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.gv
\(\chi_{8023}(19,\cdot)\) \(\chi_{8023}(75,\cdot)\) \(\chi_{8023}(80,\cdot)\) \(\chi_{8023}(180,\cdot)\) \(\chi_{8023}(192,\cdot)\) \(\chi_{8023}(296,\cdot)\) \(\chi_{8023}(363,\cdot)\) \(\chi_{8023}(405,\cdot)\) \(\chi_{8023}(413,\cdot)\) \(\chi_{8023}(429,\cdot)\) \(\chi_{8023}(432,\cdot)\) \(\chi_{8023}(435,\cdot)\) \(\chi_{8023}(462,\cdot)\) \(\chi_{8023}(464,\cdot)\) \(\chi_{8023}(499,\cdot)\) \(\chi_{8023}(507,\cdot)\) \(\chi_{8023}(546,\cdot)\) \(\chi_{8023}(571,\cdot)\) \(\chi_{8023}(632,\cdot)\) \(\chi_{8023}(666,\cdot)\) \(\chi_{8023}(712,\cdot)\) \(\chi_{8023}(785,\cdot)\) \(\chi_{8023}(796,\cdot)\) \(\chi_{8023}(861,\cdot)\) \(\chi_{8023}(881,\cdot)\) \(\chi_{8023}(901,\cdot)\) \(\chi_{8023}(916,\cdot)\) \(\chi_{8023}(927,\cdot)\) \(\chi_{8023}(950,\cdot)\) \(\chi_{8023}(972,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{560})$ |
| Fixed field: | Number field defined by a degree 560 polynomial (not computed) |
Values on generators
\((6894,3054)\) → \((e\left(\frac{31}{35}\right),e\left(\frac{87}{112}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 8023 }(405, a) \) | \(-1\) | \(1\) | \(e\left(\frac{89}{140}\right)\) | \(e\left(\frac{451}{560}\right)\) | \(e\left(\frac{19}{70}\right)\) | \(e\left(\frac{153}{560}\right)\) | \(e\left(\frac{247}{560}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{127}{140}\right)\) | \(e\left(\frac{171}{280}\right)\) | \(e\left(\frac{509}{560}\right)\) | \(e\left(\frac{263}{280}\right)\) |