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: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8023.go
\(\chi_{8023}(24,\cdot)\) \(\chi_{8023}(29,\cdot)\) \(\chi_{8023}(89,\cdot)\) \(\chi_{8023}(146,\cdot)\) \(\chi_{8023}(150,\cdot)\) \(\chi_{8023}(273,\cdot)\) \(\chi_{8023}(320,\cdot)\) \(\chi_{8023}(334,\cdot)\) \(\chi_{8023}(393,\cdot)\) \(\chi_{8023}(486,\cdot)\) \(\chi_{8023}(555,\cdot)\) \(\chi_{8023}(570,\cdot)\) \(\chi_{8023}(586,\cdot)\) \(\chi_{8023}(651,\cdot)\) \(\chi_{8023}(657,\cdot)\) \(\chi_{8023}(658,\cdot)\) \(\chi_{8023}(675,\cdot)\) \(\chi_{8023}(737,\cdot)\) \(\chi_{8023}(746,\cdot)\) \(\chi_{8023}(753,\cdot)\) \(\chi_{8023}(830,\cdot)\) \(\chi_{8023}(845,\cdot)\) \(\chi_{8023}(858,\cdot)\) \(\chi_{8023}(892,\cdot)\) \(\chi_{8023}(983,\cdot)\) \(\chi_{8023}(1142,\cdot)\) \(\chi_{8023}(1154,\cdot)\) \(\chi_{8023}(1176,\cdot)\) \(\chi_{8023}(1196,\cdot)\) \(\chi_{8023}(1210,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{560})$ |
| Fixed field: | Number field defined by a degree 560 polynomial (not computed) |
Values on generators
\((6894,3054)\) → \((e\left(\frac{34}{35}\right),e\left(\frac{89}{112}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 8023 }(29, a) \) | \(-1\) | \(1\) | \(e\left(\frac{51}{140}\right)\) | \(e\left(\frac{29}{560}\right)\) | \(e\left(\frac{51}{70}\right)\) | \(e\left(\frac{87}{560}\right)\) | \(e\left(\frac{233}{560}\right)\) | \(e\left(\frac{23}{70}\right)\) | \(e\left(\frac{13}{140}\right)\) | \(e\left(\frac{29}{280}\right)\) | \(e\left(\frac{291}{560}\right)\) | \(e\left(\frac{257}{280}\right)\) |