Basic properties
| Modulus: | \(8024\) | |
| Conductor: | \(8024\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(464\) | 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 8024.cz
\(\chi_{8024}(3,\cdot)\) \(\chi_{8024}(27,\cdot)\) \(\chi_{8024}(75,\cdot)\) \(\chi_{8024}(107,\cdot)\) \(\chi_{8024}(139,\cdot)\) \(\chi_{8024}(147,\cdot)\) \(\chi_{8024}(163,\cdot)\) \(\chi_{8024}(243,\cdot)\) \(\chi_{8024}(299,\cdot)\) \(\chi_{8024}(363,\cdot)\) \(\chi_{8024}(371,\cdot)\) \(\chi_{8024}(379,\cdot)\) \(\chi_{8024}(403,\cdot)\) \(\chi_{8024}(411,\cdot)\) \(\chi_{8024}(435,\cdot)\) \(\chi_{8024}(499,\cdot)\) \(\chi_{8024}(507,\cdot)\) \(\chi_{8024}(547,\cdot)\) \(\chi_{8024}(619,\cdot)\) \(\chi_{8024}(635,\cdot)\) \(\chi_{8024}(643,\cdot)\) \(\chi_{8024}(675,\cdot)\) \(\chi_{8024}(771,\cdot)\) \(\chi_{8024}(779,\cdot)\) \(\chi_{8024}(787,\cdot)\) \(\chi_{8024}(843,\cdot)\) \(\chi_{8024}(907,\cdot)\) \(\chi_{8024}(947,\cdot)\) \(\chi_{8024}(963,\cdot)\) \(\chi_{8024}(979,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{464})$ |
| Fixed field: | Number field defined by a degree 464 polynomial (not computed) |
Values on generators
\((2007,4013,3777,3129)\) → \((-1,-1,e\left(\frac{1}{16}\right),e\left(\frac{25}{29}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(19\) | \(21\) | \(23\) |
| \( \chi_{ 8024 }(3, a) \) | \(1\) | \(1\) | \(e\left(\frac{77}{464}\right)\) | \(e\left(\frac{457}{464}\right)\) | \(e\left(\frac{327}{464}\right)\) | \(e\left(\frac{77}{232}\right)\) | \(e\left(\frac{459}{464}\right)\) | \(e\left(\frac{63}{116}\right)\) | \(e\left(\frac{35}{232}\right)\) | \(e\left(\frac{147}{232}\right)\) | \(e\left(\frac{101}{116}\right)\) | \(e\left(\frac{171}{464}\right)\) |