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.fz
\(\chi_{8023}(144,\cdot)\) \(\chi_{8023}(217,\cdot)\) \(\chi_{8023}(262,\cdot)\) \(\chi_{8023}(277,\cdot)\) \(\chi_{8023}(303,\cdot)\) \(\chi_{8023}(430,\cdot)\) \(\chi_{8023}(513,\cdot)\) \(\chi_{8023}(578,\cdot)\) \(\chi_{8023}(750,\cdot)\) \(\chi_{8023}(760,\cdot)\) \(\chi_{8023}(817,\cdot)\) \(\chi_{8023}(926,\cdot)\) \(\chi_{8023}(1004,\cdot)\) \(\chi_{8023}(1006,\cdot)\) \(\chi_{8023}(1139,\cdot)\) \(\chi_{8023}(1155,\cdot)\) \(\chi_{8023}(1284,\cdot)\) \(\chi_{8023}(1305,\cdot)\) \(\chi_{8023}(1378,\cdot)\) \(\chi_{8023}(1428,\cdot)\) \(\chi_{8023}(1444,\cdot)\) \(\chi_{8023}(1480,\cdot)\) \(\chi_{8023}(1571,\cdot)\) \(\chi_{8023}(1591,\cdot)\) \(\chi_{8023}(1669,\cdot)\) \(\chi_{8023}(1777,\cdot)\) \(\chi_{8023}(2188,\cdot)\) \(\chi_{8023}(2296,\cdot)\) \(\chi_{8023}(2386,\cdot)\) \(\chi_{8023}(2497,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{280})$ |
| Fixed field: | Number field defined by a degree 280 polynomial (not computed) |
Values on generators
\((6894,3054)\) → \((e\left(\frac{3}{35}\right),e\left(\frac{25}{56}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 8023 }(144, a) \) | \(1\) | \(1\) | \(e\left(\frac{61}{70}\right)\) | \(e\left(\frac{27}{40}\right)\) | \(e\left(\frac{26}{35}\right)\) | \(e\left(\frac{127}{280}\right)\) | \(e\left(\frac{153}{280}\right)\) | \(e\left(\frac{23}{35}\right)\) | \(e\left(\frac{43}{70}\right)\) | \(e\left(\frac{7}{20}\right)\) | \(e\left(\frac{13}{40}\right)\) | \(e\left(\frac{97}{140}\right)\) |