Basic properties
| Modulus: | \(8023\) | |
| Conductor: | \(8023\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(112\) | 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.es
\(\chi_{8023}(247,\cdot)\) \(\chi_{8023}(318,\cdot)\) \(\chi_{8023}(394,\cdot)\) \(\chi_{8023}(406,\cdot)\) \(\chi_{8023}(690,\cdot)\) \(\chi_{8023}(815,\cdot)\) \(\chi_{8023}(875,\cdot)\) \(\chi_{8023}(949,\cdot)\) \(\chi_{8023}(962,\cdot)\) \(\chi_{8023}(1020,\cdot)\) \(\chi_{8023}(1159,\cdot)\) \(\chi_{8023}(1248,\cdot)\) \(\chi_{8023}(1375,\cdot)\) \(\chi_{8023}(2029,\cdot)\) \(\chi_{8023}(2110,\cdot)\) \(\chi_{8023}(2653,\cdot)\) \(\chi_{8023}(2732,\cdot)\) \(\chi_{8023}(2749,\cdot)\) \(\chi_{8023}(2792,\cdot)\) \(\chi_{8023}(3147,\cdot)\) \(\chi_{8023}(3573,\cdot)\) \(\chi_{8023}(3589,\cdot)\) \(\chi_{8023}(3655,\cdot)\) \(\chi_{8023}(3804,\cdot)\) \(\chi_{8023}(4169,\cdot)\) \(\chi_{8023}(4228,\cdot)\) \(\chi_{8023}(4441,\cdot)\) \(\chi_{8023}(4453,\cdot)\) \(\chi_{8023}(4514,\cdot)\) \(\chi_{8023}(4656,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{112})$ |
| Fixed field: | Number field defined by a degree 112 polynomial (not computed) |
Values on generators
\((6894,3054)\) → \((e\left(\frac{11}{14}\right),e\left(\frac{9}{112}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 8023 }(247, a) \) | \(1\) | \(1\) | \(e\left(\frac{19}{28}\right)\) | \(e\left(\frac{57}{112}\right)\) | \(e\left(\frac{5}{14}\right)\) | \(e\left(\frac{75}{112}\right)\) | \(e\left(\frac{3}{16}\right)\) | \(e\left(\frac{3}{7}\right)\) | \(e\left(\frac{1}{28}\right)\) | \(e\left(\frac{1}{56}\right)\) | \(e\left(\frac{39}{112}\right)\) | \(e\left(\frac{17}{56}\right)\) |