Basic properties
| Modulus: | \(8023\) | |
| Conductor: | \(8023\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(280\) | 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.ge
\(\chi_{8023}(18,\cdot)\) \(\chi_{8023}(95,\cdot)\) \(\chi_{8023}(131,\cdot)\) \(\chi_{8023}(157,\cdot)\) \(\chi_{8023}(182,\cdot)\) \(\chi_{8023}(357,\cdot)\) \(\chi_{8023}(434,\cdot)\) \(\chi_{8023}(521,\cdot)\) \(\chi_{8023}(547,\cdot)\) \(\chi_{8023}(583,\cdot)\) \(\chi_{8023}(722,\cdot)\) \(\chi_{8023}(860,\cdot)\) \(\chi_{8023}(973,\cdot)\) \(\chi_{8023}(1148,\cdot)\) \(\chi_{8023}(1174,\cdot)\) \(\chi_{8023}(1225,\cdot)\) \(\chi_{8023}(1287,\cdot)\) \(\chi_{8023}(1338,\cdot)\) \(\chi_{8023}(1564,\cdot)\) \(\chi_{8023}(1600,\cdot)\) \(\chi_{8023}(1626,\cdot)\) \(\chi_{8023}(1651,\cdot)\) \(\chi_{8023}(1713,\cdot)\) \(\chi_{8023}(1764,\cdot)\) \(\chi_{8023}(1790,\cdot)\) \(\chi_{8023}(1852,\cdot)\) \(\chi_{8023}(1990,\cdot)\) \(\chi_{8023}(2052,\cdot)\) \(\chi_{8023}(2078,\cdot)\) \(\chi_{8023}(2216,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{280})$ |
| Fixed field: | Number field defined by a degree 280 polynomial (not computed) |
Values on generators
\((6894,3054)\) → \((e\left(\frac{8}{35}\right),e\left(\frac{7}{8}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 8023 }(2078, a) \) | \(1\) | \(1\) | \(e\left(\frac{61}{70}\right)\) | \(e\left(\frac{229}{280}\right)\) | \(e\left(\frac{26}{35}\right)\) | \(e\left(\frac{1}{40}\right)\) | \(e\left(\frac{193}{280}\right)\) | \(e\left(\frac{8}{35}\right)\) | \(e\left(\frac{43}{70}\right)\) | \(e\left(\frac{89}{140}\right)\) | \(e\left(\frac{251}{280}\right)\) | \(e\left(\frac{117}{140}\right)\) |