Basic properties
| Modulus: | \(8023\) | |
| Conductor: | \(8023\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(560\) | 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.gi
\(\chi_{8023}(130,\cdot)\) \(\chi_{8023}(134,\cdot)\) \(\chi_{8023}(140,\cdot)\) \(\chi_{8023}(197,\cdot)\) \(\chi_{8023}(205,\cdot)\) \(\chi_{8023}(305,\cdot)\) \(\chi_{8023}(312,\cdot)\) \(\chi_{8023}(315,\cdot)\) \(\chi_{8023}(336,\cdot)\) \(\chi_{8023}(407,\cdot)\) \(\chi_{8023}(481,\cdot)\) \(\chi_{8023}(485,\cdot)\) \(\chi_{8023}(491,\cdot)\) \(\chi_{8023}(518,\cdot)\) \(\chi_{8023}(575,\cdot)\) \(\chi_{8023}(702,\cdot)\) \(\chi_{8023}(721,\cdot)\) \(\chi_{8023}(732,\cdot)\) \(\chi_{8023}(745,\cdot)\) \(\chi_{8023}(754,\cdot)\) \(\chi_{8023}(812,\cdot)\) \(\chi_{8023}(865,\cdot)\) \(\chi_{8023}(883,\cdot)\) \(\chi_{8023}(951,\cdot)\) \(\chi_{8023}(979,\cdot)\) \(\chi_{8023}(1027,\cdot)\) \(\chi_{8023}(1029,\cdot)\) \(\chi_{8023}(1107,\cdot)\) \(\chi_{8023}(1147,\cdot)\) \(\chi_{8023}(1157,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{560})$ |
| Fixed field: | Number field defined by a degree 560 polynomial (not computed) |
Values on generators
\((6894,3054)\) → \((e\left(\frac{3}{70}\right),e\left(\frac{5}{112}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 8023 }(130, a) \) | \(1\) | \(1\) | \(e\left(\frac{111}{140}\right)\) | \(e\left(\frac{89}{560}\right)\) | \(e\left(\frac{41}{70}\right)\) | \(e\left(\frac{507}{560}\right)\) | \(e\left(\frac{533}{560}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{53}{140}\right)\) | \(e\left(\frac{89}{280}\right)\) | \(e\left(\frac{391}{560}\right)\) | \(e\left(\frac{177}{280}\right)\) |