \(e\left(\frac{2}{7}\right)\) | \(e\left(\frac{9}{14}\right)\) | \(e\left(\frac{3}{28}\right)\) | \(e\left(\frac{5}{56}\right)\) | \(e\left(\frac{3}{28}\right)\) |