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.gp
\(\chi_{8023}(35,\cdot)\) \(\chi_{8023}(42,\cdot)\) \(\chi_{8023}(65,\cdot)\) \(\chi_{8023}(78,\cdot)\) \(\chi_{8023}(153,\cdot)\) \(\chi_{8023}(155,\cdot)\) \(\chi_{8023}(184,\cdot)\) \(\chi_{8023}(186,\cdot)\) \(\chi_{8023}(266,\cdot)\) \(\chi_{8023}(268,\cdot)\) \(\chi_{8023}(274,\cdot)\) \(\chi_{8023}(291,\cdot)\) \(\chi_{8023}(297,\cdot)\) \(\chi_{8023}(410,\cdot)\) \(\chi_{8023}(417,\cdot)\) \(\chi_{8023}(487,\cdot)\) \(\chi_{8023}(494,\cdot)\) \(\chi_{8023}(525,\cdot)\) \(\chi_{8023}(530,\cdot)\) \(\chi_{8023}(630,\cdot)\) \(\chi_{8023}(636,\cdot)\) \(\chi_{8023}(743,\cdot)\) \(\chi_{8023}(833,\cdot)\) \(\chi_{8023}(944,\cdot)\) \(\chi_{8023}(975,\cdot)\) \(\chi_{8023}(982,\cdot)\) \(\chi_{8023}(1057,\cdot)\) \(\chi_{8023}(1059,\cdot)\) \(\chi_{8023}(1178,\cdot)\) \(\chi_{8023}(1195,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{560})$ |
| Fixed field: | Number field defined by a degree 560 polynomial (not computed) |
Values on generators
\((6894,3054)\) → \((e\left(\frac{29}{70}\right),e\left(\frac{13}{16}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 8023 }(35, a) \) | \(1\) | \(1\) | \(e\left(\frac{33}{140}\right)\) | \(e\left(\frac{327}{560}\right)\) | \(e\left(\frac{33}{70}\right)\) | \(e\left(\frac{3}{80}\right)\) | \(e\left(\frac{459}{560}\right)\) | \(e\left(\frac{32}{35}\right)\) | \(e\left(\frac{99}{140}\right)\) | \(e\left(\frac{47}{280}\right)\) | \(e\left(\frac{153}{560}\right)\) | \(e\left(\frac{271}{280}\right)\) |